text:
WHAT THE SCOTTISH GOVERNMENT KNEW AND WHEN THEY KNEW IT
Part Three of A Very Scottish Coup is nearly done and I'll post it tomorrow. In the meantime, here are a couple of things I've discovered while writing it. The first thing is this: The Scottish Government have always claimed that the requirement in their procedure for an Investigating Officer to have "no prior involvementContinue reading "WHAT THE SCOTTISH GOVERNMENT KNEW AND WHEN THEY KNEW IT"
Mar 11, 2021 - 20:00
Part Three of A Very Scottish Coup is nearly done and I'll post it tomorrow. In the meantime, here are a couple of things I've discovered while writing it.
The first thing is this:
The Scottish Government have always claimed that the requirement in their procedure for an Investigating Officer to have "no prior involvement with any aspect of the matter being raised" was interpreted by them throughout the development of the procedure to mean "no prior involvement in the subject matter of the complaint".
They have always denied having the slightest inkling that the phrase could, and would, be interpreted by the courts to mean "no prior knowledge of the details of the case".
The Scottish Government's unique interpretation of the phrase is of course what enabled Judith Mackinnon – who had prior knowledge of the complaints against Alex Salmond coming out of her ears – to be appointed as Investigating Officer for those complaints on 16 and 24 January 2018.
I can tell you now that, as at 12 December 2017, the Scottish Government were in fact well aware of the proper interpretation of this crucial phrase in the procedure being developed by them.
Their claims that they didn't know what their own policy actually meant are just more lies, and in what follows, I'll tell you why.
The second thing is this:
The Scottish Government officials instructing the defence of the judicial review were well aware by 19 October 2018 that Judith Mackinnon had prior knowledge of the Salmond complaints such as to make the whole procedure unlawful from the moment she was appointed.
They were well aware that her prior knowledge of the details of the complaints extended not only to receiving Ms A's full statement on 22 November 2017, and to meeting personally with Ms A and Ms B on 5 December 2017 to discuss their complaints, but also to taking Ms B's complaint directly from Ms B prior to being appointed Investigating Officer of that complaint.
Among many other things which horrified the Scottish Government's external counsel when the true extent of all of this started finally to emerge from the veil of lies thrown over it by Leslie Evans and others during the judicial review process was the revelation that Ms A had met with Mackinnon on the very day she made her formal complaint, and prior to lodging it with Nicola Richards.
It's unclear, however, whether counsel were ever told that Ms B's formal complaint owed its very existence to Judith Mackinnon.
In what follows, I'll give you a rare glimpse into the Scottish Government's withholding of evidence from their own external counsel during the judicial review process – a calculated and deliberate strategy which they're continuing to pursue successfully to thwart the pitiful Fabiani inquiry.
Mackinnon's unlawful meeting with Ms A
On a date redacted by the Scottish Government, Judith Mackinnon sent Ms A a letter which she signed as "Investigating Officer" and which began:
"We met on [Redacted] to discuss your experience about the alleged misconduct of a former minister. Following this meeting you submitted a formal written complaint to Nicola Richards, Head of People Directorate. … I have been designated as the investigating officer" (my emphasis).
I have no idea what legitimate reason there could possibly be for redacting the date on this letter. It seems likely, however, that the letter was sent immediately after Mackinnon was appointed Investigating Officer on 16 January 2018, the same day that Ms A lodged her formal complaint.
It also seems likely that the redacted date of her meeting with Ms A prior to the lodging of her formal complaint was also 16 January 2018, since it was the eventual discovery of a meeting between Mackinnon and Ms A on that date that so horrified external counsel.
When Judith Mackinnon then gave evidence on oath at the Court of Session in December 2018 that she could not remember this meeting, counsel's horror turned to barely concealed anger.
If I'm right that the meeting referred to in Mackinnon's redacted letter is the meeting of 16 January 2018 that she cannot now remember, this is a truly remarkable failure of memory, even by Scottish Government standards.
Imagine if you can writing in a formal letter about a clearly important meeting that has just taken place in January 2018 and then being unable to remember even having that meeting, far less the details of it, later that same year. Imagine further that the other person at the meeting cannot remember it either or, for some reason that we can only again imagine, cannot be asked about it.
If you can't imagine how any of this could be possible then join the club, because I can't either.
What is clear is that all of Mackinnon's prior contact and meetings with Ms A rendered her subsequent appointment as Investigating Officer wholly unlawful on that ground alone.
Mackinnon's unlawful meeting with Ms B
The text messages between Mackinnon and Ms B which have been disclosed by the Scottish Government to the inquiry are, as usual, redacted and again for no legitimate reason that I can think of, even the dates of them have been redacted.
However, the contents of the messages make clear that they were exchanged prior to the lodging of Ms B's formal complaint on 24 January 2018. The context makes it similarly likely that the exchanges occurred after Mackinnon and Richards met with Ms A and Ms B on 5 December 2017.
On a redacted date, then, Mackinnon texts Ms B:
"[Ms B] – just checking if you got my email on Friday? Judith"
Ms B replies:
"Hi Judith, yes sorry i did. [Redacted] I'm still having a think about it if that's ok, but will come back to you later today. Thanks for all your help with this, [Ms B]"
Mackinnon texts back:
"No problem [Ms B]. And no rush either – was thinking that maybe you take time over Christmas and come back to me in January? Judith"
In the format released by the Scottish Government, that same exchange then appears to continue, but again the content of the messages indicates that we are now at a later time period, and very likely one close to the date of the lodging of Ms B's formal complaint on 24 January 2018.
Mackinnon now texts to Ms B:
"[Ms B] Nicky Richards has let me know that you have decided to make a formal complaint. In order to discuss the logistics it would be good to talk. Can you advise when you would be free for a telephone conversation? Best wishes in the meantime, Judith Mackinnon, SG"
There follows some to-ing and fro-ing about times to call, which ends with Ms B texting:
"Thanks Judith, speak to you tomorrow. [Ms B]"
And then, with the usual redaction of the date:
"[Ms B] – we are [Redacted] currently at [Redacted] See you soon. Judith"
Who "we" might be can only be guessed at, but it's clear that Mackinnon and Ms B were about to meet on the day that text was sent.
And so, unless there was a yet further meeting between the two that has not been disclosed, these texts must have been exchanged on 24 January 2018, and the meeting must have been for the express purpose of Mackinnon herself taking Ms B's complaint.
We know this because of this one-sentence email, sent by Mackinnon herself:
"[Ms B] raised her complaint directly with me."
As with Ms A, it's quite clear that all of Mackinnon's prior contact and meetings with Ms B rendered her subsequent appointment as Investigating Officer wholly unlawful on that ground alone.
What those instructing the judicial review defence knew and when
As I've detailed in previous posts, Leslie Evans knew from the very start that Mackinnon had been provided with a copy of the full statement taken from Ms A on 22 November 2017 – the statement which, with only minor revisions, later became Ms A's formal complaint – because Richards and Mackinnon advised her of that fact, in writing, on 23 November 2017.
Evans knew from the very start that Mackinnon had then met with Ms A and Ms B on 5 December 2017 because Evans personally directed Mackinnon to have those meetings.
And Evans must also have known from the very start that Mackinnon had met Ms A again prior to lodging her formal complaint on 16 January 2018 because, as is detailed above, Mackinnon had referred to that meeting in her formal letter to Ms A immediately after she was appointed Investigating Officer of Ms A's complaint, and that letter must have formed part of Mackinnon's report to Evans.
The position is less clear for Ms B, which is one reason why Mackinnon's one-sentence email confirming that she, and she alone, took Ms B's complaint directly is of such significance.
Mackinnon's email forwards on to Nicola Richards an email exchange she had with Ms B at around the same time as the texts detailed above were being exchanged regarding Ms B's formal complaint.
On a date which has been redacted, Mackinnon emails Ms B to thank her for "talking to me". She then sets out various options to progress a formal complaint, and, by way of encouragement, advises that "there may be other individuals who are also prepared to submit a complaint" (my emphasis).
Ms B replies, on a date also redacted:
"Dear Judith,
"As discussed, I have decided to make a formal complaint but would not like my name to be attached to this.
"Sorry this is a bit of a ramble.
"Happy to discuss anything in more detail but will wait to hear back from you about [Redacted].
[Ms B]"
The information in this exchange and the later confirmation from Mackinnon that Ms B had "raised her complaint directly with me" are each significant enough in evidencing Mackinnon's improper interactions with Ms B.
What is even more significant, though, is the date of Mackinnon's later email, forwarding the exchange on to Richards and confirming how the complaint was then raised, so let me set out the whole thing:
From: Mackinnon J (Judith)
Sent: 19 October 2018 10:28
To: Richards, N (Nicola)
Subject: FW: Options
There can only be one reason why Mackinnon was forwarding this earlier exchange about Ms B's complaint "options" to Richards, and reminding Richards that it was Mackinnon herself who took Ms B's complaint directly from her.
The reason can only be that, in October 2018, Richards and Mackinnon were being asked by Evans and the others instructing the defence of the judicial review for relevant information and that Mackinnon, to her credit, was providing this highly relevant information to be passed on up the chain.
Just this one email, if it had been passed on as it should have been, would have been enough for external counsel to give in October 2018 the unequivocal advice they later gave in December 2018, that the case had to be conceded.
But of course it's inconceivable that this was the only such email sent at this stage, and sent what's more on the very clear understanding that it would be passed on to external counsel.
So where is Richards's email forwarding on in turn this important information from Mackinnon to whomever had asked her for it?
And where are all the other emails in September and October and November and December 2018 from all the other participants who, like Mackinnon, must have been forwarding on relevant information as it was requested of them by Evans and her accomplices?
They're buried of course – shredded for all we know, since nothing can be put past this lot – and, if it's left up to the hopeless Fabiani inquiry and the incompetent Scottish media, buried is where they'll stay.
How the Scottish Government knew in December 2017 that Mackinnon could not lawfully serve as Investigating Officer
Which brings me back finally to where I started: what the Scottish Government knew about their unlawful procedure, and when they knew it.
In their Statement to the Fabiani inquiry, the Scottish Government were keen to emphasise the significance of guidance produced by the UK Government Civil Service Employee Policy team (CSEP), a high-powered unit located in the UK Cabinet Office whose specific job it is to provide authoritative HR advice to the whole of the UK civil service.
As the Scottish Government are at pains to note in their Statement, their civil service officials:
"… received a draft copy of guidance on handling of historic allegations of harassment developed by the UK Government Civil Service Policy team on 17 November and a later copy with Frequently Asked Questions (FAQ) on 12 December during the development of the procedure."
It seems that their reason for focusing on these documents is the highly dubious – in fact, laughable – claim that the documents illustrate some superiority of the Scottish Government over the UK Government because we ended up with an unlawful procedure that has by now cost us well into the millions and the UK Government didn't:
"The lack of a published process for handling complaints about current or former Ministers in the UK Government confirmed to the Scottish Government that it had been the correct course of action to have started to develop its own procedure."
However, on the way to making this hilarious claim, the Statement does – probably by accident – manage to say some true and important stuff about the CSEP documents, namely the guidance they contain that:
"… in complex and sensitive cases of historical allegations, it is advisable to appoint either an experienced investigator or refer the case to the HR Director, who may handle the investigation within HR."
Of course, the Scottish Government neglect to point out that this advice is intended to cover historical allegations made by one serving civil servant against another, and says nothing at all about such allegations against a former Minister, but let that pass. The important point for present purposes is that, out of all of the guidance on which they might have chosen to hang their hats, the Scottish Government chose to quote specifically from these CSEP documents, and in particular, from Answer 23 of the CSEP "Frequently Asked Questions":
"In complex and sensitive cases of historical allegations, it is advisable to appoint either an experienced investigator or refer the case to the HR Director, who may handle the investigation within HR. If such cases involve a senior member of staff…, departments may want to go outside their own department to ensure somebody appropriately senior and independent is appointed" (my emphasis).
Question 23, which the above paragraph partly answers, is in the following terms:
"Who should handle investigations and what training is available for investigators?"
I wouldn't dispute for a moment that an authoritative civil service "FAQ" document which asked and answered that question should be given this level of prominence by the Scottish Government, especially since it's clear that the "FAQ" was received and read by Nicola Richards and Judith Mackinnon, exactly as the Scottish Government Statement are at pains to aver.
The "FAQ" was received by Richards as an email attachment on 12 December 2017 and sent on by her to Mackinnon and others that same day under subject heading "Guidance on handling allegation of harassment FAQ". We know that Richards, Mackinnon, Evans and others read it thoroughly because it is given such significance in the Scottish Government's own Statement to the inquiry.
So in the context of the procedure for handling harassment complaints which Richards and Mackinnon were at the very heart of developing at exactly the time the guidance was received it is simply inconceivable that they did not read and understand the most important sentence in Answer 23:
"In every case, the investigator will need to be impartial, and have no prior knowledge of the details of the case."
Let me repeat that: no prior knowledge of the details of the case.
I've written before on this blog about how basic this principle is and how utterly untenable it is for anyone, let alone an experienced HR professional or lawyer, to try to argue, as the Scottish Government still try to argue, that the phrase "no prior involvement" was thought by them to mean no prior involvement as a participant in, or witness to, the actual events comprising the complaint.
As Jerry Seinfeld once said, dry-cleaners should hardly need the Dry-Cleaner's Code to tell them not to wear your clothes, and Evans, Richards and Mackinnon shouldn't have needed Answer 23 to tell them that "no prior involvement" means – and only means – no prior knowledge of the details of the case.
But as it happens, we now have Answer 23 too.
And it is therefore beyond a shadow of a doubt that Evans, Richards, Mackinnon and the whole Scottish Government were made aware on 12 December 2017 at the very latest that appointing Mackinnon to the role of Investigating Officer would be unlawful.
As we know, and as external counsel found out many months too late, they went ahead and did it anyway.
In some other Scotland, one where laws and rules actually meant something, someone would have had to resign for that by now.
Continue reading on the Gordon Dangerfield Blog...
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Law I'm a Scottish Solicitor Advocate whose clients include Tommy Sheridan. I'll be writing on this blog about Tommy's cases, and other legal matters. Culture I've been a student and teacher of literature, and taught Freshman Composition at the University of California for seven years while I studied for my Master's and Ph.D in English. One of these days I'll finish my Dissertation. My main academic interests are in Romanticism, philosophy of language and theories of meaning. I'll be writing about those here too. I also write fiction. You can read more about me in that capacity here, and about my novel A Thousand Hearts here. I'll be using this blog shamelessly to tell you about my book and to try to talk you into buying it. Politics I'm a supporter of Scottish independence and a libertarian socialist with a deep belief in free speech as the foundation of all political struggle. I deplore the authoritarian streak on the Left that wants to suppress this most basic freedom. While our masters continue to wage the class war, we're busy fighting identity wars with ourselves. They can't believe their good luck. I'll be writing about that here too. https://gordondangerfield.com
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All Under One Banner – plans for 2021


