Excited leptons at ATLAS, a cut ow analysis

Excited leptons at ATLAS, a cutflow analysis

Max Oosterbeek

10168877

July 9, 2014

Supervisor: J¨

orn Mahlstedt

Second assessor: Paul de Jong

Report of the bachelor research (15 EC)

conducted between the seventh of april and the third of july, 2014

at the research institute NIKHEF

as student Physics and Astronomy

of the science faculty FNWI

Abstract

Research is conducted into the optimal cutflow on kinematic variables using Monte Carlo simulations to improve the exclusion limits set on excited lepton model parame-ters by the ATLAS Excotics Multilepton search. Two mechanisms are considered for the production and decay of excited leptons, the Gauge field interaction mechanism and the Contact interaction mechanism. Cuts are considered on three kinematic variables, being the effective mass Mef f, the scalar sum of the three leptons with the highest transverse

momentum H_Tlepton and the three lepton mass M3l, which adds the requirement of a

particle-antiparticle pair among the three leptons to H_Tlepton. By quantifying the signal significance as function of the peak cut values, optimal cut values are found as a combi-nation of cuts on the effective mass and H_Tlepton and used to estimate the improvement of the exclusion limits due to the cuts.

Contents

1 Dutch popular scientific summary 4

2 Introduction 6

3 Theory 7

3.1 Gauge field interaction . . . 7 3.2 Contact interaction . . . 8 3.3 GM vs CI . . . 8

4 ATLAS Exotics Multilepton search 9

5 Method and results 10

5.1 Method uncertainties . . . 12 6 Discussion 14 7 Conclusions 14 8 Acknowledgment 15 9 Sources 15 10 Appendix 16

1

Dutch popular scientific summary

Volgens de huidig aanvaarde theorie¨en van de deeltjefysica zijn deeltjes zoals elektro-nen ondeelbare elementaire bouwsteelektro-nen van materie. Om de theorie¨en te testen en om te zoeken naar nieuwe fenomenen wordt er onderzoek gedaan naar het model van ge¨exciteerde leptonen. In dit model zijn deeltjes zoals elektronen niet ondeelbaar en elementair maar opgebouwd uit nieuwe, nog kleinere elementaire deeltjes genaamd preonen. De combi-naties van preonen die het minste energie kosten om te vormen zijn de electronen en andere deeltjes die we al kennen en noemen we de grondstaat combinaties. Maar er zouden dan ook combinaties moeten zijn die meer energie kosten om te maken. Deze zogenoemde ge¨exciteerde staat deeltjes zouden snel na dat ze gemaakt zijn weer moeten vervallen tot grondstaat deeltjes door een ander deeltje uit te zenden. Als het model van ge¨exciteerde leptonen klopt zouden er bij deeltjesbotsingen, zoals in de Large Hadron Collider in Zwitserland, meer deeltes zoals elektronen moeten worden waargenomen dan als het model niet klopt. Dit overschot aan deeltjes, en daarmee ge¨exciteerde leptonen, is nog niet gevonden. Maar er is inmiddels wel al zoveel data bekeken dat limieten kun-nen worden gezet op de waardes van eigenschappen van mogelijk ge¨exciteerde leptonen. Deze limieten staan weergegeven in het onderstaande figuur. De twee eigenschappen waar limieten op worden gezet zijn de massa van het ge¨exciteerde deeltje, weergegeven op de x-as, en de samenstellingschaal, weergegeven op de y-as, welke de door het model maxi-mum toegestane energie weergeeft. Om het overschot aan deeltjesproductie te vinden en om anders de uitsluitingslimieten de versterken wordt in dit onderzoek met behulp van computersimulaties gezocht naar de beste limieten op de zoekparameters. Deze zoekpa-rameters zijn kinematische variabelen waarvan aan de toegelaten waardes limieten worden gesteld. Zo wordt er bijvoorbeeld een minimumwaarde gezet op het transversaal momen-tum van deeltjes. Als het ge¨exciteerde model klopt zouden de deeltjes die extra worden geproduceerd bij botsingen bijna allemaal een transversaal momentum hebben hoger dan deze minimumwaarde. Doordat de deeltjes die een transversaal momentum hebben onder deze minimumwaarde niet meer in beschouwing worden genomen bij de analyse is het overschot aan deeltjes, als het er is, makkelijker te vinden. Het nieuwe limiet, gevonden met de beste limieten op de zoekparameters, staat in de figuur in het rood aangegeven en het oude limiet in het zwart.

