text:
What are the 4 stages of COPD?
Chronic obstructive pulmonary disease (COPD) is a chronic condition that affects the lungs and gets progressively worse over time. Restricting air in and out of the lungs, it's thought that about 90% of cases are caused by smoking.
Because it's a progressive condition, symptoms (such as wheezing, coughing and shortness of breath) get worse over time and their severity can be split into 4 stages.
Stage 1 of COPD - Mild
Symptoms at this stage can often go unnoticed or mistakenly passed off as something else (such as allergies, the common cold or a smokers cough). During the mild stage of COPD, lung function is down to around 80% and you may begin to cough more and produce a larger amount of phlegm.
This most important thing to do at this stage is to stop smoking. If you have previously tried to quit smoking by going cold turkey or using other ineffective methods, you may benefit from stop-smoking medication or a nicotine replacement product.
Other things you can do to treat COPD at this stage is to switch to a healthier diet, increase the amount of exercise you do and try to avoid triggers like pollution, dust and strong chemicals. You may also be prescribed a fast-acting reliever inhaler (such as Ventolin) to assist when symptoms occur.
Stage 2 of COPD - Moderate
Stage 2 of COPD is where it's most often caught, because this is when symptoms become more persistent and harder to ignore. These symptoms are the same ones as during stage 1, but typically worse. The cough becomes chronic, phlegm is harder to cough up and the condition can start disrupting your sleep.
During the moderate stage, lung function is down to 50-79% and a spirometry test will clearly show if you're in stage 2. To manage ongoing symptoms, you may be prescribed a preventer inhaler (such as Clenil Modulite) that is designed to be used daily instead of as and when you need it.
Stage 3 of COPD - Severe
Lung function at this stage is now down to 30-49% of their normal capacity, so symptoms will continue to worsen and may appear more frequently. Respiratory infections are also common at this stage, as the lungs cannot expel bacteria and viruses.
It can become harder to continue with normal activities (particularly exercise) and you may benefit from a dual-action inhaler (such as Aerivio Spiromax), which works to both reduce inflammation and to help the airways in the lungs to stay open.
Other treatment options can be discussed with your doctor, as quality of life can decrease considerably during stage 3 of COPD.
Stage 4 of COPD - Very severe
This stage is often called "end stage COPD" because it is the most severe stage and can be life-threatening. However, it does not mean that death is imminent and the title can scare people a little; plenty of stage 4 COPD patients live for years if their condition is properly managed.
However, symptoms do continue to get worse and your overall health will deteriorate. Most people experience sudden weight loss as their body struggles to pump oxygen properly (given that lung capacity is down to 30% or less).
At this stage, some patients may wish to undergo lung surgery or transplant surgery but these options don't come without risks and a list of qualifications to meet.
Explore related products
Salamol


text:
\section{Introduction}
\label{sec:intro}

The electroweak symmetry is broken in the present Universe, but is supposed to be restored in the early Universe~\cite{KIRZHNITS1972471}.
In the Standard Model~(SM), the electroweak symmetry-breaking occurs through a crossover transition~\cite{kajantie1997non},
while it can be first-order phase transition~(FOPT) in presence of Beyond-the-SM (BSM) physics.
Studying of FOPT has been of heightened interest, because it could have provided the conditions needed for explanation of the baryon asymmetry of the Universe~(BAU)~\cite{Trodden:1998ym,Cline:2006ts,10.1088/978-1-6817-4457-5,Morrissey:2012db}
and generated detectable gravitational wave~(GW)~\cite{PhysRevLett.69.2026,Kamionkowski:1993fg}.

The BAU is characterized by the baryon-to-entropy density ratio $Y_B \equiv n_{B}/s$ and the most precise measurement is given by Planck~\cite{Planck:2015fie}
\begin{equation}
    Y_B =
    8.65\pm0.09 \times 10^{-11},
\end{equation}
which is consistent with the value obtained from measurements of primordial abundance for light elements~\cite{Workman:2022ynf}. The BSM physics to explain it must satisfy the so-called Sakharov criteria: C- and CP-violation, baryon number violation and departure from equilibrium~\cite{sakharov1998violation}. Many mechanisms have been proposed following such criteria~\cite{PhysRevLett.92.061303,PhysRevLett.93.201301,PhysRevD.43.984,PhysRevD.56.6155, PhysRevD.64.063511,RevModPhys.71.1463}. The electroweak baryogenesis is one of the most attractive scenarios and has been widely studied ~\cite{RevModPhys.71.1463, PhysRevD.45.2685, PhysRevD.53.4578, Ghosh_2021, Prokopec_2019, Baldes_2019, Wang:2022dkz}, which requires an electroweak FOPT. The transition occurs when the bubbles of the symmetry-broken phase nucleate in plasma of the symmetry-restored phase. More baryons are produced than antibaryons in the regions around the expanding bubble walls. To avoid washing out the created baryons, the transition has to be strongly first-order.

The collisions, sound waves and turbulence from expanding bubbles of the broken phase can generate detectable GWs~\cite{Maggiore:1999vm,Weir:2017wfa,Alanne:2019bsm}. The observation of GW signal~\cite{LIGOScientific:2016aoc} has opened up a new window to probe BSM, especially in the situation that the LHC searches for BSM have merely given null results so far. The GW generated through strong FOPT is within coverage of future GW detectors, such as the Laser Interferometer Space Antenna~(LISA)~\cite{2017arXiv170200786A} and the Taiji program~\cite{10.1093/nsr/nwx116}.

The other by-product of strong FOPT is the change of Dark Matter~(DM) density. When the Universe evolved from the symmetric phase to the broken phase, there was an entropy injection and latent heat release, which could dilute the DM density. The DM relic density in the present Universe has been measured precisely by astrophysical and cosmological experiments: $\Omega_{DM} h^2 = 0.120\pm0.001$~\cite{Planck:2018vyg}. The DM models, such as the Weakly Interacting Massive Particle (WIMP)\cite{PhysRevD.100.115050, PhysRevD.82.055026, PhysRevD.80.055012}, right hand neutrino \cite{PhysRevD.101.095005, PhysRevD.79.033010, PhysRevD.81.085032, PhysRevD.90.013007} and axion\cite{PhysRevLett.120.211602, PhysRevLett.108.061304, PhysRevD.91.065014}, should give the correct relic density. Assuming a multi-component DM, the proportions of different DM candidates also affect the interpretation of DM direct and indirect searching results \cite{PhysRevD.103.063028, PhysRevD.100.015040, PhysRevLett.119.181301}.

For those DM models in which the FOPT occurs after DM freeze out in the evolution history of the Universe, it is mandatory to take the dilution of DM density into consideration.
The dilution effect can be induced by the entropy injection, which may come from heavy states decaying to the thermal bath~\cite{Dine_1996, Banks_1994} or the electroweak FOPT~\cite{megevand2004first, megevand2008supercooling,wainwright2009impact,chung2011probing}.
Refs.~\cite{megevand2004first, megevand2008supercooling} first showed some general information on the amounts of supercooling and reheating as well as the duration of the phase transition using thermodynamic method.
Then in a model-independent way Ref.~\cite{wainwright2009impact} found that the FOPT may dilute the thermal relic abundance of DM if the decouple process finished before the electroweak transition. Further, Ref.~\cite{chung2011probing} systematically studied various imprints of the phase transitions on the relic abundance of TeV-scale DM. The above studies showed that the dilution factor, $ d=(a_f/a_i)^3$ with $a_i(a_f)$ being the  scale factor of the Universe at the beginning (ending) of the phase transition, can be as large as 50. It will distinctly affect the DM signal expectations in relevant experiments.  However, the above studies focused on the dilution effect by using the toy-model-like effective potential such as adding large degree of freedom from hidden sector. In the studies of realistic models emphasizing DM aspect~\cite{bian2018thermally,bian2019two,Han:2020ekm, blinov2015electroweak,mcdonald2012secluded}, the dilution effect has been neglected by a rough estimation.

In this work, we aim to study in detail the dilution of DM relic density caused by FOPT in realistic models. Therefore we focus on singlet extension models, including the scalar singlet extension of the SM~(xSM), of two-Higgs-doublet model~(2HDM+S) and the next-to-minimal supersymmetric Standard Model~(NMSSM). These models are well motivated and popular in studying electroweak phase transition and DM. The introduced singlet can both trigger FOPT and provide a good DM candidate. We will calculate the magnitude of the dilution factor and find out the conditions of successful dilution of DM relic density in these models.

This paper is organized as follows. In \cref{sec:mechanism} we introduce the dilution mechanism caused by FOPT and deduce formulas for calculating the dilution factor. We describe the models and present results for xSM in \cref{sec:xsm}, for 2HDM+S in \cref{sec:2HDM+S}, and for NMSSM in \cref{sec:nmssm}.

\section{Dilution of DM density by first-order phase transition}
\label{sec:mechanism}

\subsection{Electroweak first-order phase transition}

The amount of dilution on DM density depends upon the relative entropy injected into the broken phase during the FOPT. Two special temperatures of the FOPT, the critical temperature ($T_c$) and nucleation temperature ($T_n$) defined in the following, are the vital features in determining the dilution factor.

In the hot and radiation-dominated early Universe, the electroweak symmetry is restored, i.e. the minimum of Higgs potential locates at origin $v_{\rm origin}$. As the temperature of the Universe drops, a second minimum $v_{\rm broken}$ away from the origin develops with higher free energy.
With the Universe further cooling, the symmetry-broken minimum becomes degenerate with the origin, which gives the definition of critical temperature
\begin{equation}
    V_{\rm eff} (v_{\rm origin};T_c) = V_{\rm eff} (v_{\rm broken};T_c).
\end{equation}
Then, with temperature falling below $T_c$, some regions of the symmetric plasma tunnel to the deeper broken minimum and nucleate bubbles.
Most of the bubbles are too small to grow and they just collapse, because the energy difference between the two vacuums is not large enough to overcome the surface tension of the bubble walls.
As the Universe further cools, the nucleation rate of large bubbles increases dramatically.
The phase transition begins once the probability to nucleate a supercritical bubble in one Hubble volume is of order one, at the so-called nucleation temperature $T_n$.

Quantitatively, the tunneling probability per unit time per unit volume can be roughly estimated as~\cite{linde1983decay}
\begin{equation}
    \Gamma \sim T^4~e^{-\frac{S_{E}}{T}},
\end{equation}
where $S_{E}$ is the three-dimensional Euclidean action given by
\begin{equation}
    S_{E} =  4 \pi \int^{+\infty}_{0}r^2{\rm d}r~\left[\frac{1}{2}\left(\frac{\partial \phi}{\partial r}\right)^{2} + V_{\rm eff}(\phi;T)\right].
\end{equation}
The bubble configuration $\phi(r)$ in the integral is fixed from the corresponding Euclidean equation of motion
\begin{equation}
    \frac{{\rm d}^2 \phi}{{\rm d} r^2} + \frac{2}{r}\frac{{\rm d} \phi}{{\rm d}r} = \frac{\partial V_{\rm eff}(\phi;T)}{\partial \phi},
\end{equation}
subjecting to the boundary conditions $\lim \limits_{r \to \infty} \phi(r) = 0 $ and ${\rm d} \phi/{\rm d} r|_{r=0}=0$ (see \cite{rubakov2009classical} for details). The $\mathcal{O}(1) $ probability of nucleating a supercritical bubble in one Hubble volume is expressed as
\begin{equation}
    \int^{+\infty}_{T_{n}} \frac{{\rm d} T}{T}(\frac{2\zeta M_{PI}}{T})^4 e^{-\frac{S_{E}}{T}} = \mathcal{O}(1),
\end{equation}
where $M_{PL}$ is the reduced Planck mass, $\zeta = \frac{1}{4 \pi}\sqrt{\frac{45}{\pi g^{*}}}$ with $g^{*}$ being the effective number of relativistic degrees of freedom \cite{quiros1998finite}. From this definition, we can get an estimated formula for $T_{n}$
\begin{equation} \label{eq: S/T}
    \frac{S_{E}}{T_{n}} \sim \mathcal{O}(130-140).
\end{equation}

\subsection{Dilution mechanism via entropy injection}

There are two situations for the dilution of DM density due to entropy injection. In the first situation, the transition temperature $T_n$ is near the critical temperature $T_c$, and the supercooling process is negligible.
The system is almost in equilibrium and thus the total entropy $(\sim a^3 s)$ is conserved, where $s$ indicates the entropy density and $a$ is the scale factor of the Universe. With entropy injection, the density changes as $s_- = (a_i/a_f)^3 ~ s_{+}$, where the subscripts ${+}$ and ${-}$ denote the high-temperature symmetric phase and low-temperature broken phase, and the subscripts $f$ and $i$ indicate the
beginning and ending of the phase transition. Therefore we can get the dilution factor
\begin{equation}  \label{eq: entropy scale}
    d \equiv \left(\frac{a_{f}}{a_i}\right)^{3} = \frac{s_{+}(T_c)}{s_{-}(T_n)},
\end{equation}
for the transition in this situation.