text:
Arno Luboldt (* 10. Juni 1866 in Gera; † 6. März 1915 bei Davia in Südlitauen) war ein deutscher Fabrikant und Politiker (NLP).

Leben
Luboldt war der Sohn des Kaufmanns und Kommerzienrats Hermann August Lubold aus Gera und dessen Ehefrau Ida Marie geborene Lantz aus Arnstadt. Er war evangelisch-lutherischer Konfession und heiratete am 1. Dezember 1891 in Gera Marie Louise Adele Gladitsch (* 26. Februar 1870 in Weida; † 6. Februar 1944 in Gera), die Tochter des Kaufmanns Paul Hermann Gladitsch in Gera. Aus der Ehe gingen der Sohn Hermann sowie die Töchter Elisabeth und Louise hervor.

Luboldt lebte als Textilfabrikant (Fa. Focke & Luboldt) in Gera. Er war dort Mitglied der Gesellschaft von Freunden der Naturwissenschaft. Politisch vertrat er liberale Positionen und war im Vorstand der NLP tätig. Vom 27. Juli 1907 bis zum 27. November 1913 war er für die Gruppe der Höchstbesteuertsten Abgeordneter im Landtag Reuß jüngerer Linie.

Im Ersten Weltkrieg leistete er Kriegsdienst. Er fiel am 6. März 1915 bei Davia in Südlitauen als Hauptmann durch einen Kopfschuss.

1913 wurde er mit dem fürstlichen Ehrenkreuz III. Klasse mit Krone ausgezeichnet.

Literatur
 Reyk Seela: Landtage und Gebietsvertretungen in den reußischen Staaten 1848/67–1923. Biographisches Handbuch (= Parlamente in Thüringen 1809–1952. Tl. 2). G. Fischer, Jena u. a. 1996, ISBN 3-437-35046-3, S. 276.
 Christel Gäbler: "Du bist es, die ich liebe..." – Das Bild der Stadt Gera in den Gedichten Hermann Luboldts (1892–1862); in: Alexander Krünes, Uwe Schirmer, Hans-Werner Hahn, Holger Böning (Hrsg.): Medien – Kommunikation – Öffentlichkeit: Vom Spätmittelalter bis zur Gegenwart. Festschrift für Werner Greiling zum 65. Geburtstag, Band 58 von Veröffentlichungen der Historischen Kommission für Thüringen, S. 366 ff., Digitalisat

Landtagsabgeordneter (Reuß jüngerer Linie)
NLP-Mitglied
Unternehmer (19. Jahrhundert)
Person (Gera)
Deutscher
Geboren 1866
Gestorben 1915
Mann

redpajama_set_name: RedPajamaWikipedia


text:
River Tungufljot,
Fishing Permits
TUNGUFLJOT
Buses-Flights
Ferries-Car rentals
During the last few years, the proprietors of this river have been testing its possibilities for becoming a salmon river by releasing smolt into it. It is a traditional brown trout and char river and the fishing spots the waterfall Faxi. and abov. A salmon ladder was built by the side of the waterfall to facilitate the salmon runs upriver. Seasonal changes between the sources, the glacier Langjokull and Lake Sandvatn, make it more or less a mixture of a spring fed and a glacial river. Its branch from the lake is called Asbrandsa. Further downriver the River Tungufljot name takes over. Eventually it joins the main river of the area, River Hvita, near the farm Braedratunga. Most rivers of the country remained unbridged to the end of the 19th century. River Tungufljot was first bridged in 1907 to facilitate King Frederik's the VIII his travels during his official visit the same year.
It was a custom to take all esteemed visitors to the Parliamentary Plains, the Geysir Area and the Golden Waterfalls, and River Tungufljot sometimes became an obstacle. This wooden bridge was swept away by a sudden flooding during summer in 1929. Another bridge was built soon afterwards and in 1966 it was enlarged for car traffic.The sheep pen Tungurettir is just above the beautiful waterfall Faxi and still further upriver a car bridge was built in 1929. It was repaired in the year 2000 and counts among the oldest still standing bridges of the country.
See fishing Statistic
The distance from the capital is about 100 km.
BACK Nat.is - Box 8593 108 Reykjavik- tel.: +354-898-0355 - nat@nat.is - about us - sources HOME

