text:
\section{Introduction}
\label{sec:intro}
The search for non-gravitational dark matter (DM) interactions is one of the chief enterprises in modern experimental particle physics and observational astrophysics~\cite{Jungman:1995df,*Bergstrom:2000pn,*Bertone:2004pz,*Feng:2010gw}. While not required on general grounds, such interactions find strong motivation in the context of a cosmological origin of the dark matter abundance. Indeed, a compelling hypothesis is that DM is a thermal relic from the hot Big Bang, which requires non-gravitational couplings between DM and the Standard Model (SM) to ensure thermal contact and deplete the DM abundance. These couplings in turn predict a variety of novel phenomena associated with DM that can be sought through experiment and observation, offering the prospect of testing the thermal relic hypothesis. The most popular possibility for the non-gravitational couplings is the ordinary electroweak gauge interactions. This scenario is theoretically attractive due to the coincidence of the predicted and observed DM abundance for a TeV-mass relic with electroweak interactions and its potential connection to the Higgs naturalness problem, and has inspired an expansive and diverse experimental search program that has probed a significant portion of the parameter space.

Nevertheless, thermal relic DM need not have SM gauge interactions. It is quite plausible that DM is instead a new electroweak gauge singlet particle, in which case an additional mediator particle is generally required to couple the dark and visible sectors~\cite{Boehm:2003hm,*Boehm:2003ha}.
While there are in principle many ways that this mediation can occur, three renormalizable {\it portal} couplings stand out on account of their economy and uniqueness.
These are the well-known vector portal~\cite{Okun:1982xi,*Galison:1983pa,*Holdom:1985ag}, Higgs portal~\cite{Silveira:1985rk,*Patt:2006fw}, and neutrino portal~\cite{Minkowski:1977sc,*Yanagida:1979as,*GellMann:1980vs,*Glashow:1979nm,*Mohapatra:1979ia,*Schechter:1980gr}:
\begin{eqnarray}
B_{\mu\nu} \, V^{\mu\nu} , ~~~~~  H^\dag H \, S, ~~~~~ \bar L H N +{\rm h.c.},
\end{eqnarray}
where $V_\mu$, $S$, and $N$ are new vector, scalar, and fermionic mediators, respectively, which can be straightforwardly coupled to the singlet DM particle.
It is possible to distinguish two cases according to the dominant DM annihilation channel~\cite{Pospelov:2007mp}. The first case is {\it secluded annihilation},
in which dark matter annihilates directly to mediator particles. This occurs when DM is heavier than the mediator. The second, more predictive case, is {\it direct annihilation}, in which the dark matter annihilates through the mediator to SM particles. This occurs when DM is lighter than the mediator. In the secluded regime, the annihilation rate is set entirely by dark sector couplings. The mediator need only have a minuscule coupling to the SM to ensure kinetic equilibrium between the sectors, making it challenging to robustly test the scenario. In contrast, efficient direct annihilation necessitates a substantial mediator-SM coupling to avoid DM overproduction, leading to a predictive and experimentally testable scenario. For the predictive case of thermal DM directly annihilating to SM particles, a broad experimental effort is developing that will decisively test vector portal mediation~\cite{Alexander:2016aln}, while the case of Higgs portal mediation is already strongly constrained~\cite{Krnjaic:2015mbs}.

Neutrino portal DM has been studied only a handful of times, despite sterile neutrinos $N$ being arguably the best motivated mediator candidate due to their role in neutrino mass generation.
One likely reason for this is a theoretical prejudice for tiny neutrino Yukawa couplings, which in the simplest Type I seesaw with Majorana sterile neutrinos are generally far too small to allow efficient direct DM annihilation to SM neutrinos.
Most studies have therefore focused on the secluded regime, in which DM annihilates directly to the sterile neutrino mediators~\cite{Pospelov:2007mp,*Tang:2015coo,*Tang:2016sib,*Escudero:2016tzx,*Escudero:2016ksa,*Allahverdi:2016fvl,*Campos:2017odj,Batell:2017rol}. In this case the most robust signatures are indirect, and include cosmic gamma-rays antiprotons, and imprints of DM annihilation on the cosmic microwave background (see e.g., the recent study of Ref.~\cite{Batell:2017rol}).

However, the case of direct annihilation to SM neutrinos can also be viable if the Yukawa couplings are large. Small neutrino masses are easily compatible with large neutrino Yukawa couplings provided sterile neutrinos are pseduo-Dirac states and an approximate $U(1)_L$ global lepton number symmetry is present.
A model incoporating these basic ingredients was first studied in Ref.~\cite{Bertoni:2014mva}, where the implications of a large neutrino-DM interaction for small scale structure were investigated. A similar model was analyzed in Ref.~\cite{Macias:2015cna,*Gonzalez-Macias:2016vxy}, where the focus was on heavy DM phenomenology. For other dark matter studies utilizing the neutrino portal, see Ref.~\cite{Falkowski:2009yz,*Falkowski:2011xh,*Cherry:2014xra}.

Our aim in this work is to provide a systematic analysis of thermal neutrino portal DM in the direct annihilation regime, over the entire cosmologically viable DM mass range from 1 MeV$-$1 TeV.
The basic model consists of a dark sector containing a Dirac fermion DM $\chi$ and a complex scalar $\phi$, along with a Dirac sterile neutrino mediator $N$, and is essentially the one constructed in Ref.~\cite{Bertoni:2014mva}. Beyond the particular motivation of Ref.~\cite{Bertoni:2014mva}, this model is of interest more generally as a scenario in which dark sector interactions with light neutrinos lead to thermalization and annihilation. We derive the existing constraints and future sensitivity projections from direct detection experiments, colliders, rare meson and tau decays, electroweak precision tests, cosmology. We also indicate the parameter regions that are favored by perturbativity and technical naturalness. In analogy with predictive vector and Higgs portal models, we also present a transparent strategy to compare these constraints and projections with the thermal relic target, under minimal and conservative assumptions on model parameters. We identify new probes of this model that can be undertaken with existing or near future experiments, including 3-body decays of stopped kaons and transverse momentum distributions of charged leptons in $W$ boson production at colliders. Furthermore, we emphasize the impact that a high statistics $\tau^+\tau^-$ sample at a future $B$-factory could have on testing this scenario.

The rest of this paper is organized as follows. In Sec.~\ref{sec:framework}, we outline the basic ingredients of the model, discuss its simple cosmology, and the decay modes of the new states. Section~\ref{sec:Npheno} describes constraints and probes of the heavy, mostly sterile neutrino in this scenario. The phenomenology of the DM in this model and ways to test it are in Sec.~\ref{sec:DMpheno}. In Sec.~\ref{sec:outlook} we conclude and discuss future prospects.

\section{Framework}
\label{sec:framework}
In this section we begin by defining a simple model in which DM couples to SM neutrinos through mixing generated with a neutrino portal coupling. We then discuss the cosmology and define the thermal relic target. We also discuss some basic features of the model that will be needed to understand the phenomenology, including the decays of the new heavy states, and the radiative couplings. We conclude this section with a brief discussion of technical naturalness in this scenario.

\subsection{Model}
\label{sec:model}
As discussed in the introduction, the basic scenario we have in mind is thermal DM annihilating directly to SM neutrinos through the neutrino portal.\footnote{More precisely, the dark matter annihilates into very light, mostly SM flavor neutrinos which we refer to here as ``SM neutrinos'' for simplicity.} To allow for a large neutrino Yukawa coupling, and in turn an efficient annihilation rate, we take our mediator $N$ to be a Dirac particle. The dark sector is very minimal, and consists of a Dirac fermion DM candidate $\chi$ and a complex scalar $\phi$.
Along with the kinetic terms, the Lagrangian is given by~\cite{Bertoni:2014mva}
\begin{align}
-{\cal L} & \supset  m_\phi^2 \, |\phi|^2  +  m_\chi \, \bar \chi \chi  + m_N \, \bar N N   \nonumber  \\
&  + \left[ \lambda_\ell \, \bar L_\ell {\hat H} N_R +\phi \, \bar\chi\left(y_L N_L+y_R N_R\right)+{\rm h.c.} \right],
\label{eq:Lagrangian}
\end{align}
where $H\ (\hat H = i\tau_2 H^*)$ is the Higgs doublet, $L_\ell=({\nu_\ell}_L,\ell_L)^T$ are SM lepton doublets with $\ell=e$, $\mu$, $\tau$ labeling the charged lepton mass eigenstates, $\lambda_\ell$ are the neutrino Yukawa couplings, and $y_{L, R}$ are couplings of the sterile neutrino mediator to the dark sector fields. The Lagrangian of Eq.~(\ref{eq:Lagrangian}) respects a global $U(1)_L$ lepton number symmetry, under which $L_\ell$, $N$ and $\phi^*$ have equal charges, as well as a global $U(1)_D$ dark matter number symmetry under which $\chi$ and $\phi$ have equal charges. At the level of Eq.~(\ref{eq:Lagrangian}), the lepton number symmetry forbids light SM neutrino masses, allowing us to take $\lambda_\ell$ as free parameters and in particular much larger than the usual naive Type I seesaw expectation.

We will assume $m_\chi < m_\phi$, such that $U(1)_D$ symmetry ensures the stability of $\chi$. If, instead, $m_\chi > m_\phi$ then the $U(1)_D$ symmetry would render $\phi$ stable and it would be a good DM candidate. The phenomenology in this case would be essentially the same. The main difference is that the DM annihilation cross section is velocity-suppressed (in the limit that either $y_L$ or $y_R$ dominates), requiring larger couplings to provide efficient annihilation. Since the fermionic DM scenario can tolerate smaller couplings, it is more conservative. For this reason, we specify that $m_\chi < m_\phi$ and the fermion is the DM  for definiteness in our detailed study.

In the electroweak vacuum, $\langle H \rangle = v  = 174$ GeV, the SM neutrinos $\nu_i$ mix with $N$.
Diagonalizing the Lagrangian, we find a heavy sterile Dirac neutrino state, which we label $\nu_4$. The  physical mass of this state is $m_4=\sqrt{m_N^2+\sum_\ell\lambda_\ell^2v^2}$, and
its left chiral component is a combination of sterile and active flavors,
\begin{align}
\nu_4=
\left(
\begin{array}{c}
U_{N4}^\ast N_L+\sum_\ell U_{\ell4}^\ast{\nu_\ell}_L \\
N_R
\end{array}
\right),
\end{align}
where the mixing angles are given by
\begin{align}
\label{eq:angle}
U_{\ell 4}=\frac{\lambda_\ell v}{m_4}, ~~~~~~ \left|U_{N4}\right| = \frac{m_N}{m_4}=\sqrt{1-\sum_\ell\left|U_{\ell4}\right|^2}.
\end{align}
This is the crucial feature of the model:
the mixing angles are not proportional to the light neutrino masses (in this limit, zero) and can be viewed as more or less free parameters.

The linear combinations of $N_L$ and ${\nu_\ell}_L$ that are orthogonal to ${\nu_4}_L$ are the light neutrinos, ${\nu_i}_L$ with $i=1$, $2$, $3$, which remain massless at this level. $N_L$ contains an admixture of light neutrinos, and so the light neutrinos interact with the DM via Eq.~(\ref{eq:Lagrangian}):
\begin{align}
\label{eq:Lagrangian2}
 &y_L \, \phi \, \bar\chi_R \, N_L+{\rm h.c.}        \\
& \to  y_L \left|U_{N4}\right|  \phi \, \bar\chi_R \, {\nu_4}_L - y_L \, \sqrt{1\!-\!\left|U_{N4}\right|^2} \, \phi \, \bar\chi_R \, {\nu_l}_L+{\rm h.c.} \nonumber
\end{align}
where $\nu_l$ is an admixture of light neutrinos $\nu_{1,2,3}$ with unit norm. The active neutrinos get an orthogonal admixture of heavy and light neutrinos,
\begin{align}
{\nu_\ell}_L= \sum_{i=1,2,3}U_{\ell i}{\nu_i}_L+U_{\ell 4}{\nu_4}_L
\end{align}
for $\ell=e$, $\mu$, $\tau$.

