hiro/bachelor_thesis
1
0
Fork 0
mirror of https://github.com/vale981/bachelor_thesis synced 2025-03-04 17:11:39 -05:00
Code Issues Projects Releases Packages Wiki Activity Actions

final touches

Browse source
This commit is contained in:
hiro98 2020-06-10 18:07:32 +02:00
parent bb83c272bc
commit f1dadb5131
2 changed files with 51 additions and 45 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

76
latex/tex/pheno/discussion.tex
View file

@ -91,19 +91,20 @@ events. Because the \(\pt\) distribution of the photons
produce photons with low \(\pt\) that a prone to falling under the
cuts and so this effect is substantial. The fraction of events that
have been discarded by the phase space cuts are listed in
\cref{tab:xscut} which shows an increase for all stages after \stone,
contributing to the drop in fiducial cross section for the \sttwo\ and
\stthree.
\cref{tab:xscut} which shows an increase in the fraction of discarded
events for all stages after \stone, contributing to the drop in
fiducial cross section for the \sttwo\ and \stthree stages.
The isolation cuts do affect the observed cross section as well, as is
demonstrated in \cref{tab:xscut}. The fiducial \stfour\ cross section
is a bit higher than the \stthree\ one, because the hardonization
favors isolation of photons by reducing the collinearity of the
particles in the final state and may create particles like neutrinos
that show in the detectors at all or can be 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.
shown in \cref{tab:xscut}. The fiducial \stfour\ cross section is a
bit higher than the \stthree\ one, because the hadronization favors
isolation of photons by reducing the collinearity of the particles in
the final state and may create particles like neutrinos which are not
detected in the calorimeter or can be easily identified (muons). The
opposite effect can be seen with MI, where the number of final state
particles and thus the hadronic activity in the isolation cone is
increased. This effect leads to another drop in the fiducial cross
section.
The transverse momentum of the photon system (see
\cref{fig:disc-total_pT}) now becomes non trivial, as both the \sttwo\
@ -112,44 +113,43 @@ radiation generated by the parton showering algorithm kicks the quarks
involved in the hard process and thus generates transverse momentum.
In regions of high \(\pt\) all but the \stone\ stage are largely
compatible, falling off steeply at
\(\mathcal{O}(\SI{10}{\giga\electronvolt})\). Because parton showers
are modeled in the collienar limit, they cannot necessarily be trusted
in higher \(\pt\) regions~\cite{buckley:2011ge}.
\(\mathcal{O}(\SI{10}{\giga\electronvolt})\). Because the parton
shower approximation is only valid in the collinear limit, it can't
necessarily be trusted in higher \(\pt\)
regions~\cite{buckley:2011ge}. The fact that the distribution has a
maximum and falls again towards lower \(\pt\) is related to the nature
of parton shower algorithms, which approximately sum over all terms of
a perturbation series~\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 the cross section of the \stthree\ stage.
\SI{1}{\giga\electronvolt} and below, the effects of primordial
\(\pt\) show as an enhancement in the cross section of the \stthree\
stage.
% 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.
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~\cite{buckley:2011ge}.
Related effects can be seen in the distribution for the azimuthal
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
separation of the photons in \cref{fig:disc-azimuthal_angle}. Back to
back photons are favored by all stages because deviations from
this configuration are purely higher order 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.
In the \(\pt\) distribution of the leading photon (see
\cref{fig:disc-pT}) the boost of the leading photon towards higher
\(\pt\) in all stages but the \stone\ originates from the parton
\(\pt\) in all stages but the \stone\ stage originates from the parton
showering and thus the distribution of those stages are largely
compatible beyond \gev{1}. Again, the effect of primordial \(\pt\)
becomes visible transverse momenta smaller than \gev{1}.
becomes visible for transverse momenta smaller than \gev{1}.
The \(\pt\) distribution for the sub-leading photon (see
\cref{fig:disc-pT_subl}) shows remarkable resemblance to the \stone\
@ -157,17 +157,19 @@ 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.
effects of primordial \(\pt\) are not very visible.
In leading order, the phase space cuts impose a hard lower bound to
the invariant mass of the photon system. Parton showers can give
the invariant mass of the photon system. Higher order effects 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.
PDF-induced decline towards higher energies. High \(\pt\) boost in a
are very rare, which supports the reasoning about the drop in fiducial
cross section. Also, due to the implementation of the showering
algorithm, it may be that only the rather small intrinsic \(\pT\)
changes the center of momentum energy at all.
The angular distributions of the leading photon in
\cref{fig:disc-cos_theta,fig:disc-eta} are most affected by the
@ -183,7 +185,7 @@ grow larger, as this is the region where the cuts have the largest
effect. In the CS frame, the cross section does not converge to zero
for \sttwo\ and subsequent stages. With non-zero \(\pt\) of the photon
system, the z-axis of the CS frame rotates out of the region that is
affected by cuts. The ration plot also shows, that the region where
affected by cuts. The ratio plot also shows, that the region where
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.
@ -194,9 +196,9 @@ 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.
good qualitative picture, but in most other observables higher order
effects introduce considerable deviations and have to be taken into
account for a realistic study, even with this simple process.
%%% LOCAL Variables:
%%% mode: latex

20
latex/tex/summary.tex
View file

@ -7,20 +7,24 @@ the \sherpa\ event generator. Subsequently some Monte Carlo methods
for integration and sampling were mathematically motivated,
implemented and applied to the diphoton process, resulting in the
implementation of a simple event generator for proton-proton
scattering. Good sampling efficiency was achieved, at the cost of
accuracy.
scattering. Good sampling efficiency was achieved and potential
problems with the employed algorithm were highlighted.
Finally a phenomenological study of the diphoton process in
proton-proton scattering was performed by incrementally enabling
additional effects in the \sherpa\ event generator. Even with the
simplistic leading order matrix element, NLO effects like parton
showering showed significant impact on certain observables.
additional effects in the \sherpa\ event generator. Albeit the leading
order matrix element gives a good qualitative picture for the shape of
some observables, higher order effects like parton showering proved to
have a significant impact on certain observables.
The simplistic implementation of the diphoton process could be
developed further by using NLO matrix elements for the hard
process. This would lead extra emissions and new requirements for
photon isolation and a plethora of new effects. Furthermore the impact
of hard photons from parton showers can be studied.
process. This would lead to extra emissions and new requirements for
photon isolation and a plethora of new effects. Another avenue of
refinement of the simulation would be to allow the creation of photons
in parton showers. The impact of increased photon activity could lead
to additional observable effects.
%%% LOCAL Variables:
%%% mode: latex