redpajama_set_name: RedPajamaCommonCrawl


Our client has lived in his neighborhood for a long time. He knows most of his neighbors, and everyone is generally friendly. Many families live there, and children frequently play in the front yards and street. So, when some new people moved into the neighborhood, our client was extremely worried about a habit of one of the new residents, a young man, of driving through the streets at a high speed. He decided to go meet the new neighbor and express his concern in a friendly fashion. He was extremely surprised, then, when the man answered his door with a gun in his hand. He would not let our client in his house or open the door all the way. Our client tried to have a conversation with the man, but the gun went off and shot him in the abdomen.
The injuries were severe, and our client's medical bills were in excess of $150,000. Uninsured, our client had no way to pay that amount. Because the injury resulted from a crime, he was able to get help from Victim's Assistance for $20,000 of his medical expenses. Many of his other expenses were written off, but he still was coping with the remainder, in addition to lost wages and the pain and suffering caused by the traumatic experience. It was at this point that the client contacted our expert personal injury lawyers to get help settling his case.
Upon taking the case, I investigated and learned that the gun-wielding neighbor had renter's insurance. I contacted the insurance carrier and submitted our client's medical records and bills.
was able to clear up his outstanding medical bill balances and move on with his life after this terrible experience.


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

Several phenomenological models have been formulated in order to describe the dynamics of multi-particle production in high-energy hadron collisions.  Examples include  the string \cite{Andersson:1987} and cluster \cite{Morel:1974} models,  but all have proven to be incomplete since they provide only limited explanations for the observed production of soft particles. The study of correlations between final-state particles is a powerful method for investigating the underlying mechanisms of particle production, as demonstrated by previous experiments \cite{Eggert:1975,UA5:1988,PHOBOS:2007}.  Phenomenological models of soft particle production are encapsulated in a variety of different Monte Carlo (MC) generators. Particle correlation measurements provide useful input for discriminating between such models and for tuning their parameters in order to better describe non-perturbative physics. Model features that are sensitive to measurements of correlations include fragmentation, resonance decays, multi-parton interactions, and the emergence of jets. The measurement of correlated particle production in proton-proton collisions is also very useful for studies of heavy ion collisions; any deviation in the latter from the behaviour seen in the former can be attributed to the fact that partons experience additional interactions, and other collective effects, in the hot and dense medium present in heavy ion collisions.

This study focuses on the two-particle angular correlations in pseudorapidity, $\eta$, and azimuthal angle, $\phi$, using proton-proton collision data collected by the ATLAS experiment\footnote[1]{ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the $z$-axis along the beam pipe. The $x$-axis points from the IP to the centre of the LHC ring, and the $y$-axis points upwards. Cylindrical coordinates $(r,\phi)$ are used in the transverse plane, $\phi$ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle $\theta$ as $\eta=-\ln\tan(\theta/2)$.} at the Large Hadron Collider (LHC).  A measurement of the inclusive two-particle angular correlation function is performed for charged particles produced in the kinematic region defined by $\ensuremath{p_\mathrm{T}}>100$\ MeV~\footnote[2]{The quantity $\ensuremath{p_\mathrm{T}}$ corresponds to the component of the charged-particle momentum transverse to the beam direction.} and $|\eta|<2.5$ in proton-proton collisions at centre-of-mass collision energies of $\sqrt{s} =$ 900 GeV and 7 TeV. For the 7 TeV centre-of-mass energy, an additional region of phase space is considered for which the charged-particle multiplicity per event is at least twenty.

The paper is organised as follows: the two-particle correlation definition used here is described in section \ref{sec:definition}, while a brief description of the ATLAS detector is presented in section \ref{sec:detector}. Section \ref{sec:montecarlo} summarises the different Monte Carlo models used in this study and the data samples and event selection are described in section \ref{sec:selection}. In section \ref{sec:correction} the data-driven procedure for unfolding the effect of the detection apparatus from the physics is presented. The sources of systematic uncertainty affecting the analysis are discussed in section \ref{sec:systematics}. Finally, the corrected two-particle angular correlation functions and a comparison to a variety of different Monte Carlo predictions are shown in section \ref{sec:results}.

\section{Definition of the two-particle correlation}
\label{sec:definition}

The correlation function is defined using two different distributions that are dependent on $\eta$ and $\phi$. The foreground distribution, $F(n_{ch}, \Delta\eta,\Delta\phi)$, describes the angular separation in azimuth ($\Delta\phi$) and pseudorapidity ($\Delta\eta$) between pairs of particles emitted in the same event of charged multiplicity $n_{ch}$.  $F(n_{ch}, \Delta\eta, \Delta\phi)$ is defined for all events with $n_{ch}$ greater than one and  contains correlations due to both the underlying physics processes and detector effects such as geometrical acceptance. The expression for $F(n_{ch}, \Delta\eta, \Delta\phi)$ is given by

\begin{equation}
F\left(n_{ch}, \Delta\eta, \Delta\phi\right)=\left<\frac{2}{n_{ch}\left(n_{ch}-1\right)}\sum_{i}\sum_{j\ne i}\delta(\eta_{i}-\eta_{j}-\Delta\eta)\delta(\phi_{i}-\phi_{j}-\Delta\phi)\right>,\label{eqn:F}
\end{equation}

\noindent where the summation is over all charged particles in a single event and the average is taken over an ensemble of many events, all having the same charged-particle multiplicity of $n_{ch}$. The delta functions, $\delta(\eta_{i}-\eta_{j}-\Delta\eta)$ and $\delta(\phi_{i}-\phi_{j}-\Delta\phi)$, select particle pairs with the $\Delta\eta$ and $\Delta\phi$ separation that is appropriate for $F(n_{ch}, \Delta\eta, \Delta\phi)$.  The total number of charged-particle pairs in an event is $n_{ch}\left(n_{ch} - 1\right)/2 $, therefore if the factor of $2/n_{ch}\left(n_{ch} - 1\right)$ were not included then a particle in a low multiplicity event would carry a lower weight than an otherwise identical particle in a higher multiplicity event because there are fewer possible pair combinations.

Since the average charged-particle distribution, $\mathrm{d}n/\mathrm{d}\eta$, is approximately flat in $\eta$ within the acceptance of the measurement,  phase-space alone dictates that the $\Delta\eta$ distribution is peaked at $\Delta\eta=0$ and falls approximately linearly to a maximum possible value of $\Delta\eta=\pm2\eta_{max}$. This motivates the second distribution used in constructing the correlation function, the background correlation $B$, the $\Delta\eta$ dependence of which at a fixed charged-particle multiplicity is given by

\begin{equation}
\begin{split}
B\left(n_{ch}, \Delta\eta\right) =& \int_{-\eta_{max}}^{+\eta_{max}}\int_{-\eta_{max}}^{+\eta_{max}}\mathrm{d}\eta_{1}\mathrm{d}\eta_{2}\delta\left(\eta_{1} - \eta_{2} - \Delta\eta\right)\\ & \left.\frac{1}{n_{ch}}\frac{\mathrm{d}n\left(n_{ch}, \eta\right)}{\mathrm{d}\eta}\right|_{\eta=\eta_{1}}\left.\frac{1}{n_{ch}}\frac{\mathrm{d}n\left(n_{ch},\eta\right)}{\mathrm{d}\eta}\right|_{\eta=\eta_{2}},\label{eqn:B}
\end{split}
\end{equation}

\noindent where $\mathrm{d}n\left(n_{ch}, \eta\right)/\mathrm{d}\eta$ is the $\eta$ distribution of charged particles in events of fixed charged-particle multiplicity $n_{ch}$ and the factors of $1/n_{ch}$ ensure that the integral of $B$ over all $\Delta\eta$ is unity. The function $\delta(\eta_{1}-\eta_{2} -\Delta\eta)$ is a Dirac delta function.  The $\Delta\phi$ dependence of $B$ is defined analogously to, and is flatter than, the $\Delta\eta$ dependence.

The correlation function $C(n_{ch},\Delta\eta,\Delta\phi)$ can be constructed using the foreground and background distributions, and is

\begin{equation}
C(n_{ch},\Delta\eta,\Delta\phi) = F(n_{ch},\Delta\eta,\Delta\phi) - B(n_{ch},\Delta\eta,\Delta\phi).\label{eqn:C}
\end{equation}

Previous analyses \cite{Eggert:1975} have found that $(n_{ch}-1) \times C(n_{ch},\Delta\eta,\Delta\phi)$ is approximately independent of $n_{ch}$.  By multiplying equation (\ref{eqn:C}) by a factor of $\left(n_{ch} - 1\right)$ and averaging the resulting quantity over all charged particle multiplicities greater than one, we obtain the multiplicity-independent result, $\overline{C}$, given by

\begin{align}
\overline{C}\left(\Delta\eta, \Delta\phi\right) &=  \sum_{n_{ch}}P\left(n_{ch}\right)\left(n_{ch} - 1\right)\left\{F\left(n_{ch}, \Delta\eta, \Delta\phi\right)-B\left(n_{ch}, \Delta\eta, \Delta\phi\right)\right\} \notag\\
 &=\left<\left(n_{ch}-1\right)F\left(n_{ch}, \Delta\eta, \Delta\phi\right)\right>_{ch} - \left<\left(n_{ch}-1\right)B\left(n_{ch}, \Delta\eta, \Delta\phi\right)\right>_{ch}, \label{eqn:Cbar}
\end{align}
where $P\left(n_{ch}\right)$ is the probability density function for $n_{ch}$ and the notation $\left<...\right>_{ch}$ indicates that a weighted average over contributions from all charged-particle multiplicities should be made.

