finish discussion

This commit is contained in:
hiro98 2020-06-09 15:57:38 +02:00
parent eb017961c6
commit 019264c711
20 changed files with 252 additions and 139 deletions

View file

@ -44,6 +44,8 @@ captions=nooneline,captions=tableabove,english,DIV=16,numbers=noenddot,final]{sc
\input{./tex/pheno/setup.tex}
\input{./tex/pheno/discussion.tex}
\input{./tex/summary.tex}
\clearpage
\appendix
\pagenumbering{roman}

View file

@ -53,7 +53,8 @@ otherwise. The fine structure constant's value \(\alpha = 1/137.036\)
is configured in \sherpa\ and used in analytic calculations.
The compatibility of histograms is tested as discussed in
\cref{sec:comphist}.
\cref{sec:comphist} and the respective \(P\) and \(T\) values are
being included in the ratio plots.
\section{Source Code}%
\label{sec:source}

View file

@ -9,12 +9,12 @@
Monte Carlo methods for multidimensional integration and sampling of
probability distributions are central tools of modern particle
physics. Therefore some simple methods and algorithms are being
studied and implemented here and will be applied to the results from
\cref{chap:qqgg}. The \verb|python| code for the implementation can be
found as described in \cref{sec:source}. The sampling and integration
intervals, as well as other parameters have been chosen as in
\cref{sec:compsher} been chosen, so that \result{xs/python/eta} and
\result{xs/python/ecm}. This chapter is based on the
appendix~\cite{buckley:2011ge} and supplants that source with some
derivations and more methods like the \vegas~\cite{Lepage:19781an}
algorithm.
studied and implemented from scratch here and will be applied to the
results from \cref{chap:qqgg}. The \verb|python| code for the
implementation can be found as described in \cref{sec:source}. The
sampling and integration intervals, as well as other parameters have
been chosen as in \cref{sec:compsher} been chosen, so that
\result{xs/python/eta} and \result{xs/python/ecm}. This chapter is
based on the appendix~\cite{buckley:2011ge} and supplants that source
with some derivations and more methods like the
\vegas~\cite{Lepage:19781an} algorithm.

View file

@ -136,18 +136,22 @@ code. The resulting histograms of some observables are depicted in
\result{xs/python/pdf/samp_eff} using a total of
\result{xs/python/pdf/num_increments} hypercubes.
The distributions are more or less compatible with each other
The histograms are more or less compatible with each other
\footnote{See \cref{sec:comphist} for a description of the
compatibility test.}. In all cases the difference between
\(T\)-Value and the mean of the \(\chi^2\) distribution for that value
(\(=50\), the number of bins) is less then the standard deviation
(\(=10\)) of the same distribution and thus the histograms are
considered compatible. The very steep distributions for \(\pt\) and
\(m_{\gamma\gamma}\) are especially sensitive to fluctuations and the
systemic errors introduced of the weight of each hypercube. Therefore
their formal measure of compatibility, the \(P\)-Value, is rather
low. This shows that the error in the determination of the weights for
the hypercubes should be studied more carefully.
considered compatible. The angular distributions for
\(\eta, \cos\theta\) show agreeable \(P\)-values, but the very steep
distributions for \(\pt\) and \(m_{\gamma\gamma}\) are especially
sensitive to fluctuations and the systemic errors introduced of the
weight of each hypercube. Therefore their formal measure of
compatibility, the \(P\)-Value, is rather low. This indicates that the
MC error in the determination of the weights for the hypercubes should
be studied more carefully and highlights the disadvantage of the
sampling method chosen here. The kinematics and PDF values were
compared with sherpa and proved to be equivalent.
The \sherpa\ runcard utilized here and the analysis used to produce
the histograms can be found in

