Probing the Wtb vertex structure in top-quark production and decay with the ATLAS detector

Probing the Wtb vertex structure in top-quark production and

decay with the ATLAS detector

C. Escobar on behalf of the ATLAS Collaboration

Instituto de Física Corpuscular (IFIC) - CSIC/UV

Santander — October 23-25, 2017

Wtb vertex at production and decay

In top-quark pair production, the Wtb vertex can be probed through the top-quark decay.

• Top quarks are produced unpolarised.

In single top-quark production, the Wtb vertex can be studied in both the production and the decay.

• Three production mechanisms (@ LO):

t-channel

s-channel Wt

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

tt̄

• Production modes sensitive to new physics.

At hadron colliders, top quarks are produced:

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

• Alternatively, singly through the EW interaction.

L = − g

√ 2

¯ bγ

V

P

tW

+ h.c.

L

= − g

√ 2 bγ

(V

P

+ V

P

) tW

− g

√ 2 b iσ

q

m

(g

P

+ g

P

) tW

+ h.c., L = − g

√ 2

¯ bγ

V

P

tW

+ h.c.

Wtb vertex structure

In SM, the Wtb vertex has a V-A structure, described by the Lagrangian:

where Vtb is the CKM matrix element.

where VL = fLV Vtb is the left-handed vector coupling.

• Considering t→bW being, by far, the dominant top-quark decay (CKM matrix element Vtb~1).

Experimental cross-section measurements usually assume a SM-like V-A structure for the Wtb vertex.

New physics at the Wtb vertex can be described by an effective Lagrangian, which modifies the structure of the Wtb vertex, presented either by dimension-six operators in the EFT framework or by four non-renormalisable effective complex couplings called anomalous couplings:

where VR, gR and gL are the (complex) anomalous couplings.

Imaginary parts related with CP violation!

• fLV is a model-independent left-handed form factor, assumed to be real, that encapsulate non-SM contributions.

L

= − g

√ 2 bγ

(V

P

+ V

P

) tW

− g

√ 2 b iσ

q

m

(g

P

+ g

P

) tW

+ h.c., L = − g

√ 2

¯ bγ

V

P

tW

+ h.c.

How to probe the Wtb vertex structure?

These anomalous couplings can be probed by measuring different top-quark related properties:

• W boson polarisation (and related observables) in top-quark decays (either tt̄ or single top quark).

• Single top-quark production and decay observables (angular distributions, etc).

• Indirect limits from B-physics (rather model dependent).

The left-handed vector coupling VL can be measured from:

• Directly from single top-quark production cross-section measurements since they are proportional to the square of VL coupling at the Wtb production vertex.

• Indirect measurements from branching ratio measurements in tt̄ production (rather model dependent).

SM-like V-A structure for the Wtb vertex:

Non-SM V-A effective structure for the Wtb vertex:

• where fLV is a model-independent left-handed form factor, assumed to be real, that encapsulate non-SM contributions.

• In SM, the |VL| = |Vtb| ~ 1 with fLV = 1.

| V

| ≡ | f

V

| =

! σ

σ

Summary of single top-quark production cross-section

Production cross-sections have been and are being measured by ATLAS and CMS during Run 1 and 2 from all three single top-quark production processes. All are in agreement with the SM predictions.

• Various methods are used to measure the single top-quark production cross-sections.

|f

V

| measurements in ATLAS and CMS

• Independent of assumptions about the number of quark generations or about the unitarity of the CKM matrix.

Assumptions for the extraction:

• Wtb interaction is a SM-like left-handed weak coupling.

• |Vtb| ≫ |Vtd|, |Vts|, i.e. BR(t→Wb) ~ 1.

|fLV Vtb| results from all three single top-quark production processes are in agreement with the SM predictions.