Dividing equation (\ref{eqn:Cbar}) by the multiplicity-averaged background distribution then gives the multiplicity-independent two-particle correlation function

\begin{equation}
R\left(\Delta\eta, \Delta\phi\right) = \frac{\left<\left(n_{ch}-1\right)F\left(n_{ch}, \Delta\eta, \Delta\phi\right)\right>_{ch}}{\left<B\left(n_{ch}, \Delta\eta, \Delta\phi\right)\right>_{ch}} - \frac{\left<\left(n_{ch} - 1\right)B\left(n_{ch}, \Delta\eta, \Delta\phi\right)\right>_{ch}}{\left<B\left(n_{ch}, \Delta\eta, \Delta\phi\right)\right>_{ch}}.\label{eqn:R}
\end{equation}

Since the $\mathrm{d}n/\mathrm{d}\eta$ distribution, and hence the background, is not \emph{strongly} dependent on the charged particle multiplicity, the factor of $B$ approximately cancels from the second term on the right of equation\ (\ref{eqn:R}) with two caveats. First, the background \emph{does} have some multiplicity dependence at low multiplicity due to the contribution from double diffraction, which favours higher $\Delta\eta$ values compared to the non-diffractive contribution. Second, the effect of any track reconstruction inefficiency is larger in low multiplicity events compared to high multiplicity events because a small number of mis-reconstructed tracks has a proportionally larger significance in the former. As an example, consider a low multiplicity event with a small number of correlated track clusters; the loss of a small fraction of tracks could easily remove completely one of the track clusters, thus changing the overall correlation.  The loss of the same fraction of tracks in a higher multiplicity event is less likely to remove such a feature; it will instead simply reduce the overall number of track pairs. Calculating a multiplicity independent background distribution, $B\left(\Delta\eta, \Delta\phi\right)$,  using $\left<\mathrm{d}n/\mathrm{d}\eta\right>_{ch}$, which is already averaged over all multiplicities, therefore has the advantage of diluting the effect of the experimentally more troublesome lower multiplicity events. Such an approach slightly reduces the sensitivity of the observable to diffraction. However, diffraction is not the motivation for this measurement. The final expression used for the inclusive two-particle correlation function is then given by

\begin{equation}
R\left(\Delta\eta, \Delta\phi\right) = \frac{\left<\left(n_{ch}-1\right)F\left(n_{ch}, \Delta\eta, \Delta\phi\right)\right>_{ch}}{B\left(\Delta\eta, \Delta\phi\right)} - \left<n_{ch} - 1\right>_{ch}.\label{eqn:RFinal}
\end{equation}

In practice, the expression $\left<\left(n_{ch}-1\right)F\left(n_{ch}, \Delta\eta, \Delta\phi\right)\right>_{ch}$ is constructed by taking each pair of particles within a single event, calculating their absolute $\eta$ and $\phi$ separations and filling one quadrant of a two-dimensional distribution at those values using a weight of $2/n_{ch}$. The other three quadrants are filled by reflection, making the distribution symmetric around (0,0). This distribution is normalised by dividing each bin by the number of events entering the distribution. The background is determined by taking random pairs of events and, for each particle in one event, the $|\Delta\eta|$ and $|\Delta\phi|$ values with each particle in the other event are calculated and used to fill another two-dimensional distribution, in the same way as done to the foreground distribution, which is then normalised to unit integral.

Projections of the two-dimensional correlation function along both $\Delta\eta$ and $\Delta\phi$ help reveal more details of the structure of the correlations and permit easier comparisons with different models. These projections are calculated by first integrating separately the foreground and the background distributions before taking the ratio between the two, and normalising with the average track multiplicity.

\section{The ATLAS detector}
\label{sec:detector}

The ATLAS detector \cite{ATLAS:2008} is one of the two general-purpose detectors at the LHC \cite{LHC:2008}. Collision events are reconstructed by layers of tracking, calorimeter and muon systems covering almost the whole solid angle around the collision point. For the analysis presented in this paper, the tracking detectors and trigger systems are the most relevant.

At the centre of ATLAS lies the inner detector (ID), which is responsible for reconstructing the trajectories and measuring the transverse momenta of charged particles and reconstructing the vertices from which they originate. The ID has complete azimuthal coverage and consists of three sub-systems, which cover the pseudorapidity range of $|\eta| < 2.5$. The three ID sub-systems are: a silicon pixel detector, a semiconductor tracking detector (SCT) and a transition radiation tracker (TRT). They are immersed in a 2 T axial magnetic field and cover a radial distance from the nominal interaction point in the barrel of 50.5-150 mm, 299-560 mm and 563-1066 mm, respectively. The ID sensors provide a position resolution of 10, 17 and 130 $\mu$m for the $r-\phi$ coordinate and of 115 and 580 $\mu$m for the second coordinate in the case of the pixel and SCT detectors. The angular resolution of the tracks reconstructed from the pixel, SCT and TRT hits is between 40 $\mu$rad (for $\eta\simeq0.25$) and 50 $\mu$rad (for $\eta\simeq1.75$) in azimuth and between 5 and 10 in $\cot\left(\theta\right)$.

There are three levels in the ATLAS trigger system: Level-1, Level-2 and the Event Filter. The first level uses limited information to perform an initial selection of potentially interesting events, with a fixed latency of 2.5~$\mu$s. The subsequent levels use full granularity measurements to further reduce the selected events to a level acceptable for offline reconstruction. For this measurement, only the Level-1 trigger signals from the beam pickup timing devices (BPTX) and minimum bias trigger scintillators (MBTS) are used to select candidate events. The BPTX electrostatic button pick-up detectors are attached to the beam-pipe and located at $\pm175$~m from the collision point. The MBTS consists of plastic scintillators on the inner edge of the calorimeter end-caps, which lie on both sides of the detector, each at a distance of 3.56~m from the interaction point. Segmented into eight sectors in azimuth, they have a pseudorapidity coverage of $2.09 < |\eta| < 2.82$ and $2.82 < |\eta| < 3.84$. A coincidence of the BPTX signals between the two sides of ATLAS (i.e. colliding bunches) and at least one hit above threshold from either side of the MBTS (referred to as single-arm trigger) are required.

\section{Monte Carlo models}
\label{sec:montecarlo}

In order to compare the present measurement to different soft QCD models, three MC event generators are considered: {\sc{pythia}}~6.4 (versions 6.421 and 6.425) \cite{Pythia6:2006}, {\sc{pythia}}~8.150 \cite{Pythia8:2008} and {\textsc{herwig}}++ version~2.5.1 \cite{Herwig:2008}.

The {\sc{pythia}}\ approach to soft interactions uses phenomenological adaptations of the lowest-order perturbative QCD to describe low-$\ensuremath{p_\mathrm{T}}$ scattering processes in order to extend its physics description to the non-perturbative regime.\ {\textsc{herwig}}++, on the other hand, extends its eikonal concept of independent multi-partonic scatters down into the infrared region \cite{HSoft:2009}.  Other differences between {\textsc{herwig}}++ and {\sc{pythia}}\ include the hadronisation model and the ordering of the parton shower. {\sc{pythia}}\ uses a hadronisation model based upon colour strings and a \ensuremath{p_\mathrm{T}}\ or virtuality-ordered shower, while {\textsc{herwig}}++ implements a cluster hadronisation scheme and a shower that is ordered in emission angle.

Each Monte Carlo generator provides a set of parameters whose values can be altered to produce different MC tunes.  Several tunes of {\sc{pythia}}\ version 6.4 are compared to data: AMBT2B \cite{AMBT:2011}, Perugia 2011 \cite{Per11:2011} and DW \cite{DW:2002}. Version 6.425 of {\sc{pythia}}\ was used in all cases apart from tune DW at 900~GeV, for which version 6.421 was used\footnote[3]{The small differences between the minor {\sc{pythia}}\ versions do not affect the non-perturbative physics relevant for this measurement}.  Tune 4C of {\sc{pythia}}\ 8.150  \cite{P84C:2011} as well as the UE7-2 underlying-event tune at $\sqrt{s} =$ 7 TeV and the MU900-2 minimum bias tune at $\sqrt{s} =$ 900 GeV \cite{HTunes:2011} of {\textsc{herwig}}++ \cite{H25:2011} are also used for comparison.

AMBT2B is a tune of {\sc{pythia}}\ 6 that was produced by the ATLAS Collaboration as a result of optimising earlier tunes to best describe ATLAS results.  In particular, parameters controlling the initial state radiation (ISR) cut-off and evolution, plus further parameters that adjust the model for multi-parton interactions (MPI) were modified to reproduce data on jet shapes and minimum bias events from ATLAS. The tune AMBT2B with the CTEQ6L1 parton density functions (PDFs)  \cite{CTEQ6:2002} is used here, and provides one of the best available descriptions of existing minimum bias data.