In the second situation, where the transition is strongly first-order and  $T_{n}$ is consequently much smaller than $T_{c}$, the equilibrium condition is broken at a stage of the transition. For convenience, we can divide the evolution of transition into supercooling stage, reheating stage and phase coexistence stage.

In the supercooling stage, the high temperature phase always dominates the Universe, so the total entropy is conserved. Similar to the first situation, we have
\begin{equation}
\label{eq:supercooling}
    (\frac{a_{i}}{a_{m}})^{3} \simeq \frac{s_{+}(T_{n})}{s_{+}(T_{c})},
\end{equation}
where $a_{m}$ is the scale factor at a temperature near $T_n$, corresponding to the end of supercooling.

Then the latent heat is released and reheats the Universe. If the duration of the reheating stage is short compared to the expansion rate, the energy density $\rho$, instead of the total entropy, is conserved~\cite{wainwright2009impact}. When the Universe is reheated to a temperature close to $T_c$, it reaches a phase coexistence stage, and its energy density can be expressed as
\begin{equation}
\label{eq: f_define}
    \rho_-(T_c) = f \rho_{-}(T_{c}) + (1-f)\rho_{+}(T_{c}),
\end{equation}
where $f$ is the volumetric fraction of the plasma of the low-temperature phase. With energy density conservation, the energy density at the beginning of the reheating stage is given as
\begin{equation}
\begin{aligned} \label{eq: f_define}
    \rho_+(T_n) & = \rho_-(T_c) \\
    & =  \rho_{+}(T_{c}) - f[\rho_{+}(T_{c}) - \rho_{-}(T_{c})].
\end{aligned}
\end{equation}
Then we can get the fraction
\begin{equation} \label{eq: f_cal}
    f = \frac{\rho_{+}(T_{c})-\rho_{+}(T_{n})}{L},
\end{equation}
where $L = \rho_{+}(T_{c}) - \rho_{-}(T_{c}) $ is the latent heat.

During the third stage, which also happens quickly, the total entropy is again conserved. The total entropy is approximately $a_m^3 ~[(1-f)s_{+}(T_c) + f s_{-}(T_c)] $ at the beginning and $a_f^3 ~s_{-}(T_c) $ at the ending of this stage. Therefore we see
\begin{equation}
    \left(\frac{a_{f}}{a_{m}}\right)^3 = \frac{1-f\Delta s / s_{+}(T_{c})}{1 - \Delta s/s_{+}(T_{c})},
\end{equation}
where $\Delta s = s_{+}(T_c) - s_{-}(T_c)$.
Finally, combined with \cref{eq:supercooling}, we get the total expansion of dilution factor
\begin{equation} \label{eq: supercolling dilution factor}
  d \equiv \left(\frac{a_{f}}{a_{i}}\right)^3 = (\frac{1-f\Delta s / s_{+}(T_{c})}{1 - \Delta s/s_{+}(T_{c})})(\frac{s_{+}(T_{c})}{s_{+}(T_{n})}).
\end{equation}
for the second situation.

\section{Singlet extension of the SM}
\label{sec:xsm}

\subsection{Effective potential}

Firstly, we consider xSM, the simplest scalar extension of the SM,  which includes an extra $Z_{2}$ symmetric real scalar singlet field $S$.  The scalar potential is given by \begin{equation}\label{eq:xsm_tree}
    V_{0}(H,S) = -\mu_{H}^{2}H^{\dagger}H + \lambda_{H}(H^{\dagger}H)^{2} - \frac{\mu_{S}^2}{2}S^2 + \frac{\lambda_{S}}{4}S^4 + \frac{\lambda_{HS}}{2}H^{\dagger}HS^2.
\end{equation}
The Higgs doublet can be parameterized as
\begin{equation}\label{eq: parameterized H}
H = 	{\left[\begin{array}{c}
	G^{+}\\ \frac{ h + iG^{0}}{\sqrt{2}}
	\end{array}\right]},
\end{equation}
where $G^{\pm, 0}$ indicate the Goldstone bosons and $h$ stands for the SM Higgs boson. We parameterize the $S$ field as $S = s$.  The background field configurations $h$ and $s$ have vacuum expectation values (VEVs) of $(v_h,v_s)$ at zero-temperature. Substituting them into Eq~(\ref{eq:xsm_tree}), the tree level tadpole conditions are
\begin{equation}
\label{eq: tadpole conditions_tree}
\begin{aligned}
   \left<\frac{\partial V_{0}}{\partial h}\right> &= v_{h} \left(-\mu_{H}^2 + \lambda_{H}v_{h}^2 + \frac{\lambda_{HS}}{2} v_{s}^2\right) = 0,\\
    \left<\frac{\partial V_{0}}{\partial s}\right> &= v_{s} \left(-\mu_{S}^2 + \lambda_{S}v_{s}^2 + \frac{\lambda_{HS}}{2} v_{h}^2 \right) = 0,
\end{aligned}
\end{equation}
where $\left<...\right>$ represents that the quantity in between the angled brackets is evaluated in the vacuum $(h=v_h,s=v_s)$.
Among the solutions of \cref{eq: tadpole conditions_tree}, we take the $Z_2$ invariant one, $v_h = \mu_H^2/\lambda_H$ and $v_s=0$.
The scalar masses are obtained by diagonalizing the squared mass matrix
evaluated at the VEV,
\begin{equation}
\label{eq: mass matrix}
\begin{aligned}
M^2 &= {\left(
  \begin{array}{cc}
\left<\frac{\partial^2 V_{0}}{\partial^2 h^2}\right> & \left<\frac{\partial^2 V_{0}}{\partial h \partial s}\right>\\
\left<\frac{\partial^2 V_{0}}{\partial h \partial s}\right> &  \left<\frac{\partial^2 V_{0}}{\partial^2 s}\right>
  \end{array}
\right)}\\
&= {\left(
  \begin{array}{cc}
3v_{h}\lambda_{H} - \mu_{H}^2 + \frac{1}{2}\lambda_{HS}v_{s}^2 & \lambda_{HS}v_{h}v_{s}\\
\lambda_{HS}v_{h}v_{s} &  3v_{s}\lambda_{S} - \mu_{S}^2 + \frac{1}{2}\lambda_{HS}v_{h}^2
  \end{array}
\right)}.\\
\end{aligned}
\end{equation}
Since $v_{s} =0$, the off-diagonal elements of the mass matrix are eliminated, i.e. no mixing between the Higgs and singlet fields. Owing to this, the singlet scalar particle does not interact with any particle except the Higgs boson, which consequently is a good candidate for the DM.

To study the phase transition, we need the effective potential with loop corrections
\begin{equation} \label{eq: V_eff}
V_{\rm eff}(h, s; T) = V_{0}(h, s) + V_{\rm CW}(h, s) + V_{\rm CT}(h, s) +  V_{1T}(h, s; T) + V_{\rm ring}(h, s; T),
\end{equation}
where $V_{\rm CW}$, $V_{\rm CT}$, $V_{1T}$ and  $V_{\rm ring}$ are the one-loop Coleman-Weinberg potential, the corresponding counter term, the one-loop thermal correction and the resummed daisy correction, respectively.

We choose the OS-like scheme and the Landau gauge to avoid introducing dependence on renormalization scale~\cite{quiros1998finite}. The one-loop zero-temperature correction takes a form~\cite{Anderson:1991zb}
\begin{equation} \label{eq: V_CW}
\begin{aligned}
V_{1}(h, s)  =& V_{\rm CW}(h, s) + V_{\rm CT}(h, s) \\
 =& \sum_{i} (-1)^{s_{i}} \frac{g_{i}}{64 \pi^2}  \left\{ m_{i}^4(h, s)\left[\log \frac{m_{i}^2(h, s)}{m_{i}^2(v_{h}, v_{s})} -\frac{3}{2} \right] + 2m_{i}^2(h, s)m_{i}^2(v_{h}, v_{s}) \right\},
\end{aligned}
\end{equation}
where $i \in \{H,~S,~W^{\pm},~Z,~\gamma,~t$\}, $s_i$ is the spin of particle $i$, and $g_i$ is the number of degrees of freedom,
\begin{equation}
g_{H} = 1, ~~ g_{S} = 1, ~~ g_{W^{\pm}} = 6, ~~ g_{Z} = 3, ~~ g_{\gamma}=3, ~~ g_{t} = 12.
\end{equation}
$m_i^2(h, s)$ stands for the squared tree-level background-field-dependent masses,
\begin{equation}
\begin{aligned}
m_{H}^2 &= - \mu_{H}^2 + 3\lambda_{H}h  + \frac{1}{2}\lambda_{HS}s^2 \\
m_{S}^2 &= - \mu_{S}^2 + 3\lambda_{S}s  + \frac{1}{2}\lambda_{HS}h^2 \\
m_{W^{\pm}} & = \frac{1}{4} g_{SU(2)_L}^2 h^2, ~~~~~
m_{Z} = \frac{1}{4} \left(g_{SU(2)_L}^2+g_{U(1)_Y}^2\right) h^2 \\
m_{\gamma}^2 &=0, ~~~~~~~~~~~~~~~~~~~
m_{t}  = \frac{1}{2} y_t^2h^2.\\
\end{aligned}
\end{equation}
We neglect the contributions of light fermions. Goldstone bosons are not included because that second derivative of $V_{\rm CW}$ is logarithmic divergent at VEV of zero-temperature, originating from $\left.m_{G^{\pm,0}}\right|_{h=v_h,s=0}=0$ and $\left. \partial m_{G^{\pm,0}}/\partial h \right|_{h=v_h,s=0}\neq0$~\cite{elias2014taming}. The impact of fixing the Goldstone catastrophe, as well as choosing other renormalization scheme, can be found in Ref.~\cite{braathen2016avoiding,Athron:2022xxx}.

In the OS-like scheme, the position of VEV at zero-temperature and masses at VEV are not affected by loop corrections, so the renormalization conditions are imposed as
\begin{equation}
\begin{aligned}
\left< \frac{\partial (V_{0} + V_{1})}{\partial h}\right> &= \left< \frac{\partial V_{0}}{\partial h}\right> = 0, \\
\left<\frac{\partial^2 (V_{0} + V_{1})}{\partial^2 h}\right> &= \left<\frac{\partial^2 V_{0}}{\partial^2 h}\right> = m_H^2, ~~
\left<\frac{\partial^2 (V_{0} + V_{1})}{\partial^2 s}\right> = \left<\frac{\partial^2 V_{0}}{\partial^2 s}\right> = m_S^2.
\end{aligned}
\end{equation}
Thus, with $v_h=246\ensuremath{\,\text{GeV}}\xspace$ and $m_H = 125\ensuremath{\,\text{GeV}}\xspace$, we can fix $\mu_H$ with \cref{eq: tadpole conditions_tree,eq: mass matrix}. We choose $m_S$, $\lambda_S$ and $\lambda_{HS}$ as input parameters of the model.

