Physics at Hadron Colliders Part I

Marina Cobal

Università di Udine

Physics at Hadron Colliders

Part I

The Standard Model Lagrangian

gauge sector

ν mass sector EWSB sector

flavour sector

ü

ü ü

Status of the art

•  The SM (in terms of its QCD and EWK parts) WORKS PERFECTLY well, up to the

% level at the highest energies probed so far (7 and 8 TeV)

•  We have very advanced theory tools at hand

•  There is a new boson of mass ~125 GeV, with properties consistent with the SM Higgs, within the current uncertainties. More data needed to ascertain the nature of this object.

•  So far, no indications of BSM physics from direct searches at the HEF: colored SUSY particles (first generations) ruled out up to O(1 TeV), for a light LSP;

•  “natural” SUSY probed at level of a few hundred GeV of 3rd generation spartners;

•  exotica: heavy objects probed up to masses of 2-3 TeV;

a lot of room still to be explored, 14 TeV will be essential!

•  very few anomalies in the world-wide HEF data, no strongly smoking gun most

•  Precision measurements of

–  M_W =80.399 ± 0.023 GeV/c² –  M_top=173.3 ± 1.2 GeV/c²

–  Precision measurements on Z pole

•  Prediction of higgs boson mass within SM due to loop corrections

Problem I: Where is the Higgs boson?

Problem II: Where did all the Antimatter go?

•  Not explained by Standard Model

Early Universe Universe today

Problem III: Hierarchy Problem

•  Free parameter m²_H^tree needs to be “finetuned” to cancel huge corrections

–  Can be solved by presence of new particles at M ~1 TeV –  Already really bad for M~10 TeV

•  Why is gravity so weak?

m²_H ≈ (200 GeV)² = m²_H^tree + δ m²_H^top + δ m²_H^gauge + δ m²_H^higgs

(Some) More Problems …

•  Matter:

–  SM cannot explain number of fermion generations

–  or their large mass hierarchy

•  m_top/m_up~100,000

•  Gauge forces:

–  electroweak and strong interactions do not unify in SM

–  SM has no concept of gravity

•  What is Dark Energy?

“Supersymmetry” (SUSY) can solve some of these problems

Luminosity

•  Single most important quantity

–  Drives our ability to detect new processes

–  Rate of physics processes per unit time directly related:

LHC:

revolving frequency: f_rev=11245.5/s

#bunches: n_bunch=2808

#protons / bunch: N_p= 1.15 x 10¹¹ Area of beams: 4πσ_xσ_y~40 µm

f

n

N

4 π σ

σ

L=

LHC and Tevatron Machine Parameters

LHC (today)

LHC (design)

Tevatron (achieved)

Centre-of-mass energy 8 TeV 14 TeV 1.96 TeV

Number of coll. bunches 1368 2808 36

Peak Luminosity (10³⁰ cm^-2s^-1) 7700 10000 400 Integrated Luminosity: ∫Ldt 21.6 fb^-1 >100 fb^-1 ~12 fb^-1

Instantaneous Luminosity

Tevatron LHC

Integrated Luminosity

•  Tevatron: 12 fb^-1 delivered

•  LHC: almost 22 fb^-1 delivered

–  Very steeply rising due to progress in accelerator

LHC Tevatron

Example: ATLAS Detector Performance

Cross section

•  Cross section measurements in particle physics:

–  Connecting Theory and Experiment

•  Cross section: definition –  Luminosity

–  Counting the number of events

–  Efficiency & acceptance corrections –  Use of Monte Carlo simulations

–  Systematic uncertainties

–  Unfolding of measured data to quantities predicted by theory

•  Examples of cross section measurements

Motivation

•  Cross section is a fundamental physics observable

–  Cross section measurements were crucial to achieve the model of particle physics as we have it today

•  Most measurements at LHC, HERA, Tevatron are cross section measurements

•  Concepts of a cross section measurement are common to

most analyses addressed today

Cross section at fixed target

Rutherford formula

•  Perform scattering experiments

•  Measure scattering angles and energy

•  Structure has been explored down to 10^-18 m (upper limit for quark radius)

1908: Atoms have nuclei

1956: Nuclei are extended

1962: Nuclei have substructure

Since 70's: Quarks and gluons (PDF)

