Spin measurements in top-quark events at the LHC

Spin measurements in top-quark events at the LHC Jacob Linacre (FNAL on behalf of the ATLAS and CMS collaborations TOP25 5 th September 25

Outline Today I ll show recent top quark spin measurements from ATLAS and CMS top quark polarisation in t t t t spin correlations and single top (t-channel events 5/9/5 2

Introduction Top decays before QCD interactions can affect its spin top lifetime < QCD timescale spin-flip timescale 25 s < 24 s 2 s top decay products give us direct access to its spin expect top spin variables to be well predicted by perturbative QCD excellent test of SM Spin variables can be significantly modified by new physics already being used to set limits 5/9/5 3

Top polarisation 5/9/5 4

Introduction to top quark spin Top spin depends on production process and on the basis (direction for spin measurement Single top t-channel: tops % L chirality (because they have to couple to the W translates to ~95% spin up in spectator basis t t b q W t q W b l ν production via strong interaction with unpolarised incoming partons R and L tops equally likely no net polarisation at LO QCD (usually measured in helicity basis b L q L t L q L (Spectator quark 5/9/5 5

5/9/5 Polarized top quark decay The top quark s spin determines the angular distribution of its daughters when it decays spin analysing powers: lepton preferentially produced in top spin direction top rest frame θ Polarisation measures average spin: l apple` =, apple d =.97, apple u =.3, apple b =.39 A. Brandenburg, Z. G. Si, P. Uwer (22 dn d cos ( + apple cos 2 d d cos = ( + applep cos 2 cos 6

Polarisation (single top t-channel - CMS, 8 TeV BDT selects ~5% pure t-channel sample CMS-PAS-TOP-3- Reconstruct cos, subtract background (W+jets largest, unfold to parton level, and combine e and µ channels Dominant systematics from JES and background subtraction 8 6 4 data signal (t-channel s-channel tw tt DY W diboson QCD stat. + syst. CMS preliminary - s = 8 TeV, L = 2 fb Muon channel, 2JT BDT >.6 a.u. 2 3 CMS preliminary A =.42 ± unfolded data generated (POWHEG generated (CompHEP - s = 8 TeV, L = 2 fb.7 (stat. ±.5 (syst. (exp.-meas./meas. 2 - -.5.5 cos θ*.5 -.5 - - -.8 -.6 -.4 -.2.2.4.6.8 P = 2A (asymmetry - -.5.5 cos θ* Polarisation from distribution asymmetry: P = (82 ± 2 ± 32% 5/9/5 7

Polarisation ( t t - ATLAS, 7 TeV Template fit to 5/9/5 at reco-level using templates with +3% and -3% polarisation l, 2l channels and distributions (l + and l - fitted separately Two scenarios CP-conservation: P(t = P( t Maximal CP violation: P(t = -P( t Jet reconstruction dominant systematic cos PRL, 2322 (23 t, t Events /. 25 ATLAS single lepton 2 5 5 Ldt =4.7fb - -.8-.6-.4-.2.2.4.6.8 - -.8 -.6 -.4 -.2.2.4.6.8 cos θ(l + s =7TeV CP violating hypothesis: l + templates unchanged s =7TeV and l - templates flipped so benefits from maximal cancellation of systematics Data αp = Fit αp =+.3 Bkgd. αp =.3 cos θ(l Data αp = Fit αp =+.3 Bkgd. αp =.3 - -.8 -.6 -.4 -.2.2.4.6.8 cos θ(l 8

Polarisation ( t t - ATLAS, 7 TeV Results (assuming apple` =: PRL, 2322 (23 P CPC = (-3.5 ±.4 ± 3.7% P CPV = (2. ±.6 +.3 -.7 % e +jets µ + jets l +jets ATLAS Ldt =4.7fb s =7TeV e +jets µ + jets l +jets ATLAS Ldt =4.7fb s =7TeV ee ee eµ Uncertainties eµ Uncertainties µµ Statistical µµ Statistical Dilepton Total Dilepton Total Combined -.5 -.4 -.3 -.2 -...2.3.4.5 α l P CPC Combined -.5 -.4 -.3 -.2 -...2.3.4.5 α l P CPV 5/9/5 α = κ = spin analysing power 9