View file

@ -19,33 +19,13 @@
\begin{figure}[ht]
\centering
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/cos_theta}
\caption{\label{fig:disc-cos_theta}}
\end{subfigure}
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/eta}
\caption{\label{fig:disc-eta}}
\end{subfigure}
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/total_pT}
\caption{\label{fig:disc-total_pT}}
\end{subfigure}
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/inv_m}
\caption{\label{fig:disc-inv_m}}
\end{subfigure}
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/o_angle}
\caption{\label{fig:disc-o_angle}}
\end{subfigure}
\end{figure}
%
\begin{figure}[t]
\centering \ContinuedFloat
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/o_angle_cs}
\caption{\label{fig:disc-o_angle_cs}}
\rivethist{pheno/azimuthal_angle}
\caption{\label{fig:disc-azimuthal_angle}}
\end{subfigure}
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/pT}
@ -56,56 +36,76 @@
\caption{\label{fig:disc-pT_subl}}
\end{subfigure}
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/azimuthal_angle}
\caption{\label{fig:disc-azimuthal_angle}}
\rivethist{pheno/inv_m}
\caption{\label{fig:disc-inv_m}}
\end{subfigure}
\end{figure}
%
\begin{figure}[t]
\centering \ContinuedFloat
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/cos_theta}
\caption{\label{fig:disc-cos_theta}}
\end{subfigure}
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/eta}
\caption{\label{fig:disc-eta}}
\end{subfigure}
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/o_angle}
\caption{\label{fig:disc-o_angle}}
\end{subfigure}
\begin{subfigure}[t]{.49\textwidth}
\rivethist{pheno/o_angle_cs}
\caption{\label{fig:disc-o_angle_cs}}
\end{subfigure}
\caption{\label{fig:holhistos} Histograms of observables generated
by simulations with increasingly more effects turned on.}
\end{figure}
%
The results of the \sherpa\ runs for each stage with \(10^7\) events
each are depicted in the histograms in \cref{fig:holhistos} and shall
now be discussed in detail.
%TODO: high prec not possible
Because of the analysis cuts, the total number of accepted events is
smaller than the number of events generated by \sherpa, but sufficient
for proper statistics for most observables. The fiducial cross
sections of the different stages, which are compared in
\cref{fig:disc-xs}, differ as a result.
% TODO: not as result
All other histograms
are normalized to their respective cross sections.
now be discussed in detail.\footnote{A higher precision study was not
possible due to unavailability of access to the \emph{Taurus}
cluster at the time of writing.} Because of the analysis cuts, the
total number of accepted events is smaller than the number of events
generated by \sherpa, but sufficient for proper statistics for most
observables. Also the fiducial cross sections of the different stages,
which are compared in \cref{fig:disc-xs}, differ as a result of the
NLO effects that have been switched on. All histograms are normalized
to their respective cross sections.
Effects that give the photon system additional $\pt$ decrease the
cross section. This can be understood as follows. When there is no
cross section This can be understood as follows. When there is no
additional \(\pt\), then the photon momenta are back to back in the
plane perpendicular to the beam axis (transverse plane). If the system
now gets a kick then this usually subtracts \(\pt\) from one of the
photons unless that kick is near perpendicular to the photons. Because
the \(\pt\) distribution (\cref{fig:disc-pT,fig:disc-pT_subl}) is very
steep, a lot of events produce photons with low \(\pt\) and so this
effect is substantial. The fraction of events that have been discarded
by the \(\eta\) and \(\pt\) cuts are plotted in
\cref{fig:disc-cut-disc}, which shows an increase for all stages after
\stone, leading (principally) to the drop in cross section for the
\sttwo\ and \stthree.
plane perpendicular to the beam axis (transverse plane). Because
four-momentum conservation is enforced, every emission from a parton
gives a recoil momentum to that parton. If the system now gets a
