Florian Fischer

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Florian Fischer

Ludwig-Maximilians-Universität München – LS Schaile –

TAE 2019 - COST International Training School on High Energy Physics

– Benasque, September 12

^th

, 2019 –

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Physics Motivation:

t¯t Za rare Standard Model (SM) process Measurement of cross section a stringest test of Standard Model

Sensitivity to physics beyond Standard Model (BSM) t¯t Zan important background for several LHC analyses

t¯t H,t¯t t¯t+ other rare SM processes

Several BSM searches including variety of SUSY signatures, flavour-changing neutral-current processes (FCNC), . . .

⇒ Improved knowledge oft¯t Zprocess can lead to improvements in many analyses

g

g t

¯ t Z

q ¯

q t

¯ t

Z

Florian Fischer (LMU München) TAE 2019 – Benasque September 12, 2019 1 / 14

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Inclusivet¯t Zcross section measurement for decay channels with 3 and 4 leptons in final state

Successful measurements of inclusive cross section already performed by ATLAS & CMS experiments at centre-of-mass energy

√ s=13TeV

Very good agreement with theoretical prediction (cf.1609.01599,1711.02547,1901.03584) Perform unfolded differential cross section measurements as functions of kinematic variables

Will allow to further probe the top-Zcoupling of the Standard Model

Unfolding: extrapolate measurements to fiducial detector volume and full generator phase space

⇒ Correct for detector effects as well as signal acceptance & efficiency w.r.t given phase space region

⇒ Directly compare measurements with theory and other experiments

Employing the LHC 2015-2018 “Run 2” dataset taken at ATLAS experiment corresponding to 139 fb⁻¹

g

g t

¯ t Z

q ¯

q t

¯ t

Z

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[1]

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[2]

ATLAS

Largest detector ever constructed at a particle collider General-/multi-purpose detector

Many-layer design with nearly cylindrical symmetry

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[2]

[3]

Inner Detector

Charged particle track measurement

→Charge & momentum Layers of silicon pixels and strips

Tiny gas-filled drift tubes

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[2]

[3] [4]

'

&

$

%

Calorimeters

Particle energy measurement 2 sampling calorimeters:

→electromagnetic

→hadronic

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[2]

[3] [4] [5]

'

&

$

%

Muon Spectrometer

Muon track measurement

→Charge & momentum Contains 4 different detector types Same principle as for inner detector

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[2]

[3] [4] [5]

Magnet System

2 magnetic fields with different orientation, created by

→Solenoid magnetfor inner detector

→Toroid magnetfor muon measurement

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Coordinate System

Right-handed, interaction point as centre Azimuthal angleϕin transverse plane Separation from beam line via polar angleθ Instead, often use pseudorapidity

η=−ln

tan θ

2

y (upwards)

x

(LHC ring centre)

z (LHC beam line)

θ φ η

[6]

Object Features

Leptons appear as distinct objects (tracks &

calorimeter clusters)

Colour-charged particles hadronise to cone-shaped showers of uncoloured particles⇒Jets(reconstructed by anti-k_t algorithm [7])

Neutrinos leave detector unseen, only reconstructable via energy- and momentum conservation in transverse plane

E^miss_T =

−X i

~ p_T,i

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Signature:

2 jets fromb-quarks (“b-jets”) 2 jets from light quarks (u,d,c,s) 3 charged light leptons (e,µ) 1 neutrino

Dominant backgrounds:

WZ,tWZ,tZq, fake leptons

Branching:2.3 %

¯t

¯b W⁻

ν¯_l⁰

t Z

l⁻ l⁺

b

W⁺

¯ q⁰ q

⇒Requiring≥3jets,≥2b-jets and exactly 3 leptons

Event Reconstruction

Motivation:

Better probe of underlying top quark kinematics

Allow for several sensitive differential variables

Strategy:

Onlypartial reconstructionof signal signature

Focus on top quark withsubsequent leptonicW-decay(“leptonic-side”)

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Require only≥2 jets

Consider 2 leptons of opposite charge and same flavour with an invariant mass best consistent withZboson mass to beZdecay products Assume neutrino fromW-decay to be predominant source of missingtransverse energy

ApplyWmass constraint: m_l^±_ν≡m_W

→2 neutrinop_zsolutions from quadr. eq.