Figure 1: De uitsluitingslimieten op eigenschappen van mogelijke ge¨

exciteerde muonen. Op

de x-as staat de massa van het ge¨

exciteerde staat deeltje in GeV (Giga-electronVolt) en op de

y-as de samenstellingschaal in GeV. Het gebied onder de limieten is uitgesloten. Dit betekent

bijvoorbeeld dat we met grote statistische zekerheid kunnen zeggen dat ge¨

exciteerde muonen

met een massa van 500 GeV in een model met een samenstellingschaal van 4000 GeV niet

bestaan. Over ge¨

exciteerde muonen met een massa van 2000 GeV in een model met een

samenstellingschaal van 10000 GeV kunnen we dit niet zeggen.

2

Introduction

In the Standard Model of particle physics the leptons are regarded as elementary particles. The Standard Model leptons are shown in Fig. 2. In order to test the Standard Model as well as to search for so called ”Beyond Standard Model” physics, a research is conducted into the model of excited leptons, which proposes that leptons are not elementary particles, but are composed of new elementary particles called preons [1]. Standard Model leptons are regarded as ground states of preon combinations and excited state leptons exist that can decay into ground state leptons by emitting a particle, as is depicted in Fig. 3. The preon substructures could explain the observed mass hierarchy of the quarks and leptons, which currently cannot be explained by the Standard Model. Theories for excited quarks involving preon substructures also exist but are not studied in this report [1].

One analysis looking for excited leptons is the Excotics Multilepton search by the ATLAS collaboration, making use of the detector at the Large Hadron Collider in Geneva, Switzerland. The goal of the research presented in this report will be to increase the exclusion limits on the excited leptons parameters as found by the Excotics Multilepton search by determining the optimal cutflow on kinematic variables to maximize the signal significance.

To do so, the effect of the kinematic cuts on the signal significance is studied for different parameters using Monte Carlo simulations of excited leptons and background processes.

Figure 2: In this figure the Standard Model

leptons are shown with their mass, electric

charge and spin values.

Figure 3: A conceptual scheme showing the

decay of an excited lepton into a ground state

lepton by the emission of a particle [2]

3

Theory

3.1

Gauge field interaction

There have been two mechanisms proposed for the production and decay of excited leptons [1]. One is the gauge field interaction mechanism (GM), which involves the interaction of an excited lepton and a ground state lepton with a gauge field, as shown by the Feynman diagram in Fig. 4. The Lagrangian of this process is proportional to the inverse of the compositeness scale Λ, which is the models maximum allowed energy scale for the excited lepton, and has a Vector - Axial vector structure [3]. The Lagrangian density function is given by LGM= X V =γ,W,Z e 2ΛG ¯ f∗σµν(cV − dVγ5)f Vµν+ h.c.

As can be seen from the Feynman diagram by changing the time order, an excited lepton can decay by the GM mechanism into a ground state lepton by emitting a gauge boson [1]. l∗→ l + γ l∗→ l + Z l∗→ νl+ W ν∗→ ν + Z ν∗→ l + W

Figure 4: The right hand vertex is associated with the Gauge field interaction mechanism.

It shows the interaction of an excited lepton and an anti-lepton with a gauge field. The left

hand vertex belongs to the domain of the Standard model.

3.2

Contact interaction

The other mechanism is the Contact interaction (CI) mechanism, which assumes an un-known preon interaction, approximated as a lepton self-interaction. This is depicted in the Feynman diagram in Fig. 5 by the large black vertex. Here the Lagrangian is proportional to the inverse of the square of the compositeness scale,

LCI=

4π Λ2

CI

jµjµ.

It is worthwhile to note that the compositeness scales of the two models do not nec-essarily have to have the same value, ΛGM 6= ΛCI. However, in this analysis the two Λ

values are assumed to be identical.

An excited lepton can decay by the Contact interaction mechanism in to a ground state lepton and a fermion anti-fermion pair[1].

l∗→ l + f ¯f ν∗→ ν + f ¯f

Figure 5: The Feynman diagram associated with the Contact Interaction mechanism. In the

vertex some unknown preon interaction occurs.

3.3

GM vs CI

To improve the yield of this search it is beneficial to be independent of either model. The excited lepton mass ml∗ and the compositeness scale Λ are free parameters in this

theory and the unknown ml∗/Λ ratio is of large influence to which process dominates

the decay, as is shown in Fig. 6. At a low ml∗/Λ ratio the Gauge field interaction

mechanism dominates the decay, while above a ratio value of about 0.3 the Contact interaction mechanism dominates the decay of excited leptons [2].