ATLAS+CMS Preliminary LHCtopWG from single top quark production σ^meastheo

| = σ Vtb

|fLV

MSTW2008nnlo : NLO+NNLL

σtheo

PRD 83 (2011) 091503, PRD 82 (2010) 054018,

PRD 81 (2010) 054028

⊕ PDF : scale σtheo

Δ

= 172.5 GeV mtop

May 2017

including top-quark mass uncertainty

1

: NLO PDF4LHC11 σtheo

2

NPPS205 (2010) 10, CPC191 (2015) 74 including beam energy uncertainty

3

total theo

(theo) (meas) ±

| ± Vtb

|fLV

t-channel:

Wt:

s-channel:

ATLAS 7 TeV 1

1 )

PRD 90 (2014) 112006 (4.59 fb− 1.02 ± 0.06 ± 0.02

ATLAS 8 TeV 1,2

1 )

arXiv:1702.02859 (20.2 fb− 1.028 ± 0.042 ± 0.024

CMS 7 TeV

1 )

JHEP 12 (2012) 035 (1.17 - 1.56 fb− 1.020 ± 0.046 ± 0.017

CMS 8 TeV

1 )

JHEP 06 (2014) 090 (19.7 fb− 0.979 ± 0.045 ± 0.016

CMS combined 7+8 TeV

JHEP 06 (2014) 090 0.998 ± 0.038 ± 0.016

CMS 13 TeV 2

1 )

arXiv:1610.00678 (2.3 fb− 1.03 ± 0.07 ± 0.02

ATLAS 13 TeV 2

1 )

JHEP 04 (2017) 086 (3.2 fb− 1.07 ± 0.09 ± 0.02

ATLAS 7 TeV

1 )

PLB 716 (2012) 142 (2.05 fb− 1.03 ₋⁺ _0.18 ^0.15± 0.03

CMS 7 TeV

1 )

PRL 110 (2013) 022003 (4.9 fb− ^{− 0.13 − 0.04}

0.03 0.16 +

1.01 +

ATLAS 8 TeV 1,3

1 )

JHEP 01 (2016) 064 (20.3 fb− 1.01 ± 0.10 ± 0.03

CMS 8 TeV 1

1 )

PRL 112 (2014) 231802 (12.2 fb− 1.03 ± 0.12 ± 0.04

LHC combined 8 TeV 1,3

CMS-PAS-TOP-15-019 ATLAS-CONF-2016-023,

0.04 0.08 ± 1.02 ±

ATLAS 13 TeV 2

1 )

arXiv:1612.07231 (3.2 fb− 1.14 ± 0.24 ± 0.04

ATLAS 8 TeV 3

1 )

PLB 756 (2016) 228 (20.3 fb− 0.93 ₋⁺ _0.20 ^0.18± 0.04

From single top-quark production cross-section measurements, VL can be extracted:

| V

| ≡ | f

V

| =

! σ

σ

Measurement of the W boson helicity in tt ̄ events (8 TeV)

The differential decay rate of top quarks considering the angle θ^∗ℓ is given by:

∗

1 Γ

dΓ

dcosθ_ℓ^∗ = 3

8 (1 + cosθ_ℓ^∗)² F_R + 3

8 (1 − cosθ_ℓ^∗)F_L + 3

4 (sinθ_ℓ^∗)² F₀

The properties of the decay Wtb vertex in tt̄ events are determined by the structure of the weak interaction.

• Helicity fractions (FR, FL, F0) are determined by the Wtb vertex structure.

|t>

|WLbL>

|W0bL>

|W0bR>

|WRbR>

A-1,-1/2

A0,-1/2

A0,+1/2

A+1,+1/2

FL = 0.311 ± 0.005 F0 = 0.687 ± 0.005 FR = 0.0017 ± 0.0001

}

☞

☞

☞

☞

• Transition amplitudes depend on (real) anomalous couplings.

• Deviations could provide solid hints of BSM physics.

!!

!A_1,¹

2

!!

!² ∝ 2|x_WV_R −g_L|²

!!

!A_0,¹

2

!!

!² ∝ |V_R −x_Wg_L|²

!!

!A_−1,−¹

2

!!

!² ∝ 2|x_WV_L −g_R|²

!!

!A_0,−¹

2

!!

!² ∝ |V_L −x_Wg_R|²

x ≡ m /m ^{m = 0 GeV}

➡ Fractions are well predicted in the SM (Phys. Rev. D 81 (2010) 111503).

☞

☞

☞

FL + F0 + FR = 1

Measurement of W boson helicity fractions in tt̄ topology (20.2 fb^-1, 8 TeV).

• Cut-based analysis for S/B separation.

• Kinematic fitting to reconstruct tt̄ system (leptonic and hadronic side in lepton+jets events).

• Hadronic analyser less sensitive.

• Template reweighting:

• Fit truth tt̄ SM cosθ distribution before selection to obtain SM fractions.

• Reweigh final reco. distribution to produce templates for FR, FL, F0 (per-lepton channel).