The $4\times4$ matrix $U$ describes the relationship between gauge and mass eigenstates. Since the light neutrinos are all degenerate (i.e. massless) at the level we are dealing with them now, we can ignore mixing amongst the active neutrinos. Thus, the upper-left $3\times 3$ block of this matrix, corresponding to the usual Pontecorvo-Maki-Nakagawa-Sakata matrix~\cite{Pontecorvo:1967fh,*Pontecorvo:1957cp,*Maki:1962mu} and which governs ordinary neutrino oscillations, is unimportant for our purposes and the phenomenology is determined by the active-sterile mixing angles $U_{\ell 4}$.\footnote{See Sec.~\ref{sec:nu_osc}, however, for a discussion of atmospheric neutrino oscillations in the context of a large $\tau$-sterile mixing.}

There are a few simple ways to extend the model to incorporate light neutrino masses.
The most interesting possibility is to endow $N$ with couplings that violate lepton number.
For example, one can add the Majorana mass term, $\mu \, \bar  N^c_R \, N_L +{\rm h.c.}$ as in the ``inverse seesaw'' scenario~\cite{Mohapatra:1986aw,*Mohapatra:1986bd}, or the Yukawa couplings, $\lambda'_\ell \, \bar L_\ell {\hat H}  N^c_R +{\rm h.c.}$ as done in~\cite{Malinsky:2005bi}.
This will lead to small neutrino masses, of order $\lambda_\ell^2 v^2 \mu/m_N^2$ or $\lambda'_\ell\lambda_\ell v^2/m_N$
respectively, governed by $U(1)_L$ breaking interactions, while the $\Delta L=0$ neutrino Yukawa coupling, $\lambda_\ell$, in Eq.~(\ref{eq:Lagrangian})
may still be large. These possibilities give $N$ the dual responsibility of generating neutrino masses and mediating DM interactions. In fact, only one Dirac sterile neutrino (made up of two Weyl fermions) is required to produce phenomenologically viable neutrino masses and mixings. Another possibility is that there are additional states $N'$ that participate in the mass generation, in either lepton-number--preserving or --violating ways with some other UV dynamics.
In any event, generating realistic neutrino masses while keeping the Yukawa couplings $\lambda_\ell$ large requires that $N$ is a Dirac or pseudo-Dirac state; in the latter case, the small mass splitting between the mass eigenstates will, however, have no significant phenomenological consequences for the parameter choices of interest to us.

Note that we have not written the renormalizable operator $\lambda_{\phi H} |\phi|^2 |H|^2$ which is allowed by the symmetries in Eq.~(\ref{eq:Lagrangian}) and is generated radiatively. After electroweak symmetry breaking, this operator contributes to the $\phi$ mass and to decays of the Higgs boson to $\phi\phi^\ast$ (which as we show in Sec.~\ref{sec:decays} are invisible at colliders). In a natural theory, we would expect the coefficient of this operator to be at least as large as the radiative contributions $\lambda_{\phi H}\gtrsim\delta_{\lambda_{\phi H}}\sim (y_L^2\lambda_\ell^2/16\pi^2)\log(\Lambda_{\rm UV}^2/m_4^2)$ where $\Lambda_{\rm UV}$ is a cutoff of the theory. However, given this estimate of the value of this operator, its effects on $m_\phi$ and the invisible Higgs width are subdominant to other contributions.

\subsection{Cosmology}
\label{sec:cosmo}
As is well-known, the relic density obtained through thermal freezeout is determined by the thermally averaged DM annihilation cross section $\langle  \sigma v \rangle$. The relevant process in this case is annihilation into light neutrinos, $\chi \bar \chi \rightarrow \nu \bar \nu$, and the cross section can be computed from the interaction Lagrangian, Eq.~(\ref{eq:Lagrangian2}):
\begin{align}
\label{eq:sigv}
\langle\sigma v\rangle&=\frac{y_L^4}{32\pi}\left(\sum_\ell\left|U_{\ell 4}\right|^2\right)^2\frac{m_\chi^2}{m_\phi^4}\left(1+\frac{m_\chi^2}{m_\phi^2}\right)^{-2}
\\
&\simeq
1\,{\rm pb} \,
{\left(\! \frac{y_L\! \sqrt{\sum_\ell\left|U_{\ell 4}\right|^2}}{0.2} \right)}^{\!\!\! 4}\!
{\left(\!\frac{ 10\, \rm GeV}{m_\chi }\right)}^{\!\! 2}\!
{\left(\frac{3}{m_\phi/m_\chi}\right)}^{\!\! 4}, \nonumber
\end{align}
where in the second step we have normalized the cross section to the canonical value $\langle\sigma v\rangle  = 3\! \times \! 10^{-26}$ cm$^3/$s $\simeq 1$ pb, which yields a DM abundance that is in close agreement with the measured value.

In analogy with simple vector portal DM scenarios~\cite{Izaguirre:2015yja,Alexander:2016aln}, it is useful to define a dimensionless parameter $Y$ that governs the annihilation rate,
\begin{align}
Y&\equiv y_L^4\left(\sum_i\left|U_{i4}\right|^2\right)^2\frac{m_\chi^4}{m_\phi^4}.
\label{eq:Y}
\end{align}
In terms of this parameter Eq.~(\ref{eq:Y}), $\langle\sigma v\rangle \approx Y/(32 \pi m_\chi^2)$ and constraints on the model can be conveniently compared to the thermal relic target in the $m_\chi - Y$ plane.
In Fig.~\ref{fig:Yvsm} we show in this parameter space where the cross section Eq.~(\ref{eq:sigv}) is $3\times10^{-26}~\rm cm^3/\rm s=1~\rm pb$ as a function of DM mass $m_\chi$ with solid, dark gray diagonal lines.
Along this line, the DM thermal relic density is close to the observed value.
Above this line, the relic density is smaller than the measured density if DM is symmetric (equal populations of particles, $\chi$, and antiparticles, $\bar\chi$),
but it is easy to imagine obtaining the correct abundance in this region through an initial asymmetry (i.e., exactly what happens in the baryon abundance case).
Below this line, if the DM is in thermal equilibrium then it naively overcloses the Universe, and obtaining the correct DM density here requires a more complicated nonthermal cosmology.
From this point of view, parameter space above the $\langle\sigma v\rangle=1~\rm pb$ line is a well motivated target. Accordingly, we shade the region where $\langle\sigma v\rangle<1~\rm pb$ to indicate that it is disfavored in a simple thermal cosmology.
Our goal in this work is to place conservative bounds and projections on the cosmologically motivated region of parameter space, which suggests a particular set of benchmark model parameter choices.

\begin{figure*}
\begin{centering}
\includegraphics[width=0.99\linewidth]{Yvsm.pdf}
\caption{Limits and constraints on the parameter $Y=y_L^4\left(\sum_i\left|U_{i4}\right|^2\right)^2\left(m_\chi/m_\phi\right)^4$ as a function of the DM mass $m_\chi$, assuming mixing dominantly with the $e$, $\mu$, $\tau$ flavors from top to bottom. We have fixed the mediator mass to be $m_\phi=3m_\chi$. On the left we take the heavy neutrino's mass to be $m_4=10m_\chi$ and on the right we fix it to $m_4=400~\rm GeV$. The blue lines show the limit on $Y$ given the upper limit on $\left|U_{i4}\right|^2$ (which are functions of $m_4$, see Fig.~\ref{fig:Ulimit}) and two different upper limits on $y_L$: 1) the perturbative limit $y_L<4\pi$ (solid) and 2) the fine tuning limit $y_L<4\pi m_\phi/m_4$ (dashed) where we require that radiative corrections to the $\phi$ mass are not larger than the $\phi$ mass itself and assume that $m_4$ is the cutoff scale. The  orange lines show where the heavy neutrino's visible branching ratio (through weak interactions) is $10^{-3}$ for the same two upper limits on $y_L$, pertubativity (solid) and fine-tuning (dashed); below these lines for either of these values of $y_L$ the visible branching ratio is smaller than $10^{-3}$. The solid gray line shows where the annihilation cross section is $1~\rm pb$, roughly the value required for a thermal relic. Above this line, the correct DM density can be easily explained by an initial asymmetry while below it requires a more intricate cosmological story. We also show direct detection limits through the effective DM coupling to the $Z$ (red, solid), as well as the direct detection cross sections corresponding the the ``$\nu$ floor'' (red, dotted). Future direct detection prospects are shown as red, dashed curves. Values of the coupling required to obtain small scale structure cutoff masses of $10^{7,9}M_\odot$, relevant for addressing the missing satellites problem are shown as dashed green lines. The ``$N_{\rm eff}$'' limit on the DM mass, $m_\chi\gtrsim 10~\rm MeV$, comes from CMB and BBN measurements of the effective number of relativistic degrees of freedom. See text for details.}
\label{fig:Yvsm}
\end{centering}
\end{figure*}

We also display a variety of experimental constraints in Fig.~\ref{fig:Yvsm}, which will be surveyed in detail below.
The first class of constraints, including direct detection experiments and the small scale structure of dark matter, scale in approximately the same way on $Y$, $m_\chi$ as the annihilation cross section and can be compared to the thermal target without further assumption on the model parameters. However, there are a number of other constraints on sterile neutrinos which limit the mixing angle as a function of the heavy neutrino mass and thus require further assumptions about the model parameters to obtain a constraint on $Y$. Noting Eq.~(\ref{eq:Y}), we see that for this class of constraints, the weakest (and thus most conservative) constraint on $Y$ as a function of $m_\chi$ is obtained by 1) saturating the experimental bound on the mixing angle, 2) taking $y_L$ close to nonperturbative values, and 3) maximizing the ratio of masses $m_\chi/m_\phi$ while keeping $m_\chi <m_\phi$.
For these limits, we therefore fix a set of conservative benchmark values of $y_L = 4 \pi$ and $m_\chi/m_\phi =1/3$.

Note that to represent the constraints on the invisible heavy neutrino in the $m_\chi - Y$ plane, we further require an assumption about the heavy neutrino mass.
There are two important comments in this regard, First, these constraints become stronger in the low $m_4$ regime. Thus to place conservative bounds we should take $m_4$ to be heavy.
Second the dark scalar $\phi$ suffers from then usual naturalness problem associated with light scalar particles. The scalar receives a quadratically divergent correction to its mass coming from the same Yukawa coupling that enters into the DM annihilation cross section, $\delta m_\phi^2 \sim y_L^2 \Lambda_{\rm UV}^2/16 \pi^2$.
To conservatively implement a naturalness ``bound,'' we choose to cut this off at the scale $\Lambda_{\rm UV} = m_4$ (typically the heaviest particle in the low energy theory). Further UV contributions could be screened in  a low scale UV completion which stabilizes the $\phi$ mass, e.g. supersymmetry or compositeness. The operator $\lambda_{\phi H} |\phi|^2 |H|^2$ gives a contribution $\lambda_{\phi H} v^2$ to $m_\phi^2$. Given the radiative estimate of $\lambda_{\phi H}$ above, this contribution is suppressed by the relative factor $(|U_{\ell4}|^2 m_4^2/\Lambda_{\rm UV}^2)\log(\Lambda_{\rm UV}^2/m_4^2)$ so we do not include it in our ``bound.''