The decay of an excited lepton by either model can produce a final state containing at least three leptons. By looking for an excess of processes with a final state containing at least three leptons, an analysis can be made independent of either model.

Figure 6: The branching fraction of the Gauge field interaction and the Contact interaction

as a function of the ratio of the excited leptons mass to the models compositeness scales [2].

4

ATLAS Exotics Multilepton search

The Exotics Multilepton search by members of the ATLAS collaboration consists of an analysis looking for excess event, compared to the Standard Model, containing at least three charged leptons. It employs a series of basic cut selections, like cuts on kinematic variables and overlap removal, to ensure a clean signal of prompt leptons and uses a data-driven method to estimate fake leptons. The analysis provides model independent upper limits and fiducial efficiencies, which describe the detectors efficiency of measuring the leptons [4].

The Exotics Multilepton search uses data obtained by the ATLAS1 _{experiment, one}

of the experiments at CERNs Large Hadron Collider. The LHC is a 27 kilometer long ring shaped proton-proton collider build underground near Geneva, Switzerland. The ATLAS detector is one of four large experiments at the LHC. It consists of inner tracking chambers, electromagnetic and hadronic calorimeters and muon chambers, making the ATLAS detector versatile due to being able to detect most particles.

Currently, excited leptons remain to be discovered. But enough events have been studied to be able to exclude some parameter values of the models. The 95% confidence level exclusion limits on excited muon parameters as set by the ATLAS collaboration are shown in Fig. 7.

Figure 7: The (m

, Λ) parameter space showing the exclusion limits as set by the Multilepton

search.

5

Method and results

The Monte Carlo data used in this research has been generated with Pythia 8 and analyzed using RIVET 2[5]. In this research only the excited muon parameter grid was studied. The excited muon mass extended in this grid from 250 GeV to 2250 GeV in increments of 250 GeV and the compositeness scale ran from 500 GeV to 14000 GeV in increments of 500 GeV.

To determine the optimal cut values, the signal significance is defined by the following formula,

signif icance =√ S S + B.

Here, S stands for the normalised amount of signal events left after the cuts and B for the normalised amount of background events left after the cuts. This definition of significance is optimized for setting exclusion limits.

Three kinematic variables were chosen for study. H_Tlepton, the scalar sum of the trans-verse momenta of the three leptons with the highest transtrans-verse momentum. The effective mass Mef f, which is the scalar sum of all missing transverse energy ETmiss, the transverse

momenta of the jets H_Tjets and the transverse momenta of all the leptons H_Tall leptons. The third variable is the three lepton mass M3l, which is H

lepton

T with the additional

requirement of a particle anti-particle pair among the three leading leptons. The cuts on

the effective mass Mef f are measured in increments of 100 GeV. The cuts on H lepton T and

the three lepton mass M3l are measured in increments of 50 GeV.

Figure 8: On the left side is the effective mass distribution of the background. On the right

side is the effective mass distribution of the signal parameter point with m

= 2000 GeV and

Λ = 3000 GeV. In both distribution, the most effective cut is shown as determined from the

peak in Fig. 9.

The t¯t,W Z,W W and ZZ backgrounds were tested with the basic cut selection. The W Z and ZZ backgrounds gave a nonzero result. The ZZ background gave a small contribution and dropped to zero at a cut on the effective mass at 500 GeV. Therefore only the WZ background is used for the cutflow optimization.

As can be seen in Fig. 8, the distribution of the effective mass Mef f is different for the

background and signal and signal significance can be increased by cutting on the lowest effective mass values. By determining the signal significance as a function of the cut value a peak can be found, as is seen in Fig. 9.

By doing this for many points in the parameter space and by plotting the found peak values as a function of the parameter space, the contour plot, as shown in Fig. 10, could be made using Origin 8. The points in the parameter space used are shown in the Appendix. The contour plot gives an indication of the optimal cut value on the effective mass for a point in the parameter space.

To further increase significance, cuts on H_Tlepton are made on top of the cuts on the effective mass. Following the same procedure as described above for the effective mass, a contour plot was obtained of the optimal cut value for H_Tlepton, shown in Fig. 11.

The optimal cut value for points in the parameter space was also determined for the three lepton mass M3l, as shown in Fig. 12.

Figure 9: The signal significance as a function of the cut value on the effective mass for the

point with m

= 2000 GeV and Λ = 3000 GeV. A peak can be seen at a value of 1000 GeV.

Figure 10: A contour graph indicating the optimal cut value on the effective mass for every

point in the parameter space. The values assigned to the contour lines are arbitrarily chosen

by Origin 8.