• Use combined likelihood fit (8 inputs) to extract FR, FL, F0 from data.

Measurement of the W boson helicity in tt ̄ events (8 TeV)

• Results:

• FL = 0.299 ± 0.008 (stat.+bkg. norm.) ± 0.013 (syst.)

• F0 = 0.709 ± 0.012 (stat.+bkg. norm.) ± 0.015 (syst.)

• FR = −0.008 ± 0.006 (stat.+bkg. norm.) ± 0.012 (syst.)

• Dominant systematics: template stat., JER and JES.

In agreement with SM predictions.

• Very precise measurement of FR, FL, F0.

• Impossible to fully constrain the four top-quark decay amplitudes from FR, FL, F0 (just two independent) without more information.

Templates from truth Post-fit recons. distribution

Using the previous results, set limits on anomalous Wtb couplings with EFTFitter tool (Bayesian approach).

• Limitations: only place limits on combinations of (real) coupling pairs (other couplings set to their SM values).

• This implies loosing generality.

Measurement of the W boson helicity in tt ̄ events (8 TeV)

Regions excluded by taking into account the t-channel single top-quark cross-section measurements

L

= − g

√ 2 bγ

(V

P

+ V

P

) tW

− g

√ 2 b iσ

q

m

(g

P

+ g

P

) tW

+ h.c.,

Re[VR] ∈ [−0.24, 0.31] @ 95 CL Re[gL] ∈ [−0.14, 0.11] @ 95 CL

Re[gR] ∈ [−0.02, 0.06] and [0.74, 0.78] @ 95 CL Allowed ranges:

PRD81 (2010) 111503

|t>

|WLbL>

|W0bL>

|W0bR>

|WRbR>

FL

F0-

FR

A full description of the top-quark decay has to include four amplitudes (three independent parameters) and their phases.

• This breaks the degeneracy (not measured in W boson helicity fractions measurement in tt̄ events).

• In addition, the top-quark polarisation can be considered in single top-quark events.

F0+

Very small amplitudes.

Phase δ+ not observable.

• Dependence of the transition amplitudes on anomalous couplings

!!

!A_1,¹

2

!!

!² ∝ 2|x_WV_R −g_L|²

!!

!A_0,¹

2

!!

!² ∝ |VR − xWgL|²

!!

!A_−1,−¹

2

!!

!² ∝ 2|xWVL − gR|²

!!

!A_0,−¹

2

!!

!

2 ∝ |VL − xWgR|²

xW ≡ mW/mt

mb = 0 GeV

! 2

2x²_W + 1 (x_WV_R −g_L) = A_1,¹

2e^iδ+

! 1

2x²_W + 1 (V_R −x_Wg_L) = A_0,¹

2

! 2

2x²_W + 1 (x_WV_L − g_R) = A_−1,−¹

2e^iδ−

! 1

2x²_W + 1 (V_L −x_Wg_R) = A_0,−¹

2

Imaginary terms related with CP violation A-1,-1/2

A0,-1/2

A0,+1/2

A+1,+1/2

}

☞

☞

☞

☞

☞

☞

☞

☞

} δ

δ

FL + F0- + F0+ + FR = 1

Full description of the top-quark decay using single top-quark events

Measurement of the top-quark and W boson polarisation observables in t-channel single-top-quark events from angular asymmetries (20.2 fb^-1, 8 TeV).

• Cut-based analysis for S/B separation.

• Observables extracted from asymmetries in various angular distributions unfolded at parton level.

Measurement of top-quark and W boson spin observables (8 TeV)

helicity fraction basis

• W boson spin observables: <S1>, <S2>, <S3>, <A1>, <A2> and <T0>

Polarised top quarks are required to measure these observables.

• The <A2> and <S2> observables related with CP violation (i.e. imaginary anomalous couplings)

‣ Phys. Rev. D 93 (2016) 011301

JHEP04 (2017) 124

Measurement of top-quark and W boson spin observables (8 TeV)

Im[gR] ∈ [−0.18, 0.06] @ 95 CL

• The angular distributions, from which AFBN and AFBl are extracted, are sensitive to Im[gR].

• Use an interpolation technique (based on non-SM Protos sim.) for deriving model-independent unfolding corrections.

• Combine AFBN and AFBl (including their correlations) to set limits to Im[gR]:

• AFBN (@ LO) = 0.64 P Im[gR] (Nucl. Phys. B (2010) B840) where the dependence of P on Im[gR] is neglected.