Probing the Structure of Matter

Theory and Experiment

•  Cross Section: A measure of the number of collisions

–  Experiment: Measurement of rate of events in particular final state –  Theory: Calculation of transition probability using matrix elements and

phase space

19

Theory predicts cross section (number of events per luminosity)

Standard Model Cross Section calculations known up to NNLO (accuracy 5-10%)

Production Cross Section

Theory and Experiment

Example: Calculation of H → ZZ → 4 leptons

Notreviewed,forinternalcirculationonly

Higgs Production at the LHC

3

Gluon fusion process (87%) Vector Boson fusion (7%) Associated production with W/Z (5%)

Associated production with top (1%)

[GeV]

MH

80 100 200 300 400 1000

H+X) [pb] →(pp σ

10-2

10-1

1 10 102

= 8 TeV s

LHC HIGGS XS WG 2012

H (NNLO+NNLL QCD + NLO EW) pp →

qqH (NNLO QCD + NLO EW) pp →

WH (NNLO QCD + NLO EW) pp →

ZH (NNLO QCD +NLO EW) pp →

ttH (NLO QCD) pp →

Cross section [pb] at m_H = 125.5 GeV

ggF VBF WH ZH ttH

LHC Higgs Cross Section Working Group

[GeV] MH

80 100 120 140 160 180 200

Higgs BR + Total Uncert

10-4

10-3

10-2

10-1

1

LHC HIGGS XS WG 2013

b b

µ µ c c

gg

Z

WW

ZZ

BR [%] at m_H = 125.5 GeV

Parton Distribution Functions

(PDF)

Branching Ratios

Z Z

l

l l l

Theory and Experiment: Higgs

Notreviewed,forinternalcirculationonly

Higgs Production at the LHC

3

Gluon fusion process (87%) Vector Boson fusion (7%) Associated production with W/Z (5%)

Associated production with top (1%)

80 100 200 300 400 1000

H+X) [pb] →(pp σ

10-2

10-1

1 10 102

= 8 TeV s

LHC HIGGS XS WG 2012

H (NNLO+NNLL QCD + NLO EW) pp →

qqH (NNLO QCD + NLO EW) pp →

WH (NNLO QCD + NLO EW) pp →

ZH (NNLO QCD +NLO EW) pp →

ttH (NLO QCD) pp →

LHC Higgs Cross Section Working Group

Higgs BR + Total Uncert

10-3

10-2

10-1

1

LHC HIGGS XS WG 2013

b b

µ µ c c

gg

Z

WW

ZZ

Hadron collision physics

Protons are complex objects:

Partonic substructures:

Quarks and Gluons Q²: ~(M²+p_T²)

Björken-x:

Fraction of proton momentum carried by the parton

Hard scattering processes are a small fraction of the total inelastic cross section

•  Hard scattering processes: high momentum transfer (Q²)

•  Quark-quark

•  quark-gluon

•  gluon-gluon scattering or annihilation

•  PDF can not be calculated, but are universal (assumed and proven)

–  within given approximation and scheme (e.g. NNLO DGLAP)

•  Determined from different experiments

–  mostly from HERA, now from LHC data

•  High energy proton collisions are really parton collisions, mostly gluons

–  parton luminosity

•  Generic pp cross section is sum of partonic cross sections

Theory and Experiment

Parton Distribution Functions (PDF)

PDF Fits at HERA Amanda Cooper-Sarkar

/ GeV

model

mc

1.2 1.3 1.4 1.5 1.6 1.7 1.8

2 χ

520 540 560 580 600 620 640 660 680

flexible param standard param

/ndf2χ

0.9 0.95 1 1.05 1.1 1.15 H1 and ZEUS (prel.)

HERAPDF1.0 RT standard

0.100 GeV (opt)=1.308 ±

model

mc

/ GeV

model

mc

1.2 1.3 1.4 1.5 1.6 1.7 1.8

2χ

600 700 800 900 1000

flexible param standard param

/ndf2χ

1 1.2 1.4 1.6 H1 and ZEUS (prel.)