The Perugia series of tunes predates the availability of LHC data; however, the most recent Perugia 2011 tune has been adjusted to take account of measurements made at the LHC.  Differences between the Perugia 2011 and AMBT2B tunes include the ISR evolution and the parameters controlling the reconnection of outgoing string fragments to the beam remnants.  Perugia 2011 is shown here with the CTEQ 5L PDFs.

Both AMBT2B and Perugia 2011 use a $\ensuremath{p_\mathrm{T}}$-ordered parton shower and a model in which multi-parton interactions are interleaved with ISR. DW, on the other hand, is a tune that uses a virtuality-ordered parton shower and a MPI model that is not interleaved with the initial state shower. It is optimised to describe underlying event and Drell-Yan data from the Tevatron.

{\sc{pythia}}\ 8 adds to the MPI model of {\sc{pythia}}\ 6 by interleaving not only the ISR, but also the final state radiation (FSR) with the MPI.  {\sc{pythia}}\ 8 includes an updated model of diffraction that includes harder colour singlet exchange;  compared to {\sc{pythia}}\ 6, this allows for harder $\ensuremath{p_\mathrm{T}}$ and particle multiplicity distributions from the single- and double-diffractive contributions.  Like the version of AMBT2B shown here, tune 4C of {\sc{pythia}}\ 8 uses the CTEQ6L1 PDFs.   While {\sc{pythia}}\ 8 has not yet been tuned to data as extensively as {\sc{pythia}}\ 6, tune 4C was the result of comparisons to early LHC data after {\sc{pythia}}\ 8 had already been tuned to give reasonable agreement with Tevatron minimum bias data.  The result is that tune 4C has a reduced diffractive contribution and more realistic average \ensuremath{p_\mathrm{T}}\ per particle compared to earlier tunes of {\sc{pythia}}\ 8.

{\textsc{herwig}}++ is used here with the MRST2007LO* PDFs \cite{MRTS:2008}. The current version of {\textsc{herwig}}++ does not have a model for diffraction, so it has been tuned to diffraction-suppressed LHC data. {\textsc{herwig}}++ has a model for hadronisation that is based on cluster decay, rather than the string fragmentation used by {\sc{pythia}}.  It is therefore interesting to test {\textsc{herwig}}++ against the present measurement in order to compare the two hadronisation models and to ascertain the importance of a diffractive model in describing two-particle correlations.

In addition to these models, the older Perugia 0 \cite{Per0:2009} and ATLAS MC09 \cite{MC09:2010} {\sc{pythia}}\ 6 tunes, the Tune 1 of {\sc{pythia}}\ 8.130 and the {\textsc{phojet}}\ \cite{Phojet:1995} generator are used for systematic studies.

Samples containing non-diffractive and diffractive components, mixed according to the generator cross sections, are used when appropriate for those models that provide a separate diffractive contribution. Particles with a mean decay length ($c\tau$) greater than 10~mm are not decayed by the generator. As a consequence, secondary particles (such as the decay products of neutral kaons) are excluded from the generator-level distributions. This setting also defines the hadronic final state to which the measured distributions are corrected. The generated events are processed through the GEANT~4 \cite{Geant4:2002} based ATLAS detector simulation program \cite{ATLASsim:2010}.  In addition to simulating the detector, GEANT~4 also handles the decays of particles whose mean decay length is longer than 10~mm. Having been fully simulated, MC events are then reconstructed and analysed in the same manner as the data.

\section{Data samples and event selection}
\label{sec:selection}

This study uses the same selection criteria as the charged-particle multiplicity analysis carried out at $\sqrt{s} =$ 900~GeV and 7~TeV \cite{MB2:2011}. In total, approximately 7~$\mu$b$^{-1}$  of 900~GeV data and 190~$\mu$b$^{-1}$ of 7~TeV data are analysed. The events were collected during 2009 and 2010 using low instantaneous luminosity proton beams such that the mean number of interactions per bunch crossing was around 0.01. Only events in which the inner detector was fully operational and the solenoidal magnet was on are used.

Tracks are selected for analysis if they have:
\begin{itemize}
		\item $\ensuremath{p_\mathrm{T}} >$ 100 MeV,
		\item $|\eta| <$ 2.5,
		\item at least 1 hit in the innermost layer of the pixel detector,
		\item at least 1 hit in any of the layers of the pixel detector,
		\item at least 2, 4 or 6 hits in the SCT for tracks with $\ensuremath{p_\mathrm{T}} > $~100,~200 and 300~MeV, respectively,
		\item a transverse impact parameter with respect to the primary vertex, $d_{0}^{\mathrm{PV}}$,  of $|d_{0}^{\mathrm{PV}}| <$ 1.5 mm,
		\item a longitudinal impact parameter with respect to the primary vertex, $z_{0}^{\mathrm{PV}}$, of $|z_{0}^{\mathrm{PV}}\sin\theta| <$ 1.5 mm (where $\theta$ is the angle between the track and the $z$-axis),
		\item a track-fit $\chi^{2}$ probability of at least 0.01 for those tracks with  $\ensuremath{p_\mathrm{T}} >$ 10 GeV (to remove tracks with mis-measured $\ensuremath{p_\mathrm{T}}$ due to misalignment or interactions within the detector material).
	\end{itemize}

To reduce the contribution from background events (such as beam-halo, beam-gas interactions and cosmic rays) and non-primary tracks, events are required:
\begin{itemize}
	\item to have been triggered by the single-arm trigger,
	\item to contain at least one primary vertex.  Primary vertices are required to be associated with at least two tracks with $\ensuremath{p_\mathrm{T}} >$ 100 MeV with a transverse impact parameter with respect to the beam spot\footnote[4]{The beam spot is defined as the centre of the luminous region in which the proton beams interact.} of  $\left|d_{0}^{\mathrm{BS}}\right| <$ 4 mm,
	\item not to have a second interaction vertex associated to more than four tracks (to remove events with more than one proton-proton interaction in a single bunch crossing),
	\item to contain a minimum number of tracks, depending on the phase-space region, passing the track selection criteria previously described.
\end{itemize}

For data taken at $\sqrt{s} =$ 7 TeV, two different phase-space regions with varying contributions from diffractive events are explored: $n_{ch} \geq 2$ and $n_{ch} \geq 20$. For data taken at $\sqrt{s} =$ 900 GeV, only the particle multiplicity requirement of $n_{ch} \geq$ 2 is used. The total numbers of selected events and tracks are shown in table \ref{tab:Nevents_data}.

\begin{table}[t]
\begin{tabular}{|l|c|c|c|}
\hline \hline
Phase-Space Region						& $\sqrt{s}$ [TeV]	& Selected Events	& Selected Tracks	\\
\hline
$n_{ch}\geq2$, $\ensuremath{p_\mathrm{T}} >$ 100 MeV, $|\eta| <$ 2.5	& 0.9			& 357,523			& 4,532,663		\\
\cline{2-4}
		         							& 7				& 10,066,072		& 209,809,430		\\
\hline
$n_{ch}\geq20$, $\ensuremath{p_\mathrm{T}} >$ 100 MeV, $|\eta| <$ 2.5	& 7				& 4,029,565		& 153,553,766       	\\
\hline \hline
\end{tabular}
\centering
\caption{Total number of selected events and tracks in 900 GeV and 7 TeV data.}
\label{tab:Nevents_data}
\end{table}

\section{Correction procedure}
\label{sec:correction}

In order to disentangle the effects caused by the apparatus and the reconstruction algorithms from the true physics processes, the following corrections are applied to the reconstructed data.

First, the foreground and multiplicity distributions are weighted with the inverse of the trigger and vertex reconstruction efficiencies. These efficiencies, taken directly from ref.~\cite{MB2:2011}, are calculated before a requirement on the vertex is made. The efficiencies were determined in ref.~\cite{MB2:2011} from data by using a trigger independent of the Level 1 MBTS (for the trigger efficiency) and by relaxing the requirement on the presence of a reconstructed vertex (for the vertex efficiency). These efficiencies depend on the track multiplicity, where the total number of selected tracks is obtained by applying all of the selection criteria  described in section \ref{sec:selection} apart from  the $d_{0}^{\mathrm{PV}}$ and $z_{0}^{\mathrm{PV}}\sin\theta$ requirements.  A requirement on the transverse impact parameter with respect to the beam spot position, $d_{0}^{\mathrm{BS}}$, is made instead such that $|d_{0}^{\mathrm{BS}}| <$ 1.8 mm.  The trigger efficiency is determined using a test trigger that selects events from random proton bunch crossings and uses information from the pixel and SCT detectors at Level 2.

