Project Report

Kinematics Comparison of Monte Carlo to Real

Data for Z

Kunal GargNISER

School of Physical Sciences

Abstract

This project involved an extensive usage of ROOT framework, an Object Ori-ented C++ framework. As a first step gaining familiarity with ROOT had beenessential. Using the ROOT framework, Z events are analysed from the4.7fb1 of proton-proton collision data recorded by the ATLAS experiment. Insuch events, detailed kinematics comparison between the data and Monte-Carlo(simulated and reconstructed with the ATLAS detectors and software) are pre-sented here.

0.1 Introduction

The basic physical process we study here is called Drell-Yan process. It is anelectromagnetic effect that takes place in high energy hadron-hadron scattering.When a quark from one hadron and anti-hadron from another hadron annihilate,in the process creating a virtual Z0 boson which then decays into a pair ofoppositely charged leptons. This process was first suggested by Sidney Drell andTung-Mow Yan in 1970 to describe the production of leptonanti-lepton pairs inhigh-energy hadron collisions. Experimentally, this process was first observed byJ.H. Christenson et al. in protonuranium collisions at the Alternating GradientSynchrotron.

Figure 1: Drell-Yan Process

The ATLAS experiment identifies and reconstructs muons with two highprecision tracking systems, the Inner Detector (ID) and the Muon Spectrometer(MS) which provide independent measurements of the muon momentum. In thisreport, we compare the performance of the reconstruction algorithm and data asderived from the dataset corresponding to an integrated luminosity of 4.7 fb1

of 7 TeV pp collisions recorded in 2011. Also there is described the correctionsto be applied to the simulation to reproduce the momentum resolution and scaleobserved in experimental data.

0.2 Drell-Yan Process

The partons

The strongly interaction particles such as pi mesons and nucleons are not elemen-tary. They are made up from simpler particles: quarks, antiquarks and gluons,known collectively as partons. The quarks are point like, spin- 12 fermions, prop-erties they share with other class of matter particles, the leptons. Quarks differfrom leptons in that they interact strongly via gluon exchange, whilst leptons

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only feel electroweak force. Evidence of internal structure of hadrons has comefrom deep inelastic lepton scattering of nucleons and from hadron spectrum(Gell-Mann 1964, Zweig 1964).

Colour

Electroweak and gravitational forces are known to be gauge interactions trans-mitted by gauge fields. In this case of electroweak interactions, the fields arequantised as spin-1 particles, namely photons and intermediate vector bosons.It is expected that the quark-quark strong interaction is also a gauge force.Greenberg (1964) deduced evidence for a new symmetry called colour, whichturned out to be the gauge symmetry. He pointed out that if the account istaken of the spin, flavour and relative motion, then the quarks inside baryons

with spin parity 32+

are in totally symmetric state. This contradicts the Pauliexclusion principle. In order to resolve this dilemma.Greenberg proposed thata further three-fold symmetry existed, SU(3) of colour, with the quarks as-signed to the fundamental three-representation (red, blue and green). Then ifthe quarks in a baryon are arranged in an antisymmetric colour state with nonet colour, the difficulty disappears. The solution is to have one red, one blueand one green quark inside each; in the mesons a quark of one colour is pairedwith an antiquark of the same colour. The state of the pi+ meson in this schemebecomes

(1/

3)[u(r)d(r) + u(b)d(b) + u(g)d(g)

]The parton model

The interactions of leptons with hadrons lend themselves to a treatment byan impulse approximation when the relative four-momentum squared |q|2 islarge. Figure 2 shows the form this takes for (a) the Drell-Yan process, (b)e+e annihilation and (c) deep inelastic lepton scattering. The lepton (line) issupposed to interact instantaneously with a single quark (line), and any parton-parton interactions are ignored. On a longer time scale the partons interactto give the hadronic final state. This impulse approximation leads to simpleelectromagnetic calculations of the cross sections. Bjorken originally provedthe model for lepton scattering at large energies and introduced the Bjorkenx variable (Bjorken 1969); x is the fraction of longitudinal momentum of thehadron that is carried by a given parton, and must lie in the range 0-1. Theasymptotic freedom limit gives a theoretic basis to the impulse approximationinside QCD. When the inelastic momentum transfer to a hadron is large enough,it will appear to be made up of quasi-free point-like partons.