(prel.)

c c

HERAPDF1.0 + F2

RT standard

0.018 GeV (opt)=1.572 ±

model

mc

/ GeV

model

mc

1.2 1.4 1.6 1.8

2 χ

600 800 1000 1200

RT standard RT optimised ACOT-full

χ S-ACOT- ZMVFNS

H1 and ZEUS (prel.) (prel.)

c c

HERAPDF1.0 + F2

HERA Inclusive Working Group August 2010

/ GeV

model

mc

1.2 1.4 1.6 1.8

/ nb+ Wσ

52 54 56 58 60 62 64

RT standard RT optimised ACOT-full S-ACOT-χ ZMVFNS

) = 7 TeV (s

W+

(prel.)

c c

HERAPDF1.0 + F2

HERA Inclusive Working Group August 2010

Figure 1: The χ² of the HERAPDF fit as a function of the charm mass parameter m^model_c . Top left; using the RT-standard heavy-quark-mass scheme, when only inclusive DIS data are included in the fit. Top right;

using the RT-standard heavy-quark-mass scheme, when the data for F₂^{c c} are also included in the fit. Bottom left; using various heavy-quark-mass schemes, when the data for F₂^{c c} are also included in the fit. Bottom right: predictions for the W⁺ cross-sections at the LHC, as a function of the charm mass parameter m^model_c , for various heavy-quark-mass schemes.

H1 and ZEUS

HERA Inclusive Working GroupAugust 2010

x = 0.02 (x300.0) x = 0.032 (x170.0)

x = 0.05 (x90.0) x = 0.08 (x50.0)

x = 0.13 (x20.0) x = 0.18 (x8.0)

x = 0.25 (x2.4)

x = 0.40 (x0.7)

x = 0.65

Q²/ GeV² σr,NC(x,Q2 )

HERA I+II NC e⁺p (prel.) HERA I+II NC e^-p (prel.)

HERAPDF1.5 e⁺p HERAPDF1.5 e^-p

±

10^-2 10^-1 1 10 10² 10³

10² 10³ 10⁴ 10⁵

0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1

0.2 0.4 0.6 0.8 1

HERAPDF1.0 (HERA I) HERAPDF1.5 (prel.) (HERA I+II)

x

xf ₂

= 10 GeV Q2

xuv

xdv

xS xg

0.2 0.4 0.6 0.8 1

HERA Structure Functions Working GroupJuly 2010

H1 and ZEUS Combined PDF Fit

Calculation of a cross section

•  Cross section is convolution of pdf’s and Matrix Element

23

§  Calculations are done in perturbative QCD

§  Possible due to factorization of hard ME and pdf s

§  Can be treated independently

§  Strong coupling (α

) is large

§  Higher orders needed

§  Calculations complicated

The Proton Composition

•  It’s complicated:

–  Valence quarks, Gluons, Sea quarks

•  Exact mixture depends on:

–  Q²: ~(M²+p_T²) –  Björken-x:

•  fraction or proton momentum carried by parton

•  Energy of parton collision:

The structure of an event: PDFs

Initially two beam particles are coming in towards each other. Normally each particle is characterized by a set of parton distributions, which defines the partonic substructure in terms of flavour composition and energy

sharing. This determines the energy of the interacting partons (x1, x2)

partonic x-section:

Incoming beams:

Parton Kinematics

§  Examples:

§  Higgs: M~100 GeV/c²

§  LHC: <x_p>=100/14000≈0.007

§  TeV: <x_p>=100/2000≈0.05

§  Gluino: M~1000 GeV/c²

§  LHC: <x_p>=1000/14000≈0.07

§  TeV: <x_p>=1000/2000≈0.5

pdf’s measured in deep-inelastic scattering

PDFs

•  Describe energy distribution of partons inside proton.

•  There are several PDF’s

parametrizations, determined by the data from ep

experiments at Hera or from Tevatron or fixed target.

•  u- and d-quarks dominate at large x, while gluons

dominate at low x.

Physics Cross Sections

Process M_X σ(LHC @ 7 TeV)

qq→W 80 GeV 3

qq→Z’_SM 1 TeV 50

gg→H 120 GeV 20

qq/gg →tt 2x173 GeV 15 gg → gg 2x400 GeV 1000

_ _

_ _ ^{101 102 103}

1 10 100

1000 ^{WJS 2010}

!qq

ratios of parton luminosities at 7 TeV LHC and Tevatron

luminosity ratio

M_X (GeV)

gg

MSTW2008NLO

From where do we know x?