The naturalness ``constraint''  becomes weaker as $m_4$ is lowered. It is clear that the naturalness consideration is complementary to the invisible neutrino experimental constraints, since the latter prefer large $m_4$ while the former prefer small $m_4$. We thus show two sets of plots in Fig.~\ref{fig:Yvsm} with the following assumptions: 1) light $\nu_4$, fixing $m_\chi:m_\phi:m_4 = 1  :  3  :  10$, in the left column and 2) heavy $\nu_4$, fixing $m_4 = 400$ GeV, in the right column.

We also derive limits under the assumption that one of the mixing angles $|U_{e4}|$, $|U_{\mu4}|$, $|U_{\tau4}|$ dominates, while the others are negligible. This assumption is not necessarily conservative in terms of constraining the thermal target, since some of the limits may be weakened by ${\cal O}(1)$ factors while still obtaining a viable DM cosmology if two or more sizable mixing angles are present. This concern is relatively minor in our view, and is outweighed by the transparency of this assumption, which allows us to clearly display the flavor dependence inherent in certain limits. In this case we specify the flavor content of the coupling relevant for DM annihilation in Eq.~(\ref{eq:Y}) via $Y_\ell\equiv y_L^4|U_{\ell 4}|^4m_\chi^4/m_\phi^4$ for $\ell=e$, $\mu$, $\tau$.

Only the coupling $y_L$ enters the annihilation cross section Eq.~(\ref{eq:sigv}). The coupling $y_R$ does not lead to a tree-level DM-SM interaction, and for most DM masses plays no role in the cosmology. For simplicity, we therefore will assume in this work that $y_R$ is small and can be neglected.  However, we note that for $m_\chi \sim m_Z/2$ or $m_\chi \sim m_h/2$, DM can annihilate at one loop through an $s$-channel $Z$ or Higgs to the SM, which can potentially compete with the tree level process due to the resonant enhancement. It is easy to see that the radiative coupling of DM to the Higgs, $h \bar \chi \chi$, vanishes in the limit $y_R \rightarrow 0$.
As discussed further below, a radiative $Z \bar \chi \chi$ coupling, proportional to $y_L^2$, is still generated in this limit. For the benchmark choices described above, we have checked that annihilation through the $Z$ on resonance is subdominant to the tree level annihilation process Eq.~(\ref{eq:sigv}). It would be worthwhile to explore in more detail these resonance regions under different parameter assumptions, as this may allow certain constraints to be relaxed. However, these are fairly special regions of parameter space and their detailed exploration goes beyond our scope here. See Ref.~\cite{Macias:2015cna,*Gonzalez-Macias:2016vxy} for work in this direction.

Light DM that is in thermal equilibrium with neutrinos can affect the number of relativistic degrees of freedom, $N_{\rm eff}$, as inferred by measurements of the cosmic microwave background (CMB)~\cite{Ade:2013zuv} and primordial light element abundances. The agreement of these with standard CMB and big bang nucleosynthesis (BBN) expectations can be used to set a lower limit on the DM mass of around $10~\rm MeV$~\cite{Serpico:2004nm,*Boehm:2013jpa,*Nollett:2014lwa,Iocco:2008va} which we show in Fig.~\ref{fig:Yvsm} with vertical dot-dashed lines.

\subsection{Decays of new states}
\label{sec:decays}
From the interactions in Eq.~(\ref{eq:Lagrangian2}) we can obtain the partial decay widths of the new unstable particles. The dark scalar $\phi$ decays to $\chi$ and a light anti-neutrino with a rate
\begin{align}
\Gamma_{\phi\to\chi \bar \nu_l}=\frac{y_L^2}{16\pi}\sum_i\left|U_{i4}\right|^2 m_\phi\left(1-\frac{m_\chi^2}{m_\phi^2}\right)^2.
\end{align}
The heavy neutrino $\nu_4$ decays (invisibly) to $\chi$ and $\phi$ through either $y_L$ or $y_R$. Assuming that $y_R$ is negligible, the rate for this is
\begin{equation}
\begin{aligned}
\Gamma_{\nu_4\to\chi\phi^\ast}& =
\frac{y_L^2}{32\pi}\left|U_{N4}\right|^2m_4\left(1-\frac{m_\phi^2}{m_4^2}+\frac{m_\chi^2}{m_4^2}\right)
\\
&\quad\quad\times \lambda^{1/2}\left(1, \frac{m_\phi^2}{m_4^2},\frac{m_\chi^2}{m_4^2} \right),
\label{eq:decN-dark}
\end{aligned}
\end{equation}
where $\lambda(a,b,c)\equiv a^2+b^2+c^2-2ab-2ac-2bc$. This rate should be compared with the usual weak decay rate that occurs due to active-sterile mixing.
The weak decay rate is negligible for $m_4 \ll m_W$, as it must proceed via off-shell weak bosons. For $m_4>m_W$, two body weak decays are kinematically allowed, and the rate for $\nu_4 \rightarrow \ell^- W^+$ is
\begin{align}
\Gamma_{\nu_4\to\ell^- W^+}&=\frac{G_F m_4^3}{8\pi\sqrt2}\left|U_{\ell 4}\right|^2\left(1-\frac{m_W^2}{m_4^2}\right)^2\left(1+\frac{2m_W^2}{m_4^2}\right)  \nonumber  \\
  &\simeq \frac{\lambda_\ell^2 m_4}{32 \pi},
  \label{eq:decN-weak}
\end{align}
where in the second step we have assumed $m_W \ll m_4$ and used the mixing angle relation Eq.~(\ref{eq:angle}). Comparing Eqs.~(\ref{eq:decN-dark}) and (\ref{eq:decN-weak}), we see that weak decays can be competitive if $\lambda_\ell$ is as large as $y_L$.
However, given the mixing angle relation in Eq.~(\ref{eq:angle}), this only occurs in practice when $m_4$ is very large, of order 1 TeV or more.
Therefore, weak decays of $\nu_4$ are subdominant over the entire parameter space consistent with thermal dark matter. To illustrate this, in Fig.~\ref{fig:Yvsm} we show contours where the weak branching fraction of the heavy neutrino is $10^{-3}$, fixing $y_L$ to either its perturbative maximum, $y_L=4\pi$ (orange, solid curves), or to its ``bound'' from naturalness, $y_L=4\pi m_\phi/m_4$ (orange, dashed curves). Below these lines, values of the weak branching fraction can be chosen to be less than $10^{-3}$, which is sufficient to reduce the limits derived from visible decays of the heavy neutrino (see, e.g.~\cite{Atre:2009rg}) to be subdominant. In this setup, where $N$ is Dirac or pseudo-Dirac, $\Delta L=2$ decays of the heavy neutrino are either absent or highly suppressed. In the two specific possibilities mentioned in Sec.~\ref{sec:model} where the light neutrino masses are due to either a lepton-number--violating Majorana mass $\mu$ or Yukawa coupling $\lambda^\prime_\ell$, the $\Delta L=2$ decay rate is suppressed relative to the $\Delta L=0$ rate by the factor $(\mu/m_N)^2$ or $(\lambda^\prime_\ell v/m_N)^2$, respectively.

\section{Sterile Neutrino Constraints}
\label{sec:Npheno}

As discussed in the previous section, the sterile neutrino mediator $\nu_4$ decays invisibly into the dark sector in our scenario. In Ref.~\cite{Bertoni:2014mva}, the limits on the mixing angle for invisibly decaying heavy neutrinos were presented (see also Ref.~\cite{deGouvea:2015euy}). These limits impact the cosmologically motivated DM parameter space since the annihilation cross section Eq.~(\ref{eq:sigv}) (or equivalently the $Y$ parameter in Eq.~(\ref{eq:Y})) depends on this mixing angle. In this section we briefly review the existing limits and take note of a few updates due to recent searches. The limits are summarized in the $m_4-|U_{i4}|^2$ plane in Fig.~\ref{fig:Ulimit}.

\subsection{$\mu,\tau$ decays}

A massive neutrino with non-vanishing $|U_{e4}|$ and/or $|U_{\mu4}|$ leads to a modified value of the Fermi constant extracted from the muon lifetime. Because the Fermi constant governs a host of precision electroweak and high-energy observables, the general agreement of this data~\cite{Tishchenko:2012ie,Olive:2016xmw} with the SM predictions constrains these mixing angles (labelled $\tau_\mu$/EWPT in Fig.~\ref{fig:Ulimit}). Similarly, the Fermi constant enters into the semi-leptonic weak decays used to measure the CKM elements, $V_{ud}$ and $V_{us}$, and CKM unitarity can therefore be used to derive limits on $|U_{\mu4}|$~\cite{Olive:2016xmw,Bertoni:2014mva}.
Furthermore, the lack of distortions in the $e^+$ energy spectrum in $\mu^+$ decays measured by the TWIST collaboration~\cite{Bayes:2010fg} can be used to constrain $|U_{e4}|$ and $|U_{\mu4}|$ for masses $m_4 < m_\mu-m_e$~\cite{Gninenko:2010pr,Bertoni:2014mva,deGouvea:2015euy}.

The constraints on mixing in the $\tau$ sector are generally much weaker than in the $e$ and $\mu$ sector. Relevant limits on $|U_{\tau 4}|$ can be derived from $\tau$ decays, including the leptonic decays $\tau\rightarrow e \bar \nu \nu$, $\tau\rightarrow \mu \bar \nu \nu$~\cite{Olive:2016xmw,Belous:2013dba,*Pich:2013lsa}, as well as certain hadronic modes like $\tau \rightarrow \nu 3 \pi$~\cite{Barate:1997zg,Bertoni:2014mva}.

\subsection{Rare meson decays}

 Rare meson decays, $M^+ \rightarrow \ell^+ \nu_4$, provide some of the best probes of an invisible heavy neutrino.
One striking signature is a peak in the energy spectrum of the outgoing lepton in the meson rest frame due to the two-body kinematics. Strong limits on $|U_{e4}|$ arise from peak searches in $\pi \rightarrow e \nu$~\cite{Britton:1992xv,*PIENU:2011aa,*Ito:2016nxh}, $K \rightarrow e \nu$~\cite{Yamazaki:1984sj}, and $B\rightarrow e \nu$~\cite{Park:2016gek} decays, while similar searches in the decays $\pi \rightarrow \mu \nu$~\cite{Abela:1981nf}, $K \rightarrow \mu \nu$~\cite{Hayano:1982wu,Artamonov:2014urb,Lazzeroni:2017fza}, and $B\rightarrow \mu \nu$~\cite{Park:2016gek} decays constrain $|U_{\mu4}|$.
Furthermore, a comparison of the experimental value of the ratio $\Gamma_{\pi \rightarrow e \nu}/\Gamma_{\pi\rightarrow \mu\nu}$ to its SM prediction can be used to set constraints on $|U_{e4}|$ and $|U_{\mu4}|$~\cite{Britton:1992pg,*Czapek:1993kc,*Marciano:1993sh}.