Polarisation ( t t - CMS, 8 TeV cos (dilepton channel P measured from distribution unfolded to parton level asymmetry of distribution Two measurements per event (l + and l - Combined assuming CP conservation and violation /σ dσ/d(cos θ* l.6.55.5.45 CMS Preliminary W. Bernreuther & Z.-G.Si (SM, µ = m t P = 2A CMS TOP-4-23 - 9.5 fb Data (stat. unc. Syst. uncertainty (8 TeV MC@NLO parton level P CPC = ( 2.2 ± 5.9 % JES dominant systematic P CPV = (. ±.7 % cancellation of systematics Data/Simulation.5.95 - -.5.5 cos θ* l 5/9/5

t t spin correlations 5/9/5

Introduction to spin correlations Same and opposite helicity gluon fusion contributions impart different spin correlations to the top quark pairs g R t R in t t CM frame, speed of tops β g R g R t R g L t R Same helicity gluons Positive spin correlations Same helicity contribution is dominant near threshold t L Opposite helicity gluons Negative spin correlations Opposite helicity dominant when E t >> m t (helicity conservation Expected net spin correlation strength of about +3% at the LHC modified in many new physics scenarios 5/9/5 2

Dilepton ϕ distribution Spin correlations in same-helicity gluon fusion result in aligned lepton decays alignment strongest in ϕ (lab frame azimuthal angle between two leptons l + l - ϕ l+l- /σ dσ/d( φ.44.42.4.38.36.34.32.3.28.26.24 5/9/5 ϕ distribution in presence and absence of spin correlations (parton level W.Bernreuther & Z.G.Si W.Bernreuther (SM, µ=m & Z.G.Si (SM, µ=m t t W.Bernreuther & Z.G.Si (uncorrelated, µ=m W.Bernreuther & Z.G.Si (uncorrelated, µ=m ~6% enhancement here t.5.5 2 2.5 3 φ l+l- t ~6% suppression here Kinematically, large ϕ is preferred because tops are produced back to back relative enhancement at low ϕ due to spin correlations Lepton angles have excellent experimental resolution ϕ most precise probe of spin correlations (unique to LHC 3

ϕ - ATLAS, 8 TeV Select t t events in dilepton final state data-driven prediction for dominant Z/γ +jets background Quantify spin correlation strength as fraction f SM of SM expectation template fit using simulated correlated and uncorrelated t t f SM =.2 ±.5 ±.3 Events/. Ratio 6 4 2 8 6 4 2.2..9 Data SM tt tt (A= Background ~ ~, 8 GeV t t Fit PRL 4, 42 (25 s ATLAS - = 8 TeV, 2.3 fb.8.2.4.6.8 φ [rad] / π 5/9/5 4

Probing SUSY with spin correlations Supersymmetric top squark pair production looks like t t + MET Squarks have spin-zero daughter top quarks look similar to uncorrelated t t events but only ~/6 of the t t cross 5/9/5 section for m stop = m t Total cross section measurement also sensitive to stops Combining the two, ATLAS excludes m t < m stop <9 GeV [GeV] m χ t t t t P 2 t t t t b bw t + W t b W + PRL 4, 42 (25 Important region to probe based on naturalness considerations t t b b ± ± b bw + W ~ ~ ~ ~ ~ t χ W b χ c χ t t production, t / t / t 6 5 4 3 2 ATLAS Preliminary L int L int P c χ W b χ ~ t t χ ~ t t χ ~ t t χ ~ t W b χ ~ t c χ m ~ = 2.3 fb - t Observed limits All limits at 95% CL = 2.3 fb < m c - + m χ m ~ t < m b + m W + m χ t - L int = 2 fb L [46.22] L [47.583] Expected limits m ~ t +m χ < m t - = 4.7 fb L int s=8 TeV 2L [43.4853], 2L [42.4742] L [47.583], 2L [43.4853] L [47.68] - = 2 fb L int Status: Feb 25 - = 4.7 fb L int L [28.447] L [28.259] 2L [29.486] 2 3 4 5 6 7 t [GeV] m χ 4 3 2 - - b W m~ t E T mis MET Direct searches insensitive when χ soft ~ s=7 TeV 7 8 9 2 2 [GeV] m~ t [GeV] 5 χ

ϕ - CMS, 8 TeV ϕ distribution unfolded to parton level Compared to theoretical predictions at NLO with and without spin correlations The data agree with the SM prediction top p T modelling dominant experimental systematic f SM =.8 ±.8 dominant uncertainty from scale uncertainties in the NLO predictions /σ dσ/d( φ l + l - Data/Simulation.5.45.4.35.3.25.5.95 CMS Preliminary W. Bernreuther & Z.-G.Si (SM, µ = m t W. Bernreuther & Z.-G.Si (uncorrelated, µ = m t CMS TOP-4-23 - 9.5 fb Data (stat. unc. Syst. uncertainty (8 TeV MC@NLO parton level π /6 π /3 π /2 2 π/3 5π/6 π φ l + l - 5/9/5 6