The proton structure was investigated in the Deep Inelastic Scattering experiments:

Important role played in the past by: HERA ep collider at DESY Scattering of 30 GeV electron on 900 GeV protons :

→ Test of the proton structure up to 10

m

HERA ep acceleratore, 6.3 km of circumference

What are the results on the value of x?

QCD Approach: Quarks & Gluons

Parton Distribution Functions

Q² dependence predicted from QCD

Quark & Gluon Fragmentation Functions

Q² dependence predicted from QCD

Quark & Gluon Cross- Sections

Proton-Proton Collisions at the LHC

Elastic Scattering

σ _tot = σ _EL + σ _SD + σ _DD + σ _ND

1.8 TeV: 78mb = 18mb + 9mb + (4-7)mb + (47-44)mb

The Min-Bias trigger picks up most of the hard core The Non diffractive

component contains

σ _tot = σ _EL + σ _IN

Proton-Proton Collisions at the LHC

Elastic Scattering

σ _tot = σ _EL + σ _SD + σ _DD + σ _ND

σ _tot = σ _EL + σ _IN

•  Diffractive events typically produce particles in the very forward region

•  A large fraction of these events goes undetected

•  Characterised experimentally by large rapidity gaps

·•  

Cross Section Measurement

•  Luminosity: Number of incident particles per area per time (unit: cm^-2s^-1) –  Example: LHC design luminosity LHC: 10³⁴ cm^-2s^-1

•  Cross section equals number of events per time-integrated luminosity –  depends on particle and process type (unit: barn, 1 b = 10^-28m²)

Experimentally, we need to:

subtract background events

Number of Events

4 4 Background determination

Events

0 2000 4000 6000 8000 10000

12000 ^Data_VV

Non W/Z Single t DY

t t

Uncertainty = 8TeV, L = 5.3 fb-1

s CMS

channel µ±

e±

Jet multiplicity

1 2 3 ≥ 4

Obs/Exp _0.6

1 1.4

Events

0 2000 4000 6000 8000

Data VV Non W/Z Single t DY

t t

Uncertainty = 8TeV, L = 5.3 fb-1

s CMS

channel µ±

e±

b-jet multiplicity

0 1 2 ≥ 3

Obs/Exp _0.6

1 1.4

Figure 2: Jet multiplicity (left) in events passing the dilepton criteria, and (right) b-jet multi- plicity in events passing the full event selections but before the b-jet requirement, for the e^±µ^⌥ channel. In the right figure, the hatched bands show the total statistical and b-jet systematic uncertainties in the event yields for the sum of the tt and background predictions. The hatched bands in the left figure show only the total statistical uncertainty on the predicted event yields.

The ratios of data to the sum of the expected yields are given at the bottom.

4 Background determination

Backgrounds in this analysis arise from single-top-quark, DY and VV events, in which at least two prompt leptons are produced from Z or W decays. Other background sources, such as tt or W+jets events with decays into lepton+jets and where at least one jet is incorrectly re- constructed as a lepton (which mainly happens for electrons) or a lepton from the decay of bottom or charm hadrons (which mainly happens for muons), are grouped into the non-W/Z lepton category. Background yields from single-top-quark and VV events are estimated from simulation, while all other backgrounds are estimated from data.

The DY background is estimated using the “Rout/in” method [3, 4, 24] in which the events outside of the Z mass window are obtained by normalising the event yield from simulation to the observed number of events inside the Z mass window. The data-to-simulation scale factor is found to be 1.3±0.4 for the e^±µ^⌥ channel. This value is compatible with 1.5±0.5, which is estimated using a template fit as described in [4]. For the e⁺e and µ⁺µ channels the factors are found to be 1.7±0.5 and 1.6±0.5, respectively.

Non-prompt leptons can arise from decays of mesons or heavy-flavour quarks, jet misidentifi- cation, photon conversions, or finite resolution detector effects whereas prompt leptons usually

29

CMS arXiv:1312.7582

Number of Events: Cut and Count

Works if good separation of signal and background.

Advantage: simple & robust

Example: top pair production cross section measured in the di-lepton channel at LHC

8 7 Summary

corresponding to 5.3 fb ¹. The result obtained by combining the three final states is s_tt = 239±2 (stat.)±11 (syst.)±6 (lum.) pb, in agreement with the prediction of the standard model for a top-quark mass of 172.5 GeV.