The one-loop finite temperature correction is deduced from the finite-temperature field theory~\cite{quiros1998finite}
\begin{equation} \label{eq: one-loop effective potential at finite temperature}
    V_{1T}(h, s) = \frac{T^{4}}{2 \pi^2} \left[\sum_{B} g_{B}J_{B}\left(\frac{m_{B}(h, s)}{T}\right) + \sum_{F} g_{F}J_{F}\left(\frac{m_{F}(h, s)}{T}\right)\right],
\end{equation}
where $J_{B}$, $J_{F}$ are the relevant thermal distribution functions for the bosonic and fermionic contributions, respectively,
\begin{equation} \label{eq: J_BJ_F}
    J_{B,F}(x) = \pm \int_{0}^{+\infty} {\rm d}y ~y^2 \log \left(1\mp e^{-\sqrt{x^2 + y^2}}\right).
\end{equation}
In the high-temperature limit, they can be expanded as
\begin{equation}
\label{eq:high-temperature JBF}
\begin{aligned}
J_{B}(x) &= -\frac{\pi ^4}{45} + \frac{\pi^2}{12}x^2 -\frac{\pi}{6}x^3 - \frac{x^4}{32}\log\frac{x^2}{a_b},\\
J_{F}(x) &= -\frac{7\pi^4}{360} + \frac{\pi^2}{24}x^2 + \frac{x^4}{32}\log\frac{x^2}{a_f},
\end{aligned}
\end{equation}
where $\log(a_{b})=\frac{3}{2}-2\gamma + 2\log(4\pi)$, $\log({a_{f})=\frac{3}{2}-2\gamma+2\log(\pi)}$, with $\gamma$ being the Euler constant~\cite{PhysRevD.45.2685}.

Owning to the zero-mode contribution, the multi-loop diagrams will dominate if the temperature is high enough, which makes the perturbation condition broken~\cite{curtin2018thermal, senaha2020symmetry}. To make the expansion reliable, the dominant thermal pieces must be resummed. Here we adopt the Parwani method~\cite{Parwani:1991gq} by replacing the tree-level masses $m_{i}^2$ in \cref{eq: V_CW,eq: one-loop effective potential at finite temperature}) through the thermal masses $m_{i}^2(T) = m_{i}^2 + d_{i}T^2$, where $d_{i}T^2$ is the leading contribution in temperature to the one-loop thermal mass, where
\begin{equation} \label{eq: deby mass correction}
\begin{aligned}
d^{L}_{W^{\pm,3}}&=\frac{11}{6}g_{SU(2)_L}^2, ~~~~~~
d^{T}_{W^{\pm,3}}=0, ~~~~~~
d_{B}^{L}=\frac{11}{6}g_{U(1)_Y}^{2},\\
d_{HH} &= \frac{3g_{SU(2)_L}^2}{16} + \frac{1}{16}g_{U(1)_Y}^2+\frac{1}{2}\lambda_{H}+\frac{1}{4}y_{t}^2+\frac{1}{24}\lambda_{HS},\\
d_{SS} &= \frac{1}{4}\lambda_{S} + \frac{1}{6}\lambda_{HS}.
\end{aligned}
\end{equation}

\subsection{Scan results}

We performed a scan in the following ranges,
\begin{equation} \label{eq: scan_area}
    10\ensuremath{\,\text{GeV}}\xspace \le m_{S} \le 1\ensuremath{\,\text{TeV}}\xspace, ~~0 \le \lambda_{HS} \le 10, ~~0 \le \lambda_{S} \le 1.
\end{equation}
The upper bounds on $\lambda_S$ and $\lambda_{HS}$ are set because of perturbation limits. We will see later that the upper bound on $m_S$ is large enough for achieving strong FOPT. \textbf{Cosmotransition}~\cite{WAINWRIGHT20122006} and \textbf{PhaseTracer}~\cite{Athron:2020sbe} are used to calculate the physical quantities related to the phase transition, and \textbf{MicrOmega} \cite{belanger2002micromegas} is used to get the freeze-out temperature $T_{f}$ and DM observables. In the following, we study samples that can achieve successfully FOPT in the thermal history of the Universe.
The bound on DM relic density from Planck~\cite{Planck:2015fie} and limits from DM direct detection XENON1T~\cite{PhysRevLett.119.181301} are discussed later taking the dilution effect into consideration. For other possible constraints on xSM, see Refs.~\cite{Athron:2018ipf}.

\subsubsection{Dilution factor}

\begin{figure}[t]
\centering
\includegraphics[width=0.48\textwidth]{fig/10.8_dilusion_factor.pdf}
\hfill
\includegraphics[width=0.48\textwidth]{fig/10.8_delta_T.pdf}
\hfill
\includegraphics[width=0.48\textwidth]{fig/DM_before_dilution.pdf}
\hfill
\includegraphics[width=0.48\textwidth]{fig/DM_after_dilution.pdf}
\caption{{\bf Top:} the dilution factor (left) and supercooling information (right) in the plane of
input parameters. {\bf Bottom:} the cross section of spin-independent scattering of DM on nucleon without (left) and with (right) dilution of DM relic density caused by FOPT taken into consideration, along with the 90\% CL limit from XENON1T.}
\label{fig:dm}
\end{figure}