recoil from parton showering, then this usually subtracts \(\pt\) from
one of the photons unless that recoil is near perpendicular to the
photons. Because the \(\pt\) distribution
(\cref{fig:disc-pT,fig:disc-pT_subl}) is very steep, a lot of events
produce photons with low \(\pt\) and so this effect is
substantial. The fraction of events that have been discarded by the
\(\eta\) and \(\pt\) cuts are plotted in \cref{fig:disc-cut-disc},
which shows an increase for all stages after \stone, leading
(principally) to the drop in cross section for the \sttwo\ and
\stthree.
The isolation cuts do affect the cross section as well, as is
demonstrated in \cref{fig:disc-iso-disc} which shows the fraction of
events discarded due to the isolation cuts. The \stfour\ cross section
is a bit higher than the \stthree\ one, because the hardonization
favors isolation of photons by reducing the number of particles in the
final state and clustering them closer together. The opposite effect
can be seen with MI, where the number of final state particles is
increased and this effect leads to another substantial drop in the
cross section.
% TODO: analysis plot of rejected events?
% TODO: link to CS frame
% TODO: iso cuts
% TODO: hadr isolation? why
% TODO: teilchen aufgefaechert, weniger in cone, teilchen ohne calo
favors isolation of photons by reducing the collinearity the of
particles in the final state and may create particles like neutrinos
that show in the detectors at all or can easily identified
(muons). The opposite effect can be seen with MI, where the number of
final state particles is increased and this effect leads to another
substantial drop in the cross section.
Also the NLO nature of the effects in the stages after \stone\ reduces
cross section, for instance by ``adding coupling constants'' for each
shower emission or multiple interaction.
The transverse momentum of the photon system (see
\cref{fig:disc-total_pT}) now becomes non trivial, as both the \sttwo\
@ -115,24 +115,34 @@ involved in the hard process and thus generates transverse momentum
and primordial \(\pt\) is simulated by the \stthree\ stage. In regions
of high \(\pt\) all but the \stone\ stage are largely compatible,
falling off steeply at
\(\mathcal{O}(\SI{10}{\giga\electronvolt})\). In the region of
\(\mathcal{O}(\SI{10}{\giga\electronvolt})\). Because parton showers
are modeled in the collienar limit, they cannot necessarily be trusted
in higher \(\pt\) regions~\cite{buckley:2011ge}.
The partons in a proton are somewhat localized and thus the
uncertainty principle demands that those partons have some momentum
perpendicular to the proton motion. The default parameters in \sherpa\
assign transverse momenta according to a Gaussian distribution with a
mean and standard deviation of \gev{.8}. In the region of
\SI{1}{\giga\electronvolt} and below, the effects primordial \(\pt\)
show as an enhancement in cross section. This is consistent with the
mean of the primordial \(\pt\) distribution which was off the order of
\gev{1}. The distribution for MI is enhanced at very low \(\pt\) which
could be an isolation effect or stem from the fact, that other partons
can emit QCD bremsstrahlung and showers as well, decreasing the
showering probability for the partons involved in the hard scattering.
show as an enhancement in cross section.
% The distribution for MI is
% enhanced at very low \(\pt\) which could be an isolation effect or
% stem from the fact, that other partons can emit QCD bremsstrahlung and
% showers as well, decreasing the showering probability for the partons
% involved in the hard scattering.
% TODO: clarify, Frank
The fact that the distribution has a maximum and falls off towards
lower \(\pt\) relates to the fact, that parton shower algorithms
effectively sum over all terms of the perturbation series and is
nontrivial~\cite{buckley:2011ge}.
effectively sum over all terms of the perturbation
series~\cite{buckley:2011ge}.
Related effects can be seen in the distribution for the azimuthal
separation of the photons in \cref{fig:disc-azimuthal_angle}. Albeit