The effect of tracks lost due to inefficiencies in the reconstruction is corrected for using the model-independent Hit Backspace Once More (HBOM) method described in ref.~\cite{Monk:2011pg}. Figure \ref{fig:cmethod7TeV} illustrates this correction procedure, in which the observable is first computed using all reconstructed tracks that satisfy the analysis selection criteria (solid circles in figure \ref{fig:cmethod7TeV}a). The track reconstruction efficiency as a function of the track $\ensuremath{p_\mathrm{T}}$ and $\eta$ is taken from ref.~\cite{MB2:2011}.  For each track, a random number, $r_{i}$, uniformly distributed between zero and one, is generated and compared to the track reconstruction efficiency, $\epsilon_{i}(\ensuremath{p_\mathrm{T}},\eta)$. A track is removed from the sample if the random number is greater than the track reconstruction efficiency. This results in a subset of the original tracks, defined by all those tracks satisfying

\begin{equation}
\epsilon_{i}(\ensuremath{p_\mathrm{T}},\eta) > r_{i}.
\end{equation}

Tracks removed from the sample in this way are lost with the same probability as they would be lost by the detector reconstruction.  The reduced  sample of tracks, which now expresses an exaggerated detector reconstruction effect, is used to compute the observable again. This defines one iteration of the track-removal procedure (the full set of uncorrected tracks is the 0th iteration). A second iteration takes as input the tracks used in the first iteration and again uses a new set of random numbers to remove additional tracks according to their track reconstruction efficiency. The observable is then determined from this third sample of tracks that shows a larger detector effect than the first two samples. Further iterations are carried out in the same way.

\begin{figure}[t]
\begin{center}
\begin{overpic}[height=53.5mm]{fig_01a}
\put(53,-3){\small(a)}
\end{overpic}
\begin{overpic}[height=53.5mm]{fig_01b}
\put(53,-3){\small(b)}
\end{overpic}
\caption{(a) Two-particle pseudorapidity correlation function, $R(\Delta\eta)$, after each iteration of the probabilistic track removal correction method. (b) Example of a third-degree polynomial fit to the values of $R(\Delta\eta)$ in a central bin.  Plots of $R(\Delta\eta)$ shown here and throughout this paper are symmetric around $\Delta\eta$ = 0 by construction.}
\label{fig:cmethod7TeV}
\end{center}
\end{figure}

Using this probabilistic track removal method, it is possible to quantify the effect that detector inefficiencies have on an observable; each iteration corresponds to an additional application of the detector effect to the data. The value of each bin of the observable can be plotted as a function of the iteration number (0, 1, 2, ..., $N$) and a function can be fitted to the resulting set of points. By extrapolating the fit to the $N$=$-1$ iteration, an estimate of the observable at the particle level, without detector effects, can be made. In this analysis the fit and subsequent extrapolation use a third-degree polynomial, with six track removal iterations in total used as the input, as illustrated in figure \ref{fig:cmethod7TeV}b for one particular $\Delta\eta$ bin.

\begin{figure}[t]
\begin{center}
\begin{overpic}[height=70mm]{fig_02a}
\put(52,-3){\small(a)}
\end{overpic} \\
\vspace{5mm}
\begin{overpic}[height=70mm]{fig_02b}
\put(52,-3){\small(b)}
\end{overpic}
\begin{overpic}[height=70mm]{fig_02c}
\put(52,-3){\small(c)}
\end{overpic}
\caption{Comparison between the generated and corrected two-particle correlation functions $R(\Delta\eta)$ at (a) $\sqrt{s} =$ 900 GeV and 7 TeV for the phase-space regions (b) $n_{ch} \geq 2$ and (c) $n_{ch} \geq 20$ for the Monte Carlo MC09 tune. The absolute difference between the generated and corrected MC as a function of $\Delta\eta$ is shown underneath each distribution.}
\label{fig:closure}
\end{center}
\end{figure}

No specific correction is made for tracks arising from the secondary decays of longer lived particles nor from material interactions. The effect of secondary particles is discussed in section \ref{sec:systClosure}.

In order to test the correction procedure, Monte Carlo studies are performed in which the distributions at the generated particle level are recovered from a fully detector-simulated and reconstructed Monte Carlo sample. This is shown in figure \ref{fig:closure} for the {\sc{pythia}}\ 6 MC09 tune at $\sqrt{s} =$ 900 GeV and 7 TeV for $R(\Delta\eta)$ with $0 < \Delta\phi < \pi$. The size of the correction that must be applied to the uncorrected correlation function depends on the value of $\Delta\eta$ and $\Delta\phi$; in general the correction has an absolute value of around 0.5.  At high $\left|\Delta\eta\right|$ the correction is negative, while at low $\left|\Delta\eta\right|$ the correction is positive, so the overall effect is that the peak at $\Delta\eta=0$ is narrowed significantly.  The generated and corrected distributions are generally in good agreement with each other, showing an absolute difference of approximately 0.05 in all but a few bins. The remaining differences are considered as a systematic uncertainty, as discussed in section \ref{sec:systClosure}.

All the distributions presented in this paper, both one- and two-dimensional, have been corrected using this procedure. No correction is made for the effects of angular smearing because the resolution of the tracking detector is much better than the bin size used. Any such correction would be insignificant in comparison to the uncertainty on the efficiency correction that is applied.

\section{Statistical and systematic uncertainties}
\label{sec:systematics}

The sources of uncertainty identified for this measurement are described in this section. The most significant contributions to both the one- and two-dimensional distributions are associated with the track reconstruction efficiency and with the correction procedure (arising from the small differences between the generated and corrected Monte Carlo distributions).

\subsection{Statistical uncertainty}

Each of the parameters in the third-degree polynomial fits in the probabilistic track removal method carries a statistical error. The statistical uncertainty in the corrected values is the result of propagating these uncertainties, using the full covariance matrix, when evaluating the third-degree equation at $N$=$-1$. In general, this uncertainty is negligible compared to the ones associated to the track reconstruction efficiency and the non-closure of the correction method.  The exceptions to this are the highest $\Delta\eta$ bins where, due to reduced statistics, the uncertainty on the fit parameters is of the same magnitude as the other uncertainties.

\subsection{Uncertainties on the efficiencies}

In order to evaluate the systematic uncertainty that is associated with uncertainties in the trigger, vertex and track reconstruction efficiencies, the complete analysis is repeated varying each of these quantities, one at a time, according to their uncertainties.  It is assumed there is no difference in the size of these uncertainties between the different collision energies, as discussed in ref.~\cite{MB2:2011}.

The systematic uncertainties associated with the track reconstruction efficiency come from various sources: material effects, track selection, momentum resolution and badly measured high-$\ensuremath{p_\mathrm{T}}$ tracks. The tracking efficiency is obtained in ref.~\cite{MB2:2011} by matching MC generated  charged particles to tracks reconstructed after the full detector simulation.  Uncertainties on the efficiency are determined by varying the parameters of the detector simulation.   These uncertainties are summarised in table \ref{tab:systTrack}. All of these uncertainties are added in quadrature to obtain the total uncertainty on the tracking efficiency in each ($\ensuremath{p_\mathrm{T}}$,$\eta$) bin.

In the case of the trigger and vertex reconstruction efficiencies, the systematic uncertainties are of the order of 1\% for events with a track multiplicity of two and decrease rapidly as the multiplicity increases.

\begin{table}[t]
\begin{tabular}{|l|l|}
\hline \hline
Source					& Uncertainty	\\
\hline
Material description in MC	& Increases at high-$|\eta|$ and decreases at high-$\ensuremath{p_\mathrm{T}}$; \\
						& max. 15\% in the range $2.3 < |\eta| < 2.5$ \\
						& and 100 MeV $< \ensuremath{p_\mathrm{T}} < 150$ MeV	\\
\hline
Track selection				& 1\% in all ($\ensuremath{p_\mathrm{T}}$,$\eta$) bins	 \\
\hline
$\ensuremath{p_\mathrm{T}}$ resolution in MC		& 5\% in the first $\ensuremath{p_\mathrm{T}}$ bin (100 MeV $< \ensuremath{p_\mathrm{T}} < 150$ MeV)	\\
\hline
High-$\ensuremath{p_\mathrm{T}}$ tracks			& 10\% due to the requirement on the track-fit $\chi^{2}$ probability \\
\cline{2-2}
						& $\eta$ and $\ensuremath{p_\mathrm{T}}$ dependent uncertainty due to \\
						& mis-measured tracks	\\
\hline \hline
\end{tabular}
\centering
\caption{Uncertainties associated to the track reconstruction efficiency. Values are taken from and are identical to those in ref.~\cite{MB2:2011}, which provides a more complete discussion on this subject.}
\label{tab:systTrack}
\end{table}

\subsection{Uncertainty due to lack of closure using Monte Carlo samples}
\label{sec:systClosure}

The absolute difference between the generated and corrected Monte Carlo distributions is used as the systematic uncertainty resulting from the small non-closure of the correction procedure. From this it is possible to derive an estimate for the non-closure uncertainty in data as a function of the corrected value of $R$.

This is illustrated in figure \ref{fig:closureSyst7} for $R(\Delta\eta)$ (where $\Delta\phi$ was integrated from 0 to $\pi$) for different tunes at $\sqrt{s} =$ 7 TeV for $n_{ch}\geq2$. The absolute amount of non-closure does not depend strongly on either the Monte Carlo model or on the value of $R(\Delta\eta)$ and, for this example, lies generally in the region between $\pm$0.05.  Therefore in this case a systematic uncertainty of 0.05 is assigned to all bins in the data distribution.

\begin{figure}[t]
\begin{center}
\includegraphics[height=80mm]{fig_03}
\caption{Difference between the generated and corrected two-particle correlation functions as a function of $R(\Delta\eta)_{corr}$ for various Monte Carlo tunes at $\sqrt{s} =$ 7 TeV for $n_{ch}\geq2$.}
\label{fig:closureSyst7}
\end{center}
\end{figure}

The systematic uncertainty associated with the non-closure of the correction method is calculated in this manner for each of the one-dimensional projections and the two-dimensional distributions. In most cases the systematic uncertainty has a value of 0.05 or smaller and has very little dependence on $R$; however, in a small number of cases for some of the $n_{ch}\geq20$ distributions, the uncertainty can be as large as 0.2.