The top left panel of \cref{fig:dm} displays the results of the dilution factor as a function of the model parameters.
It finds that the dilution effect can be neglected in most of the parameter space that can achieve FOPT, except at the upper edge on $(m_s,\lambda_{hs})$ plane.
In the upper edge, the phase transition happens mostly between minimums of $(v_h^{\rm high}=0,v_s^{\rm high}\neq 0)$ and $(v_h^{\rm low}\neq 0,v_s^{\rm low}=0)$, which is strong first-order and corresponds to a large difference between $T_c$ and $T_n$.
It can be seen from the top panels of \cref{fig:dm}, the larger the difference is, the more obvious the dilution is.
This is consistent with the results in previous studies that the dilution can be neglected when $T_{c} \sim T_{n}$~\cite{bian2018thermally, bian2019two}, and is significant if supercooling occurs~\cite{wainwright2009impact,megevand2008supercooling}. The impact of supercooling can be expected from \cref{eq: supercolling dilution factor}. At high temperatures, the dominant part of effective potential is the quartic term of temperature provided by Eq~(\ref{eq: one-loop effective potential at finite temperature}). Thus the dilution factor can be estimated as
\begin{equation} \label{eq: dilution approx}
  s = - \frac{{\rm d} V_{\rm eff}}{{\rm d} T},
  ~~~~~~~~~~
  (\frac{a_{f}}{a_{i}})^3 \sim (\frac{T_{c}}{T_{n}})^3 \sim (1 + \frac{\Delta}{T_{n}})^3.
\end{equation}

In the bottom panels of \cref{fig:dm}, we present the cross section of spin-independent scattering of DM on nucleon for the above samples, along with the 90\% CL limit from XENON1T~\cite{PhysRevLett.119.181301}. In the case of singlet DM relic density $\Omega_{S} h^2$ smaller than the observed value $\Omega_{DM} h^2 = 0.120$, which means that the singlet DM is only a fraction of DM, we re-scale the cross section by a factor of $f_{\rm rel} = \Omega_{S}/ \Omega_{DM}$. The bottom panels show the results without and with the dilution of $\Omega_{S} h^2$. One can see that the dilution can salvage some samples excluded by DM direct detection. This is the reason why the dilution caused by FOPT should be taken into consideration in DM studies.

\begin{figure}[t]
\centering
\includegraphics[width=0.48\textwidth]{fig/lowmass_T.pdf}
\hfill
\includegraphics[width=0.48\textwidth]{fig/lowmass_f.pdf}
\caption{The critical temperature $T_c$, the nucleation temperature $T_n$ and the dilution factor $d$ as functions of the input parameter $\lambda_{HS}$, with fixed $m_s = 129.5070$ GeV and $\lambda_{S} = 0.5286$.}
\label{fig:bk1}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=0.6\textwidth]{fig/action_T_2.pdf}
\caption{The ratio of the Euclidean action to the temperature $S/T$ versus the temperature for different $\lambda_{HS}$ values. Other input parameters are same as in \cref{fig:bk1}.}
\label{fig:bk2}
\end{figure}

The largest value of the dilution factor in our scan is $2.8$, which may be raised a little with more sophisticated scan. However, as it is correlated with the difference $T_c - T_n$, we find that it is hard to obtain  a dilution factor larger than $3$. In \cref{fig:bk1} we displace $T_c$, $T_n$ and the dilution factor $d$ as functions of the model parameter $\lambda_{HS}$ for a benchmark point with $m_s = 129.5070$\ensuremath{\,\text{GeV}}\xspace and $\lambda=0.5286$.
We see in the left panel that the critical temperature $T_c$ and the nucleation temperature $T_n$ both decrease but with different speeds as $\lambda_{HS}$ increases. Theoretically, the lowest value of $T_c$ can reach to zero by fine tuning the parameter $\lambda_{HS}$, as discussed in Ref.~\cite{Athron:2022xxx}. However, the nucleation temperature has a lower bound around 50\ensuremath{\,\text{GeV}}\xspace. The reason of existing this lower bound is displaced in \cref{fig:bk2}, where the colored solid curves indicate the ratio of the Euclidean action to the temperature as functions of the temperature for different $\lambda_{HS}$ values. The nucleation temperature is obtained from condition $S/T=140$, namely the intersection of the colored curves and the horizontal black dashed line. With $\lambda_{HS}$ increasing, the intersection moves to the left and the slope of $S/T$ decrease. When $\lambda_{HS}>0.9250$, the $S/T$ curve looks U-shaped and there is no more intersection with the horizontal line, which means that the FOPT can not finish in the history of the Universe.

The difference between $T_{c}$ and $T_{n}$ increases with $\lambda_{HS}$ increasing as well, and stops at about $50\ensuremath{\,\text{GeV}}\xspace$ because of no nucleation temperature for larger $\lambda_{HS}$. Therefore, the dilution factor increases with increasing $\lambda_{HS}$ and has an upper bound about 3 for this benchmark point, as shown in the right panel of \cref{fig:bk1}.

\subsubsection{Constraints on dilution process}

Although the dilution in xSM is sizable to affect DM properties, there are two essential prerequisites in the calculation of dilution factor discribed in \cref{sec:mechanism}. In the case of supercooling the liberated latent heat reheats the system back to a temperature close to $T_c$, and the phase transition happens after the singlet DM freeze-out. Now we check the two conditions for the above scan result.

In \cref{eq: f_define}, the volumetric fraction of the low temperature phase during the reheating stage $f$ must be smaller than 100\%. However, using \cref{eq: f_cal}, it can exceed 100\% especially for samples of large dilution factor. It is because \cref{eq: f_cal} assumes that a large amount transition latent heat brings temperature of the system from $T_n$ back to near $T_c$, which fails when $T_c\gg T_n$. In this case, $T_{n}$ appearing in \cref{eq: supercolling dilution factor} should be replaced by reheating temperature $T_{r}$. The calculation of $T_{r}$ involves processing specific kinetic processes~\cite{megevand2008supercooling}, which is out of the scope of this paper. Neglecting the term including $f$, i.e. setting $f=100\%$, \cref{eq: supercolling dilution factor} approaches to \cref{eq: dilution approx} and gives a larger dilution factor.  Moreover, friction and collisions in the walls of bubbles would also release entropy and increase the dilution~\cite{wainwright2009impact}, which are not included in \cref{eq: supercolling dilution factor}. Thus, breaking of this assumption does not indicates reduction of dilution factor.

\begin{figure}[t]
\centering
\includegraphics[width=0.6\textwidth]{fig/10.8_delta_T2.pdf}
\caption{The difference between DM freeze-out temperature $T_{f}$ and the nucleation temperature $T_{n}$ in the plane of input parameters. }
\label{fig:diff}
\end{figure}

As for the second prerequisite, in order to avoid the DM reequilibrate with other thermal species, the nucleation temperature $T_{n}$ shall be smaller than the singlet DM freeze-out temperature $T_{f}$. As discussed in \cref{fig:bk2}, there is a lower bound on $T_{n}$, and the lowest $T_{n}$ in our scan is about 50\ensuremath{\,\text{GeV}}\xspace. On the other hand, the variable $x_{f} = m_S/T_f $ used in solving the Boltzmann transport equation of matter lies in range of $\mathcal{O}(20 \sim 40)$ in xSM. We see from \cref{fig:dm} that $m_S$ is smaller than 600\ensuremath{\,\text{GeV}}\xspace when $d>1.5$ and $\lambda_{HS}<10$, which indicates $T_f<30\ensuremath{\,\text{GeV}}\xspace<T_n$, i.e. the dilution process happens before the DM freeze-out and can not affect the current singlet DM density. This can be seen from \cref{fig:diff} which shows that for the samples of FOPT the DM freeze-out temperature is always lower than the nucleation temperature. The mass of singlet DM is bounded because large dilution factor requires transition between minimums $(0,v_s^{\rm high}\neq 0)$ and $(v_h^{\rm low}\neq 0,0)$. The upper bound can be estimated using high temperature approximation.

Using \cref{eq:high-temperature JBF} and neglecting the zero-temperature corrections and the finite temperature corrections beyond $T^2$ terms, we can get the approximate effective potential~\cite{vaskonen2017electroweak}
\begin{equation}
    V_{\rm HT}(h,s;T) = \frac{1}{2}(-\mu_{H}^2 + c_HT^2)h^2 + \frac{1}{4} \lambda_{H}h^4
    +\frac{1}{2}(-\mu_{S}^{2}+ c_ST^2)s^2 + \frac{1}{4} \lambda_{S}s^4
    + \frac{1}{4} \lambda_{HS} h^2s^2,
\end{equation}
where
\begin{equation}
\begin{aligned}
& c_S = \frac{2\lambda_{HS} + 3\lambda_S}{12},\\
& c_H = \frac{9g_{SU(2)_L}^2 + 3g_{U(1)_Y}^2 + 12y_t^2 + 24\lambda_H + 2\lambda_{HS}}{48}.
\end{aligned}
\end{equation}
In order to obtain FOPT between minimums
\begin{equation}
\begin{aligned}
\left(0,~v_s^{\rm high} = \frac{-\mu_{S}^{2}+ c_ST^2}{\lambda_S} \neq 0 \right)
{\rm ~~~and~~~}
\left(v_h^{\rm low}=\frac{-\mu_{H}^{2}+ c_HT^2}{\lambda_H} \neq 0 ,~0\right),
\end{aligned}
\end{equation}
with temperature decreasing from high value, $v_s^{\rm high}$ must become non-zero before $v_h^{\rm low}$ become non-zero. It gives
\begin{equation} \label{eq: contrain_1}
\begin{aligned}
 \frac{\mu_H^4}{c_H^2} < \frac{\mu_S^4}{c_S^2}.
\end{aligned}
\end{equation}

On the other hand, $(v_h^{\rm low},~0)$ must be deeper than $(0, ~v_s^{\rm high})$ when $T<T_c$, such as $T=0$ at zero-temperature minimum, which implies
\begin{equation}  \label{eq: contrain_2}
\begin{aligned}
\frac{\mu_H^4}{\lambda_H} > \frac{\mu_S^4}{\lambda_S}.
\end{aligned}
\end{equation}

Combining the two constraints, we can obtain
\begin{equation}
\begin{aligned}
\frac{\mu_H^4}{c_H^2}c_S^2 < \mu_S^4 < \frac{\mu_H^4}{\lambda_H}\lambda_S &\rightarrow \frac{\mu_H^2}{c_H}c_S < \mu_S^2 < \frac{\mu_H^2}{\sqrt{\lambda_H}}\sqrt{\lambda_S}.
\end{aligned}
\end{equation}
Note that $\mu_S^2$, $\mu_H^2$ are positive.
Then recalling $\mu_S^2 = \lambda_{HS}\frac{v_{h}^2}{2} - m_{S}^2$, the constrain on $m_{S}$ reads
\begin{equation} \label{eq: ms contrain}
\begin{aligned}
\frac{-\mu_H^2}{\sqrt{\lambda_H}}\sqrt{\lambda_S} + \lambda_{HS}\frac{v_{h}^2}{2} < m_S^2 < \frac{-\mu_H^2}{c_H}c_S + \lambda_{HS}\frac{v_{h}^2}{2}.
\end{aligned}
\end{equation}

\begin{figure}[t]
\centering
\includegraphics[width=0.48\textwidth]{fig/path_one_lambda-ms-0.1.pdf}
\includegraphics[width=0.48\textwidth]{fig/path_one_lambda-ms-1.pdf}
\caption{The lower and upper bounds on $m_S$ obtained from high-temperature approximated potential for transition between $(0,v_s^{\rm high}\neq 0)$ and $(v_h^{\rm low}\neq 0,0)$.}
\label{fig:mass limit}
\end{figure}

In \cref{fig:mass limit}, we display the upper bound and lower bound on $m_S$ for $\lambda_S=0.1$ and $\lambda_S=1$ with varying $\lambda_{HS}$. The upper bound and lower bound meet in a point, i.e. maximal value of $m_s$. Taking perturbation limits on $\lambda_S$ and $\lambda_{HS}$ into consideration, there is no way that $m_S$ in \cref{eq: ms contrain} exceeds 600\ensuremath{\,\text{GeV}}\xspace. Even without perturbation limits, it is hard to obtain $m_S>1\ensuremath{\,\text{TeV}}\xspace$, namely $T_f>50\ensuremath{\,\text{GeV}}\xspace$.

By and large, the phase transition always happens after the singlet DM freeze-out in xSM, because the strong FOPT and the perturbation limits set an upper bound of $30\ensuremath{\,\text{GeV}}\xspace$ on $T_f$, while the lowest $T_n$ is above $50\ensuremath{\,\text{GeV}}\xspace$. The dilution of the current singlet DM density in the xSM can be neglected.

\section{Singlet extension of two-Higgs-doublet model}
\label{sec:2HDM+S}

Since the obstacle to achieve the dilution of DM relic density in the xSM is the mass upper bound on the singlet DM, we now turn to the singlet extension of the 2HDM (for a recent review on various 2HDM, see, e.g., \cite{Wang:2022yhm}) to see whether this constraint can be avoided. The 2HDM itself can achieve a strong electroweak FOPT in the early Universe~\cite{Su:2020pjw,Wang:2021ayg}, so the extended singlet, as the DM candidate, can be independent of the FOPT. For instance, Ref.~\cite{Han:2020ekm} systematically studied the electroweak FOPT and the DM in the type-II 2HDM, taking the relevant constraints into consideration. It showed the surviving parameter space
where the FOPT happens between the symmetric phase and the broken phase (with $v_s = 0$, and non-zero $v_{h_1}$ and/or $v_{h_2}$), and the singlet field configuration keeps zero in evolution of the Universe. This strongly indicates that the singlet scalar may not be related to the transition temperature.

We focus on the dilution of DM density in this type-II 2HDM. The tree-level scalar potential is given as
\begin{equation}
\begin{aligned}
    V_0^{\rm 2HDM+S} &= m_{11}^2(\Phi_{1}^{\dagger}\Phi_{1}) + m_{22}^2(\Phi_{2}^{\dagger}\Phi_{2}) - [m_{12}^2\Phi_{1}^{\dagger}\Phi_{2} + h.c.] \\
    &+ \frac{\lambda_{1}}{2}(\Phi_{1}^{\dagger}\Phi_{1})^2 + \frac{\lambda_{2}}{2}(\Phi_{2}^{\dagger}\Phi_{2})^2 + \frac{\lambda_{3}}{2}(\Phi_{1}^{\dagger}\Phi_{1})(\Phi_{2}^{\dagger}\Phi_{2}) +
    \frac{\lambda_{4}}{2}(\Phi_{1}^{\dagger}\Phi_{2})(\Phi_{2}^{\dagger}\Phi_{1})\\
    &+ [\frac{\lambda_{5}}{2}(\Phi_{1}^{\dagger}\Phi_{2})^2 + h.c.] + \frac{1}{2}S^2(\kappa \Phi_{1}^{\dagger}\Phi_{1}+\kappa\Phi_{2}^{\dagger}\Phi_{2}) + \frac{m_{0}}{2}S^2 + \frac{\lambda_{S}}{4!}S^4.
\end{aligned}
\end{equation}
Here we parameterize the two Higgs-doublets in a similar way as in the xSM, assuming all parameters are real, and construct the one-loop effective potential using the OS-like scheme~\cite{Han:2020ekm}. After spontaneous electroweak symmetry breaking, the scalar field $S$ gets a mass
\begin{equation}\label{eq: 2HDM+S_ms}
    m_{S} = m_{0}^2 + \frac{1}{2}\kappa_{1} v^2 \cos^2\beta + \frac{1}{2}\kappa_{2} v^2 \sin^2\beta,
\end{equation}
where $v=\sqrt{v_{h_1}^2 + v_{h_2}^2} = 246$ GeV. The CP-even neutral Higgs couplings can be reorganized as
\begin{equation}
\begin{aligned}
    \lambda_{h} &= -\kappa_{1}~\sin\alpha ~\cos\beta + \kappa_{2} ~\cos\alpha ~\sin\beta,\\
    \lambda_{H} &= -\kappa_{1}~\cos\alpha ~\cos\beta + \kappa_{2} ~\sin\alpha ~\sin\beta.
    \end{aligned}
\end{equation}
Therefore we choose the input model parameters as $\tan \beta$, $\sin(\beta-\alpha)$, $m_H$, $m_{H^\pm}$, $m_{12}$, $m_{0}$, $\lambda_h$, and $\lambda_H$.