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Structure Functions

The structure functions are the covariant scalar quantities used to describedeep inelastic scattering from nucleons. Most determinations of the structurefunctions of nucleons have been made in deep inelastic scattering experimentsfor the reactions:

l + nucleon l + hadrons + nucleons l + hadrons

and their analogues. Under the assumption that a single vector boson ex-change dominates, the dynamics of the reaction is described by the three struc-ture functions F1, F2 and F3, which are in turn functions of the two covariantkinematic quantities:

x = q2/2p.q and q2

where q is the four-momentum transfer between the leptons and the targetnucleons and p is the incident nucleon four-momentum.

Of central interest to us here is the interpretation of x and the structurefunctions in the parton model; x is to be interpreted as the fraction of longitu-dinal momentum of the parent hadron (Bjorken x) that is carried by the active,struck quark in the overall centre-of-mass frame. If n(x)dx overall centre-of-mass frame. If n (x) dx is the number of quarks carrying longitudinal momentumfractions between x and x+ dx, then

F l2(x) =i

Q2ixni(x) (charged leptons)

F 2 (x) =i

xni(x) (neutrinos)

where the sums are taken over all quark flavours. The difference betweencharged lepton and neutrino scattering arises from the difference between theweak and electromagnetic forces at usual experimental energies. The electro-magnetic coupling requires the appearance of the quark charge, namely Q inunits of e. In addition, the model requires exact relationships to hold betweenthe structure functions:

F l2 = 2xFl1 and F

2 = xF 3 = 2xF 1

where the sign is positive for neutrino-quark and antineutrino-antiquark scatter-ing and negative for the other choices. Bjorken (1969) argued that the structurefunctions at large q2 and finite x are functions of x alone (Bjorken scaling).

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Dynamics of Drell-Yan process

Drell and Yan (1970a, 1971) proposed a simple electromagnetic process to ac-count for the production of the continuum of dilepton pairs from hadron-hadroncollisions:

A+B l+ + l + anythingThe essential steps are the annihilation of a single antiquark from one hadron

on a single quark from the other hadron to produce a virtual photon. Subse-quently the virtual photon converts to a pair of leptons. If the mass M of thedilepton is large compared to the nucleon mass, then the Heisenberg uncer-tainty principle tells us that the time of interaction is short on the nuclear scale.There is thus no opportunity for annihilating quark-antiquark pair to interactwith other components of the parent hadrons. The other partons can be treatedpurely as spectators. Subsequently, on a time scale that is long compared to theannihilation, the spectators rearrange themselves into outgoing hadrons. Gen-erally the leptons alone are detected and momentum-analysed. This proceduremeasures the inclusive cross section for the dilepton production and sums overall possible combinations of the final-state hadrons. Thus in the calculation ofthe cross section the factor expressing the probability that the spectators con-vert to hadrons us simply unity. The dilepton kinematic variables and xF aredirectly related to the Bjorken x values (longitudinal momenta) of the parentquark and anti-quark. Suppose the active quark (antiquark) in the beam par-ticle has a Bjorken x of x1, and the active antiquark (quark) in the target hasa Bjorken x of x2. Then in the CM frame of beam plus target the annihilat-ing pair have longitudinal momenta x1

s/2 and x2

s/2, respectively. If the

quarks are massless their energies are x1s/2 and x2

s/2. Then equating the

four-momentum of the annihilating pair to the dilepton four-momentum (E, pl)gives