\subsection{Three body decays}
\label{sec:3body}
One of the most sensitive probes of sterile neutrinos comes from decays of a charged meson, $M^+$, to a charged lepton, $\ell^+$, and heavy, mostly sterile neutrino, as discussed in Sec.~\ref{sec:Npheno}. If the mass of the heavy neutrino, $m_4$, is larger than $m_M-m_\ell$, this two-body decay is kinematically forbidden from happening. However, in this model, if $m_\chi+m_\phi<m_M-m_\ell$, then three-body decays $M^+\to\ell^+\chi\phi$ can proceed through off-shell (heavy and light) neutrinos. In the limit that $m_4\gg m_M$, the rate for this decay is
\begin{align}
&\frac{1}{\Gamma_{M^+\to\ell^+\nu_\ell}}\frac{d\Gamma_{M^+\to\ell^+\phi\chi}}{dx}=\frac{y_L^2\left|U_{\ell 4}\right|^2}{32\pi^2}\left(1-\left|U_{\ell 4}\right|^2\right) \nonumber
\\
&\quad\frac{\sqrt{x^2-4x_\ell}}{x_\ell\left(1-x_\ell\right)^2}\frac{\left(1-x\right)x+2x_\ell}{\left(1+x_\ell-x\right)^3}\left(1+x_\ell-x-x_\phi+x_\chi\right) \nonumber
\\
&\quad\quad\times\lambda^{1/2}\left(1+x_\ell-x,x_\phi,x_\chi\right),
\label{eq:3body}
\end{align}
where $x=2E_\ell/m_M$ is the energy fraction carried by the charged lepton in the meson rest frame and $x_{\chi,\phi,\ell}=m_{\chi,\phi,\ell}^2/m_M^2$.

The signature of this decay is a charged lepton recoiling against something unobserved ($\chi$ and $\phi$ are both invisible) with a momentum different from the value expected for the standard decay into a charged lepton and massless neutrino, just as in the two-body case (where the decay products of the heavy neutrino are unobserved). The $\ell^+$ momentum is distributed over a range of values in the three-body case instead of being monochromatic as in the two-body case.

Armed with the expression in Eq.~(\ref{eq:3body}) (including terms that survive with finite $m_4$) for the decay rate, we can use the search for heavy neutrinos in $K^+\to\mu^++{\rm inv.}$ by the E949 experiment~\cite{Artamonov:2014urb} to set an upper limit on $y_L^2\left|U_{\mu 4}\right|^2$ or, equivalently, $Y_{\nu\mu}$. To perform this estimate we assume that the $\mu^+$ momentum distribution in the $K^+$ rest frame measured by E949 is well described by a power law background (dominantly from the radiative decay $K^+\to\mu^+\nu\gamma$) and ask what level of signal, $K^+\to\mu^+\chi\phi$, is allowed. We show the resulting 90\% CL upper limits on $Y_{\nu\mu}$ as a function of $m_\chi$ (assuming $m_\phi=3m_\chi$) for both the light $m_4$ and large $m_4$ cases in Fig.~\ref{fig:Yvsm}. In both cases, E949 data appear to be sensitive to an interesting region of parameter space close to thermal relic annihilation cross sections. The NA62 experiment plans to collect about $10^{13}$ kaon decays~\cite{Lazzeroni:2017fza,NA62:2017rwk} and could, assuming systematic errors can be kept under control, probe values of $Y_{\nu\mu}$ about an order of magnitude smaller than E949.

\subsection{Neutrino oscillations}
\label{sec:nu_osc}

Given the rather weak direct constraints on mixing in the $\tau$ sector, it is interesting to consider the consequences of mixing on neutrino oscillations.
Notably, atmospheric neutrino oscillations are affected by $\nu_\tau - \nu_4$ mixing due to a suppression of the matter potential by the factor $(1-|U_{\tau_4}|^2)$ (see \cite{Bertoni:2014mva} for a detailed discussion). An analysis by Super-Kamiokande using the atmospheric muon neutrino zenith angle distribution leads to constraints on $|U_{\tau_4}|$~\cite{Abe:2014gda}.

If the heavy neutrino is light, it can affect the number of relativistic species present during BBN. This sets a lower bound of $m_4\gtrsim 10~\rm MeV$~\cite{Iocco:2008va} which we show in Fig.~\ref{fig:Ulimit}, labelled ``$N_{\rm eff}$''.

\subsection{Invisible Higgs and $Z$ decays}

In addition to the flavor-specific constraints discussed above, invisible Higgs and $Z$ boson decays can be used to constrain the mixing angles. These are most relevant for larger values of $m_4$ where they become competitive with other constraints. We show the limit on the mixing angles from the constraint that the invisible branching of the Higgs is less than $0.24$ at $95\%$~C. L.~\cite{Khachatryan:2016whc} as solid blue lines in Fig.~\ref{fig:Ulimit}. We also show the reach that a future limit of $5\%$~\cite{Peskin:2013xra} on this branching could achieve as dotted blue lines. In setting these limits, we only consider decays of the Higgs to neutrinos through the Yukawa coupling with a rate proportional to $\lambda_\ell^2$. Since $\phi$ decays invisibly, $h\to\phi\phi^\ast$ decays generated by the operator $\lambda_{\phi H} |\phi|^2 |H|^2$ also contribute to the invisible Higgs width. However, this mode is suppressed relative to the neutrino mode by at least a further factor of $\lambda_\ell^2$ given the radiative estimate of the coefficient $\lambda_{\phi H}$ and we therefore ignore it.

The effect on the invisible branching of the $Z$ due to heavy sterile neutrinos that mix with the active neutrinos is well-known. The $90\%$~C. L. limits on the mixing angles that comes from the measurement of the invisible $Z$ width of $499.0\pm1.5~\rm MeV$~\cite{Olive:2016xmw} are shown in Fig.~\ref{fig:Ulimit} as solid, orange lines.

\subsection{LHC searches}

Furthermore, a heavy neutrino with a relatively large admixture of active flavors can be produced in large numbers in leptonic $W^\pm$ decays. Since, in the case we consider here, the heavy neutrino decays invisibly into the dark sector the only effect is a distortion of the kinematics of this decay. In particular, at a hadron collider, the $W$ transverse mass ($M_T^W$) endpoint or the transverse momentum ($p_T$) spectra of electrons and muons measured in Drell-Yan production of $W^\pm$ would be affected.
For heavy neutrinos light enough to be produced on-shell in $W^\pm\to\ell^\pm$ decays, this would appear as a kink in the lepton $p_T$ at $p_T^{\rm peak}$ with the $M_T^W$ endpoint, $M_T^{\rm peak}$, shifted as
\begin{equation}
M_T^{\rm peak} = M_W \left(1-{m_4^2\over M_W^2}\right) , \quad
p_T^{\rm peak} = {1\over 2} M_T^{\rm peak}.
\end{equation}
The relative size of the kink in this spectrum is at the level $\sim|U_{\ell 4}|^2$ for neutrinos kinematically allowed in $W$ decay. Neutrinos that are heavier than the $W$ simply dilute the rate by the factor $1-|U_{\ell 4}|^2$. Lepton $p_T$ spectra in $W^\pm$ production and decay at a hadron collider are very well studied because accurate measurements of these spectra, in particular their endpoints, are crucial in determining the $W^\pm$ mass. Since the recent ATLAS measurement of the $W^\pm$ mass~\cite{Aaboud:2017svj} has $e^\pm$ and $\mu^\pm$ $p_T$ spectra that agree with theoretical expectations at the subpercent level, we can reasonably expect a sensitivity to mixing angles of ${\cal O}(10^{-2})$ or smaller. This would be comparable to the limit from electroweak precision tests and therefore very interesting.

To estimate the sensitivity of the measurement of lepton $p_T$ spectra at the LHC to $|U_{e4}|$ and $|U_{\mu 4}|$, we generated samples of $pp\to W^+\to e^+,\mu^++{\rm inv.}$ including massless and massive neutrinos~\cite{Alva:2014gxa,*Degrande:2016aje} corresponding to $4.1~\rm fb^{-1}$ of $7~\rm TeV$ $pp$ collisions using MadGraph5~\cite{Alwall:2014hca}, interfaced with Delphes~\cite{deFavereau:2013fsa} to model the detector response. We examine the resulting $e^\pm$ and $\mu^\pm$ $p_T$ distributions between $30~\rm GeV$ and $50~\rm GeV$ with bins of $0.5~\rm GeV$. Assuming that the standard model expectation describes these data and that statistical errors dominate (which are ${\cal O}({\rm few}\times 0.1\%)$ as in Ref.~\cite{Aaboud:2017svj}) aside from the overall normalization, we perform a fit to the underlying theory expectation (a function of $|U_{e4}|$ and $|U_{\mu 4}|$) at each value of $m_4$. We allow the overall measured cross section to vary by 2\% from the theoretical prediction to take the systematic error on the overall normalization, which comes mainly from the measurement of the total luminosity, into account.

In Fig.~\ref{fig:Ulimit} we show the resulting regions of parameter space ruled out at $90\%$ C.L.~with dashed brown lines labeled ``$W\to e$'' and ``$W\to \mu$''. As anticipated, the limit on the mixing angle for heavy neutrinos that can be produced on-shell is at the level of the statistical errors which dominate the shape of the $p_T$ spectra while for $m_4>m_W$ the limit corresponds to the uncertainty on the overall cross section. For lighter neutrino masses the difference in the lepton $p_T$ is difficult to distinguish from that for a massless neutrino so the limit is weakened.

\begin{figure}
\begin{centering}
\includegraphics[width=1.15\linewidth]{Ulim.pdf}
\caption{90$\%$ C.L. upper limits on the mixing angles $\left|U_{\ell 4}\right|^2$ as functions of the heavy neutrino mass $m_4$ in the case that the heavy neutrino decays invisibly. Constraints on the mixing angle $|U_{e4}|$ (top) are obtained from searches in $\pi  \rightarrow e \nu$ and $K  \rightarrow e \nu$ decays, the ratio  $\Gamma_{\pi\rightarrow e\nu}/\Gamma_{\pi\rightarrow \mu\nu}$, electroweak precision tests (labelled $\tau_\mu/$EWPT), the lack of distortions in the $e^+$ spectrum in $\mu^+$ decays (labelled ``TWIST''), decays of $B$ mesons, and invisible $Z$ and Higgs decays.
Constraints on $|U_{\mu4}|$ (middle) come from peak searches in $\pi  \rightarrow \mu \nu$  and $K\rightarrow \mu \nu$ decays, electroweak precision and the $e^+$ spectrum in $\mu^+$ decays, decays of $B$-mesons, unitarity of the CKM matrix, and invisible $Z$ and Higgs decays. For $|U_{e4}|$ and $|U_{\mu 4}|$, we show our estimate of the reach from a search for massive, invisible neutrinos in Drell-Yan production of $W$ bosons at LHC, labelled ``$W\to e$'' and ``$W\to \mu$''.
Constraints on $|U_{\tau4}|$ (bottom) come from leptonic and hadronic $\tau$ decays, atmospheric neutrino oscillation studies, and invisible $Z$ and Higgs decays. The solid blue curves correspond to the limit ${\rm Br}_{h\to{\rm inv.}}<0.24$ while the dotted blue curves show the reach of a future limit ${\rm Br}_{h\to{\rm inv.}}<0.05$. This figure has been adapted and updated from Ref.~\cite{Bertoni:2014mva}. See text for further discussion and references.}
\label{fig:Ulimit}
\end{centering}
\end{figure}

\section{Dark Matter Phenomenology}
\label{sec:DMpheno}

\subsection{Direct Detection}
\label{sec:dirdet}
At one loop $\chi$ picks up an effective coupling to the $Z$ boson, which can be written after EWSB as
\begin{align}
\label{eq:Z-coupling1}
 {\cal L} \supset \, a_Z \, \frac{g}{c_W}  \,Z_\mu \, \bar \chi \gamma^\mu P_R \chi,
\end{align}
where the coupling $a_Z$ is given by
\begin{align}
\label{eq:Z-coupling2}
a_Z = |U_{N4}|^2(1-|U_{N4}|^2) \frac{y_L^2}{16 \pi^2} G\left(\frac{m_\phi^2}{m_4^2} \right) ,
\end{align}
with $G(x) = (x-1-\log{x})/(4(1-x)^2)$. In Eqs.~(\ref{eq:Z-coupling1}) and (\ref{eq:Z-coupling2}) we work in the limit $m_\chi \ll m_\phi, m_4$ and zero external momentum (we use the full loop integral for our numerical results). This coupling mediates spin-independent scattering of DM with nuclei vis $Z$ boson exchange, and therefore direct detection experiments provide an important probe of the model. The effective DM-nucleon spin-independent scattering cross section is given by
\begin{align}
\sigma_n = \frac{\mu_n^2}{\pi}\frac{(Z f_p+(A-Z)f_n)^2}{A^2}
\end{align}
where $ f_n = G_F a_Z /\sqrt{2},\  f_p = -(1-4 s_W^2) G_F a_Z/\sqrt{2}$.