• AFBl = 0.5αlP where the quadratic variation of P and αl as a function of Im[gR] (Phys. Rev. D 89 (2014) 114009) is taken into account when setting the limit.

assuming VL = 1 and VR = gL = Re[gR] = 0

• Dominant systematics: tt̄ modelling, JES, MC statistics.

• These measurements represent a consistency check of the SM.

• Unfolding corrections based on a SM Protos simulation except for AFBN.

Analysis of the Wtb vertex in production and decay

helicity fraction basis

M_k,l^m (✓,✓^⇤, ^⇤) = p

2⇡Y_k^m(✓,0)Y_l^m(✓^⇤, ^⇤)

Finite series of orthonormal M-functions

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

• The generalised helicity fractions (three independent: f1, f1+, f0+) and phases (δ+, δ-) + P (nuisance) are determined simultaneously, including all correlations.

Analysis of the Wtb vertex from the measurement of triple-differential angular decay rates of single top quarks produced in the t-channel (20.2 fb^-1, 8 TeV).

• Normalised triple-differential angular (θ, θ^∗, φ^∗) decay rate using the helicity formalism.

• Relative phases can only be measured with polarised top quarks.

• Polarisation (P) can only be measured in single top-quark events.

• Terms in Black: measured by W-boson helicity analysis (PRD81 (2010) 111503).

• Terms in Blue: added by two-angle analysis (JHEP 04 (2016) 023).

• Terms in Red: even more with three-angle analysis (arXiv:1707.05393).

arXiv:1707.05393

%(✓,✓^⇤, ^⇤;P) = 1 N

d³N

dcos✓d⌦^⇤ = 1 8⇡

(3

4 A_1,¹

2

2(1 + P cos✓) (1 + cos✓^⇤)²

+ 3

4 A _1, ¹

2

2 (1 P cos✓) (1 cos✓^⇤)²

+ 3

2

✓

A_0,¹

2

2(1 P cos✓) + A_0, ¹

2

2(1 + P cos✓)

◆

sin² ✓^⇤ 3p

2

2 P sin✓sin✓^⇤ (1 + cos✓^⇤) Reh

e^{i ⇤}A_1,¹

2A^⇤_0,¹

2

i 3p

2

2 P sin✓sin✓^⇤ (1 cos✓^⇤) Reh

e ^{i ⇤}A _1, ¹

2A^⇤_0, ¹

2

i)

= X2

k=0

X2

l=0

Xl

m= l

a_k,l,mMM_k,lk,l^mm (✓,✓^⇤, ^⇤) = p

2⇡Y_k^m(✓,0)Y_l^m(✓^⇤, ^⇤) Angular coefficients

to be determined

Analysis of the Wtb vertex in production and decay

Global fit to extract generalised helicity fractions and phases → Likelihood function with all correlations (cov. matrix).

• Distributions (profiles and contours) are obtained from numerical calculations of the likelihood function.

Interpretation in terms of anomalous couplings by propagating the statistical and systematic uncertainties.

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

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

• Covariance matrix fully available.

• No assumptions on values of the other anomalous couplings.

|V_R/V_L| < 0.37 @ 95 CL

|g_L/V_L| < 0.29 @ 95 CL

Re[gR] ∈ [−0.12, 0.17] @ 95 CL

As this analysis yields no constraint on δ+, no constraint can be placed on the relative phase between VL and g^L.

}

Summary

The Wtb vertex has been carefully probed during Run 1.

• The most precise measurements have been discussed in this talk.

• The left-handed vector coupling of the SM-like Wtb vertex has been extracted from the measurement of single top-quark cross-sections.

• Limits on the Wtb anomalous couplings have been presented by:

• W boson helicity fraction measurements in top-quark decays (either tt̄ or single top quark).

• Multi-dimensional analysis are performed using single top-quark production and decay observables in order to set simultaneous limits to the couplings without loosing generality (i.e. assuming values on other

couplings).

• All measurements are so far consistent with the SM predictions.

• Measurements dominated by systematic uncertainties.

• No sign of new physics has been found yet.

• Run 2 data being studied nowadays ⟹ Even more interesting results!!!

• ATLAS Top Physics Results: https://twiki.cern.ch/twiki/bin/view/AtlasPublic/TopPublicResults.

Backup slides

Top quark

Top quark is unique!

• Heaviest known fundamental particle.