The small non-closure of the corrected samples with the hadron-level Monte Carlo distributions is primarily caused by the introduction of additional particles in the detector simulation that are not produced by the Monte Carlo generator. Such secondary particles can be produced either by the decays of longer-lived particles that are set stable by the generator (primarily neutral kaons), or by interactions between primary particles and the detector material.\  Both sources of secondary particles produce  correlated pairs of tracks, and as such contribute to the non-closure in the same manner;  however, the pairs of secondary particles initiated by detector interactions produce an effect that is between five and ten times as large as the effect produced by neutral decay products.

Using the reconstruction efficiency to remove tracks from the data sample provides an approximation to the effect that the detector has on the observable.  This approximation does not account for the effect of fake tracks or of tracks that arise from secondary decays and material interactions.  In order to apply a correction for these small effects, the probabilities that such particles are produced would need to be assessed so that they could be used to add  additional particles probabilistically in each iteration of the correction procedure.  Studies using the full detector simulation show that the size of such corrections would be small in comparison to the correction for tracking inefficiencies and would be of a similar size to other systematic uncertainties present in this measurement.  This justifies the approach of  applying a correction for tracking inefficiencies, which is the largest detector effect, and assigning a non-closure systematic based on studies using the full detector simulation.

\section{Results and discussion}
\label{sec:results}

The corrected inclusive two-particle angular correlation functions for data and the {\sc{pythia}}\ 6 AMBT2B Monte Carlo tune are shown in figures \ref{fig:2D900} and \ref{fig:2D7} for $\sqrt{s} =$ 900 GeV and 7~TeV, respectively.

\begin{figure}[t]
\begin{center}
\begin{overpic}[height=70mm]{fig_04a.png}
\put(45,-3){(a)}
\end{overpic}
\begin{overpic}[height=70mm]{fig_04b.png}
\put(45,-3){(b)}
\end{overpic}
\caption{Corrected $R(\Delta\eta,\Delta\phi)$ two-particle correlation functions for (a) data and (b) the AMBT2B Monte Carlo tune, at $\sqrt{s} =$ 900 GeV.}
\label{fig:2D900}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\begin{overpic}[height=70mm]{fig_05a.png}
\end{overpic}
\begin{overpic}[height=72mm]{fig_05b.png}
\end{overpic}
\begin{overpic}[height=70mm]{fig_05c.png}
\put(45,95){(a)}
\put(45,-3){(c)}
\end{overpic}
\begin{overpic}[height=72mm]{fig_05d.png}
\put(45,95){(b)}
\put(45,-3){(d)}
\end{overpic}
\caption{Corrected $R(\Delta\eta,\Delta\phi)$ two-particle correlation functions at $\sqrt{s} =$ 7 TeV for $n_{ch}\geq2$ (a) data and (b) Monte Carlo (AMBT2B), and for $n_{ch}\geq20$ (c) data and (d) Monte Carlo (AMBT2B). These plots are symmetric around $\Delta\eta$ = 0 by construction.}
\label{fig:2D7}
\end{center}
\end{figure}

At both energies a complex structure can be observed across the full $\Delta\eta$ and $\Delta\phi$ range. Several components can be identified that reflect the contributions from different underlying processes to the correlation structure. Most obvious are the near-side correlations,  which are seen as a sharp peak around (0,0) that can be attributed  to particles originating from the same (relatively) high-$\ensuremath{p_\mathrm{T}}$ process.  Such closely correlated particles indicate the  emergence of jet-like structures within this minimum bias event selection. Another prominent structure in the two-dimensional distribution is the away-side correlation, which is seen as a ridge extending across the whole of the $\Delta\eta$ range near $\Delta\phi \sim \pi$.  This away-side activity arises from the recoil of one particle against another and would be seen quite strongly in, for example, back-to-back jet production.  A third distinct structure  is the broad Gaussian-like structure spanning the $\Delta\phi$ domain at $\Delta\eta=0$ with a width of $\Delta\eta\simeq2$.  This last structure can be related to processes such as the decays of resonances, clusters or string fragmentation.

As the centre-of-mass energy increases, so too does the height of the peak at (0,0).  This peak becomes even more pronounced for the set of events with a higher charged-particle multiplicity (figure \ref{fig:2D7}c). Conversely, the height of the away-side ridge is constant regardless of the collision energy or multiplicity. {\sc{pythia}}~6 AMBT2B exhibits similar structures to those observed in data; however it does not reproduce the strength of the correlations.

\subsection{Projections in $\Delta\eta$ and $\Delta\phi$}

In all of the following figures, the solid markers correspond to the corrected data values, the error bars are statistical only (after correcting for track detection inefficiency) and the solid bands correspond to the total uncertainty in the bin, which is obtained by adding in quadrature the statistical and systematic uncertainties described in section \ref{sec:systematics}. The data distributions are compared to different Monte Carlo tunes. In general, none of the models reproduce the strength of the correlations seen in data. Some approximate the shape of the distributions more closely than others, but for all distributions {\textsc{herwig}}++ is the most discrepant with the data.

The corrected pseudorapidity correlation distributions are shown in figure \ref{fig:deta0pi} and were obtained by integrating separately the foreground and background functions over $\Delta\phi$ between 0 and $\pi$. The AMBT2B and Perugia~2011 tunes of {\sc{pythia}}~6 together with tune 4C of {\sc{pythia}}~8 show the best agreement with the data distributions for events with $n_{ch}\geq2$ at both collision energies.  For the sample of events satisfying $n_{ch}\geq20$ the AMBT2B tune shows the closest agreement to the data over the entire $\Delta\eta$ range, although the agreement cannot be considered satisfactory.

\begin{figure}[t]
\begin{center}
\begin{overpic}[height=70mm]{fig_06a}
\put(85,85){(a)}
\end{overpic} \\
\begin{overpic}[height=70mm]{fig_06b}
\put(85,85){(b)}
\end{overpic}
\begin{overpic}[height=70mm]{fig_06c}
\put(85,85){(c)}
\end{overpic}
\caption{Corrected $R(\Delta\eta$) two-particle correlation functions obtained by integrating the foreground and background distributions over $\Delta\phi$ between 0 and $\pi$ for data and several different Monte Carlo tunes at (a) $\sqrt{s} =$ 900 GeV and 7 TeV for events with a charged-particle multiplicity (b) $n_{ch}\geq2$ and (c) $n_{ch}\geq20$.}
\label{fig:deta0pi}
\end{center}
\end{figure}

In order to separate the $\eta$ correlations on the near side ($\Delta\phi\simeq0$) from those on the away side ($\Delta\phi\simeq\pi$), the pseudorapidity correlation function was also calculated by integrating the foreground and background functions over $\Delta\phi$ within the more limited ranges of  $\big(0:\frac{\pi}{2}\big)$ (near side) and $\big(\frac{\pi}{2}:\pi\big)$ (away side).  Figure \ref{fig:deta0pi2} shows that, when only the near side is included, the peak at (0, 0) becomes narrower, higher and more pronounced, which indicates a stronger correlation between nearby particles.\ Tune 4C of {\sc{pythia}}~8 provides the best description of the data across the entire $\Delta\eta$ range for the $n_{ch}\geq2$ event samples at both energies, while the AMBT2B tune provides the most reasonable description of events for which $n_{ch}\geq20$.

\begin{figure}[t]
\begin{center}
\begin{overpic}[height=70mm]{fig_07a}
\put(85,85){(a)}
\end{overpic} \\
\begin{overpic}[height=70mm]{fig_07b}
\put(85,85){(b)}
\end{overpic}
\begin{overpic}[height=70mm]{fig_07c}
\put(85,85){(c)}
\end{overpic}
\caption{Corrected $R(\Delta\eta$) two-particle correlation functions obtained by integrating the foreground and background distributions over $\Delta\phi$ between 0 and $\frac{\pi}{2}$ for data and the different Monte Carlo tunes at (a) $\sqrt{s} =$ 900 GeV and 7 TeV for events with a charged-particle multiplicity (b) $n_{ch}\geq2$ and (c) $n_{ch}\geq20$.}
\label{fig:deta0pi2}
\end{center}
\end{figure}

The $\eta$ correlations on the away side are shown in figure  \ref{fig:detapi2pi}, and here most of the tunes (with the exception of {\textsc{herwig}}++) display a better agreement with data.  The Perugia~2011 tune shows a particularly good agreement with data across the $\Delta\eta$ range at both collision energies.

\begin{figure}[t]
\begin{center}
\begin{overpic}[height=70mm]{fig_08a}
\put(85,85){(a)}
\end{overpic} \\
\begin{overpic}[height=70mm]{fig_08b}
\put(85,85){(b)}
\end{overpic}
\begin{overpic}[height=70mm]{fig_08c}
\put(85,85){(c)}
\end{overpic}
\caption{Corrected $R(\Delta\eta$) two-particle correlation functions obtained by integrating the foreground and background distributions over $\Delta\phi$ between $\frac{\pi}{2}$ and $\pi$ for data and the different Monte Carlo tunes at (a) $\sqrt{s} =$ 900 GeV and 7 TeV for events with a charged-particle multiplicity (b) $n_{ch}\geq2$ and (c) $n_{ch}\geq20$.}
\label{fig:detapi2pi}
\end{center}
\end{figure}

