Measurement of the quadruple-differential angular decay rates of single top quark produces in the t-channel at TeV s =13

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Measurement of the quadruple-differential angular decay rates of single top quark produces in the t-channel at s = 13 TeV

@FlipPhysics workshop

Mar 23, 2022

Mariam Chitishvili

Instituto de Física Corpuscular (IFIC) - CSIC/UV

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@Flip Physics 2022

Mariam Chitishvili

Introduction to top-quark physics

Unique properties of the top quark:

• Heaviest known elementary particle

• Strongest Yukawa coupling (almost unity)

• Smallest cross-section of all of the SM particles

• Short lifetime (τt ~ 5 · 10^-25 s) → top-quark decays into high pT particles before hadronizing

• Only quark whose most of its properties can be directly measured!!!

• The top quark decays almost exclusively (>99%, i.e. |Vtb| ≈ 0.999) to t → Wb (@LO)

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The top quark was discovered by the Tevatron experiments, CDF and D0, at Fermilab in 1995

• Tevatron Run-II (10³² cm^-2 s^-1 @ 1.96 TeV): ~2 top-quark pairs (tt̄) every hour The LHC is a top quark factory:

• At low luminosity (i.e. 10³² cm^-2 s^-1 @ 7 TeV): ~60 tt̄ every hour

• At design luminosity (i.e. 10³⁴ cm^-2 s^-1 @ 14 TeV): ~8 tt̄ every second

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At hadron colliders, top quarks are produced:

• Predominantly in pairs (tt̄) via the flavor-conservation strong interaction

• The tWb vertex can be probed only through the top-quark decay

• Top quarks are produced unpolarised because of parity conservation in QCD

• Alternatively, singly through the EW interaction

• The tWb vertex can be studied in both the production and the decay

• Top quarks are produced highly polarised due to V-A nature

• Lifetime (~10^-25 s) ≪ depolarization timescale (~10^-21 s)

• Only source of polarised top quarks!

• The decay products preserve the spin information of the top quark

→ accessible via angular distributions (in top-quark rest frame)

• Single top-quark production rates are lower but comparable with tt̄ production rate

• Production modes are sensitive to new physics!

• t-channel is the dominant process at LHC

Top quark production

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t-channel

s-channel tW

Top quarks predominantly decay through the EW interaction to an on-shell W boson and a b-quark

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4

Single top-quark t-channel process

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The degree of the polarisation in each axis depends on the mixture of the leading and subleading processes

Top quarks

Top antiquarks

t-channel

Polarised along spectator quark Polarised along the beam axis dominant sub-process

Peculiarities of the t-channel single top-quark process polarisation:

• Due to the fact that the valence u-quark density of the proton is about twice as high as the valence down-quark density → top quarks vs. top antiquarks in t-channel:

‣ Different cross-sections

‣ Different background levels (S/B)

‣ Different subprocesses

‣ Different polarisations

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@Flip Physics 2022

Peculiarities of the t-channel single top-quark process polarisation:

• Due to the fact that the valence u-quark density of the proton is about twice as high as the valence down-quark density → top quarks vs. top antiquarks in t-channel:

‣ Diﬀerent cross-sections

‣ Different background levels (S/B)

‣ Different subprocesses

‣ Diﬀerent polarisations

Production cross-section of single top quarks is about twice as high as the cross-section of top-antiquark production

Eur. Phys. J. C 77 (2017) 531

Phys. Rev. D89 (2014) 114009 top-quark rest frame

Single top-quark t-channel process

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• φ, θ are spherical coordinates of the W boson momentum in the top quark rest frame

• φ^*, θ^* spherical coordinates of the charged lepton momentum in the W boson rest frame

• Top quark → Lifetime (~10^-25 s) ≪ depolarization timescale (~10^-21 s) → decay products preserve the spin information of the top quark → accessible via angular distributions (in top-quark rest frame)

• The top-quark decay differential distribution is determined by four angles (Eur. Phys. J. C77, 200 (2017)):

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Full description of the single top-quark decay

Quantum mechanics:

• The fully differential decay rate can be written analytically by applying the helicity formalism of Jacob and Wick to polarised top quarks in the t-channel production, considering the transition amplitudes (in the narrow width approximation)

• The angular dependence of the amplitude for two-body decay (t → Wb → lν) is

Wigner D-function Transition amplitudes

(written as a in the next slides)

arXiv:1304.5639 [hep-ex]

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• φ, θ are spherical coordinates of the W boson momentum in the top quark rest frame

• φ^*, θ^* spherical coordinates of the charged lepton momentum in the W boson rest frame