The strongest constraints in the high DM mass region come from recent results of XENON1T~\cite{Aprile:2017iyp} and PandaX-II~\cite{PandaXII} searching for spin-independent scattering of DM on nuclei, and are shown as a solid red curve in Fig.~\ref{fig:Yvsm}. These constraints rule out the thermal DM benchmark for DM masses heavier than about 15 GeV. We also show projections from SuperCDMS SNOLAB~\cite{Agnese:2016cpb}, which will cut further into $m_\chi \sim$ GeV mass region, as a dashed red curve. In addition, to get a sense of what region of parameter space can potentially be probed with direct detection, we show values of the coupling that correspond to a direct detection cross section at the ``neutrino floor''~\cite{Ruppin:2014bra} as a dotted red curve.

Clearly, direct detection experiments provide a powerful probe of the high DM mass region in this scenario, but it is important to note that these limits can be weakened or evaded altogether if the DM obtains a mass splitting. This can be implemented by softly breaking $U(1)_D$ to $Z_2$ by a Majorana mass terms for the chiral components of $\chi$. In this case upper limits on the DM mass are provided by constraints on the mixing angles for heavy, invisibly decaying neutrinos, notably electroweak precision tests as well as decays of electroweak bosons. Thus, these searches provide a complimentary probe of this scenario to direct detection.

There has been a significant effort devoted to exploring new methods of direct detection to probe low mass DM candidates~\cite{Battaglieri:2017aum}, although in our scenario the scattering cross section with electrons is unfortunately too small to be detected.

\subsection{DM structure}
\label{sec:structure}
There has been growing evidence that observations of dark matter structure on subgalactic scales differs from the expectation from $N$-body simulations that assume that dark matter only interacts gravitationally (which, with respect to structure formation, essentially corresponds to the expectation for standard cold DM candidates). One of the longstanding problems in this area is the so-called ``missing satellites''~\cite{Klypin:1999uc,*Moore:1999gc,*Bullock:2010uy} problem---the apparent observation of fewer satellite galaxies of the Milky Way than expected. While the gravitational feedback of normal matter at small scales, resulting from complicated astrophysics, could resolve this discrepancy, it is also possible to address these issues with nongravitational interactions of dark matter. One such possibility is if the dark matter is relatively strongly coupled to the light neutrinos as in this scenario~\cite{Boehm:2000gq}.

A large coupling of dark matter to light (relativistic) neutrinos produces a pressure that that resists the gravitational collapse of the dark matter. Because both the number density of light neutrinos and the interaction cross section are larger at high temperatures, this pressure is important at early times when the Universe is hotter and eventually becomes unimportant at some critical temperature determined by the strength of the dark matter-neutrino interaction. Structures in the Universe form hierarchically, with smaller structures forming before larger ones, since only density perturbations with wavelengths smaller than the (expanding) horizon size can grow. The structures formed gravitationally by dark matter before matter-radiation equality provide the seeds for the growth of objects containing normal matter that we later observe. At early times when the dark matter-neutrino interactions are important, the pressure felt by the dark matter means that structures do not efficiently grow due to gravity, while, after the dark matter-neutrino interactions become unimportant, structures can form~\cite{Boehm:2001hm,*Boehm:2003xr}.

In other words, dark matter-neutrino interactions can address the missing satellites problem by suppressing the growth of small scale structures. The scale below which structures do not efficiently form in this scenario can be characterized in terms of a cutoff mass, $M_{\rm cut}$, which is the mass of dark matter inside the horizon at the critical temperature when DM-neutrino interactions become unimportant (for detailed discussion of these issues, see, e.g.,~\cite{Green:2005fa,*Loeb:2005pm}). This mass is a useful heuristic expected to correspond roughly to the size of the smallest gravitationally bound objects at late times. In this model the cutoff mass is estimated to be~\cite{Bertoni:2014mva}
\begin{equation}
\begin{aligned}
M_{\rm cut}\simeq 10^8M_\odot\left(\frac{g_\ast}{3.36}\right)^{-7/8}\left(\frac{0.1~\rm GeV}{m_\chi}\right)^{-14/4}Y^{3/4},
\end{aligned}
\label{eq:Mcut}
\end{equation}
assuming $m_\phi\gg m_\chi$. In this expression, $g_\ast$ refers to the effective number of relativistic degrees of freedom at the time of decoupling which we will always take to be $3.36$ which is relevant for the phenomenologically interesting case where the decoupling happens when the Universe's temperature is around a $\rm keV$.

We take values of the cutoff, $M_{\rm cut}$, between about $10^7$ and $10^9M_\odot$ to roughly represent DM-neutrino interactions strong enough to explain the missing satellites problem. An upper bound on $M_{\rm cut}$ of around $10^9M_\odot$ can be obtained analyzing Milky Way satellites~\cite{Strigari:2008ib,*Jethwa:2016gra}, looking for small scale structures in the Lyman-$\alpha$ forest~\cite{Viel:2013apy}, or through gravitational lensing of small, distant objects~\cite{Vegetti:2012mc,*Vegetti:2014lqa}.

\section{Summary and Outlook}
\label{sec:outlook}
We have presented a general analysis of thermal relic DM that annihilates directly to SM neutrinos through the neutrino portal. This possibility is very well motivated theoretically but has been relatively less well studied than other scenarios involving vector or scalar mediators.

The model described in Sec.~\ref{sec:model} is simple and economical, adding just three new states, fermions $N$ and $\chi$ and a scalar $\phi$, with masses from about $10~\rm MeV$ to ${\cal O}(100~\rm GeV)$. It allows for a very simple cosmological history, detailed in Sec.~\ref{sec:cosmo}, with the DM number density being set either by annihilation to light neutrinos or by an initial asymmetry, with annihilation reducing the number density to the measured level. The relatively large dark matter-light neutrino coupling needed for annihilation requires that the sterile neutrino mediator $N$ be (pseudo-)Dirac. We discussed the impact of radiative corrections to the scalar mass, identifying regions of parameter space that do not require fine-tuning.

In Sec.~\ref{sec:decays}, we pointed out an interesting  feature of this scenario: the fact that the heavy (mostly $N$) neutrino decays primarily invisibly into the dark sector, allowing for relatively larger active-sterile mixing angles. Sections~\ref{sec:Npheno} and \ref{sec:DMpheno} were devoted to fully exploring the model. We discussed and updated limits on the sterile neutrino in this scenario where it decays invisibly in Sec.~\ref{sec:Npheno}.
The direct detection signature of this model was examined in Sec.~\ref{sec:dirdet} and we find that it sets an upper limit on the DM mass of around $10~\rm GeV$ in the simplest scenario. The impact on the small scale structure of DM, which could signal strong interactions between light neutrinos and DM, was also presented in Sec.~\ref{sec:structure}. Addressing this would likely imply a large mixing with the $\tau$ neutrino.

We identified several new measurements or analyses that can be done to probe large regions of viable parameter space in this setup.
First, we discussed the possibility that the heavy, invisibly decaying neutrino required for this scenario can affect the kinematics of charged leptons in Drell-Yan $W^\pm$ production at the LHC. The sizable active-sterile mixing angle needed as well as the large number of $W$ bosons produced at the LHC could allow for unconstrained regions of viable parameter space to be probed by such a measurement. In our simple mock analysis, we only considered $e^+$ and $\mu^+$ transverse momenta above $30~\ensuremath{\mathrm{GeV}}$ as in the ATLAS measurement of the $W$ mass~\cite{Aaboud:2017svj}. Including smaller $p_T$ values in this analysis would extend sensitivity to smaller values of the heavy neutrino mass $m_4$ and we urge any experimental analysis to push the lepton $p_T$ threshold as low as possible while still being able to deal with, e.g., issues from pile up.

Secondly, we discussed the sensitivity of three-body decays of kaons into the dark sector to this scenario. One virtue of this search is that it scales on the parameters of the model in the same way as the DM annihilation cross section and can therefore probe the parameter space without having to assume particular values of some parameters. We estimated the region of parameter space ruled out by the E949 experiment which collected around $10^{12}$ stopped kaon decays--this includes a large region of parameter space consistent with thermal relic DM that is unconstrained by other experiments. The NA62 experiment will collect around an order of magnitude more kaons and will therefore be able to probe even more of the viable thermal relic parameter space, providing a excellent test of this scenario.

Additionally, the active-sterile mixing angle is relatively less well constrained when it involves the $\tau$ flavor, particularly for $m_4\lesssim 300~\rm MeV$, which can allow for DM-neutrino interactions to be strong enough to affect small scale structure. In this region, the dominant constraint comes from the impact of nonstandard matter effects on the oscillation of atmospheric neutrinos as measured by Super-Kamiokande~\cite{Abe:2014gda}. It is important to note that this measurement is statistics limited and further data will probe a very interesting region, especially from the point of view of small scale structure effects. Lastly, the strongest limits on the mixing with the $\tau$ neutrino come from measurements of leptonic widths in $\tau^+\tau^-$ production at LEP~\cite{Abbiendi:1998cx,*Abreu:1999rb,*Acciarri:2001sg,*Abbiendi:2002jw,*Schael:2005am} and CLEO~\cite{Anastassov:1996tc} which involve samples of $10^5$ to $10^6$ $\tau^+\tau^-$ pairs. The upcoming Belle II experiment will collect roughly $4\times10^{10}$ $\tau^+\tau^-$ pairs with $50~\rm ab^{-1}$ of data. The possibility that the $\tau$ neutrino mixes with a sterile neutrino that decays into a dark sector provides strong motivation for studying $\tau$ decay rates and their kinematics with as much precision as possible. The extremely large data sample at Belle II could allow for much more parameter space to be probed or for a discovery to be made. We urge detailed experimental studies to be undertaken. Improving the reach on $|U_{\tau 4}|$ at collider experiments would test the possibility that DM-neutrino interactions affect small scale structure.

Models in which dark matter annihilates directly to light neutrinos are well-motivated, simple and far-reaching phenomenologically, in both particle physics and cosmology. New ideas to probe this class of models should be strongly encouraged. It could well herald a discovery that uncovers the particle nature of dark matter.