5.1

Method uncertainties

Uncertainties in the results arise from the increments used in the parameters as well as in the kinematic variables. Optimal peak values are only determined to values which are integer multiples of the variable increment size, and is only determined for a finite amount of points. In the contour graphs, the optimal cut values for all other points are

Figure 11: A contour graph showing the optimal cut value for H

when an optimal cut

on the effective mass is already present.

Figure 12: The optimal cut value on the three lepton mass plotted as a function of the

parameter space.

interpolated by Origin 8. Statistics on the background gave rise to anomalous occurrences when cut values were reached that there were only few absolute events left. This led to unnatural bumps in the significance as function of the cut value, mostly at the cut value where the background dropped of to zero. Due to this uncertainty, the optimal cut value for high value parameter points could not be determined accurately.

6

Discussion

The significances under the effect of different optimal cuts on kinematic variables are shown in Table 1 for the parameter point with an excited lepton mass of 2000 GeV in a model with compositeness scale of 3000 GeV. Demanding a particle anti-particle pair among the three leading leptons leads to a small increase in significance compared to no cuts on kinematic variables. If then a cut is made on the three lepton mass M3l,

significance is doubled compared to no cuts. An optimal cut on the effective mass has a higher significance. If an optimal cut on H_Tlepton is added to the effective mass cut, the highest significance is gained. If then the particle anti-particle pair among the three leading leptons is required, effectively changing H_Tlepton into the three lepton mass M3l,

the significance is lowered some.

Cutflow

Significance

No kinematic cuts

0.066

Particle anti-particle pair requirement only

0.07463

M

> 550 GeV

0.13265

M

> 1000 GeV

0.13315

M

> 1000 GeV & H

> 350 GeV

0.13351

M

> 1000 GeV & M

> 350 GeV

0.13229

Table 1: A table comparing the significance due to different cutflows for the (l

mass,Λ) point

(2000 GeV, 3000 GeV)

The effect of the increase in significance on the exclusion limits has been approximated by using the increase in significance for three parameter points. The approximation in the increase of the exclusion limits is shown in Fig. 13. The new limit, indicated by the red line, is between the one and two standard deviation lines of the old limit. For the approximation the (ml∗/Λ) data points (250 GeV, 8000 GeV), (1000 GeV, 8000 GeV)

and (2000 GeV, 3000 GeV) were used to approximate the increase of the limits for the range (100 - 800 GeV), (800 - 1400 GeV) and (1400 - 2500 GeV) respectively.

7

Conclusions

The optimal cutflow on kinematic variables has been determined by quantifying the signal significance as a function of the cut value for different points in the parameter space. The combination of cuts on the effective mass Mef f and HTleptongives the highest significance.

The requirement of a particle anti-particle pair amongst the three leading leptons only adds to the significance if no other cuts are present. Using the best combination of cuts on kinematic variables the exclusion limits on parameters of excited lepton models have been increased significantly and the exclusion limits as previously obtained by the ATLAS

Figure 13: The excited muon parameter space showing the old limits in black and the new

limits in red. The new exclusion limits are between the one and two standard deviation lines

of the old limit, meaning the confidence level of the old limit has been increased.

collaboration have been strengthened.

8

Acknowledgment

I’d like to thank J¨orn Mahlstedt for his supervision and guidance and I wish him luck in his continuing search for excited leptons. I have very much enjoyed being part of this quest. I’d like to thank Olya Igonkina for proposing the project and for supervising my supervisor. I’d like to thank Paul de Jong for taking the time to act as second assessor. I’ve tried to keep it short. I’d like to thank all the people at the NIKHEF institute for the warm academic atmosphere and for providing me the chance to get a taste of real scientific research.

9

Sources

[1] Baur,Spira & Zerwas, Excited-quark and -lepton production at hadron colliders, Au-gust 1990, Physical review D, volume 42, number 3

[2] J¨orn Mahlstedt, Poster for Veldhoven conference 2014, NIKHEF institute, http://www.nikhef.nl/∼jmahl/Veldhoven2013/Poster Veldhoven 2013.pdf

[3] Mark Thomson, Modern Particle Physics, Cambridge University Press, 2013

[4] The ATLAS Collaboration, Search for New Phenomena in Events with Three Charged Leptons at √s = 8T eV with the ATLAS detector, ATLAS NOTE ATLAS-CONF-2013-070,July 2013

[5] A. Buckley et al., Rivet user manual, arXiv:1003.0694 [hep-ph], Feb 2013

10

Appendix

Figure 14: The parameter space showing the points for which the optimal effective mass cut

was determined.