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Helicity fractions

tt̄ Single top quark

|t>

|WLbL>

|W0bL>

|W0bR>

|WRbR>

FL

FR

F0

a-1,-1/2

a0,-1/2

a0,+1/2

a+1,+1/2

}

☞

☞ FL

F0-

FR

F0+

}

^δ⁻

δ

₊

Transition amplitudes

69%

30%

Quantum mechanics:

Full description of the single top-quark decay

• Top quark → Lifetime (~10^-25 s) ≪ depolarization timescale (~10^-21 s) → decay products preserve the spin information of the top quark → accessible via angular distributions (in top-quark rest frame)

• The top-quark decay differential distribution is determined by four angles (Eur. Phys. J. C77, 200 (2017)):

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Quadruple-differential (θ, φ, θ*, φ*) decay rate of (polarised) top quarks using single top quark events:

• Where are transition amplitudes for W boson and b-quark helicities

• Normalized such that

a

_λ_w_,λ_b

λ

_w

, λ

_b

| a

_1,¹₂

|

²

+ | a

_−1,−¹₂

|

²

+ | a

_0,¹₂

|

²

+ | a

_0,−¹₂

|

²

= N

30%

Full description of the single top-quark decay

Eur. Phys. J. C77, 200 (2017)

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Finite series of orthonormal functions (generally named M-functions) that in case of

four angles are based on Wigner D functions

Angular coefficients to be determined

First analysis aiming a full and simultaneous description of the tWb structure!!!

• Constrain of the full space by performing a global fit to simultaneously extract:

• Five generalized W boson helicity fractions

• Two phases (relative phases can only be measured with polarised top quarks)

• The polarisation in three orthogonal directions of the produced top quark (introduced in PRD89 (2014) 114009)

• (Hopefully, also) t-channel production cross-section

Measurement of the full top-quark decay

Eur. Phys. J. C77, 200 (2017)

= ∑

j₁j₂m′m

c_m′^j¹^j_m² M_m′^j¹^j_m²(ϕ,θ,ϕ*,θ*)*

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Measurement of the full top-quark decay

Eur. Phys. J. C77, 200 (2017)

Finite series of orthonormal M-functions

24 angular coefficients to be determined

Because of the orthonormality of the M functions, the different coefficients can be determined by projecting the differential distribution

1

Γ dΓ

dΩdΩ* = ∑

j₁j₂m′m

c_m′^j¹^j_m² M_m′^j¹^j_m²(ϕ,θ,ϕ*,θ*)*

10

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Measurement of the full top-quark decay

Because of the orthonormality of the M functions, the different coefficients can be determined by projecting the differential distribution

Extremely challenging analysis!!!

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Previous analyses

Triple-differential (θ, θ^∗, φ^∗) decay rate in the t-channel (20.2 fb^-1, 8 TeV) (JHEP 12 (2017) 017)→ M-functions become spherical harmonics!

• Determined simultaneously, including all correlations

• Detector effects are deconvoluted from data by measuring differential rates using Fourier techniques (OSDE)

• Distributions (profiles and contours) are obtained from numerical calculations of a unique likelihood function

Interpretation in terms of EFT

• Overall normalisation (VL) set by cross-section measurements

• Limits are placed simultaneously on complex values of the ratio of the anomalous couplings

• No assumptions on values of the other anomalous couplings

• Dominant systematics: signal modelling, Jet Energy Scale and data statistics

• In agreement with SM predictions

Re[gR]/VL ∈ [−0.12, 0.17] @ 95 CL Im[gR]/VL ∈ [−0.07, 0.06] @ 95 CL

|V_R/V_L| < 0.37 @ 95 CL

|g_L/V_L| < 0.29 @ 95 CL Pz > 0.72 @ 95 CL

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1.5 1 0.5 0 0.5 1 1.5 1.5

1 0.5

0 0.5 1 1.5

ATLAS

=13 TeV, 139 fb-1

s

top antiquark

top quark

best Fit

68% CL stat. only 68% CL stat.+syst.