Consider both solutions and combine with either of 2b-jets

Assign output weight to reconstructed top quark candidates based on interpolated value from:

m_jlνdistribution Invariant mass distribution of correctly reconstructed top quarks in simulatedt¯t Zevents MC generator-level neutrino

Reconstructed lepton and jet (MC)

⇒ Only consider top quark candidate with maximum output weight per event

y

x z

b1?

b₂? E_T^miss

ν

`^± mW

m_jlνdistribution

Plot kindly provided by T. McCarthy (MPI Munich)

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0 100 200 300 400 500 600 700 800 900 1000 blν M 0

0.2 0.4 0.6 0.8 1

(Scaled to Same Peak Height)Normalised Entries / 25 GeV

tWZ tZq WZ

=13 TeV s

3j 3l-Z-2b≥

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

blν W 0

0.2 0.4 0.6 0.8 1 1.2

(Scaled to Same Peak Height)Normalised Entries / 0.02

Z t t tWZ tZq WZ (80.0% Signal Efficiency)

> 0.021 blν W

ATLASWork in Progress Simulation

=13 TeV s

3j 3l-Z-2b≥

backgrounds by setting cut on resulting distribution, e.g. at80 % signal efficiency Focus on minimisation of signal and background uncertainties as they enter both the inclusive and the differential cross section measurement Note:inclusive cross section measured with fit, use calculation to estimate effect of cut

Cross Section Calculation

Estimate uncertainties with cross section formula

σ_t^obs_¯_tZ = N_t^obs_¯_tZ

L · BR ·ε_t¯tZ , N_t^obs_¯_tZ ≡NData−N_Bkg^MC

Withε_t¯tZas the fraction of selected reconstructed MC eventsN_t^MC_¯_tZamong the total number of generated events, the formula for the observed cross section becomes

σ_t^obs_¯_tZ =N_t^obs_¯_tZ N_t^MC_¯_tZ

·σMC=σ_t^obs_¯_tZ(NData,N_Bkg^MC,N_t^MC_¯_tZ)

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70 75 80 85 90 95 Signal efficiency [%]

9.4 9.6 9.8 10 10.2 10.4 [%]σ / σ∆ 10.6

blν Cut on W No Cut ATLAS Work in Progress

Simulation

=13 TeV

s Full systematic (detector, theory) and

statistical uncertainties applied Minimum uncertainty on cross section at signal efficiency of 84 %

⇒ Most dominantWZbackground reduced by 42 %

Values scattered in range of only 0.8 % However, certain trend towards minimum noticable

Relative cross section uncertainty:

∆σ

σ = 1

NData−N_Bkg^MC

· vu ut

(∆N_Data)²+

∆N_Bkg^MC2 +







NData−N_Bkg^MC N_t^MC_¯_tZ





 2

∆N_t^MC_¯_tZ2

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Inclusive and di ff erential measurement of t ¯ t Z cross section with full LHC Run 2 dataset taken by ATLAS Performed partial reconstruction of t ¯ t system to exploit top quark kinematics restricting to top quark with subsequent leptonic W decay

Used relative cross section uncertainty as measure to find optimum cut value on reconstruction output weight Minimised uncertainties entering inclusive t ¯ t Z cross section measurement by setting a cut at certain signal e ffi ciency

For differential measurement applying cut might get very harmful to precision due to reduced data statistics

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(p_`+p_ν)²=m_W²

Expanding the left-hand side

p_`²+p²_ν+2p_`·p_ν=m_W²

E_`E_ν−~p_`·~p_ν=m_W²−m²_` 2 E_`E_ν−p_`xp_νx−p_`yp_νy−p_`zp_νz=m_W²−m²_`

2 Treating the neutrino as massless (E²=p²

T+p_z²), and with polar coordinates

q

p_Tν² +p_νz²E_`=m_W²−m²_` 2 +p_Tν

p_`xcosφ_ν+p_`ysinφ_ν +p_`zp_νz

Squaring and definingα≡^m 2 W−m2

2 ` +p_Tν

p_`xcosφ_ν+p_`ysinφ_ν

p²_Tν+p²_νz

E_`²=α²+2αp_`Zp_νz+p_`z²p_νz²

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Collecting the terms in powers ofp_νz

Ap_νz² +Bp_νz+C=0

With

A=E_`²−p_`z² B=−2αp_`z C=p_Tν² E_`²−α² If discriminantB²−4AC>0, two real solutions can be evaluated

p_νz,1/2=−B±

√ B²−4AC 2A

In case of no real solution, two options exist:

SmearingE_T^missuntil discriminat becomes positive again Find value ofp_Tνsuch thatB²=4AC

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σ_t¯^obs_{t Z}=

N_Data−N_Bkg^MC L · BR ·εt¯t Z where the product of signal acceptance and efficiency can be written as

εt¯t Z= N_t¯^MC_{t Z} σ_MC· L · BR

The Monte Carlo have been produced inclusively int¯tdecay so that only theZbranching fraction matters. The Monte Carlo production cross sectionσ_MCincluded also higher order calculations.