• Short lifetime (~10^-25 s) ⟹ top-quark decays before hadronising.

• The only quark whose most of its properties can be directly measured.

At hadron colliders, top quarks are produced:

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

• At the LHC gg→tt̄ dominates, while qq̄→tt̄ dominated at Tevatron.

• Alternatively, singly through the EW interaction.

Facts:

‣ The top quark was discovered (tt̄ production) in pp̄ collisions by CDF/D0, at Tevatron (Fermilab) in 1995.

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

LHC is also known as the top-quark factory:

• Top-quark pair production:

• Tevatron (1.96 TeV, 10³² cm^-2 s^-1): ~3 evt/h.

• LHC (13 TeV, 10³³ cm^-2 s^-1): ~1 evt/s.

• Single top-quark production:

• Tevatron (1.96 TeV, 10³² cm^-2 s^-1): ~30 evt./day.

• LHC (13 TeV, 10³³ cm^-2 s^-1): ~1000 evt./h.

Tevatr on (tt

̄)

LHC (tt

̄)

ATLAS and CMS detectors

ATLAS (general purpose detector)

• Length: 44 m, diameter: 25 m

• Mass: ~7.0 ktons

• Two magnet fields:

• Solenoid (ID): 2 T

• Toroid (Muon System): 2-8 Tm

CMS (general purpose detector)

• Length: 21 m, diameter: 15 m

• Mass: ~ 12.5 ktons

• Solenoid: 4 T

Single top-quark production modes and signature

t-channel signature:

• 1 isolated and high-pT lepton.

• 1 high-pT and forward |η| jet (light jet).

• 1 high-pT and central |η| jet (b-jet).

• An additional soft b-quark with high |η| (not usually detected).

• MET from the neutrino.

• Main backgrounds: tt̄ and W+jets.

tW signature:

• 2 isolated and high-pT leptons.

• 1 high-pT and central |η| jet (b-jet).

• MET from the two neutrinos.

• Main backgrounds: tt̄.

s-channel signature:

• 1 isolated and high-pT lepton.

• 2 high-pT and central |η| jets (b-jets).

• MET from the neutrino.

• Main backgrounds: tt̄, W+jets and t-channel.

t-channel

s-channel tW

Three production mechanisms (@ LO):

Golden channel

Observed at the LHC

Challenging at the LHC σt-ch (8 TeV) = 87.7 pb σt-ch (13 TeV) = 217.0 pb

σWt (8 TeV) = 22.4 ± 1.5 pb σWt (13 TeV) = 71.7 ± 3.8 pb

σs-ch (8 TeV) = 5.6 ± 0.2 pb σs-ch (13 TeV) = 10.3 ± 0.4 pb

Summary of the W boson helicity fractions

W boson helicity fractions

−1.5 −1 −0.5 0 0.5

ATLAS+CMS Preliminary LHCtopWG May 2017

FR F_L F₀

=7 TeV s

LHC combination,

=20.2 fb-1

=8 TeV, Lint

s ATLAS 2012 single lepton,

-1 *

=2.2 fb

=7 TeV, Lint

s CMS 2011 single lepton,

=5.0 fb-1

=7 TeV, Lint

s CMS 2011 single lepton,

=35 pb-1

=7 TeV, Lint

s ATLAS 2010 single lepton,

=1.04 fb-1

=7 TeV, Lint

s ATLAS 2011 single lepton and dilepton,

=19.7 fb-1

=8 TeV, Lint

s CMS 2012 single top,

=19.8 fb-1

=8 TeV, Lint

s CMS 2012 single lepton,

=19.7 fb-1

=8 TeV, Lint

s CMS 2012 dilepton,

ATLAS-CONF-2013-033, CMS-PAS-TOP-12-025

EPJC 77 (2017) 264 CMS-PAS-TOP-11-020

JHEP 10 (2013) 167 ATLAS-CONF-2011-037

JHEP 1206 (2012) 088

JHEP 01 (2015) 053 PLB 762 (2016) 512

CMS-PAS-TOP-14-017

* superseded by published result

Theory (NNLO QCD)

PRD 81 (2010) 111503 (R) 0)

L/F

R/F Data (F

total stat

• Measurements based on tt̄ events are the most precise measurements of the W boson helicity fractions (FR, FL, F0).

• Unfortunately, it is impossible to fully constrain the four top-quark decay amplitudes from FR, FL, F0 (just two independent) without more information.