NNLO SM Prediction

Pz'

Px'

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Previous analyses

Diﬀerential cross-section measurements (θ; but different projections) for Px, Py and Pz carried out

separately for top quark and top antiquarks at particle level in a fiducial region (arXiv:2202.11382 [hep-ex])

0.81 1.2

Pred./Data

0.3 0.4 0.5 0.6 0.7 0.8 0.9

lx'dcos d tot1

ATLAS

= 13 TeV , 139 fb-1

s

DataStat. only uncertainty Stat.+Syst. uncertainty Powheg-Box+Pythia8 Protos+Pythia8 MG5_aMC@NLO+Pythia8 Powheg-Box+Herwig7

Parameter Extracted value (stat.) t-channel norm. +1.045±0.022 (±0.006) W+ jets norm. +1.148±0.027 (±0.005) tt¯norm. +1.005±0.016 (±0.004) P_x^t0 +0.01 ±0.18 (±0.02 ) P_x^t^¯0 0.02 ±0.20 (±0.03 ) P_y^t0 0.029±0.027 (±0.011) P_y^t^¯0 0.007±0.051 (±0.017) P_z^t0 +0.91 ±0.10 (±0.02 ) P_z^t^¯0 0.79 ±0.16 (±0.03 )

First measurement of the full polarisation vector {Px,Py,Pz} for top quark and antiquark separately in the t-channel (139 fb^-1, 13 TeV) (arXiv:2202.11382 [hep-ex]) → θ (but different projections)

• Results interpreted within an EFT framework to manifest possible deviations from the SM

Submitted to JHEP

• Dominant systematics: Jet Energy Resolution and signal modelling

• In agreement with theoretical and SM predictions

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Analysis of the Quadruple-differential (θ, φ, θ^∗, φ^∗) decay rate in the t-channel (139 fb^-1, 13 TeV) being performed nowadays!!!

• Previous experience has been crucial and now working on the necessary improvements:

• Event selection being optimized trying to reduce the dominant systematics

• Top-quark reconstruction is very important (KLFitter-based reconstructions with custom transfer functions for our phase space)

• Fakes estimation for the best background selection

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Measurement of the full top-quark decay

• Carefully studying the dependence of the angular distributions with different EFT coefficients for the t-channel signal process and for tt̄ (main) background process

0 1 2 3 4 5 6

phi_star

0.850.80.9 0.951 1.051.1 1.151.2

ratio

0 1 2 3 4 5 6

phi_star 0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

0.2 MADGRAPH LO

MADGRAPH ctW=2 MADGRAPH ictW=1.5

Simulation ATLAS

= 13 TeV, 139 fb-1

s

0 1 2 3 4 5 6

phi

0.850.80.9 0.951 1.051.1 1.151.2

ratio

0 1 2 3 4 5 6

phi 0

0.02 0.04 0.06 0.08 0.1

0.12 MADGRAPH LO

MADGRAPH ctW=2 MADGRAPH ictW=1.5

= 13 TeV, 139 fb-1

s

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

cos_theta_star

0.850.80.9 0.951 1.051.1 1.151.2

ratio

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 cos_theta_star 0

0.05 0.1 0.15

0.2 0.25

MADGRAPH LO MADGRAPH ctW=2 MADGRAPH ictW=1.5

= 13 TeV, 139 fb-1

s

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

cos_theta

0.850.80.9 0.951 1.051.1 1.151.2

ratio

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 cos_theta 0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

MADGRAPH LO MADGRAPH ctW=2 MADGRAPH ictW=1.5

= 13 TeV, 139 fb-1

s

ATLAS Simulation Work in progress ATLAS Simulation Work in progress

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Analysis of the Quadruple-differential (θ, φ, θ^∗, φ^∗) decay rate in the t-channel (139 fb^-1, 13 TeV) being performed nowadays!!!

• Previous experience has been crucial and now working on the necessary improvements:

• Event selection being optimized trying to reduce the dominant systematics

• Top-quark reconstruction is very important (KLFitter-based reconstructions with custom transfer functions for our phase space)

• Fakes estimation for the best background selection

Measurement of the full top-quark decay

• Carefully studying the dependence of the 24 angular coefficients (cj1j2m’m) (Eur. Phys. J. C77, 200 (2017)) with different MC generators and EFT coefficients

• Also doing this for the dominant background (tt̄) as will impact some of the EFT coefficients being considered

ATLAS work in progress

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• Top quark has unique properties!

• The LHC gives the best opportunities to use it to test the SM and as a window for new physics

• t-channel production allows to use the single top-quark decay product to exploit spin information

• The analysis of the quadruple-differential angular decay of single top quark in t-channel is the most complete study of the top quark properties that will be performed so far (based on Eur. Phys. J. C77, 200 (2017))

• This challenging analysis has become now possible because of the novel model-independent framework (proposed in arXiv:1304.5639 [hep-ex] and Eur. Phys. J. C77, 200 (2017)) and the necessary and important experience gained in previous analyses:

• Triple-differential analysis: JHEP 12 (2017) 017

• Polarization analysis: arXiv:2202.11382 [hep-ex] (submitted to JHEP)

• Quadruple-differential analysis research has newly started !!!