Together with the number of observed eventsN_t¯^obs_{t Z}≡N_Data−N_Bkg^MCthe cross section formula can be rewritten:

σ_t^obs_¯_{t Z}=N^obs t¯t Z N_t¯^MC_{t Z}

|{z}

µt¯t Z

·σMC

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With Gaussian error propagation

∆y(x_i) = vu t

X

i

∂y

∂xi∆x_i

!2

the error on the cross section evaluates to

∆σ= vu uu uu t



 σ_MC N_t¯^MC_{t Z}∆N_Data





 2

+





 σ_MC N_t¯^MC_{t Z}∆N_Bkg^MC





 2

+





 N_Data N_t¯^MC_{t Z}2σ_MC





 2

∆N_t¯^MC_{t Z}2

=σ_MC N_t¯^MC_{t Z}

vu uu t

(∆N_Data)²+

∆N_Bkg^MC2 +







N_Data−N_Bkg^MC N_t¯^MC_{t Z}





 2

∆N_t¯^MC_{t Z}2

Hence, the relative uncertainty on the cross section can be written as

∆σ σ =

vu t

(∆N_Data)²+

∆N_Bkg^MC2 +







NData−NMC Bkg NMC

t¯t Z





 2

∆N_t¯^MC t Z 2

N_Data−N_Bkg^MC

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Select events featuring characterisitcs of signal signature

Possibly perform reconstruction to better probe underlying kinematics Get total cross section inclusive in by

Calculating according to a certain formula

Performing a fit (single or multiple bins) to extract signal strength Differential Approach:

Measure cross sections as functions of certain variables

Unfold detector-level distributions of variables to particle- and parton level, respectively

Correction of detector effects, as well as signal acceptance and efficiency w.r.t. given phase space region dσ

dXⁱ = 1

L · BR ·∆Xⁱ·f_accⁱ X

j

R_ij⁻¹·_eff^j ·

N_Data^j −N_Bkg^j

withithe bin index of observableXⁱwith bin width∆Xⁱ. Background contribution estimated from Monte Carlo,N_Bkg^j , is subtracted from observed data,N_Data^j , providing estimated observed signal in binj.

Correction terms:eff=N^reco^∧^truth/N^reco, f_acc=N^reco^∧^truth/N^truth

Inversion of response matrixRdone iteratively by applying repeatedly Bayes’ theorem:

Fold:x^(k_i ⁾=P jR_ijµ^(k)_j Unfold:µ^(k_j ⁺¹⁾=¹

i P

iR_ijµ^(k_j ⁾





 xi x(k)

i





 Updating guess by applying Bayes:

µˆ_i=_i¹P

jP(generated in bini|observed in binj)n_j=_i¹P j

_{Rij pi} P

k Rjk pk

n_j

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tWZ :

g

b¯ t→(W⁺→`⁺ν_`)b

Z→`⁺`⁻

W⁺→`⁺ν`

tZq:

q

g

¯b t→(W⁺→`⁺ν_`)b

Z→`⁺`⁻ q⁰

WZ :

¯ q⁰

q

W⁺→`⁺ν_`

Z→l⁺l⁻ b

¯b

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CERN - Août 2018”.General Photo. 2018.url:http://cds.cern.ch/record/2636343.

[2] Joao Pequenao.“Computer generated image of the whole ATLAS detector”.2008.url: http://cds.cern.ch/record/1095924.

[3] Joao Pequenao.“Computer generated image of the ATLAS inner detector”. 2008.url: http://cds.cern.ch/record/1095926.

[4] Joao Pequenao.“Computer Generated image of the ATLAS calorimeter”.2008.url: http://cds.cern.ch/record/1095927.

[5] Joao Pequenao.“Computer generated image of the ATLAS Muons subsystem”. 2008.url: http://cds.cern.ch/record/1095929.

[6] Joao Pequenao.“Event Cross Section in a computer generated image of the ATLAS detector.” 2008.url:https://cds.cern.ch/record/1096081.

[7] Matteo Cacciari, Gavin P. Salam, and Gregory Soyez.“The anti-k_tjet clustering algorithm”.

In:JHEP04 (2008), p. 063.doi:10.1088/1126-6708/2008/04/063. arXiv:0802.1189 [hep-ph].