Here $m_0$ is a free parameter which is independent of the phase transition properties, so  $m_{S}$ can be large enough to enhance the freeze-out temperature $T_{f}$ to above the transition temperature $T_{n}$.

\begin{figure}[t]
\centering
\includegraphics[width=0.48\textwidth]{fig/2HDMS_ms_T.pdf}
\includegraphics[width=0.48\textwidth]{fig/2HDMS_dilution.pdf}
\caption{The critical temperature $T_c$, the nucleation temperature $T_n$ and the freeze-out temperature $T_f$ as functions of $m_{S}$ (left), and the dilution factor $f$ as a function of $m_{12}$ (right) for the 2HDM+S.}
\label{fig:2HDM+S}
\end{figure}

In \cref{fig:2HDM+S} we display $T_c$, $T_n$ and $T_f$ with a varying $m_0$ in the left panel, and the dilution factor $d$ with a varying mixing parameter $m_{12}$ in the right panel around the benchmark point~\cite{Han:2020ekm}
\begin{equation}
\begin{aligned}
&\tan \beta = 1.87,~~~ \sin(\beta-\alpha)=0.9991,~~~ m_H=387.97\ensuremath{\,\text{GeV}}\xspace,~~~ m_{H^\pm} = 618.31\ensuremath{\,\text{GeV}}\xspace,\\
&m_{12} = 231.41\ensuremath{\,\text{GeV}}\xspace,~~~~ m_S= 501.7\ensuremath{\,\text{GeV}}\xspace,~~~~ \lambda_H=-0.129,~~~~ \lambda_S = 10.93
\end{aligned}
\end{equation}
We see clearly that the transition temperatures $T_c$ and $T_n$ are independent of $m_0$, and there is no upper bound on  $m_s$. The light brown band indicates the possible range of $T_f$ due to the variation of the parameter $x_f=m_S/T_f$ from $20$ to $40$ with the changing DM coupling. When $m_S>2\ensuremath{\,\text{TeV}}\xspace$, $T_c$ becomes lower than $T_f$ in the parameter space for this benchmark point. The right panel shows that the dilution factor increases with $m_{12}$ decreasing, so does the difference between $T_{c}$ and $T_{n}$. The biggest dilution factor value can reach 1.77. If $m_{12}$ further decreases, there is no more $T_{n}$, as shown in \cref{fig:bk1} for the xSM.

\section{Next-to-minimal supersymmetric standard model}
\label{sec:nmssm}

In the singlet extension of the 2HDM, the strong FOPT can also be triggered by the broken singlet vacuum expectation value. A special realization of this FOPT case is the next-to-minimal supersymmetric standard model (NMSSM) \cite{Ellwanger:2009dp}, which is a popular scenario of low energy supersymmetry. Despite of null search results of superparticles at the LHC, so far the low energy supersymmetry still remains as a compelling BSM candidate (for recent reviews, see, e.g.,  \cite{Wang:2022rfd,Baer:2020kwz}).
Besides addressing the baryon asymmetry and the DM issue as well as the hierarchy problem of the electroweak scale~\cite{WITTEN1981267}, the low energy supersymmetry can give a joint explanation for the muon and electron $g-2$ anomalies \cite{Li:2022zap,Li:2021koa,Cao:2021lmj} (it can even marginally  explain the CFD II measurement of the W-boson mass~\cite{Yang:2022gvz,Tang:2022pxh}).
The NMSSM introduces a SM gauge-singlet chiral superfield to generate the $\mu$-term dynamically and the singlet scalar can couple with the Higgs doublets to sizably  enhance the tree-level mass of the SM-like Higg boson with no need of large radiative effects from heavy top-squarks. So from the point of 125 GeV Higgs boson mass, the NMSSM is more favored than the MSSM (minimal supersymmetric standard model)~\cite{Cao:2012fz}.

The NMSSM can be treated as a special case of the singlet extension of the 2HDM, where the strong FOPT is triggered by the broken singlet vacuum expectation value and hence relevant to the $\mu$ parameter (the higgsino mass).
In this model, assuming R-parity symmetry,  the lightest neutralino is usually taken as the DM candidate, which is the mixing of neutral higgsinos, gauginos and singlino. As studied in \cite{Athron:2019teq,Chatterjee:2022pxf,Baum:2020vfl},
to achieve a strong FOPT in the NMSSM, the $\mu$ parameter must be smaller than 1\ensuremath{\,\text{TeV}}\xspace . As a result, the neutralino DM must be lighter than 1\ensuremath{\,\text{TeV}}\xspace and the freeze-out temperature $T_f < 50\ensuremath{\,\text{GeV}}\xspace$ is lower than the nucleation temperature as in the xSM.
In conclusion, the strong FOPT happens before the neutralino DM freeze-out, so the dilution of DM relic density can be neglected in the NMSSM.

\section{Conclusions}
\label{sec:conclusions}

We systematically analyzed the dilution of DM relic density caused by the FOPT in the singlet extension models, including the xSM, 2HDM+S and NMSSM.
We found that in case of supercooling the released entropy can dilute the DM density to 1/3 at most.
However, the singlet field configure in the xSM is relevant to the strength of the phase transition, which sets an upper limit of 600\ensuremath{\,\text{GeV}}\xspace on the singlet DM mass and an upper limit of 30\ensuremath{\,\text{GeV}}\xspace on the singlet DM freeze-out temperature. Meanwhile, the nucleation temperature is larger than 50\ensuremath{\,\text{GeV}}\xspace from our scan. Thus, the strong FOPT happens before the singlet DM freeze-out and the dilution effect is negligible for the current DM density in the xSM.
In the type-II 2HDM+S, the singlet scalar can be independent of the phase transition, so there is no upper bound on the singlet DM freeze-out temperature. As a result, the DM relic density, as well as the DM direct detection, can be affected by the FOPT in the type-II 2HDM+S.
In the NMSSM with FOPT, the neutralino DM freeze-out temperature is lower than the nucleation temperature as in the xSM and thus the dilution of the DM relic density can be neglected.

\acknowledgments
YZ thanks Institute of Theoretical Physics of Chinese Academy of Sciences (CAS) and YX thanks Zhengzhou University for hospitality during various stages of this work.
JMY is supported by the National Natural Science Foundation of China (NNSFC) under grant numbers 11821505 and 12075300,
by Peng-Huan-Wu Theoretical Physics Innovation Center under grant number 12047503,
by a Key R\&D Program of Ministry of Science and Technology of China under grant number 2017YFA0402204,
by the Key Research Program of the Chinese Academy of Sciences under grant number XDPB15,
and by the CAS Center for Excellence in Particle Physics (CCEPP).
YZ is supported by the NNSFC under grant number 12105248, by
CAS Peng Huanwu Junior Visiting Professor Program and by Zhenghou University Young Talent Program.

\addcontentsline{toc}{section}{References}
\bibliographystyle{JHEP}

redpajama_set_name: RedPajamaArXiv


The extraordinary image below, is segment of 2019 BMW Appleplay Picture editorial which is sorted within Car News, and posted at June 3rd, 2018 03:09:38 AM by admin.
Here is crucial knowledge on . We have the best resources for . Check it out for yourself! You can acquire 2019 Honda Insight Mulitmedia System Apple Carplay Motor Trend Spy Shoot guide and look the latest 2019 BMW Appleplay Picture in here.
Through the thousands of pictures on the net about 2019 BMW Appleplay, we selects the very best series having best resolution exclusively for you all, and now this pictures is actually one of photos series in your greatest photographs gallery about 2019 BMW Appleplay Picture. I really hope you can think it's great.
This kind of image (2019 Honda Insight Mulitmedia System Apple Carplay – Motor Trend Spy Shoot) above will be branded using.


text:
/ Talking Europe
Former WTO head Lamy: 'Brexit is like trying to get an egg out of an omelette'
Issued on: 15/01/2018 - 15:34
By: Catherine NICHOLSON Follow
He says Brexit is like "trying to get an egg out of an omelette" and a "stupid mistake". Our guest Pascal Lamy knows the issues involved better than most – he served as chief-of-staff to EU Commission President Jacques Delors, and was at the eye of the Eurosceptic storm as Britain's The Sun newspaper published its notorious "Up Yours Delors" front page in 1990. More recently he served as Director-General of the World Trade Organization (WTO).
Pascal Lamy tells FRANCE 24 what he makes of the UK's departure from the EU; what kind of trade deal could be possible; and what it would mean for the UK to have a "no deal Brexit" and fall back on WTO rules. We also discuss the impact of Germany's political uncertainty on Europe, and ask why France is bidding to host the 2025 World Expo.
Produced by Isabelle Romero and Roxane Runel
Left out in the cold: Covid-19 puts the freeze on Alpine ski resorts
Corina Cretu: Binding Europe together with ring roads, museums and much more
Bulgaria takes the helm: Deputy PM Donchev on taking over the EU presidency
Estonia at 100: President Kaljulaid on risks, opportunities and Europhilia
Did the WannaCry cyber attack make you... want to cry?
2018 begins: A happy new year for Europe?
Astronaut Thomas Pesquet: To the ISS and beyond
Talking Europe in 2017: Brexit, French elections and Catalonia separatism
Europe's 'soft power': EU Commissioner Tibor Navracsics on European identity

redpajama_set_name: RedPajamaCommonCrawl


Hans Staden (c. 1525 – c. 1579) was a German soldier and explorer who voyaged to South America in the middle of the sixteenth century, where he was captured by the Tupinamba people of Brazil. He managed to survive and return safe to Europe. In his widely read account describing his travel and captivity, he claimed that the native people that held him captive practiced cannibalism.


While the renovation of Wrigley Field had been years in the making, the blueprint for the Cubs' makeover took a somewhat unexpected turn last October when Joe Maddon opted out of his contract with the Rays.
Sprung by Andrew Friedman's defection to the Dodgers, Maddon signed with the Cubs in a matter of days, dumping small-market Tampa Bay for a chance to end the 106-year title drought on the North Side.
Grabbing the charismatic Maddon was a great start to the offseason, but it was only the beginning for the Cubs, who made a statement on the first night of December's winter meetings by signing Jon Lester to a six-year, $155-million deal. That got everyone's attention -- especially the team in Boston -- and the Cubs soon followed by bringing back Jason Hammel for the rotation.
But the strength of the Cubs remains their wealth of young talent, which looks to be developing ahead of schedule. Kris Bryant had eight homers in his first 10 Grapefruit League games but is likely to open the season in the minors so the Cubs can stall his free agency. There are plenty more in the pipeline: outfielder Jorge Solder and infielders Addison Russell and Javier Baez, to name a few.
It's been a long wait, but the future is quickly becoming now for the Cubs.
Health remains the only thing that could derail the Cardinals' rotation, and that's becoming more of an issue after Adam Wainwright's offseason elbow surgery. Michael Wacha was bothered by shoulder problems last year. St. Louis traded Shelby Miller to the Braves to get slugger Jason Heyward, who adds serious thump.
After the Pirates lost Russell Martin to the Blue Jays, what did they do? They signed another Yankees catcher, of course, in Francisco Cervelli, who joins another Bronx backstop, Chris Stewart. The Pirates have offense everywhere -- with 2013 MVP Andrew McCutchen at the core -- and spent $39 million to keep Francisco Liriano in their rotation, which features Gerrit Cole at the front.
After 76 wins last season, the Reds' big offseason acquisition was Marlon Byrd, who really isn't a game-changer. Cincy has a talented roster; it's just a matter of keeping the players on the field. A year ago, Joey Votto was limited to 62 games -- after 162 the season before -- so that should be a major upgrade.
While their top Central rivals improved, the Brewers figured they could stand pat with a solid offensive nucleus of Ryan Braun, Carlos Gomez and Jonathan Lucroy. Matt Garza fronts a decent rotation, but depth is an issue as Milwaukee hopes to avoid a repeat of last season's fade.


text:
Show all stories
Set up a search alert
Raegan Carey
Raegan has always had a fondness of Performance Art, Theatre and Dance. After 15 years of studying ballet, tap, and jazz, Raegan began her dance journey at Marsha Woody's Dance Company in Beaumont, Texas at the tender age of three. After attending a national dance workshop in Houston, she was then invited to train and competitively dance with Steven Boyd Houston Dance Company. After moving with her family to Houston to further pursue Theatre and Dance, Raegan then attended Houston's proclaimed High School for the Performing and Visual Arts where she studied theatre, film, and performed several plays during her education and training there. In her spare time, she loves helping others and is a co- founder of the Oriska Foundation, a family founded Christian non-profit. She is also a member of HYPA- Houston Young People of the Arts, Houston's Downtown Alliance, YPC- Houston Health Museum's Young Professional Circle and Inter-nations: Houston.org where she serves as a local scout for all Performance Art in Houston.
A graduate of the University of Houston with a B. S. from the College of Education, and a former contributor to Houston's Urban Beat Magazine, Raegan is thrilled to bring her passion and experience to Houston Style Magazine.
It was a Jolly-filled Night at Joy to the World!
The Bayou City Performing Arts presented Joy to the World, a holiday concerto commemorating 40 fabulous seasons. It was a special night featuring the Gay Men's Chorus of Houston and the Bayou City Women's Chorus held on National Worlds Aids Day. It celebrated inclusivity, diversity, and the spirit of Christmas while reflecting on the worldwide AIDS crisis and how we still have much too accomplished with awareness and prevention.
By Raegan Carey
Legacy Lapels Brings the Power of the Suit
"It's not about the suit. It's about the man in the suit." ~ Ramon Smothers
Houston's TCWF Empowers a Community of Women Entrepreneurs