• Single top-quark events are needed to break the degeneracy ( ).f₁, f₁⁺, f₀⁺, ₊,

Measurement of W boson helicity fractions in tt̄ topology (20.2 fb^-1, 8 TeV).

• Cut-based analysis for S/B separation.

• Kinematic fitting to reconstruct tt̄ system (leptonic and hadronic side in lepton+jets events).

• Hadronic analyser less sensitive.

• Template reweighting:

• Fit truth tt̄ SM cosθ distribution before selection to obtain SM fractions.

• Reweigh final reco. distribution to produce templates for FR, FL, F0 (per-lepton channel).

• Use combined likelihood fit (8 inputs) to extract FR, FL, F0 from data.

Measurement of the W boson helicity in tt ̄ events (8 TeV)

• Results:

• FL = 0.299 ± 0.008 (stat.+bkg. norm.) ± 0.013 (syst.)

• F0 = 0.709 ± 0.012 (stat.+bkg. norm.) ± 0.015 (syst.)

• FR = −0.008 ± 0.006 (stat.+bkg. norm.) ± 0.012 (syst.)

• Dominant systematics: template stat., JER and JES.

• In agreement with SM predictions.

• Very precise measurement of FR, FL, F0.

• Impossible to fully constrain the four top-quark decay amplitudes from FR, FL, F0 (just two independent) without more information.

Templates from truth Post-fit recons. distribution

|t>

|WLbL>

|W0bL>

|W0bR>

|WRbR>

FL

F0-

FR

Full description of the top-quark decay has to include four amplitudes (three independent parameters) and their phases.

• In addition, the top-quark polarisation can be considered in single top-quark events.

F0+

Very small amplitudes.

Phase δ+ not observable.

• Generalised helicity fractions and phases:

f }1, f1+, f0+, +,

F_R = f₁f₁⁺ F0 = 1 f1

FL = f1(1 f₁⁺)

}

relative phases between amplitudes

Dependence of the transition amplitudes on anomalous couplings

!!

!A_1,¹

2

!!

!² ∝ 2|x_WV_R−g_L|²

!!

!A_0,¹

2

!!

!² ∝ |VR −xWgL|²

!!

!A_−1,−¹

2

!!

!

2

∝ 2|xWVL−gR|²

!!

!A_0,−¹

2

!!

!² ∝ |VL −xWgR|²

x_W ≡ m_W/m_t mb = 0 GeV

! 2

2x²_W + 1 (x_WV_R −g_L) = A_1,¹

2e^iδ+

! 1

2x²_W + 1 (V_R −x_Wg_L) = A_0,¹

2

! 2

2x²_W + 1 (x_WV_L−g_R) = A_−1,−¹

2e^iδ−

! 1

2x²_W + 1 (V_L−x_Wg_R) = A_0,−¹

2

related with CP-violating terms A-1,-1/2

A0,-1/2

A0,+1/2

A+1,+1/2

}

☞

☞

☞

☞

☞

☞

☞

☞

} δ

δ

FL + F0- + F0+ + FR = 1

This breaks the degeneracy (not measured in W

Full description of the top-quark decay using single top-quark events

How can we improve things?

Note that a joint PDF is not equivalent to the sum of its projections!

Which is the best method to study the Wtb vertex in production and decay?

1.Do individual (1D) analysis like: W boson helicity fractions, asymmetries from angular distributions, etc…

2.Multi-dimensional analysis ⟹ simultaneous parameter extraction (with its covariance matrix).

Easily explained and understood thanks to the “Sheldon” distribution.

Physics (“real” life)

“Sheldon” distribution

Option 1

“tradicional method”

Option 2

“novel techniques”

Orthogonal series density estimation

(OSDE)

ρ(⃗x) = !

n

a_nφ_n(⃗x)

The coefficients are computed by averaging basis functions over a dataset (Fourier technique).

a_n =

!

dxⁿρ(⃗x)φ_n(⃗x)^∗ = ⟨φ_n(⃗x)^∗⟩

;

Dependence of α

P on Im[g

]

AFBN (@ LO) = 0.64 P Im[gR]

(Nucl. Phys. B (2010) B840) AFBl = 0.5αlP

PRD89 (2014) 114009

LO Protos (4FS) @ 8 TeV

JHEP04 (2017) 124

Measurement of top-quark and W boson spin observables (8 TeV)

Im[gR] ∈ [−0.18, 0.06] @ 95 CL

• The angular distributions AFBN and AFBl are sensitive to Im[gR].