\subsubsection*{\bf Acknowledgements}
We thank Dorival Gon\c{c}alves and Satyanarayan Mukhopadhyay for helpful discussions.
The work of BB and BSE is supported in part by the U.S. Department of Energy under grant No. DE-SC0015634, and in part by PITT PACC.
The work of TH and BSE is supported in part by the Department of Energy under Grant No. DE-FG02-95ER40896, and in part by PITT PACC.
The work of DM is supported by PITT PACC.

redpajama_set_name: RedPajamaArXiv


Ok, definitely going to be making dolls for the girls for Christmas. Rapunzel style for the older girl (hopefully I have enough left over from the Rapunzel dress I made for her birthday - check out the previous post).
I am going to use felt for the face, arms and feet (as Rapunzel is barefooted - at least in "Tangled"). I chose felt as it came in the colour I am happy with (and the fabric I really wanted was £12.50 a metre...I couldn't justify that for a doll!). I have chosen a pale purple fabric for the 'vest' and 'tights' - although I may go for something stripey!
Have finally finished the big Roman Blind - pictures to follow. Unfortunately the small one was a smidge (literally 1cm) too wide...so I had to unpick all my hard work and re-hem :( BOO! I am hoping that they both fit now.... I have seen the curtains and I think they look great in-situ.
Halloween is drawing near...we don't celebrate it as such - but I wonder if any of you lot have great Halloween ideas? Do you make your own outfits?


BACKGROUND: Studies looking at acquired drug resistance (ADR) are diverse with respect to geographical distribution, HIV co-infection rates, retreatment status and programmatic factors such as regimens administered and directly observed therapy. Our objective was to examine and consolidate evidence from clinical studies of the multifactorial aetiology of acquired rifamycin and/or isoniazid resistance within the scope of a single systematic review. This is important to inform policy and identify key areas for further studies. METHODS: Case-control and cohort studies and randomised controlled trials that reported ADR as an outcome during antitubercular treatment regimens including a rifamycin and examined the association of at least 1 risk factor were included. Post hoc, we carried out random effects Mantel-Haenszel weighted meta-analyses of the impact of 2 key risk factors 1) HIV and 2) baseline drug resistance on the binary outcome of ADR. Heterogeneity was assessed used I 2 statistic. As a secondary outcome, we calculated median cumulative incidence of ADR, weighted by the sample size of the studies. RESULTS: Meta-analysis of 15 studies showed increased risk of ADR with baseline mono- or polyresistance (RR 4.85 95% CI 3.26 to 7.23, heterogeneity I 2 58%, 95% CI 26 to 76%). Meta-analysis of 8 studies showed that HIV co-infection was associated with increased risk of ADR (RR 3.02, 95% CI 1.28 to 7.11); there was considerable heterogeneity amongst these studies (I 2 81%, 95% CI 64 to 90%). Non-adherence, extrapulmonary/disseminated disease and advanced immunosuppression in HIV co-infection were other risk factors noted. The weighted median cumulative incidence of acquired multi drug resistance calculated in 24 studies (assuming whole cohort as denominator, regardless of follow up DST) was 0.1% (5 th to 95 th percentile 0.07 to 3.2%). CONCLUSION: Baseline drug resistance and HIV co-infection were significant risk factors for ADR. There was a trend of positive association with non-adherence which is likely to contribute to the outcome of ADR. The multifactorial aetiology of ADR in a programmatic setting should be further evaluated via appropriately designed studies.


MEMPHIS: August 10, 2017. FedEx has awarded the Grand Prize in its 2017 small business grant competition to Sword & Plough founders Emily Núñez Cavness and Betsy Núñez.
FedEx is providing US$100,000 in funding and US$20,500 in grant and business services to its first, second and third place winners of its latest annual competition.
Growing up at West Point, where her father Joseph Núñez taught political science, not only inspired Cavness to become an officer in the U.S. Army, but to create a company with her sister to give back to military veterans.
In 2012 they founded upcycling company Sword & Plough to transform military tents, sleeping bag covers, bullet casings and other military surplus into fashion clothing and accessories.
"From the beginning, Sword & Plough has been about more than just creating bags. We've always been excited to create high quality products, but our hope was that these products could be used as a platform to promote change," said Cavness.
In less than four years the company, with its quadruple bottom line goal of people, planet, profit and purpose, has supported 65 veteran jobs, repurposed more than 35,000 pounds of military surplus and worked to bridge the civilian-military divide by donating $35,000 in-kind and 10 percent of its profits to veteran organizations.
"Sword & Plough's 'repurpose with a purpose' model positively impacts our military veterans, our environment, and promotes greater understanding between the military and civilian world," commented Bonnie Voldeng, director of Go-to-Market and Content Strategy at FedEx. "This company, and the visionary entrepreneurs behind it, represent just how important small businesses are, not only to the U.S. economy, but to society as a whole."
Other FedEx small business winners include: second place Flexfrost Protein Ice Cream - more protein than Greek yogurt but less sugar; third place Yellow Scope – makers of science kits for girls; Terra Klay – handcrafted teaware by female artists from India; Nurdle in the Rough jewelry - crafted in Hawaii from ocean plastic debris and recycled precious metals; Brian Bogge Chairmakers – handmade furniture from Asheville, NC; Scratch & Peck Feeds - soy-free, organic and non-GMO animal feed; Funky Fresh Spring Rolls – handcrafted, grilled and made from local ingredients; G.Joannou Cycle – quality bicycles for every age group; and The Konery – makers of hand-rolled waffle cones, bowls and fortune cookies in a variety of flavors.


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Shareholders of BLA ask FSA to stop politicians from speaking about institution
An agreement has been reached between the Financial Services Authority (FSA) and the committee elected to represent shareholders of the Building and Loan Association (BLA) to influence politicians to refrain from engaging in chatter over the troubled financial institution.
This was one of the issues discussed when the committee met with the FSA on March 12, Junior Bacchus, chairman of the committee, said.
A call was also made for economist Luke Browne, who, in January, wrote the letter to a local newspaper which triggered a run on the BLA, to refrain from making public comments on the issue.
Bacchus made the point on Tuesday at a shareholders meeting at the Methodist Church Hall, and the point was reinforced at a press conference on Wednesday.
"We believe that that chatter is not helping to build the confidence that is so necessary for the survival and rebuilding of Building and Loan," Bacchus said.
"We know that following the intervention of the Financial Services Authority that there was a lot of talk on both sides of the political fence — a lot of information that we thought should not have been public — people's personal business, so to speak," he continued.
According to Bacchus, from time to time the prime minister may report on progress made, as he had done recently, and that information may be needed to help build confidence.
He further explained that the committee was referring to chatter that will give investors a feeling that they will take their business away from the BLA.
"Right now the way to go forward is to allow the FSA to do what it is doing and allow the FSA to report back to the public and its shareholders and we as a committee will interface with the FSA from time to time," the chairman said.
Jerry George, Public Relations Officer (PRO) for the group, said that immediately following the publication of the letter by Luke Browne, an economist in the Ministry of Finance, a situation arose where there "were seeds for politicking".
"And that took place; there's no ifs, and or buts about that — politicians were brought into this and it was being used for political purposes," he said.
Therefore, a decision was made and agreed upon by both sides that that should stop, George explained.
The committee's PRO said further that following the March 12 meeting with the FSA, Browne appeared on a television programme.
"And we thought since there had been agreements on both sides that the chatter should stop that the person who started this should be influenced to stop speaking on the matter, because every time that person appears, it refreshed people's mind on the hurt, and we wrote to the FSA to ask them to do that also, to use their influence to stop Mr Luke Browne from being out there, engaging in various public forums on the subject," George said.
Browne, who is employed in the civil service as an economist, is also a politician, having unsuccessfully contested the East Kingstown seat for the Unity Labour Party in 2010. (DD)

redpajama_set_name: RedPajamaCommonCrawl


Rare Find First Floor 2 Br/2 Ba/2 Parking Luxury Condominium, at best location in the Park Towers, ground level offers Large Private Patio with direct access to Pool and Deck. Beautifully Remodeled, Turn Key Move In Condition. Conveniently located adjacent to the Grand Formal lobby with on site 24 hour security personnel. Spacious floor plan has Formal double door Entry, Formal Living rm, Dining Area, Master suite w/ walk-in closet, 2nd br w/ sliding door to patio, inside the suite laundry rm. Amenities include 2 oversized Pools & storage rm (1st fl). 8th floor-rooftop Tennis Courts, rooftop Spa, BBQ deck, fully equipped Gym, Saunas, 2 story Entertainment Hall overlooking skyscrapers in DT Glendale & LA. Spacious Kitchen, Dining Area, Living Room with high ceiling, Comfortable Master, Newly refurbished area: Wood Floors, Interior Painted, Cabinets, Quartz Counter Tops, Appliances...Lots of Cabinets, inside-individual Laundry Room (W/D will stay), Master has walkin+regular closet+ extended tub size stall shower with sitting place, south facing bright unit, living room accessible to rear patio/gravel for garden rest, bbq. 2 exclusive car parking at 3rd Fl. Enjoy Resort like Living for your dream Nest! Immaculate! A must see!


I am from Ogden Utah. I began my ceramics career in 1994 as a junior in high school. I had flunked out of calculus and was looking to make up the credits with an easy class. Pottery, while not as simple as I anticipated, proved to be a successful match. I continued on to earn a BFA in ceramics from Weber State University in 2005 and a MFA in ceramics from the Rhode Island School of Design in 2008.
I completed a two-year residency at the Archie Bray Foundation in Helena, Montana as well as one year at the Roswell Artist in Residence program in New Mexico.
Sara, my wife, is my main pillar of support and often helps in the laborious process of sorting and glazing the tens of thousands of extrusions that I produce for a project. Our eleven-year-old son, Braxton, entertains us all the while. His ceramic skills have yet to manifest but his sword skills are notable. Leena is seven years old and is quite useless as a studio assistant but adorable nonetheless. Our newest member, Deklan, is four. Currently we reside in Elgin, Texas.


This is just a short list of the apps we use, but there are many available to help you stay on top of Twitter. Did we miss your favourite app? Did you stop using the apps above because you didn't like them? Let us know what apps you use in the comments!
IF YOU LIKE THIS POST, YOU MIGHT BE INTERESTED IN How To Start Your Work Day Productively OR Writing and Fear.


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The hilarity continues this season when Stan becomes a street racer to impress Francine and tries to put the spice back into their marriage. The Smiths breathe a sigh of relief when Steve heads off to camp — until they realize it's a refugee camp. Meanwhile, Haley and Jeff break up, and it takes a trip through the Dungeons and Dragons world of Steve and his friends to get them back together — and then break them up again.
American Dad, Season 2
© 2005 - 2006 Twentieth Century Fox Film Corporation
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Trump calls on Russia to hack Clinton's emails
By Natalie Huet • last updated: 27/07/2016
No stranger to controversy, Republican presidential candidate Donald Trump has just invited a foreign government to spy on his Democratic opponent, Hillary Clinton.
Russia, if you're listening, I hope you're able to find the 30,000 emails that are missing
Donald Trump Republican presidential candidate
Specifically, the brash billionaire called on Russia to find and release the thousands of emails Clinton did not disclose to officials investigating how she handled classified information when she was secretary of state. Clinton has said the emails she did not turn over were private.
"Russia, if you're listening, I hope you're able to find the 30,000 emails that are missing," Trump told reporters.
If Russia or any other country or person has Hillary Clinton's 33,000 illegally deleted emails, perhaps they should share them with the FBI!
Whether or not it was a joke, it did not amuse the Clinton camp, which already believes Russia orchestrated a leak of embarrassing Democratic party emails last week to help Trump.
Clinton camp: Trump actively encourging Russia to spy on us is a "national security issue" https://t.co/u0LKS7ou8mpic.twitter.com/qfpBUTf3Gc
The New York Times? said intelligence officials are pretty sure Moscow was behind the email theft, but not so sure whether this was just routine spying or meant to influence the election.
Russian foreign minister Sergei Lavrov brushed aside suggestions it was involved: "I don't want to use four-letter words," he told reporters.
The FBI is now investigating the leak of some 19,000 emails that showed the Democratic National Committee favoured Clinton over the more left-wing Bernie Sanders for the party's presidential nomination.
'Just move on': US Republicans grapple with post-Trump future as Biden becomes president
In pictures: Joe Biden becomes the 46th US president
Donald Trump leaves the White House for the final time


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Q: use IXAudio2 to play sound mix? I write a MFC project . I use IXAudio2 to play wav file.
my code is like this :
pSourceVoice->SubmitSourceBuffer( &buffer );

hr = pSourceVoice->Start( 0 );

but in this way I only can play one sound by a time. It must wait this .wav file play over. I can play the second file. How can I play the file I need and not wait for the first one is over, likes mixing sounds?
How can I achieve this function?