E = (x1 + x2)s/2 (1)

and

pl = (x1 x2)s/2 (2)

The dilepton mass squared is

M2 = E2 p2l = sx1x2 (3)Two basic relations between quark variables and the observables now emerge

= M2/s = x1x2 (4)

and

xF = 2pl/s = x1 x2 (5)

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0.3 ATLAS detectors

ATLAS (A Toroidal LHC Apparatus) is one of the seven particle detector ex-periments (ALICE, ATLAS, CMS, TOTEM, LHCb, LHCf and MoEDAL) con-structed at the Large Hadron Collider (LHC). ATLAS is 45 metres long, 25metres in diameter, and weighs about 7,000 tons. The detector consists of aseries of ever-larger concentric cylinders around the interaction point where theproton beams collide. It can be divided into four major parts: the Inner De-tector, the calorimeters, the Muon Spectrometer and the magnet systems. Ofspecial interest to us are the Inner Detector (ID) and the Muon Spectrometer(MS) and to a lesser extent the calorimeter.

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Radiation shield

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Resistive plate chambers

14161820 21012 468 m

Figure 2: ATLAS design

0.3.1 Inner Detector

The Inner Detector begins a few centimetres from the proton beam axis, extendsto a radius of 1.2 metres, and is 6.2 metres in length along the beam pipe. Itsbasic function is to track charged particles by detecting their interaction withmaterial at discrete points, revealing detailed information about the types ofparticles and their momentum. The magnetic field surrounding the entire innerdetector causes charged particles to curve; the direction of the curve revealsa particles charge and the degree of curvature reveals its momentum. Thestarting points of the tracks yield useful information for identifying particles aswell.

In the barrel region the high-precision detectors are arranged in concentriccylinders around the beam axis, while the end-cap detectors are mounted ondisks perpendicular to the beam axis. The barrel TRT straws are parallel to

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Figure 3: Inner Detector

the beam direction. All end-cap tracking elements are located in planes perpen-dicular to the beam direction. ID has three parts:

Pixel Detector - innermost part of the detector, contains three con-centric layers and three disks on each end-cap. It has minute pixel sizedesigned for extremely precise tracking very close to the interaction point.

Semi-Conductor Tracker (SCT) - It is similar in concept and functionto the Pixel Detector but with long, narrow strips rather than small pixels,making coverage of a larger area practical. The SCT is the most criticalpart of the inner detector for basic tracking in the plane perpendicularto the beam, since it measures particles over a much larger area than thePixel Detector.

Transition Radiation Tracker (TRT) - Its the outermost componentof the detector. The detecting elements are drift tubes (straws). Eachstraw is filled with gas that becomes ionised when a charged particle passesthrough. Between the straws, materials with widely varying indices ofrefraction cause ultra-relativistic charged particles to produce transitionradiation and leave much stronger signals in some straws. Xenon gasis used to increase the number of straws with strong signals. Since theamount of transition radiation is greatest for highly relativistic particles,and because particles of a particular energy have a higher speed the lighterthey are, particle paths with many very strong signals can be identified asbelonging to the lightest charged particles: electrons and its antiparticles,positrons.

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0.3.2 Calorimeters

The calorimeters are situated outside the solenoidal magnet that surrounds theInner Detector. Their purpose is to measure the energy from particles by ab-sorbing it. There are two basic calorimeter systems: an inner electromagneticcalorimeter and an outer hadronic calorimeter. Both are sampling calorime-ters; that is, they absorb energy in high-density metal and periodically samplethe shape of the resulting particle shower, inferring the energy of the originalparticle from this measurement.