Table 2: Number of dilepton events after applying the event selection and requiring at least one b jet. The results are given for the individual sources of background, tt signal with a top-quark mass of 172.5 GeV and stt =252.9 pb, and data. The uncertainties correspond to the statistical and systematic components added in quadrature.

Number of events

Source e⁺e µ⁺µ e^±µ^⌥

Drell–Yan 386±^{116 492}±^{148 194}±⁵⁸ Non-W/Z leptons 25±10 114±46 185±72 Single top quark 127±^{28 157}±^{34 413}±⁸⁸

VV 30±8 39±10 94±21

Total background 569±^{120 802}±^{159 886}±¹³⁰ tt dilepton signal 2728±^{182 3630}±^{250 9624}±⁵⁰⁴

Data 3204 4180 9982

Table 3: The total efficiencies etotal, i.e. the products of event acceptance, selection efficiency and branching fraction for the respective tt final states, as estimated from simulation for a top-quark mass of 172.5 GeV, and the measured tt production cross sections, where the uncertainties are from statistical, systematic and integrated luminosity components, respectively.

e⁺e µ⁺µ e^±µ^⌥

e_total(%) 0.203±0.012 0.270±0.017 0.717±0.033

s_tt(pb) 244.3±^5.2±^18.6±^{6.4 235.3}±^4.5±^18.6±^{6.1 239.0}±^2.6±^11.4±^6.2

Acknowledgments

We congratulate our colleagues in the CERN accelerator departments for the excellent perfor- mance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully ac- knowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we ac- knowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus);

MoER, SF0690030s09 and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF and WCU (Republic of Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mex- ico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS and RFBR (Russia); MESTD (Serbia); SEIDI and CPAN (Spain);

Swiss Funding Agencies (Switzerland); NSC (Taipei); ThEPCenter, IPST, STAR and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA).

Individuals have received support from the Marie-Curie programme and the European Re- search Council and EPLANET (European Union); the Leventis Foundation; the A. P. Sloan

8 7 Summary

corresponding to 5.3 fb ¹. The result obtained by combining the three final states is s_tt = 239±^{2 (stat.)}±^{11 (syst.)}±6 (lum.) pb, in agreement with the prediction of the standard model for a top-quark mass of 172.5 GeV.

Table 2: Number of dilepton events after applying the event selection and requiring at least one b jet. The results are given for the individual sources of background, tt signal with a top-quark mass of 172.5 GeV and s_tt = 252.9 pb, and data. The uncertainties correspond to the statistical and systematic components added in quadrature.

Number of events

Source e⁺e µ⁺µ e^±µ^⌥

Drell–Yan 386±^{116 492}±^{148 194}±⁵⁸ Non-W/Z leptons 25±^{10 114}±^{46 185}±⁷² Single top quark 127±^{28 157}±^{34 413}±⁸⁸

VV 30±^{8 39}±^{10 94}±²¹

Total background 569±^{120 802}±^{159 886}±¹³⁰ tt dilepton signal 2728±^{182 3630}±^{250 9624}±⁵⁰⁴

Data 3204 4180 9982

Table 3: The total efficiencies e_total, i.e. the products of event acceptance, selection efficiency and branching fraction for the respective tt final states, as estimated from simulation for a top-quark mass of 172.5 GeV, and the measured tt production cross sections, where the uncertainties are from statistical, systematic and integrated luminosity components, respectively.

e⁺e µ⁺µ e^±µ^⌥

e_total (%) 0.203 ± ^{0.012 0.270} ± ^{0.017 0.717} ±^0.033

s_tt (pb) 244.3 ± ^5.2 ± ^18.6 ± ^{6.4 235.3} ±^4.5 ± ^18.6± ^{6.1 239.0} ± ^2.6 ± ^11.4 ± ^6.2

Acknowledgments

We congratulate our colleagues in the CERN accelerator departments for the excellent perfor- mance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully ac- knowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we ac- knowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus);

MoER, SF0690030s09 and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF and WCU (Republic of Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mex- ico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS and RFBR (Russia); MESTD (Serbia); SEIDI and CPAN (Spain);

Swiss Funding Agencies (Switzerland); NSC (Taipei); ThEPCenter, IPST, STAR and NSTDA

t

ν ν l⁺ W⁺

b W^– t

b

q q'

~9% background

Data sample: 5.3fb^-1

Error: 5.4%

l- ν

Separation of signal and background

2 methods commonly used:

–  Side band fit

–  Template fit

40

σtt = 139 ± 10^stat ± 26^syst ± 3^lumi pb

Number of Events: Template Fits

Example: Top Quark Pair Production in all hadronic channel

•  Signature

–  6 or more jets –  2 b-tagged

•  Analysis

–  kinematic fit to reconstruct top mass –  background shape from b-untagged

data

•  Selected Sample

–  background is large (~75 %)

•  Measurement

–  Determine fraction of signal in sample from fit of signal plus background shapes to the data –  Correct for signal efficiency and

luminosity

20%

m(top)

4 5 Extraction of tt Signal

Table 1: Number of events and the expected fraction of tt events in the data for s_tt = 163 pb, following each consecutive selection. The expected tt fractions are taken from simulation.

Selection Events Fraction of tt At least 6 jets 786 741 0.02 At least two b-tags 21 783 0.18

Kinematic fit 3 136 0.41

2) (GeV/c mt

100 150 200 250 300 350 400 450 500 550 )2 Events / ( 10 GeV/c

0 50 100 150 200 250 300 350

0.025 = 0.351 ± fsig

CMS data: 3136 events component

t t

multijet background and multijet t

fit to t

= 7 TeV s

at CMS, 3.54 fb-1

Figure 1: Results of a fit of contributions from a MC tt component (dashed line) and MJ back- ground estimated from data (dotted line) to the distribution of the reconstructed top-quark mass in the data. The uncertainty in the signal fraction represents just the statistical uncer- tainty obtained from the fit.

5.1 Estimate of Background from Multijet Events

The background from multijet production is estimated from data containing =6 jets using the same criteria as detailed in Section 4 except for the b-tagging requirement (786 741 events, as indicated in Table 1). However, as properties of b-tagged and untagged jets differ, those events in this sample that do not have b-tagged jets are weighted to reproduce the distributions ap- propriate for b-tagged jets from MJ background in the b-tagged tt-candidate data sample. This is done through the jet-tag-rate ratio:

N(p_T,|^h|^{, d}B > 2)

7

Matching of parton showers to matrix elements: The threshold of the matching scale used for interfacing the matrix elements generated with M^ADG^RAPH and ^PYTHIA parton shower- ing in simulating tt events is changed from the default value of 20 GeV to 10 GeV and to 40 GeV, and propagated to s_tt.

Mass of the top quark: The influence of the value of m_t is estimated by shifting m_t in the tt simulation from the nominal 172.5 GeV/c² by ±^{0.9 GeV/c2}, the uncertainty in the currently accepted value of mt [32].

Pileup: The effect of pileup from simultaneous pp interactions is evaluated by superimposing additional minimum-bias events on the simulated signal (on average, ⇡8 observed in the data). To account for uncertainties associated with the measured total inelastic pp cross section, the mean number of observed interactions, and the weighting procedure, the average number of additional pileup events is changed by ±8%, and the impact of the changes extrapolated to s_tt.

Luminosity: The total integrated luminosity is determined with a precision of ±^{2.2% [33].}

An overview of the different uncertainties contributing to s_tt is given in Table 2. All uncertain- ties are reasonably symmetric around the mean value of s_tt. They are therefore averaged and presented as symmetrical excursions about the extracted value of s_tt. The total uncertainty is obtained by summing the individual uncertainties in quadrature.

Table 2: List of all non-negligible uncertainties contributing to the measurement of s_tt.

Source Relative uncertainty (%)

Jet energy scale 10.1

Background contribution 9.0

Tagging of b jets 6.0

Renormalisation and factorisation scale 5.8

Tune for underlying event 5.5

Trigger 5.0

Jet energy resolution 4.0

Matching matrix elements/parton showers 4.0

Mass of the top quark 2.1

Pileup 0.8

Total systematic 18.6

Total statistical 7.0

Luminosity 2.2

Total uncertainty 20.0

7 Results

The tt production cross section, as measured in the all-jet final state, is given by:

s_tt = ^fsig · ^N

e · ^{Lint , (3)}

where fsig is estimated from the fit in Fig. 1. The total number of candidate events is N = 3 136, as given in Table 1. The efficiency for selecting tt events as determined from simulation isε = 0.22%

Background estimate in DY:

side band fit

[GeV]

mee

60 70 80 90 100 110 120 130 140 150 160

Entries / GeV

0 2000 4000 6000 8000 10000

12000 ATLAS Preliminary

< 25 GeV ET

20 GeV <

< 0.6 0.1 < η

= 8 TeV

s ∫^{Ldt = 20.3 fb-1}

Data, all probes Background template

ee MC Z →

Expected (template + MC)

The Z->ee MC is scaled to match the total estimated signal yield in the Z-mass window.