• Some of preliminary studies have been shown and presented here but stay tune for more!

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Conclusions

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BACKUP

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Top-quark production:

• Predominantly in pairs via flavour-conserving strong interaction

• Alternatively, singly through the EW interaction in involving a vertex

• At the LHC, in proton–proton (pp) collision data, the t-channel is the dominant process

• In the process vertex can be studied in the production and the decay, using same effective couplings

(tt¯)

Wtb Wtb

t-channel

ℒ

_eff

= ℒ

_SM

+ ∑

i

c

_i

Λ

²_NP

𝒪

^(dim=6)_i

+ . . .

‣

Effective Lagrangian describing Wtb transition:

Where are eﬀective operators, are dimensionless coeﬃcients and is a new physics scale.

‣ The most general effective Wtb interaction arising from the addition of dimension-six operators to the SM Lagrangian can be parameterised as

𝒪

_i

c

_i

Λ

_NP

18

ℒ_Wtb = − g

2 b¯γ^μ(V_LP_L + V_RP_R)tW_μ⁻ − g

2 b¯ iσ^μνq_ν

M_W (g_LP_L + g_RP_R)tW_μ⁻ + h .c.

‣ Where the four non-renormalisable effective complex couplings called anomalous couplings . They can be measured by different top-quark related properties

V_R, V_L, g_R, g_L

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4-angle analysis

Introduction:

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The top quark is the heaviest known elementary particle.

At hadron colliders, top quarks are produced:

• Predominantly in pairs (tt̄) via the flavour-conserving strong interaction.

The top quark was discovered by CDF/D0 at Tevatron in 1995 in tt̄ events.

• The single top-quark production was discovered in 2009 by CDF/D0 and observed in 2011 by ATLAS/CMS.

• Alternatively, singly through the electroweak interaction.

90% (13 TeV, pp) 10% (13 TeV, pp)

t-channel (~73% at LHC) tW (~24% at LHC) s-channel (~3% at LHC)

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30%

20

3 independent helicity fractions

4 phases of the interference terms separately for top quarks and antiquarks

6 Polarization components for top quarks and antiquarks

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Parametrization of a decay

= F₀⁺ + F₀⁻

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• are angular coefficients to be determined

• In 4-angle analysis M functions are defined by Wigner D functions

• While in 3-angle analysis they were defined by spherical harmonics

c

_m^j¹

, c

_m^j²

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M function

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22

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Previous analyses

Diﬀerential cross-section measurements (θ; but different projections) for Px, Py and Pz carried out

separately for top quark and top antiquarks at particle level in a fiducial region (arXiv:2202.11382 [hep-ex])

1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 cos lx'

0.81 1.2

Pred./Data

0.3 0.4 0.5 0.6 0.7 0.8 0.9

lx'dcos d tot1

ATLAS

= 13 TeV , 139 fb-1

s

DataStat. only uncertainty Stat.+Syst. uncertainty Powheg-Box+Pythia8 Protos+Pythia8 MG5_aMC@NLO+Pythia8 Powheg-Box+Herwig7

Parameter Extracted value (stat.) t-channel norm. +1.045±0.022 (±0.006) W+ jets norm. +1.148±0.027 (±0.005) tt¯norm. +1.005±0.016 (±0.004) P^t_x0 +0.01 ±0.18 (±0.02 ) P^t_x^¯0 0.02 ±0.20 (±0.03 ) P_y^t0 0.029±0.027 (±0.011) P_y^t^¯0 0.007±0.051 (±0.017) P_z^t0 +0.91 ±0.10 (±0.02 ) P_z^t^¯0 0.79 ±0.16 (±0.03 )

0 1 2 3 4 5 6 7

Q+

0.96 0.98 1 1.02

Data / Pred.

0 5000 10000 15000 20000 25000

Events ATLAS

= 13 TeV, 139 fb-1

s

Signal Region top quark Post-Fit

Data t-channel

, tW, s-ch

tt W+jets

Z+jets, VV others Multijet Uncertainty

First measurement of the full polarisation vector {Px,Py,Pz} for top quark and antiquark separately in the t-channel (139 fb^-1, 13 TeV) (arXiv:2202.11382 [hep-ex]) → θ (but different projections)

• Results interpreted within an EFT framework to manifest possible deviations from the SM

Best limits so far from high-energy experiments!

Submitted to JHEP

• Dominant systematics: JER and signal modelling

• In agreement with theoretical and SM predictions