A: You create one IXAudio2SourceVoice for each 'playing, active' sound you want at a time. Typically games will create a few hundred source voices to manage--beyond that the sound mix is typically too muddy to hear anyhow.
Game audio engines have a mix of 'one-shot' voices that just play-on-demand until they complete--at which point that frees up that source voice for use by another one-shot sound--, 'ambients' or 'music' voices that are manipulated as they play, and 3D audio positioned sounds which have to be updated every rendering frame to track the 3D rendering object they are emitted from.
If you submit the same audio data to two distinct IXAudio2SourceVoice instances, then you'll hear it being played twice, mixed together in real-time. Typically you won't start them at precisely the same instant because the result is just a louder version of the one sound. Normally they are started at different times so you get overlapped playback.
See XAudio2 Programming Guide, GitHub, and DirectX Tool Kit for Audio.

redpajama_set_name: RedPajamaStackExchange


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Рейкин (, буквально «деньги благодарности») — единовременный невозвратный платеж, уплачиваемый арендатором арендодателю при заключении договора аренды недвижимости, считающийся подарком арендодателю и не возвращающиеся после расторжения договора аренды.

Рейкин часто равен первоначальной сумме депозита «арендного залога» (, сикикин). Однако рейкин может быть эквивалентом арендной платы за шесть месяцев (или более), но, как правило, такой же, как арендная плата за один-три месяца. Эти деньги считаются подарком арендодателю и не возвращаются после расторжения договора аренды.

Требование рейкин является обычным делом в большинстве договоров аренды. В Токио размер рейкин в размере арендной платы за один или два месяца является стандартной. Рейкин не выплачивается за аренду государственного жилья и за недвижимость, построенную на ссуду Корпорации жилищного финансирования.

В последние годы всё большее число арендодателей и агентств недвижимости начали предлагать аренду жилья без рейкина.

Выдвигаются различные теории относительно природы рейкин, объяснаяющие природу возникновения платежа. Типичными примерами являются: вознаграждение за заключение договора аренды; компенсация за неполучение арендной платы в течение периода простоя недвижимости после выезда арендатора; затраты на восстановление, связанные с естественным износом и т. д.

Примечания

Литература

Ссылки

Экономические термины
Недвижимость
Аренда

redpajama_set_name: RedPajamaWikipedia


This herb is most often used in formulas that treat bloating and congestion in the digestive tract, regulate digestion, promote urination, and treat general edema (TCM: for stagnant Qi and dampness). May also be used in some formulas to treat worms due to its paralyzing effect on tapeworms in the bowel.
Moves Qi and reduces stagnation; expels dampness; promotes urination and moves dampness.
Use cautiously where there is Qi deficiency.


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AWorkstation.com
Love, Art and Design
January 10, 2023 CreativityMartin
Sony's Project Leonardo: A PS5 Controller for Differently-Abled Gamers
Sony Interactive Entertainment's designers have rolled out a wonderful initiative to reduce barriers for differently-abled gamers. Their Project Leonardo is a freshly-designed customizable controller for the PS5, designed incorporating feedback from accessibility experts, game developers and of course gamers themselves, for some of whom the standard controller can be difficult if not impossible to use.
"It is built to address common challenges faced by many players with limited motor control, including difficulty holding a controller for long periods, accurately pressing small clusters of buttons or triggers, or positioning thumbs and fingers optimally on a standard controller," the company writes.
Listen beautiful relax classics on our Youtube channel.
To that end, the user-swappable interface features different analog stick caps and buttons of different sizes, all of which can be customized. Buttons can also have two different functions mapped onto them at once, to allow players to access two-button combos with just one button press.
Each controller can store up to three different players' settings. And conveniently, while they can be used as standalone controllers, they can also work in conjunction with another Project Leonardo controller or even a standard controller, allowing friends and family to assist with the controls.
As for the form the designers settled on:
"Project Leonardo's split, symmetric design allows players to reposition the analog sticks as close together or as far apart as they like. The controller lies flat and does not need to be held, so players can lay it on a tabletop or a wheelchair tray. It can be easily secured to AMPS mounts or tripods, and can be oriented 360 degrees for the most comfortable use. Players can also program the 'north' orientation on the analog sticks to match their preferred controller orientation."
Industrial designer So Morimoto describes the design team's overall goals:
"Project Leonardo is part of the PS5 product family and is based on the same design concept. We were inspired by the idea of all players enjoying the world of PlayStation together. Our team tested over a dozen designs with accessibility experts, looking for approaches that would help address key challenges to effective controller use. We finally settled on a 'split controller' design that allows near free-form left/right thumbstick repositionability, can be used without needing to be held, and features very flexible button and stick cap swapping.
"Because players can customize Project Leonardo according to their needs, there is no one 'right' form factor. We want to empower them to create their own configurations. The controller can also flexibly accept combinations of accessibility accessories to create a unique aesthetic. I am excited that the design will be completed through collaboration with players rather than presenting them with a single form factor."
Source: core77
Woman Gets Angry At Partner Telling Her How To Handle Job Interviews About Her Own Career, And The Internet Can't Help But Agree With Her
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text:
Q: Cities problem interpretation Cities A, B, ... , Z are connected in a loop by 26 two way roads: A to B, B to C, .... Z to A. Each road can be destroyed with probability p independently of the others.
Find the probability that, after the rain, there are two cities that are not reachable from each other.
I do not need help solving this problem. I think I may have solved it in fact. My question is with whether or not I am interpreting it correctly as English is not my native language.
Does this mean that if one of the roads are destroyed then two cities are not reachable from each other? Does reachable from each other mean both cities must be able to travel to the other? That is, we cannot have just one way.
Thanks for help.


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SEC Approves PCAOB Budget and Accounting Support Fee for 2023
On December 23rd, the SEC approved the 2023 budget of the Public Company Accounting Oversight Board (PCAOB) and the related annual accounting support fee. The PCAOB monitors the audits and auditors of the financial statements that are submitted by registered broker-dealers and issuers. Section 109 of the Sarbanes-Oxley Act of 2002 requires the PCAOB to establish, with SEC approval, a reasonable accounting support fee to fund its operations. Continue reading "SEC Approves PCAOB Budget and Accounting..." »
in Accounting, SEC at 18:14
FASB Staff Releases Proposed GAAP Taxonomy Enhancements for Proposed ASU Regarding Leases (Topic 842), Solicits Comment
On November 30th, the Financial Accounting Standards Board (FASB) released for comment the proposed GAAP taxonomy improvements for the proposed Accounting Standards Update (ASU), which is aimed at improving accounting guidance for lease arrangements between entities under common control. Continue reading "FASB Staff Releases Proposed GAAP Taxonomy..." »
in Accounting, FASB News, US GAAP Taxonomy at 08:42
Financial Accounting Foundation Releases New Strategic Plan
The Board of Trustees of the Financial Accounting Foundation (FAF) has released the final version of its new strategic plan. The FAF is the organization that oversees the Financial Accounting Standards Board (FASB) and the Governmental Accounting Standards Board (GASB). Because stakeholder feedback is the foundation of the organization's work, the new strategic plan is based on extensive engagement with stakeholders via comment letters, an online survey, and a number of individual interviews. Continue reading "Financial Accounting Foundation Releases New..." »
in Accounting, FASB News, Investor Education at 08:25
GASB Proposes Guidance to Help Stakeholders Apply its Pronouncements
On November 15th, the Governmental Accounting Standards Board (GASB) released proposed implementation guidance that uses a questions and answers format to clarify and expound on certain GASB pronouncements. Continue reading "GASB Proposes Guidance to Help Stakeholders..." »
in GASB News, US GAAP Taxonomy at 08:25
FASB Issues Proposed Investment Companies Taxonomy Implementation Guide
On November 15th, the Financial Accounting Standards Board (FASB) released a proposed Taxonomy Implementation Guide. The Guide is premised on the proposed 2023 GAAP Financial Reporting Taxonomy, which is currently awaiting SEC acceptance and subject to change until the finalized version is published. The newly proposed Guide, Financial Services—Investment Companies (Including SEC S-X Schedules for Business Development Companies), is comprised of examples intended to help users of the taxonomy understand how the reporting framework for investment companies is structured within the taxonomy. Continue reading "FASB Issues Proposed Investment Companies..." »
in FASB News, US GAAP Taxonomy at 15:21
Thursday, October 06. 2022
FASB Releases Proposed Technical and Other Improvements for 2023 GAAP Taxonomy
On October 5th, the FASB issued for a request for comment on proposed technical and other conforming improvements for the 2023 GAAP Financial Reporting Taxonomy. The comment period ends on November 3, 2022. Continue reading "FASB Releases Proposed Technical and Other..." »
in FASB News, SEC, US GAAP Taxonomy at 10:18
Thursday, September 15. 2022
FASB Releases Proposed Changes and Technical Guide for 2023 SEC Reporting Taxonomy, Solicits Comment
On September 8th, the FASB announced that it has released for public review and comment proposed technical and other conforming improvements for the 2023 SEC Reporting Taxonomy (SRT) along with the related release notes. The technical and conforming modifications made to the SRT are designed to improve its overall utility. Continue reading "FASB Releases Proposed Changes and Technical..." »
in FASB News, SEC, XBRL at 09:48
FASB Releases Proposed 2023 DQCRT for Review and Comment
On September 6th, the Financial Accounting Standards Board (FASB) staff issued the Proposed 2023 DQC Rules Taxonomy (DQCRT) for the US GAAP and SEC reporting taxonomies. Individuals and organizations may review and comment on the modifications made to the proposed DQCRT until October 6, 2022. Continue reading "FASB Releases Proposed 2023 DQCRT for Review..." »
in Data Quality Committee, FASB News, SEC, US GAAP Taxonomy at 12:20
FASB Announces Release of Proposed 2022 Q3 Supplemental GAAP Taxonomy for Public Review and Comment
The Financial Accounting Standards Board (FASB) has released the Proposed 2022 Q3 Supplemental GAAP Taxonomy for public review and comment. The publication introduces enhancements to the GAAP Financial Reporting Taxonomy and the SEC Reporting Taxonomy, collectively known as the GAAP Taxonomy. Continue reading "FASB Announces Release of Proposed 2022 Q3..." »
Friday, July 08. 2022
FASB Releases 2021 Agenda Consultation Report
On June 29th, the Financial Accounting Standards Board (FASB) issued its 2021 FASB Agenda Consultation Report. The document summarizes comments submitted by investors during the 2021 agenda consultation project and demonstrates how those responses have shaped the FASB's technical and research agendas and standard-setting process as of June 29, 2022. Continue reading "FASB Releases 2021 Agenda Consultation Report" »
in FASB News, Investor Education at 10:00
Thursday, July 07. 2022
FASB Releases ASU to Improve Fair Value Guidance for Equity Securities
On June 30th, the Financial Accounting Standards Board (FASB) published an Accounting Standards Update (ASU) that improves financial reporting for investors and other financial statement users. The ASU is designed to enhance comparability of financial information for all reporting entities with investments in equity securities measured at fair value and are subject to contractual restrictions preventing the sale of those securities. Continue reading "FASB Releases ASU to Improve Fair Value..." »
Thursday, June 09. 2022
FASB Releases Proposed Taxonomy Implementation Guide on Disclosures about Offsetting Assets and Liabilities
On June 3rd, the FASB announced that it has released a proposed Taxonomy Implementation Guide based on the 2022 US GAAP Financial Reporting Taxonomy related to disclosures about offsetting assets and liabilities. Continue reading "FASB Releases Proposed Taxonomy Implementation..." »
Friday, May 20. 2022
FASB Announces Meeting of Investor Advisory Committee
The Financial Accounting Standards Board's (FASB) Investor Advisory Committee (IAC) will convene a meeting on Tuesday, May 24th to address matters of interest to financial statement users including income tax disclosures, digital assets, segment reporting, disaggregation of income statement expenses, and ESG-linked financial instruments. Continue reading "FASB Announces Meeting of Investor Advisory..." »
The Financial Accounting Standards Board (FASB) has announced that it will convene a meeting of its Small Business Advisory Committee (SBAC). The meeting will take place on Thursday, May 12, 2022, from 1:00 p.m. – 3:00 p.m. ET. Continue reading "FASB to Hold Small Business Advisory Committee..." »
(Page 1 of 4, totaling 49 entries) next page »