• Deviations from SM values, i.e. Im[gR] = 0, would imply that the top-quark decay has a CP-violating component.

Comparison of the distributions observed in the signal region with the distributions predicted as a function of Im[gR].

• Use an interpolation technique (based on non-SM Protos simulations) for deriving model-independent unfolding corrections.

• Combine AFBN and AFBl (including their correlations) to set limits to Im[gR]:

• AFBN (@ LO) = 0.64 P Im[gR] (Nucl. Phys. B (2010) B840) where the dependence of P on Im[gR] is neglected.

• AFBl = 0.5αlP where the quadratic variation of P and αl as a function of Im[gR] (PRD89 (2014) 114009) is taken into account when setting the limit.

assuming VL = 1 and VR = gL = Re[gR] = 0

• Dominant systematics: tt̄ modelling, JES, MC statistics.

Analysis of the Wtb vertex in production and decay

Non-zero phase could imply CP-violation (at first order)

no sensitivity to this parameter since it is related to right-handed b-quarks

From these two parameters, traditional

helicity fractions (F+, F—, F0) can be extracted.

From the helicity amplitudes, five physics parameters can be constructed, representing three amplitude fractions and two phases. Observables:

Not previously measured! F0 only measures combinations of fractions but this analysis separates them.

F_R = f₁f₁⁺ F₀ = 1 f₁

Helicity fractions in terms of the generalized helicity fractions:

Analysis of the Wtb vertex in production and decay

• Relationship between the angular coefficients and the generalised helicity fractions and phases.

Analysis of the Wtb vertex in production and decay

Given a distribution:

Thanks to the orthonormality of the M-functions:

Now, using a given dataset (either simulated or real data) we can simply compute the mean value of M’-function:

And we can therefore compute all these angular coefficients having statistical uncertainties and correlations!

Finally, to interpret these coefficients as a measurement of the physics parameters, we simply pack them in a vector, v0, and their covariance matrix, obtained from OSDE, into a real-value matrix C and we just do a 𝜒² fit with MINUIT to extract 𝛼:

where

Analysis of the Wtb vertex in production and decay

Relationship between the angular coefficients and the W boson spin observables:

Analysis of the Wtb vertex in production and decay

Global fit to extract generalized helicity fractions and phases → Likelihood function with all correlations (cov. matrix).

• Distributions (profiles and contours) are obtained from numerical calculations of the likelihood function.

• Dominant systematics: signal modelling, JES and data statistics.

Deconvoluted angular coefficients from data using the migration matrix from the SM together with 2 new physics scenarios.

• The scenario with δ- = π ⟹ Re[gR/VL] ≈ 0.77.

• The scenario with f0+ = 0.2 ⟹ |VR/VL| ≈ 0.65, and |gL/VL| ≈ 0.27.

• Both scenarios allowed/consistent with W boson helicity fractions measurements in tt̄.

Coefficients than can be largely improved by a combination with W boson helicity fractions measurement from tt̄ events.

Analyse the Wtb vertex properties from the normalised quadruple-differential (θ, φ, θ*, φ*) decay rate of top-quarks.

• Simultaneously constrain of the full space of generalised helicity fractions and phases + three top-quark polarisation components.

Finite series of orthonormal M-functions

Where the M-functions are based on the Wigner D functions:

• Relative phases can only be measured with polarised top quarks.

• Top-quark polarisation can only be measured in single top-quark events.

• Similarly to the three-angle analysis, the idea is to extract all amplitudes and phases + (Px, Py, Pz) which are determined simultaneously, including all correlations.

• So, the final result will be a likelihood function with all correlations (covariance matrix).

• Exploring also the possibility of having the expansion in terms of harmonic polynomials (real functions, real coefficients).

What’s next? some thoughts…

Interpretation in terms of anomalous couplings by propagating the statistical and systematic uncertainties.

• Limits may be placed simultaneously on the possible complex values of the ratio of the anomalous couplings.

• No assumptions on values of the other anomalous couplings.

Interpretation in terms of W boson spin observables (PRD93 (2016) 011301) by propagating the statistical and systematic uncertainties.

• Limits may be placed simultaneously on the observables.

• No assumptions on any parameter.

‣ Introduced by Phys. Rev. D 93 (2016) 011301.

‣ Measured by JHEP 04 (2017) 124.

What’s next? here it is a proposal