From f1dadb5131aa94ffac3d6e778d61b60df5be1480 Mon Sep 17 00:00:00 2001 From: hiro98 Date: Wed, 10 Jun 2020 18:07:32 +0200 Subject: [PATCH] final touches --- latex/tex/pheno/discussion.tex | 76 +++++++++++++++++----------------- latex/tex/summary.tex | 20 +++++---- 2 files changed, 51 insertions(+), 45 deletions(-) diff --git a/latex/tex/pheno/discussion.tex b/latex/tex/pheno/discussion.tex index 763d5a7..9e2cec4 100644 --- a/latex/tex/pheno/discussion.tex +++ b/latex/tex/pheno/discussion.tex @@ -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 diff --git a/latex/tex/summary.tex b/latex/tex/summary.tex index 0263e53..f40ec40 100644 --- a/latex/tex/summary.tex +++ b/latex/tex/summary.tex @@ -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