Shantera Chatman, founder of The Chatman Women's Foundation (TCWF) held an incredible, enterprising event titled the PowHER Breakfast. This year's breakfast was special since it commemorated the organization's tenth year of helping others. That's ten years of inspiration, professional growth and empowering women of Houston to be future business owners.
UNICEF With Harvey On Its Mind Generously Gives Back
It was a glamorous night of Houstonians on the red carpet that led to a grandiose evening at the UNICEF Gala Houston.
Community: AVDA Acts to End Abuse
The fearless AVDA campaign "END ABUSE BEGAN AGAIN" is a strategic force against domestic violence and it has been a successful one. This past week, many well-heeled society women and a few well-suited men filled up the Junior League's Tearoom to discuss making a significant difference and furthering this much-needed cause.
Johnson 'Sets It Off' Onstage with Houston Audiences
'Set It Off Live on stage,' Je'Caryous Johnson's most recent anticipated play made its way to Houston and debuted to sold-out audiences. It was a smash hit. "Set It Off Live On Stage' is based on the original screenplay of the same name by Takashi Bufford and the stage production was written, directed, and produced by Houstonian Je'Caryous Johnson.
Memphis Makes it's Way to Houston Audiences with an All –Too Familiar Narrative
Written by Joe DiPietro and David Bryan and directed by Dan Knechtges, the story of Memphis begins in musically–rich Memphis during the 1950's south where Rock and Roll was born. It tells a story of a white radio DJ named Huey Calhoun who becomes obsessed with the taboo music of Blacks. Lured into a jute-joint by the sound of Rhythm & Blues, he starts to regularly visit a local nightclub for Blacks only and develops a crush on the nightclub's star singer, the beautiful and talented Felicia Farrell.
The Ensemble Theatre Honors King in a Magnificent Way
On April 4, 1968, the Rev. Dr. Martin Luther King Jr., 39, was shot to death in Memphis TN while standing on a hotel balcony. Dr. King, the praised civil rights leader, arrived in Memphis on April 3rd and delivered the final speech of his life, known today as the "I've Been to the Mountaintop" address, in which he spoke of his own mortality.
Love It or Not: "Lover, Beloved, Plays" Up to Small Alley Audiences
In the spirit of all things love, The Alley Theatre presents "Lover, Beloved," a musical play written and composed by Grammy award winner and singer/ songwriters Suzanne Vega and Duncan Sheik. The play is inspired by the life and writings of Carson McCullers, an outspoken, rebellious 1940's writer that became one of the brightest literary talents of the 20th century.
Galleria Unveils Its New Saks Fifth Avenue Wing With New Boutiques
The Houston Galleria opened its newest Saks Fifth Avenue Wing on Westheimer. Featuring fashion previews with live models, Pop-Up Tea and Patisserie by Yauatcha, special gifts for attendees from GVI retailers and more. The Exclusively Yours, VIP Influencer Event was a fashionable partay!


text:
Home / ADAPTATION / "POKEMON Detective Pikachu" Movie Reveals Official Title Logo
"POKEMON Detective Pikachu" Movie Reveals Official Title Logo
Ravenfox13 12:56:00 PM ADAPTATION
At the opening ceremonies of the 2018 Pokémon World Championships, The Pokémon Company, along with its partners from Legendary Entertainment, unveiled the official title and logo for the first-ever live action Pokémon movie, POKÉMON Detective Pikachu.
Mr. Tsunekazu Ishihara, president of The Pokémon Company, welcomed the movie's director, Rob Letterman, and actors Justice Smith and Kathryn Newton to the stage for the surprise reveal.
The stars also engaged the room full of the world's best Pokémon players in a chant of "Pikachu!" which was recorded for use in the upcoming film.
In Philippine cinemas June 12, 2019, POKÉMON Detective Pikachu is distributed by Warner Bros. Pictures, a WarnerMedia Company.


text:
Chasin' Crackers sets the pace in Group 1 Vic Peters Classic
Tuesday 24th October 2017 10:17 am. Staff Writer
Chasin' Crackers was brilliant in his heat of the Vic Peters Classic. PIC: Paul Munt.
VICTORIAN greyhound Chasin' Crackers (Fabregas x Lady Arko Aug '15) stamped himself as the greyhound to beat in this year's Group 1 Vic Peters Classic (520m) after an emphatic win in his heat of the series at Wentworth Park on Saturday night.
Trained at Tooradin by Glenn Rounds, Chasin' Crackers came into his heat in sensational form, having won three of his previous four starts at Sandown Park and The Meadows over the middle distance.
Drawn ideally in box two, the black dog speared the lids and raced straight to the front of the pack. Once on the bunny it was a case of times and margins as he stretched out to defeat a gallant Bogan Doonie (Spring Gun x Agni Jul '15) by three and three quarter lengths in a blistering 29.62.
Rounds said he was quietly confident his greyhound could put in a bold performance on Saturday night and noted he was not surprised to see Chasin' Crackers win so convincingly.
"I was very pleased with his run," Rounds told Australian Racing Greyhound.
"I thought he was drawn well – the inside is the place to be at Wentworth Park because if you miss it you get pushed wide around the first corner.
"I wasn't surprised at all to see him win so well – he has always been a nice dog and he has been racing very well lately."
Rounds believes his recent racing over the middle distance may have assisted his greyhound's attitude going into the race.
"I think the 600 racing helped him a lot heading into the heats – he got a lot of confidence from those runs as he was able to find the front easily and stay out of trouble," he said.
"He had been screaming out for 600 and while he was racing very well over the middle distance and beginning well, when I saw the Vic Peters coming up I decided to have a crack at it because it is an age restricted series and you only get one go."
Chasin' Crackers has now won 12 races from 30 starts with 12 minor placings, his prize money earnings now closing in on $70,000.
The 33-kilogram powerhouse was bred in NSW by Luke Miller and is owned by David and Mick Carroll, the latter also racing his mother Lady Arko which was a former top-class stayer.
Rounds says with another good box draw Chasin' Crackers will be hard to beat in his semi-final next week, with the prominent conditioner of the belief he is improving each time he races.
"Lately he has really been starting to find his best and develop into a very nice dog – although with that being said he has never really put in a bad run throughout his career," he said.
"He came out super on Saturday night – hopefully he can get another good draw in the semi-finals – box one, two or three would be perfect.
"If he can repeat what he did in his heat he is going to be right in it."
Rounds said another middle distance campaign will happen down the track, however he is unsure whether he will get any further and says Chasin' Crackers won't be pushed too far, too soon.
"I do want to have another go with him over more distance – although while he is racing well over the sprints we'll probably keep him over it," he said.
"I'd say sometime after Christmas we'll step him up – but I am not in a huge rush as I am aware that once I do step him up over more ground there is no coming back."
Six heats of the Group 1 Vic Peters Classic were run and won on Saturday night. The first qualifier went to Seona Thompson's Manila Kampyon (Fernando Bale x Solar Pak Nov '15) which debuted at Wentworth Park with a fast 29.94 win.
The second heat went to local star Mr Pupparazzi (Djays Octane x Pie Thief Sep '15) which made it four in a row when saluting in 29.66 for Jason Magri.
Heat four went the way of Group 1 National Sprint Championship finalist Bekin Street (Bekim Bale x Serisier Street Sep '15) in 29.99, whilst Chris Carl collected a double with litter mates Fast Car Driving (Kc And All x Subway To Venus Dec '15) and Rostered On in 30.14 and 30.00 respectively.
The box draw for the four semi-finals will be released on Tuesday, with the first two from each race progressing through to the $75,000 to the winner final on November 4.
Previous in category
Next post in category


Army is a medium green with a dash of silver and hint of gold in the undertones adding a rich shimmer. Applies semi sheer dry and full coverage when foiled. Especially flattering for hazel, blue and brown eyes. Especially complimentary to earth tones.


To be a premier pharmacy institute achieving excellence in teaching, value education, research and consultancy in core areas and be engaged in the service in promoting continued education.
To educate students from diverse backgrounds in the fundamental skills, knowledge through a curriculum designed by the university and to prepare them for pharmacy professional positions in service organizations, pharmaceutical industries, other healthcare fields and also to promote a spirit of innovation and entrepreneurship.
To develop competent pharmacy professionals through excellence in education.
To provide sound academic foundation to develop professional skills through a personalized and multiple learning environments both within and beyond the classroom.
2018 – Introduction of D. Pharm course with an intake of 60 students.
2017 – Reaccreditation by National Board of Accreditation, New Delhi (B. Pharm. course – July 2017 to June 2020).
2016 – Recognition Under Section2 (f) & 12 (B) of the UGC Act,1956.
2013 – Permanent Affiliation for B.Pharm course to Savitribai Phule Pune University, Pune.
2013 – Recognition as an approved center for Post Graduate Research (Ph.D.) by Savitribai Phule Pune University.
2011 – Introduction of Post Graduate (PG) Courses (M. Pharm. in Pharmaceutical Quality Assurance) with an intake of 18 students.
2010 – Introduction of Post Graduate (PG) Courses (M. Pharm. in Pharmaceutics and Pharmacognosy) with an intake of 18 students each.
2006 – Establishment of B.Pharm course with an intake of 60 students.


This is a placeholder page for Karen Hebert, which means this person is not currently on this site. We do suggest using the tools below to find Karen Hebert.
You are visiting the placeholder page for Karen Hebert. This page is here because someone used our placeholder utility to look for Karen Hebert. We created this page automatically in hopes Karen Hebert would find it. If you are not Karen Hebert, but are an alumni of Hamburg High School Hamburg, AR, register on this site for free now.


text:
iPad 4 and iPad mini performance tests
Rene Ritchie
The iPad 4 has an Apple A6X system-on-a-chip (SoC) is marketed as twice as fast, both in central and graphics processing, as the iPad 3 released only 7 short months ago. Apple's custom, manually-set ARM v7s processor -- called Swift -- remains the 32nm CMOS dual-core beast found in the iPhone 5, but it's been cranked up to 1.4 GHz. The X in the iPad 4's A6X once again represents a quad-core graphics processor, this time the PowerVR SGX554MP4. On spec, that's some serious fire-power.
The iPad mini, by contrast, has the same die-shrunk Apple A5 SoC found in the iPad 2. That's a 1GHz dual-core ARM Cortex A9 and PowerVR dual-core SGX543MP2. But the iPad mini also has the same 1024x768 display as the iPad 2. It's smaller but denser, going from 9.7-inches to 7.9 inches, and 132 ppi to 163 ppi, but it's the raw pixel count here that makes the difference.
Retina comes at a price, and that price is performance for the first generation devices that have to support it. The iPad 3, iPhone 4, the iPod touch 4, even the Retina MacBook Pros were and are maxed out trying to push all those pixels. Once that's done, though, once the price has been paid, however, performance improvements go back to where they belong -- making things feel faster.
So, even with the older, less powerful Apple A5, the iPad mini should fly. But will the new A6X help the iPad 4 do likewise?
Benchmarks aren't that useful for humans, but they do provide some amount of relative measure, and a way to tell if your particular device has a problem (i.e. it's way slower than expected.) So, here's what the difference in CPU looks like on Geekbench 2 between the iPad 1, iPad 2 (top left and right), iPad 3, and iPad 4 (bottom left and right).
Those are pretty close to Geekbench's standard listings of 454, 781, 790, and 1755.
Here're SunSpider results for JavaScript rendering, which try to give an idea of how code-heavy sites like FaceBook or Google Docs will perform.
That's 454, 781, and 790 compared with 1755, which is a numerically impressive jump.
More importantly, however, the video up top shows what the iPad 4 and iPad mini look like in real-world situations like booting up, rendering web pages, and launches apps, compared against the iPad 3, iPad 2, iPad 1, iPhone 5, and iPod touch 5. They're ludicrously unscientific, but perception is reality and how something works, day to day, is far more important than how it looks on the spec sheet.
As you can see, the difference looks much bigger in numbers than it turns out to be in daily usage. The iPad mini was, as expected, every bit as good as the iPad 2. With the iPad 4, the best way I can phrase it after using it side by side with the iPad 3, is that you don't really notice much if any speed improvement, you just notice much less lag. Everything launches and moves at about the same pace, it just doesn't stick and stutter anywhere nearly as much while doing it.
It's still not perfect, mind you, but it's better.
Sonos Beam Smart TV sound bar with 2 $50 Amazon gift cards


text:
The Comic Critic's Review of "The French Connection"