back to back photons are favored by all distributions and most events
feature an azimuthal separation of less than \(\pi/2\), the
separation of the photons in \cref{fig:disc-azimuthal_angle}.
Back to back photons are favored by all distributions because
deviations from this configuration are purely NLO effects, so most
events feature an azimuthal separation of less than \(\pi/2\). The
enhancement of the low \(\pt\) regions in the \stthree\ stage also
leads to an enhancement in the back-to-back region for this stage over
the \sttwo\ stage.
@ -145,23 +155,23 @@ compatible beyond \gev{1}. Again, the effect of primordial \(\pt\)
becomes visible transverse momenta smaller than \gev{1}.
% TODO: mention steepness again
The \(\pt\) distribution for the sub-leading photon shows remarkable
resemblance to the \stone\ distribution for all other stages, although
there is a very minute bias to lower \(\pt\). This is consistent with
the mechanism described above so that events that subtract (very small
amounts of) \(\pt\) from the sub-leading second photon are more
common. Interestingly, the effects of primordial \(\pt\) not very
visible.
The \(\pt\) distribution for the sub-leading photon (see
\cref{fig:disc-pT_subl}) shows remarkable resemblance to the \stone\
distribution for all other stages, although there is a very minute
bias to lower \(\pt\). This is consistent with the mechanism described
above so that events that subtract (very small amounts of) \(\pt\)
from the sub-leading second photon are more common. Interestingly, the
effects of primordial \(\pt\) not very visible.
The distribution for the invariant mass (see \cref{fig:disc-inv_m})
shows that events with lower c.m.\ energies than the \stone\ threshold
can pass the cuts by being \(\pt\) boosted. The decline of the cross
section towards lower energies is much steeper than the PDF-induced
decline towards higher energies. High \(\pt\) boost to \emph{both}
photons are very rare, which supports the reasoning about the drop in
total cross section. The tendency for higher \(\pt\) boosts of the
photon system in the \sttwo\ stage shows in a slight enhancement of
the \sttwo\ cross section at low \(\pt > \gev{2}\).
In leading order, the phase space cuts impose a hard lower bound to
the invariant mass of the photon system. Parton showers can give
recoil momentum to the partons in such a way, that events with lower
invariant mass pass the cuts. The distribution for the invariant mass
(see \cref{fig:disc-inv_m}) shows that effect. The decline of the
cross section towards lower energies is much steeper than the
PDF-induced decline towards higher energies. High \(\pt\) boost to
\emph{both} photons are very rare (+ NLO suppressed), which supports
the reasoning about the drop in total cross section.
The angular distributions of the leading photon in
\cref{fig:disc-cos_theta,fig:disc-eta} are most affected by the
@ -182,13 +192,15 @@ cross section distributions are similar in shape extends further. In
the CS frame effects of the non-zero \(\pt\) of the photon system are
(somewhat weakly) suppressed.
It becomes clear, that the \sttwo\ and \stthree\ have the biggest
effect on the shape of observables, as they affect kinematics
directly. Isolation effects show most with the \stfour\ and especially
the \stfive\ stages. In angular observables hard process alone gives a
reasonably good qualitative picture, but in most other observables
non-LO effects introduce considerable deviations and have to be taken
into account.
It becomes clear, that parton showering and the primordial transverse
momentum have the biggest effect on the shape of observables, as they
affect the kinematics of the diphoton process directly. Isolation
effects show most through hadronization and especially multiple
interactions. In observables that exist in leading order
(\(\eta, \pt\), \ldots), the hard process alone gives a reasonably
good qualitative picture, but in most other observables non-LO effects
introduce considerable deviations and have to be taken into account
for a realistic study. Even with this simple process.
%%% LOCAL Variables:
%%% mode: latex