Region to normalize background template

Efficiency and

Acceptance

Experimental Corrections

•  Factorization Ansatz:

•  Efficiency: selection of reconstructed signatures (detector response)

•  Acceptance: kinematic selection (phase space)

•  Branching ratio (if applicable)

Experimental corrections from data:

Tag & Probe

[GeV]

mee

1 2 3 4 5 10 20 30 100 200 1000

Entries / GeV

10-1

1 10 102

103

104

105

J/ψ

Υ Z

ATLAS Data 2010, s=7 TeV

∫^{Ldt≈40 pb-1}

2.5 3 3.5 4

104

105 J/ψ

ψ(2S)

Method:

select final state, e.g.:

Drell-Yan Z->ee, Z->µµ events J/Psi->ee, J/Psi->µµ events

W->eν

Require one particle (µ, e,ν) to be identified (“tag”)

Test  if  the  other  is  also  iden/fied  (“probe”)  

Example: ATLAS measured

Detector Efficiency

example: reconstruction of electrons in ATLAS

number of primary vertices

5 10 15 20 25 30

Efficiency

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

L dt = 20.3 fb-1

ee = 8 TeV Z s

ATLAS Preliminary > 15 GeV 2012

ET

Loose Multilepton Medium Tight

Cluster -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Reconstruction Efficiency

0.8 0.85 0.9 0.95 1 1.05

Reconstruction and track quality efficiency L dt = 4.7 fb-1

=7 TeV s 2011 data

2011 MC

L dt = 20.3 fb-1

=8 TeV s 2012 data 2012 MC

<50 GeV 15<ET

ATLAS Preliminary

efficiency between 80-97%

depending on detector region,

electron identification requirements,

electron energy and transverse momentum

Detector Acceptance

•  Experimentally accessible kinematic region is limited (can not measure very small p

and large η)

•  Measure in 'visible' range (‘fiducial’ volume)

•  Use theory to extrapolate into inaccessible phase space

47

“Visible” or “fiducial” Cross Section

Example: ttbar+jets from ATLAS:

Measure additional jets in top pair production

•  Limits theory dependent corrections

•  Particularly important for measurements with large uncertainties on the theoretical predictions

(a) q! qg (b) g! gg

(c) g! q ¯q

Figure 1.7: Leading-order (1! 2) Feynman diagrams for the splitting of quarks and gluons. Examples are shown for a quark emitting a gluon (a), a gluon emitting another gluon (b), and a gluon splitting into a quark-anti-quark pair (c).

15

(a) quark-quark (b) quark-anti-quark

(c) gluon-gluon

Figure 1.5: Leading-order (2! 2) Feynman diagrams for jet production in proton-proton scattering at the LHC. Examples are shown for quark-quark t-channel scattering (a), quark-anti-quark s-channel annihilation (b), and gluon-gluon t-channel scattering (c).

(a) Virtual loop (b) Real emission

Figure 1.6: Two types of NLO Feynman diagrams for jet production, the first being a 2! 2 diagram with a virtual loop (a) and the second being a 2 ! 3 diagram where the third outgoing parton is produced via real emission from another parton (b).

13

q_i q_j

g g α_s(Q₁) α_s(Q₂)

•  Compare with theory in form of MC models in same kinematic range

•  Calculations in limited phase space are generally more difficult

•  Provide information such that extrapolations to the full phase space can

Branching Ratio

Example: top quark pairs

all-hadronic

electron+jets electron+jets muon+jets

muon+jets

tau+jets

tau+jets

eµ ^eτ eτ µτ

µτ ττ

e⁺ µ⁺ τ⁺ ud cs e– cs udτ– µ–

Top Pair Decay Channels

W decay

eµ ee

µµ

dileptons

W decay universal e:µ:τ:jets ~ 1:1:1:6

l=e, µ t->Wb to almost 100%