The French Connection has one of the most famous car chases in movie history. Featuring a 1971 Pontiac LeMans, it was carefully choreographed stunt. Part of the reason for this choreography was because the chase was being conducted without the proper permits. That means the streets in which the scene was shot was not cleared of normal traffic. Off duty police and stunt cars were poised to stop traffic, and other stunt cars were arrange to provide the near misses. Some of the shots were angle was set low with a bumper mounted camera capturing all the trash and dirt of the street and as the car raced along. Even with precautions in place some of the near misses became crashes. An one crash was completely unpredicted as a fellow leaving his house didn't realize that a car chase was being filmed. His vehicle was paid for and all of these lucky accidents went into the final cut of the movie. What you get is a true to life reckless car race lasting five minutes and leaving you shaky at the end of it. The French Connection is also ground zero for numerous cop show tropes used so heavily since then they are considered trite. It was also the first movie that did an excellent job showing the city's true gritty underbelly and the real nature of police work. All of which have become a genre of entertainment in itself.
Nominated for eight Academy Awards it won five including Best Picture.
Labels: #moviereview, 1971, action, cop drama, Gene Hackman, Mark Monlux, The French Connection
The Comic Critic's Review of "The French Connectio...


In digital marketing, cannibalization occurs when a paid search ad "steals" traffic away from an organic listing. You'll typically find questions associated to this topic like, why should I bid on my brand name keywords? Or, why should bid on keywords that I rank #1 for organically?
Let's put these questions to rest once and for all because, in my opinion, cannibalization is a pretty harsh term to associate with paid search. So, unlike my Pac-Man example above, I prefer to view the relationship between PPC and SEO as a symbiotic one where both channels work together to achieve an overarching marketing goal. Let's look at a few examples and discuss why it's beneficial to appear in both spaces simultaneously.
Real estate consumed on the search engine results page is the most easily seen benefit of targeting identical keywords in both paid search and search engine optimization efforts. Increasing the shear visibility of your brand is always beneficial; your (1) more noticeable and (2) consumers will begin to associate your brand more often with a particular search phrase – both branded and non-branded.
I've conducted a search for the keyword sears in the example below. I am not only served an organic link (with sitelinks), a map displaying locations, and a Google+ page, but I'm also provided with a paid search ad that consumes a huge portion of the SERP. In fact, the only brand visible above the page fold is Sears®. This advertisers has certainly done their homework in both SEO and PPC.
Because the advertiser is dominating the SERP, they now have the ability to generate over a dozen different messages and ways (links) for the consumer to interact with their brand. But how do they leverage this visibility? Notice how the messaging differs between PPC and SEO, and think about how both PPC and SEO work separately. SEO is a long-term strategy, and PPC is a short-term strategy.
We see similar techniques at play here in the non-branded PPC example: ad extensions, calls-to-action, etc. are used to build upon and solidify the message presented in long-term SEO strategy.
The third benefit of targeting the same keywords in both SEO and PPC channels again harkens back to consuming real estate on the SERP. It is plain and simple; with more links pointing to your website at any given moment there is more opportunity for increased visitors.
In Scenario 1, paid search ads are not running. Organic links are responsible for 1,000 website visits. In Scenario 2, paid search ads are running. Although organic visits have decreased due to the incorporation of paid per click ads, total website visits have actually increased to 1,250. So that's 250 visits (1,250 minus 1,000) that you would not have received without the use of PPC advertising.
Since SEO and PPC strategies essentially share the same goal of increasing your overall website traffic, you should certainly consider using both strategies in conjunction with one another to achieve your marketing goals. Both digital marketing strategies are tools used to achieve your marketing goals. Learn how you can use one to strengthen the other, forming a symbiotic relationship. Once this is achieved you can start to dominate the SERP and dominate your competition. Have fun!
Questions? Comments? Leave it in the section below.


text:
Home » FAQs » What Convictions Are Eligible for Criminal Record Expungement in PA?
What Convictions Are Eligible for Criminal Record Expungement in PA?
Convictions eligible for criminal record expungement in PA include summary offenses and criminal convictions related to underage alcohol use, often following a waiting period during which the convicted party avoids further legal issues. In certain situations, a person may be granted expungement for other, more serious offenses, often after reaching a certain age or showing the court never entered a disposition on the case.
If you have a criminal record in Pennsylvania and want to explore the possibility of criminal record expungement, a criminal defense lawyer from McKenzie Law Firm, P.C. can help. Our lead attorney, David McKenzie, is a former prosecutor who understands the innerworkings of the state courts. We will evaluate your case for free and let you know how we can help.
To explore what convictions are eligible for expungement in PA, call 610-680-7842 for a free consultation.
Related: Is There Any Difference Between a 'No Contest' Vs. 'Guilty' Plea in a DUI Case in Pennsylvania?
Convictions Eligible for Criminal Record Expungement in PA
Your criminal record may be eligible for expungement in Pennsylvania. The state wipes out criminal convictions that fit into certain categories, including:
Summary Offenses
"Summary offense" is a term used in Pennsylvania to describe a minor crime. Generally, summary offenses are more severe than minor traffic violations, but less severe than even common misdemeanors. A person charged with a summary offense often never gets arrested nor spends any time in jail. This has led some in the state to refer to summary offenses as "non-traffic citations," as they more closely resemble a ticket than a criminal charge.
A few examples of summary offenses in Pennsylvania include:
Loitering
Non-violent harassment
If you receive a citation for a summary offense, you can often avoid going to court altogether by mailing in a fine, similar to a ticket for speeding or rolling a stop sign.
Summary offenses are eligible for expungement five years from the disposition date. You must be free of any other criminal convictions during those five years to have your summary offense expunged.
Underage Alcohol Offenses
If you were convicted of an alcohol-related crime at age 18 or older, but younger than 21, Pennsylvania allows you to get this conviction expunged. You may petition for expungement as soon as your 21st birthday.
If you have had no further legal issues and satisfied the terms of the sentence imposed for your conviction (e.g., paid all your fines and completed the period of driver's license suspension, if applicable), then your offense will be expunged.
Expungement Due to Advanced Age or Death
Pennsylvania also expunges most criminal records of residents who are 70 years of age or older, provided they have avoided further legal problems for at least 10 years following their most recent release from confinement.
No Disposition Entered
When you are convicted of a crime, the court must enter the disposition of the case (e.g., guilty) into the repository. If, after 18 months following your arrest, no disposition has been entered in the repository, you can have the offense expunged from your criminal record.
Related: Who is the Best Criminal Lawyer in Montgomery County?
Convictions Not Eligible for Criminal Record Expungement in Pennsylvania
There are certain criminal convictions Pennsylvania does not expunge, even if you agree to enter an Accelerated Rehabilitative Disposition program. These crimes typically are of a sexual nature or involve minor victims. For instance:
Statutory sexual assault
Involuntary deviate sexual intercourse
Aggravated indecent assault
Possession of obscene sexual materials
To find out more about whether your crime is eligible for expungement, call McKenzie Law Firm, P.C. today. Our team offers a free case evaluation and is eager to help in any way we can. Call 610-680-7842.
Related: What Are Some Punishments Given To Juvenile Offenders In Pennsylvania?
For a Free Case Evaluation with a Criminal Defense Lawyer in PA, Call McKenzie Law Firm, P.C. at 610-680-7842
David McKenzie and his dedicated legal staff at McKenzie Law Firm, P.C. want to help you with any criminal issue you are facing. Whether you have been arrested and are fighting a conviction or have a conviction and want it expunged, we fight for the rights of the accused and convicted in Pennsylvania. To schedule your free case evaluation with a member of our team, call 610-680-7842 today.
How Do I Find Someone Who Was Arrested In Pennsylvania?
If I Have an Outstanding Warrant in Pa and Moved, Am I a Fugitive?
What Is the Difference Between Stealing and Embezzlement?
How to Change Your Criminal Defense Attorney
How Long Do You Go To Jail For Drunk Driving In Pennsylvania?
Find a Friendly
Upper Moreland DUI Lawyer
Lower Makefield DUI Lawyer
Pennsylvania DUI Lawyer
Haverford DUI Lawyer
Springfield DUI Lawyer
Whitemarsh Township DUI Lawyer
Willow Grove DUI Lawyer
Criminal Defense,
What Crimes Cannot Be Expunged in Pennsylvania?
What Are My Miranda Rights?
Outstanding Warrant,
How Do You Know If You Have an Outstanding Warrant?
Can You Still Be Arrested For Public Drunkenness In PA?


One for the taste buds! A mixture of fruits from strawberry to pomegranate Fruit, passing through fresh melon. How can't you not love this bottle of pomberry?
Love this flavour so much. Best one yet.
This is one of my favourite flavours from Toxic Juice highly recommended it's a lovely mix of flavours.


Helen Keplinger is one of California's true winemaking masters! In 2012, she was named Napa Valley & The Sierra Foothills, California Winemaker of the Year by prestigious Food & Wine magazine. She has worked with wine legends such as consultant Michel Rolland, viticulturist David Abreu, and winemaker Heidi Peterson Barrett, and she was the winemaker for Bryant Family Vineyards before focusing on her own label. We are honored and excited to feature Helen's talent, showcasing her ability to masterfully craft different Rhône grape varieties.
Helen Keplinger's incredible wines will be paired with a farm-to-table menu created by d.k Steak House Executive Chef Albert Balbas.
21-DAY DRY AGED KING NATURAL STRIP LOIN with summer truffle and gruyere cheese gratin, red wine peppercorn jus, bay leaf gremolata, shaved asparagus.
or call 808-931-6280 for reservations.


Is pdvWireless Inc (PDVW) A Good Stock To Buy?
Like everyone else, elite investors make mistakes. Some of their top consensus picks, such as Micron and Anadarko Petroleum, have not done well during the last 12 months ending in October due to various reasons. Nevertheless, the data show elite investors' consensus picks have done well on an average. The top 30 S&P 500 stocks among hedge funds at the end of September 2014 yielded an average return of 9.5% during the last four quarters ending in October and sixty-three percent of these 30 stocks outperformed the market. S&P 500 Index returned only 5.2% during the same period and less than 49% of its constituents managed to beat this return. Because their consensus picks have done well, we pay attention to what elite funds think before doing extensive research on a stock. In this article, we take a closer look at pdvWireless Inc (NASDAQ:PDVW) from the perspective of those elite funds.
Is pdvWireless Inc (NASDAQ:PDVW) the right pick for your portfolio? Hedge funds are getting less bullish. The number of long hedge fund positions fell by 4 in recent months. pdvWireless Inc (NASDAQ:PDVW) was in 7 hedge funds' portfolios at the end of September. There were 11 hedge funds in our database with pdvWireless Inc (NASDAQ:PDVW) holdings at the end of the previous quarter. The level and the change in hedge fund popularity aren't the only variables you need to analyze to decipher hedge funds' perspectives. A stock may witness a boost in popularity, but it may still be less popular than similarly priced stocks. That's why at the end of this article we will examine companies such as Kadant Inc. (NYSE:KAI), Winmark Corporation (NASDAQ:WINA), and Golden Ocean Group Ltd (NASDAQ:GOGL) to gather more data points.
If you'd ask most market participants, hedge funds are viewed as unimportant, old investment vehicles of years past. While there are over 8000 funds trading at the moment, we look at the top tier of this club, about 700 funds. These investment experts shepherd bulk of the smart money's total asset base, and by keeping track of their best investments, Insider Monkey has revealed several investment strategies that have historically outpaced the market. Insider Monkey's small-cap hedge fund strategy outstripped the S&P 500 index by 12 percentage points per year for a decade in their back tests.
Now, we're going to take a look at the recent action encompassing pdvWireless Inc (NASDAQ:PDVW).
What does the smart money think about pdvWireless Inc (NASDAQ:PDVW)?
Heading into Q4, a total of 7 of the hedge funds tracked by Insider Monkey held long positions in this stock, a decline of 36% from the previous quarter. With the smart money's sentiment swirling, there exist a few notable hedge fund managers who were upping their holdings meaningfully (or already accumulated large positions).
According to Insider Monkey's hedge fund database, Stephen Feinberg's Cerberus Capital Management has the biggest position in pdvWireless Inc (NASDAQ:PDVW), worth close to $104.4 million, corresponding to 8.7% of its total 13F portfolio. On Cerberus Capital Management's heels is Jeffrey Altman of Owl Creek Asset Management, with a $51.3 million position; 2.9% of its 13F portfolio is allocated to the company. Hedge funds and other institutional investors that hold long positions consist of Daniel Gold's QVT Financial, Jody LaNasa and Vivian Lau's Serengeti Asset Management and Eric Edidin and Josh Lobel's Archer Capital Management.