View file

@ -9,11 +9,11 @@ listed below.
%
\begin{description}
\item[LO] The hard process on parton level as used in \cref{sec:pdf_results}.
\item[LO+PS] The shower generator of \sherpa, \emph{CSS}
(dipole-shower), is activated and simulates initial state
radiation. The recoil scheme proposed in~\cite{hoeche2009:ha}, which
has been proven more accurate for diphoton production at leading
order, has been enabled.
\item[LO+PS] The shower generator of \sherpa,
\emph{CSShower}~\cite{schumann2008:ap} (dipole-shower), is activated and
simulates initial state radiation. The recoil scheme proposed
in~\cite{hoeche2009:ha}, which has been proven more accurate for
diphoton production at leading order, has been enabled.
\item[LO+PS+pT] The beam remnants are simulated, giving rise to
aditional radiation and parton showers. Also the partons are being
assigned primordial \(\pt\), distributed like a Gaussian with a mean
@ -21,13 +21,14 @@ listed below.
\SI{.8}{\giga\electronvolt}\footnote{Those values are \sherpa 's
defaults.}.
\item[LO+PS+pT+Hadronization] A cluster hadronization model
implemented in \emph{Ahadic} is activated. The shower particles are
being hadronized and the decay of the resulting hadrons simulated if
they are unstable.
implemented in \emph{Ahadic}~\cite{Winter2003:tt} is
activated. The shower particles are being hadronized and the decay
of the resulting hadrons simulated if they are unstable.
\item[LO+PS+pT+Hadronization+MI] Multiple Interactions (MI) based on
the Sj\"ostrand-van-Zijl Model are simulated. The MI are parton
shower corrected, so that there are generally more particles in the
final state.
the Sj\"ostrand-van-Zijl Model are simulated with
\emph{Amisic}~\cite{Bothmann:2019yzt}. The MI are parton shower
corrected, so that there are generally more particles in the final
state.
\end{description}
%
A detailed description of the implementation of those models can be
@ -39,7 +40,7 @@ configuration can be found in \cref{sec:ppruncardfull}. The
are the same as in \cref{sec:ppxs} and the beam energies have been
chosen as \SI{6500}{\giga\electronvolt} to resemble \lhc\ conditions.
The cuts on the hard process have been loosened to
\(\pt \geq \SI{5}{\giga\electronvolt}\) and \(\abs{\eta}\leq 3\) to
\(\pt \geq \SI{5}{\giga\electronvolt}\) and \(\abs{\eta}\leq 3\)
because jets and primordial \(\pt\) can increase the final state
\(\pt\) to fall into the analysis cuts.
@ -58,19 +59,16 @@ from hadron decays, the analysis only selects prompt photons with the
highest \(\pt\) (leading photons). Furthermore a cone of
\[R = \sqrt{\qty(\Delta\varphi)^2 + \qty(\Delta\eta)^2} \leq 0.4\]
around each photon must not contain more than \SI{4.5}{\percent} of
the photon transverse momentum (\(+ \SI{6}{\giga\electronvolt}\)),
attempting to exclude photons stemming from hadron decay are filtered
out. The leading photons are required to have \(\Delta R > 0.45\), to
filter out colinear photons, as they likely stem from hadron
decays.
% TODO: only for experiments, do not overlap photon iso cones, einfach
% weglassen
In truth, the analysis already excludes such photons, but to
be compatible with experimental data, which must rely on such
the photon transverse momentum (\(+ \SI{6}{\giga\electronvolt}\)), to
simulate experimental photon isolation. The leading photons are
required to have \(\Delta R > 0.45\), to filter photons with
overlapping isolation cones, which would be hard to isolate in
experiments. In truth, the analysis already excludes such photons,
but to be compatible with experimental data, which must rely on such
criteria, they have been included. These cuts are called
\emph{isolation cuts}. The code of the analysis is listed in
\cref{sec:ppanalysisfull}.
\cref{sec:ppanalysisfull} and has been adapted from code privately
communicated by Frank Siegert and Heberth Torres.
The production of photons in showers has not been considered.

View file

@ -262,3 +262,51 @@
location = {Austin, Texas},
series = {LLVM 15}
}
@article{hoeche2009:ha,
author = {Hoeche, Stefan and Schumann, Steffen and Siegert,
Frank},
year = {2009},
month = {12},
pages = {},
title = {Hard photon production and matrix-element
parton-shower merging},
volume = {81},
journal = {Physical Review D},
doi = {10.1103/PhysRevD.81.034026}
}
@misc{porter2008:te,
title = {Testing Consistency of Two Histograms},
author = {Frank C. Porter},
year = {2008},
eprint = {0804.0380},
archivePrefix ={arXiv},
primaryClass = {physics.data-an}
}
@article{schumann2008:ap,
author = {Schumann, Steffen and Krauss, Frank},
year = {2008},
month = {03},
pages = {038},
title = {A parton shower algorithm based on Catani-Seymour
dipole factorisation},
volume = {2008},
journal = {Journal of High Energy Physics},
doi = {10.1088/1126-6708/2008/03/038}
}
@article{Winter2003:tt,
author = "Winter, Jan-Christopher and Krauss, Frank and Soff,
Gerhard",
title = "{A Modified cluster hadronization model}",
eprint = "hep-ph/0311085",
archivePrefix ="arXiv",
reportNumber = "CERN-TH-2003-272",
doi = "10.1140/epjc/s2004-01960-8",
journal = "Eur. Phys. J. C",
volume = "36",
pages = "381--395",
year = "2004"
}