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Updated by BusinessDegree Link on Feb 04, 2014
BusinessDegree Link
5 items 2 followers 0 votes 52 views
Top 5 Finance Schools In The U.S.
Listly by BusinessDegree Link
Take a look at the Top 5 Finance Schools In The U.S.
The University of Pennsylvania Wharton School, located in Philadelphia and San Francisco, is the most comprehensive source of business knowledge in the world, offering globally recognized programs at every level of business education.
The University of Chicago Booth School of Business
Moscow has a flourishing community of successful Booth alumni who do business with each other and feed a pipeline of promising students to the Executive MBA Program Europe.
NYU Stern | NYU Stern School of Business | Full-time MBA, Part-time (Langone) MBA, Undergraduate, PhD, Executive MBA ...
Explore the NYU Stern School of Business and learn more about the full-time MBA, part-time (Langone) MBA, undergraduate, PhD, and executive MBA business programs.
Even More Snow Falling on Morningside Campus ABOUT COLUMBIA
Stanford Graduate School of Business | Change lives. Change organizations. Change the world.
Connect with fellow alumni, take advantage of professional development opportunities and career services, and learn how volunteering your time and talents can connect you with current students and enrich Stanford GSB.


Thursday 4th April Annual Parish Assembly at Norton Canes Library, Burntwood Road, Norton Canes. at 7 p.m.
All meetings take place at Norton Canes Community Centre Brownhills Road, Norton Canes (unless otherwise notified).
Public participation commencing at 7 p.m. with full Council business commencing at 7.30 p.m.
There will be no less than 11 Ordinary meetings in any calendar year.


text:
Title: Heading To the Challenges-HTC
Category: 3. Business and Community Organizations
Bibliography: http://librarywork.taiwanschoolnet.org/gsh2014/gsh7650/page5_b2.html
School: Kang Chiao Bilingual Elementary School
New Taipei, , Taiwan
10 students, ages 11~12 worked together to complete this CyberFair project on February 12, 2014. They have participated in CyberFair in the following year(s): 2007,2009,2010,2011,2012,2013
Classes and Teachers: Chin-Hua Yang
Our School's Web Site: http://www.kcbs.ntpc.edu.tw/
Xindian District is located in the South of New Taipei City, which is beside the mountain with fabulous view and is the biggest district in New Taipei City. Since 1960, the government has set Xindian to be an export industrial zone because Xindian is close to Taipei City, without traffic jam, and no risk of flood. In addition, it is easy to get workers and land. That is why over time, many companies such as Yulong Motor, Taiwan General Electric, and GIGABYTE all set up their companies in Xindian. Our main focus, HTC, also set up its headquarters in Xindian. The Taipei headquarters of HTC mainly focuses on product development, marketing, and it is the decision-making center of the company. Its establishment not only provides New Taipei City an opportunity to gather passion, dream and creativity, but also gives the New Taipei city a stage of innovations and creativity to light up Taiwan.
HTC is one of the key companies that makes smartphones and PCs under its own brand. The company was founded in Taoyuan in 1997, and it started as an OEM factory of PDAs and cellphones for other global brands. In 2005, it started its own brand of HTC. In 2011, HTC became one of the top 100 brands in the world. In the year of 2012, HTC moved Taipei headquarters to Xindian. While most of Taiwan's electronics companies chose to be OEM, HTC chose to sell smartphones under its own brand and became a key player in the market. Along the way, HTC has faced a lot of challenges, but they kept focusing on "innovation" to make miracles, and "courage" to excite the world. It created a lot of surprises for Taiwan, and for itself, too! In this project, we'll research about it through reading paragraphs, visiting its factory, conducting a questionnaire survey, asking the professionals, doing hands-on activities, etc. We'll talk about how HTC used its own name to make its way to the world market, as well as the challenges and hope behind its success.
Currently, the school has sufficient host servers, and each classroom owns a desktop and internet access. There is an IT department in the school to provide teachers and students with a convenient and multi-service network environment including ample spaces for website and mail. In order to participate in this Cyberfair competition, we spent our extra-time, noon break, and after-school time to set up the website. We first uploaded the website page to FTP server of the school, which enabled us to modify Web Pages at home, making the whole process smooth.
1.Getting Permission from HTC: HTC is a busy and successful company. Thus, getting the permission from the company for sharing information with us was our first challenge. We wanted to thank Mrs. Chang because she helped us submit the research proposal to HTC and get the permission from HTC. This gave us the chance to visit the company and collect a lot of precious information. 2.Organizing the visit: Our second challenge was to complete the interview and collect all the information needed within a limited time, and leave a good impression at the same time. We divided ourselves into several small groups to prepare the topics and questions for the interview, and we also rehearsed for different situations that would likely happen during the interview. We also sought for our parents' assistance in taking photographs, making videos, and recording, in order to have a complete record of the entire process of our interviews. 3.The Busy Interviewees: In the year of 2013, the competition in the smartphone industry started to become more and more intense. HTC faced a critical challenge that they had never faced before. We could see it from the busy schedule of the HTC leaders. Thus, our visit was postponed several times, and we did not get to interview the senior executives of HTC. 4.Lack of the Knowledge of Technology: While we were discussing the history of HTC and reading information from news articles and magazines, we found many technical terms that we had never learned from text books. Through searching online and solving this problem from the interviews, we were able to overcome this. We also want to say thank you to the parents who work in computer companies, for teaching us the terminology.
Only through treating others in a humble and pleasant manner, and only through thinking creatively about the future, can a person seize the opportunity in the ever-changing world. Then the blue ocean in life will be found.
1.Language: invitation, interview, writing the content and experience/after-thought. 2.Math: making statistical charts and analyzing data by Excel software. 3.Social Studies: setting up research topic direction and framework, designing questionnaire, and organizing questions. 4.Integrated Activities: integrating manuscript, questionnaire, network, written documents and all kinds of data, the completion of the web production 5.Independent Study: studying all kinds of research skills, including brainstorming, KWHL chart, questionnaire, interview, data collection and organization, etc. 6.Nature and Life Science: We hope to include the knowledge of telecommunications and development of cell phone, so we added a subtopic, Encyclopedia. We hope the visitors of our website can learn more about this area.
Phone and E-mail: 1.Invite and contact the interviewees. 2.Collect the first hand information from HTC. Internet and Newspaper: 1.By internet, learn about the projects of previous winners. 2.Google the media information of HTC. 3.Use internet as a channel to discuss the information and share the experience with each other. Smartphone:Operate smartphones by ourselves to know the function of HTC smartphones. Computer:Use different application software to edit photos, writings, and data statistics in order to integrate them into Web Page. DV:Take photos of each visit and interview, and document our research and training process. Printer:Print out the guidelines of the interviews, online information, questionnaire, interview notice, and other related information. USB:Store the project information. Software:Computer application software: Photo Impact, Photoshop, Dreamweaver, Word, Excel, Ftp, IE, etc.
1.We not only saw the factory in our Taoyuan factory visit, but also we talked with some major employees. The thing that was most valuable was experiencing how people thought of new ideas and enjoyed the fun of brainstorming in Magic Lab. 2.With the help of Mrs. Chang, the mom of one Kang Chiao student, we got two interview sessions with Mr. John Wang talking about the mysterious Magic Lab. He also talked about the "Quietly Brilliant" that we didn't even know before. We'll put this on our website to share our deeper understanding. 3.The bulletin board outside our classroom is the place where we put our achievement in words and in diagrams, as well as get feedback and advice.
Our deepest impact would be the issues of "Quietly Brilliant" and "failure." Actually, "Quietly Brilliant" includes two meanings. They are the humble attitude and the ability to make innovation. For school, life, and work, only being modest can you see other people's goodness and find your own shortcomings. We should have no arrogance in victory and no despair in defeat. A proverb said, "From clogs to clogs is only three generation." If we want to break it, we must be very humble. "Failure is a very important thing." This is what John Wang told us. Yes, if you do not regard failure as an important issue but fear of it, you will not dare to innovate. Every unique and important invention is derived from the perseverance. Creativity and failure can help you in your entire life.
1.Mrs. Chang: She helped us connect with HTC and schedule a visit. Also, she helped us to arrange an interview with John Wang, the former CMO of HTC. 2.Mr. Chang, Deputy General Manager: He was one of the important people who helped arrange the visit for us. He also told us the philosophy of HTC. 3.Ms. Lai, the manager: She was in charge of our visit of Taoyuan factory and told us HTC's story of brand. 4.Mr. Lu, a board manger: He introduced the foundation to us and answered us many questions. 5.Director Ye: She answered us the questions about the staff benefit. 6.Mr. Kao and Mr. Lin, the engineers: They led us to experience as much as we could in the workshop and told us things about Magic Lab. 7.Mr. Wang, the former CMO: He shared with us his personal experience in HTC and Magic Lab.
HTC keeps encountering challenges, but it continues to grow and learn from the lessons and failure. This is the company that became one of the world's top 100 brands, HTC. From the time of OEM, to the time of creating its own brand, it has been a journey. Although the obstacles HTC encountered were difficult to conquer, it solved all of them. The weapon it used was innovation. While HTC was selling its phones very well, the war of patent started. Although the lawsuit between HTC and Apple ended with compromise, it still influenced the market of HTC in America. Also, the patent suit between HTC and Nokia may also lock the market of HTC phones in America and Europe. We admire the courage of turning from OEM to making its own brand. We also praise that HTC has gotten so many "number ones" throughout its life. We also trust its insight. We believe that HTC will fight its way out and find its new goal. Make another miracle for Taiwan, HTC! Go! Go!Go!