Yet another US healthcare company has reported a major data breach – this time insurance firm Excellus said hackers have stolen the personal details of 10.5 million customers.
The breach affected around 7 million "members, patients or others who've done business" with BlueCross BlueShield, with the remainder Lifetime Health Care customers.
The plans affected are BlueCard Members; BlueCross BlueShield of Central New York; BlueCross and BlueShield of the Rochester area; BlueCross BlueShield of Utica-Watertown; and Excellus BlueCross BlueShield.
This incident also affected members of other plans who sought treatment in the firm's 31-county upstate New York service area.
"Individuals who do business with us and provided us with their financial account information or Social Security number are also affected," the firm's president and CEO, Christopher Booth, said in a statement.
Booth revealed that his IT team first discovered the "sophisticated attack" on 5 August 2015, and has been working since with Mandiant and the FBI.
However, the attack actually began over a year and a half ago – on 23 December 2013 – he admitted.
As is the norm on such occasions, Excellus is offering free identity theft protection services to affected customers for two years.
However, Booth claims there's no evidence the data has been used "inappropriately" thus far.
"The hackers' ability to go unnoticed and gain unauthorized access to the company's IT systems and the personal information of potentially thousands of people does not come as a surprise," he added.
Netsurion CEO, Kevin Watson, added that Excellus would likely suffer loss of customer trust and brand equity because of the breach.
"As cyber-criminals increasingly target personally identifiable information other than credit card or financial data, more and more businesses will need to be vigilant of their data security," he argued.
Excellus is the latest in a long line of US healthcare breaches – following most notably Anthem (78 million customers) and Premera (11 million).
It's suspected that potentially state-sponsored Chinese hackers could be behind those attacks as they continue to build up a huge database containing the digital identities of US government employees.
Security experts have been warning for years that healthcare providers have under-invested in information security.
According to the Identity Theft Resource Center, healthcare providers accounted for more breaches (42.5%) than any other sector in 2014, continuing a three-year trend.


Secretary of State Brian Kemp addresses the audience and declares victory during an election watch party on July 24, 2018 in Athens, Georgia. Kemp defeated opponent Casey Cagle in a runoff election for the Republican nomination for the Georgia Governor's race.
When Georgia Republicans chose Brian Kemp, the state's voter-suppressing Secretary of State, as their nominee for governor against Democratic supernova Stacey Abrams this week, they set up a November election that will be one of the nation's most-watched and most entertaining. It will also be the nation's most comically misunderstood.
The hilarity began with the spate of insta-analysis unleashed the moment Kemp, a rich white businessman from the progressive outpost of Athens, bested Lieutenant Governor Casey Cagle in Tuesday's runoff after a primary best characterized (as Cagle did in a taped conversation that doomed him in the end) as a Trump-era slugfest to see "who could be the craziest." Not a single state-level policy issue came into play, thanks largely to Kemp, who set the tone with a slick series of political infomercials casting him as a cross between a shotgun-wielding suburbanite and an actor auditioning for the lead role in Forrest Gump II: Bounty Hunter. In case you don't know Abrams yet, she is basically the polar opposite of the character Kemp (whatever his real IQ or ideology) so convincingly portrays: an unabashedly liberal, Ivy League-educated novelist and attorney who rose to lead Georgia's House Democrats through smarts and savvy and lofty ambition she prefers to flaunt rather than conceal.
But all the many factors that'll make this such a fascinating and consequential — and potentially history-making — campaign also guarantee that it'll be nationally hyped into a whole bundle of "tests" and "referendums" that it won't be. The New York Times, among others, gave us a taste this week: "Mr. Kemp now faces Stacey Abrams, the Democratic nominee, in a November general election that will test whether this rapidly changing Southern state prefers a Trump-style conservative or a progressive black woman," opined Jonathan Martin and Alan Blinder on Tuesday night. Setting aside the esoteric matter of whether a state can actually cast a vote in an election, rather than voters in a state — or the higher-level issue of why the Times uses race to describe Abrams but leaves out Kemp's equally relevant racial identity — this is the basic template for how almost every pundit and news outlet will be getting this election wrong all summer and fall.
For starters, however you want to characterize Kemp's and Abrams's ideological profiles — "conservative" and "progressive" serve well enough as shorthand — they won't define the choice Georgia voters make in November. Nor will anything remotely resembling "policy issues," those quaint relics of pre-Trump American politics. That's not just because Kemp wants to — has to — cast the governor's race as a culture war. He already has, as his ad campaign and his victory speech on Tuesday night demonstrated.
It's also because there is not a single Democrat or Republican in Georgia (with usual exceptions for the profoundly uninformed and confused), who could conceivably give one nanosecond's thought to casting a vote for the other party's nominee. Not only are Abrams and Kemp running on platforms that are polar opposites, they've both been unusually high-profile politicians in Georgia for more than a decade now. Both have sky-high name recognition, crystal clear political identities and personalities, and every sentient human in Georgia knows they're long-time foes over voting rights. Abrams first shot to national attention by founding the New Georgia Voter Project, one of the country's most ambitious voter-registration efforts. Kemp, as the two-term secretary of state, has used every tool of his office (and then some) to block those efforts and keep Georgia's voter rolls disproportionately old, white and right.
Lazy pundit-speak about "the middle" completely misses what — and who — will actually decide the Abrams-Kemp showdown. Just as nobody should be fooled that Georgians (or Georgia itself!) will be deciding whether they (or it!) prefer "progressivism" to "conservatism," it's pure ignorance to imagine that either Kemp or Abrams will be recalibrating their messages and delivery to appeal to the "middle," or "centrists," or "moderates," or whatever term of art pundits might reach for. Why? These folks, who really don't have any leanings one way or another, are almost non-existent in Georgia nowadays, just as they are in the rest of the U.S. As any political scientist or pollster can tell you, voters who don't affiliate with a party in 21st-century America are now damn near as reliably Democratic or Republican when they go to the ballot box as registered Ds and Rs — "closet partisans," in the useful term popularized by political scientist Alan Abramowitz of Emory University.
So what will decide this epic battle in November? Voter registration and turnout. That's all, folks! But that certainly doesn't mean it won't be full of fireworks — and eminently worth watching.
Georgia isn't quite a "toss-up" state yet, though it's long been moving steadily in that direction — Trump just barely managed to top 50 percent in 2016. The only reason Georgia isn't already "leaning blue" is that potential voters who lean left — notably blacks, young whites, and Hispanics (9 percent and soaring) — do not register and vote in nearly the same numbers as whites who lean, register, or vote Republican. In purely racial terms, Georgia will soon (by 2025) become the next "minority-white" state in the country because of its long population boom, including the New Great Migration of blacks from North back to South that Jamil Smith noted in his recent Rolling Stone column on Abrams.
Abrams, who refreshingly makes no bones about her political ambitions — she aims to be the first black woman to lead any state in the union, and then to become the first such President of the United States — understands that more completely than anyone. The whole predicate of her New Georgia Project, and the great aim of her campaign, is turning Georgia blue by turning Democratic-leaning non-voters into Democratic-leaning voters. Once that happens, it'll be a very long time (i.e., a cold day in Hell) before Georgia ever elects another white conservative statewide. Just as in Texas, the Democratic advantage in Georgia will become overwhelming over the next few decades once younger folks and former "minorities" start voting in the same numbers as older white people.
Can Abrams accelerate that process in 2018? That is the only real "issue" at stake in her race against Kemp. In the simplest terms, can she make up the less than 5-point gap in 2016 between Trump and Hillary Clinton, and do it in a mid-term year, when white Republicans tend to vote in even more disproportionate numbers? It'll certainly help that Trump, who endorsed Kemp in the runoff, is increasingly unpopular in Georgia. It'll also help that Kemp will strike less-"crazy" Republicans as too Trump-like for comfort. Those folks won't vote for Abrams, by and large; they just won't vote.
Kemp showed in his primary campaign — running against other white conservatives — that he won't shy away from anything that helps him stoke old white Georgians' prejudices. Victory in November, for Kemp, hinges on whether he can turn Abrams into the fictionalized radical black woman he's already running against — not so much another Hillary Clinton or Nancy Pelosi as another "radical black leftist" like Angela Davis or (closer to home) former Georgia congresswoman and eternal GOP bete noire Cynthia McKinney.
Abrams won't have to cast Kemp as a wild-eyed racist, misogynist, religious bigot — the list could go on. Dude is already doing it for her, and his only path to victory is to keep it up.
The governor's race in Georgia will be a blast. A doozy. A humdinger. It will be "about" race, gender, and ideology — but not for the reasons you'll constantly be hearing. And the result, if Abrams pulls it off, will be historic, even if the history it makes will just be a sped-up version of where Georgia is already headed.


text:
Premier League | July 8, 2018
Mane: No contact with Madrid
Liverpool winger Sadio Mane insists he has not been in contact with Real Madrid amid reports of a potential move to the Spanish capital.
The Senegal international, who featured for his country at the 2018 World Cup, is rumoured to be on Los Blancos' radar should they need to replace Cristiano Ronaldo.
Juventus have been heavily linked with Ronaldo since Portugal were eliminated from the global showpiece in Russia, and the 33-year-old forward admitted on Friday he was "evaluating several opportunities".
#OTD in 2016, we signed Sadio Mane from Southampton for £34.5m. He has proven his worth this season after he has scored 20 goals in all competitions and has become a key player in our squad! #LFC #YNWA #LFCFamily pic.twitter.com/B3Ta2CR3CG
— TheKop.com (@TheKop_com) June 28, 2018
But Mane is adamant Real have not been in touch with his representatives and that he's focused on getting ready for the new campaign with Jurgen Klopp's side.
"These are just rumours. I am not aware of anything and haven't been contacted," the 26-year-old told reporters in Bambali.
"I remain a Liverpool player and I will join my team-mates in the United States for the pre-season tour.
"Real are a great team, but I am focused on my team, Liverpool."
Home Football Premier League Mane: No contact with Madrid


text:
HomeNewsRCMP issue statement on Human Rights Watch report
RCMP issue statement on Human Rights Watch report
Monday, Jun. 19th, 2017
The RCMP will be taking time to review the Human Rights Watch report coming out of Saskatchewan.
The New York-based group wrote a 32-page report detailing 64 cases of alleged violent abuse. The alleged attacks were done by enforcement officers, according to interviewed Indigenous women and social workers.
The report says, "Human Rights Watch found evidence of a fractured relationship between law enforcement and indigenous communities…The legacy of settler colonialism and racist assimilation policies — particularly the residential school system — still overshadow the present-day dynamics between police and indigenous communities."
In a statement, the RCMP said they are, "committed to participating fully in the implementation of the national reconciliation framework and supporting the Calls to Action resulting from the Truth and Reconciliation Commission of Canada."
They used 'Call to Action 41' as an example, where they are to provide full service to the Missing Indigenous Women's Inquiry.
Related: MMIW CONFIRMS INQUIRY WILL CONTINUE THROUGH SUMMER
In the statement, the RCMP detailed ways in which their officers are being trained to include cultural awareness. It's a wide list that includes expanded Indigenous training, de-escalation training for high pressured situations and appropriate female body searches.
The RCMP ended the statement with a reminder that police misconduct is serious. If you see a case of what you believe to be such an act, report it to either the Royal Canadian Mounted Police, or the CRCC directly.
To see the full statement, click here.