View file

@ -172,10 +172,13 @@ Viele Gruesse, Frank
** what does inclusive mean
** Normalize to XS
** y axis label for normalized histos
** TODO PDF cannot be derived: in principle?
** TODO still compatible?
** TODO cite atlas paper (analysis?)
** TODO call it distribution?
** DONE PDF cannot be derived: in principle?
** DONE still compatible?
** DONE cite atlas paper (analysis?)
** DONE call it distribution?
** DONE diphoton caps?
** DONE do remnants radiate?
** TODO ask about nlo emissions
* Work Log
** 18.03
- habe mich in manche konzeptionelle Dinge ziemlich verrannt!
@ -183,12 +186,13 @@ Viele Gruesse, Frank
* Todo
** TODO lab xs kuerzen
** TODO shower scale anpassen
** TODO effekt shower und kperp
** DONE effekt shower und kperp
** DONE y-axis a.u.!
** DONE mean, var einzeichnen
** DONE Variance of vegas weighted f!
** DONE look at xs plot -> they seem different
** DONE take new sample: still bias?
** DONE umnumerieren
* Observations
** XS
@ -264,3 +268,46 @@ Viele Gruesse, Frank
- biggest effect is the jet kick, photons are no qcd particles and
not touched after hard process
- no em radiation activated: would add more noise, here no additional photons
426 .. ref for CSS
433/436 .. refs
443 .. to zu viel
448 .. azimuthal
451 .. verb zu viel
452 .. collinear
kick -> recoil, klarer, momentum conservation am anfang! 481/6708
primordial pT, erklaeren fermi motion
figs umsortieren
484 .. often
off the orderd -> of
ok .. pT > 1e-1 MI schwer zu sagen, uninteressant, weglassen, nicht messbar
discuss -> parton shower collinear limes naeherung
(falling off steeply), kein grosses pT, keine gute naeherung in > 10 GeV
nontrivial feater of .. modeling
492 .. back to back preference -> nur folge der nlo unterdrueck
was ist LO threshhold, durch pT cuts
ist keine c.m. energy -> inv mass
very rare -> higher order (α_s kleiner) harte qcd kosten!
inv m LO+PS nicht verschieben 510 .. 511
524 .. welcher effekt
bigger picture .. lo bild -> geeignet, auch einfache betroffen (auch am anfang) uberall auswirkung
outlook very simple, nlo ME verwenden, fragmentation aus parton (dijet), neue photon iso + viel mehr
chi^2 test

View file

@ -10,7 +10,7 @@ Beams: [2212, 2212]
Energies: [6500, 6500]
#Luminosity_fb: 139.0
Description:
'An analysis used to compare different configuration of the Sherpa event generator.'
'An analysis used to compare different configurations of the Sherpa event generator.'
ValidationInfo:
'Not validated'
#ReleaseTests:

View file

@ -29,7 +29,7 @@ Title=$m_{\gamma\gamma}$ of the two leading photons
XLabel=$m_{\gamma\gamma}$ [GeV]
YLabel=$\mathrm{d}\sigma/\mathrm{d}m_{\gamma\gamma}$ [pb GeV$^{-1}$]
LogX=1
XMin=1
XMin=10.5
XMax=2000
# END PLOT
@ -73,6 +73,7 @@ XLabel=$\pT$
YLabel=$\mathrm{d}\sigma/\mathrm{d}\pT_{\gamma\gamma}$ [pb GeV$^{-1}$]
LogY=1
LogX=1
XMin=1e-1
# END PLOT
# BEGIN PLOT /MC_DIPHOTON_PROTON/xs