0.3.3 Muon Spectrometer

Muons are particles just like electrons, but 200 times heavier. They are theonly detectable particles that can traverse all the calorimeter absorbers withoutbeing stopped. The muon spectrometer surrounds the calorimeter and mea-sures muon paths to determine their momenta with high precision. The MuonSpectrometer is an extremely large tracking system, consisting of 3 parts: (1) amagnetic field provided by three toroidal magnets, (2) a set of 1200 chambersmeasuring with high spatial precision the tracks of the outgoing muons, (3) aset of triggering chambers with accurate time-resolution. Its tremendous size isrequired to accurately measure the momentum of muons, which first go throughall the other elements of the detector before reaching the muon spectrometer.

Figure 4: Muon Spectrometer

It functions similarly to the Inner Detector, with muons curving so that theirmomentum can be measured, albeit with a different magnetic field configuration,lower spatial precision, and a much larger volume. It also serves the function

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of simply identifying muons very few particles of other types are expectedto pass through the calorimeters and subsequently leave signals in the MuonSpectrometer.

0.4 - scale and Momentum Resolution

Efficient and accurate muon identification and reconstruction is of primary im-portance for the physics program of the ATLAS experiment. The experimentuses the information of MS and ID sub-detectors, and to a lesser extent, of thecalorimeter, to identify and precisely reconstruct muon produced in the pp col-lisions.The momentum resolution and scale are additional important parameters usedin the evaluation of the muon reconstruction performance. Di-muon decaysof the Z, J/ and resonances are used to determine the muon momentumresolution and scale. This allows a validation of the MC prediction for thesequantities.

0.5 Monte Carlo and Data

The results presented here are obtained from the analysis of thes = 7 TeV

pp collision events corresponding to an integrated luminosity of 4fb1 and col-lected by the ATLAS detector in 2011. Online event selection is performed bya three level trigger system. Events were accepted for the analysis documentedonly if the ID and MS detectors were in good data-taking conditions and bothsolenoidal and toroidal magnet systems were on.In the following, experimental data are compared to MC simulations. TheZ signal MCs are generated with ALPGEN. The generated signal eventsare passed through the full Geant4 simulation of the ATLAS detector, the trig-ger simulation and same reconstruction chain used for data. The simulation in-cludes a realistic evaluation of the MS detectors alignment obtained by studyingstraight muon tracks from cosmic ray events and from special runs performedwith toroidal magnetic field off.

We selected the bins during our analysis of the two data sets from the detec-tor and MC based on the detector design. And there are two peaks at = 1.05and = 1.9 and end caps at = 0 and = 2.5 So we selected three regionsbased on these numbers as

|| < 1.051.05 < || < 1.91.9 < || < 2.5

There are several different parameters which contribute to the resolution ofthe detector at different energy scales.

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Figure 5: Contribution to Resolution

0.6 Results

First we plot the Invariant Mass of the Z boson calculated from both MC aswell as Data and then fitted to a double Gaussian for different bins. Since thereare two muons and three bins, well have six different combinations of the bins.

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Now for pT comparison

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Figure 18: Combined Lepton pT

0.7 Conclusions

As we can see from the Invariant mass data and MC fitting, our theoreticalpredictions match the data quite well up to a certain statistical limit.

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Figure 19: Combined statistics

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The comparison between the data and MC for Z0 events are presentedhere. The M distributions show reasonable agreement between the data andMC. However in data peak and width of the Z - pole mass distribution areslightly different from the ones predicted by the MC. Such mismatches betweenthe data and MC may have originated from the potential mis-modelling of mul-tiple scattering, detector alignment etc. which require further investigation.

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0.8 Acknowledgements

I would like to thank very heartily Dr. Prolay Mal for all his support and help incompletion of this project. I would never have been able to complete it withouthis guidance and input.

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0.9 References

The Drell-Yan Process - I.R Kenyon (Rep. Prog. Phys., Vol. 45, 1982)

ATLAS Note, ATLAS CONF-2013-088 - Prelimanry results on themuon reconstruction efficiency, momentum resolution , and momentumscale in ATLAS 2012 pp collision data

http://www.root.cern.ch

http://www.scholarpedia.com

http://twiki.cern.ch

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