The dependence of the correlation function on the azimuthal separation can similarly be studied by integrating the foreground and background over $\Delta\eta$ for two different ranges: (0:2) (short-range correlations) and (2:5) (long-range correlations).  The short-range correlation functions, shown in figure \ref{fig:dphi02}, contain two peaks.  The first peak is at $\Delta\phi=0$ and becomes more pronounced if either the collision energy or the particle multiplicity is increased.  The second peak is at $\Delta\phi=\pi$ and has a height that is approximately independent of both the collision energy and the multiplicity.  We note the general similarity in the shape of these functions to some distributions obtained in measurements of underlying event; in particular the trough in the correlation function around $\Delta\phi\simeq\pi/2$ is somewhat analogous to the ``transverse" region of ref.~\cite{Aad:2010fh}.

\begin{figure}[t]
\begin{center}
\begin{overpic}[height=70mm]{fig_09a}
\put(85,85){(a)}
\end{overpic} \\
\begin{overpic}[height=70mm]{fig_09b}
\put(85,85){(b)}
\end{overpic}
\begin{overpic}[height=70mm]{fig_09c}
\put(85,85){(c)}
\end{overpic}
\caption{Corrected $R(\Delta\phi$) two-particle correlation functions obtained by integrating $\Delta\eta$ between 0 and 2 for data and the different Monte Carlo tunes at (a) $\sqrt{s} =$ 900 GeV and 7 TeV for events with a charged-particle multiplicity (b) $n_{ch}\geq2$ and (c) $n_{ch}\geq20$.}
\label{fig:dphi02}
\end{center}
\end{figure}

None of the Monte Carlo models provides a good description of the $\Delta\phi$ dependence of the short-range correlation function across the entire $\Delta\phi$ range. AMBT2B and Perugia~2011 tend to agree with data on the away side, but less so on the near side. DW, which has previously provided reasonable agreement with the transverse region of underlying event data, does not agree particularly well with the correlation function.  Tune 4C of {\sc{pythia}}~8 shows good agreement with data in some regions near the two peaks, but a clear disagreement in others, particularly the region around $\Delta\phi\simeq\pi/2$ at $\sqrt{s} =$ 7~TeV.

Unlike the short-range correlation function, the $\Delta\phi$ dependence of the long-range correlation function does not exhibit a peak at $\Delta\phi=0$.  This is shown in figure \ref{fig:dphi25}, which reveals a trough at $\Delta\phi=0$ while the away-side peak is still present.  With the exception of {\sc{pythia}}~6 tune DW, the difference between the Monte Carlo models and the data is approximately flat in $\Delta\phi$.  While the models here describe the \emph{shape} of the correlation function, they do not describe the \emph{strength} of the correlations.  AMBT2B, Perugia~2011 and 4C are the best of the models considered here, although 4C diverges slightly more than the other two tunes when compared to the $n_{ch}\geq20$ sample of events. This $\Delta\phi$ projection was recently studied in high-multiplicity events by the CMS Collaboration and a ridge-like structure was observed at $\Delta\phi = 0$ in a specific kinematic range, different to the one studied here \cite{CMS:2010}.

\begin{figure}[t]
\begin{center}
\begin{overpic}[height=70mm]{fig_10a}
\put(85,85){(a)}
\end{overpic} \\
\begin{overpic}[height=70mm]{fig_10b}
\put(85,85){(b)}
\end{overpic}
\begin{overpic}[height=70mm]{fig_10c}
\put(85,85){(c)}
\end{overpic}
\caption{Corrected $R(\Delta\phi$) two-particle correlation functions obtained by integrating the foreground and background distributions over $\Delta\eta$ between 2 and 5 for data and the different Monte Carlo tunes at (a) $\sqrt{s} =$ 900 GeV and 7 TeV for events with a charged-particle multiplicity (b) $n_{ch}\geq2$ and (c) $n_{ch}\geq20$.}
\label{fig:dphi25}
\end{center}
\end{figure}

CMS has also studied the $\ensuremath{p_\mathrm{T}}$-inclusive two-particle angular correlation function at $\sqrt{s} =$~900~GeV and 7 TeV. Their results \cite{CMS:2010} include the two-dimensional distributions, $R(\Delta\eta,\Delta\phi)$, and a single $R(\Delta\eta)$ projection where the correlation function has been integrated over $\Delta\phi$  between 0 and $\pi$. The phase-space used in their analysis is $\ensuremath{p_\mathrm{T}} > 100$ MeV and $|\eta| < 2.4$, a difference of 0.1 units in pseudorapidity with respect to the analysis presented in this paper.  In comparing the $\Delta\eta$ dependence of the correlation function obtained by CMS with the results shown here, one should note a small and subtle difference in the definitions of the observables used in the two analyses. Whereas the analysis presented here measures the foreground, background and final correlation function inclusively for all event multiplicities within the event selection, the CMS analysis first determines the correlation function in separate bins of multiplicity.  The weighted average of the function in each bin is then computed to give an inclusive set of distributions. In order to see good agreement between these two observable definitions, one would need to correct the correlation function in each multiplicity bin when using the CMS definition \emph{and} correct the multiplicity selection requirements used to define the multiplicity-dependent correlation function. The analysis performed by CMS was reproduced using the data presented here, and the results obtained were found to be in good agreement with those published by the CMS Collaboration.

\section{Summary and conclusions}
\label{sec:summary}

The two-particle angular correlation functions in $\Delta\eta$ and $\Delta\phi$ have been measured using charged particles with $\ensuremath{p_\mathrm{T}} >$ 100~MeV and $|\eta| <$ 2.5. Events were recorded by the ATLAS detector at the LHC from proton-proton collisions at $\sqrt{s} =$ 900 GeV and 7 TeV, using a minimum bias trigger. In total, integrated luminosities of approximately 7~$\mu\mathrm{b}^{-1}$ and 190~$\mu\mathrm{b}^{-1}$ have been analysed, respectively. At $\sqrt{s} =$ 7 TeV, two different phase-space regions defined by the charged particle multiplicity were investigated: $n_{ch}\geq2$ and $n_{ch}\geq20$. The structure of the correlation was explored in more detail by projecting the two-dimensional distributions into both $\Delta\eta$ and $\Delta\phi$. The results have been compared to Monte Carlo predictions, which show a similar complex structure but fail to reproduce the strength of the correlations seen in the data. Overall, the AMBT2B tune of {\sc{pythia}}\ 6 and the 4C tune of {\sc{pythia}}\ 8 are the models that provide the best description, while {\textsc{herwig}}++ is the most discrepant in all of the distributions.

While many of the models shown here reproduce the general features of the two-particle correlation function, none of them provide a good quantitative description of the strength of the correlations. In order to properly describe the correlations, the phenomenology of soft particle production needs further improvement.  Such improvement will, at a minimum, require the adjustment of existing models for diffraction and hadronisation.  However, it may be that the changes required to describe these data will extend beyond the re-tuning of existing models.

\acknowledgments

We thank CERN for the very successful operation of the LHC, as well as the
support staff from our institutions without whom ATLAS could not be
operated efficiently.

We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC,
Australia; BMWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP,
Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC,
China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic;
DNRF, DNSRC and Lundbeck Foundation, Denmark; EPLANET and ERC, European Union;
IN2P3-CNRS, CEA-DSM/IRFU, France; GNAS, Georgia; BMBF, DFG, HGF, MPG and AvH
Foundation, Germany; GSRT, Greece; ISF, MINERVA, GIF, DIP and Benoziyo Center,
Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO,
Netherlands; RCN, Norway; MNiSW, Poland; GRICES and FCT, Portugal; MERYS
(MECTS), Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD,
Serbia; MSSR, Slovakia; ARRS and MVZT, Slovenia; DST/NRF, South Africa;
MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of
Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal
Society and Leverhulme Trust, United Kingdom; DOE and NSF, United States of
America.

The crucial computing support from all WLCG partners is acknowledged
gratefully, in particular from CERN and the ATLAS Tier-1 facilities at
TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France),
KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain),
ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities
worldwide.

\bibliographystyle{JHEP}

\providecommand{\href}[2]{#2}\begingroup\raggedright

redpajama_set_name: RedPajamaArXiv


text:
Posted on 28 September, 2019 27 September, 2019 by admin
Airplane history essay – How to improve academic writing skills
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Q: Enforce Data Execution Prevention (DEP) in C# app I have a C# app thats going to run with admin privileges. I want to force DEP for it. Either set DEP On for the process or kill the app if DEP is disabled.
But I've failed in both.
My code is:
private static void CheckDEP()
{
    var dep = SetProcessDEPPolicy(3);

    var handle = Process.GetCurrentProcess().Handle;
    var res = GetProcessDEPPolicy(handle, out var flags, out var permanent);
}

[DllImport("kernel32.dll", SetLastError = true)]
static extern bool SetProcessDEPPolicy(uint dwFlags);

[DllImport("kernel32.dll", SetLastError = true, CallingConvention = CallingConvention.Winapi)]
static extern bool GetProcessDEPPolicy(IntPtr hProcess, out uint lpFlags, out bool lpPermanent);

Calling the function SetProcessDEPPolicy(3) always fails with error 50 (documentation says that it should return this error only when it's called from 64bit process, but this is not the case).
And I probably have some bug in GetProcessDEPPolicy, because the call fails with error 87 (parameter is incorrect). Maybe the Handle is wrong?

A: So, the solution is to change the build configuration in Configuration Manager from AnyCPU to x86. Now both methods work as expected.
The errors are the same for AnyCPU as for x64 (where DEP is enforced by default and these methods should return the mentioned errors).

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