Top Chromo-Magnetic Dipole Moment Heavy particle exchange in Model-independent effective Lagrangian: µ t = anomalous CMDM For small µ t : σ 5/9/5 L eff = L SM µ t 2 tσ µν T a tg a µν dσ d φ = ( σ dσ d φ SM dσ only sensitive to Re( µ t + ( σ dσ d φ NP Reˆµ t ll φ (/σ(dσ/d Template fit to SM+NP to extract Re(µ ^ t -.5 < Re(µ ^ t <.76 (95% CL New physics contribution to -.5.5.5 2 2.5 3.2. -. -.2 -.3 -.4 production can modify spin correlations by introducing colour dipole ttg couplings t t W.Bernreuther & Z.-G.Si (CMS TOP-4-23 σ dσ d φ arxiv:35.266 φ ll 7

Events/.25 Data Prediction 24 22 2 8 6 4 2 8 6 4 2 5/9/5.4.2.8.6 ATLAS Direct measurement - ATLAS, 7 TeV Direct measurement requires full, reconstruction Preliminary - s = 7 TeV, 4.6 fb Data tt Single top Z+jets Diboson Fake leptons - -.8 -.6 -.4 -.2.2.4 cos.6.8 cos tt t 2 Lepton directions in parent top CMs used as a proxies for the top spins C hel coefficient from distribution of product of top spins: cos `+ cos ` C hel =.35 ±.6 ±.49 - -.8 -.6 -.4 -.2.2.4.6.8 cos cos 2 cos d d(cos.5.45.4.35.3.25.2.5..5 ATLAS Preliminary - s = 7 TeV, 4.6 fb f SM =.2 ±.26 Paper in preparation Unfolded dist. SM spin corre. No spin corre. Chel = -9<cc2> 2 (unoffical 8

Direct measurement - CMS, 8 TeV Direct measurement requires full, reconstruction * - * + cos θ l l /σ dσ/d(cos θ.5 2 W. Bernreuther & Z.-G.Si Data (stat. unc. (SM, µ = m t Syst. uncertainty W. Bernreuther & Z.-G.Si MC@NLO parton level (uncorrelated, µ = m t - 9.5 fb (8 TeV Lepton directions in parent top CMs used as a proxies for the top spin CMS Preliminary D coefficient from distribution of angle between the spins: Chel = -4A t t t /σ dσ/d(cos ϕ.8.7.6.5 CMS Preliminary W. Bernreuther & Z.-G.Si (SM, µ = m t W. Bernreuther & Z.-G.Si (uncorrelated, µ = m t CMS TOP-4-23 ' = \( ˆ `+, ˆ ` - 9.5 fb Data (stat. unc. Syst. uncertainty (8 TeV MC@NLO parton level.5.4 D = -2A Data/Simulation 5/9/5..9 - -.5.5 cos θ l * + cos θ l * - - -.5.5 cos ϕ f SM =.87 ±.27 f SM =.9 ±.6 Data/Simulation.5.95 9

Differential measurements - CMS, 8 TeV Asymmetry variables measured differentially wrt A φ.4.2 CMS Preliminary W. Bernreuther & Z.-G. Si (SM, µ = m t W. Bernreuther & Z.-G. Si (uncorrelated, µ = m t - 9.5 fb Data (stat. unc. Syst. uncertainty MC@NLO (8 TeV A cos ϕ.3.2. CMS Preliminary W. Bernreuther & Z.-G. Si (SM, µ = m t W. Bernreuther & Z.-G. Si (uncorrelated, µ = m t M t t, y t t,p t t T - 9.5 fb Data (stat. unc. Syst. uncertainty MC@NLO (8 TeV CMS TOP-4-23 4 6 8 2 M tt (GeV/c SM spin correlations have most structure wrt 2 4 6 8 2 M t t M tt (GeV/c 2 Unfolding wrt minimises 5/9/5 M t t the ϕ top p T systematic: f SM =.6 ±.5 (but still limited by NLO scale uncertainties 2

5/9/5 Matrix element method - CMS, 8 TeV, l In l events, ϕ distribution is not as sensitive don t know whether light jet is u (apple =.3 or b-jet also has small spin analysing power d Use matrix element method to extract more information from each event event = P uncor P cor = Create templates using simulated correlated and uncorrelated t t normalised entries Data/MC 6 4 2 8 6 4 2.5.5-3 CMS Preliminary Data t t (signal t t (other Single Top W + jets Z/γ* + jets - -2lnλ event (apple =.39-9.7 fb (8 TeV normalised entries Data/MC 6 4 2 8 6 4 2.5.5 (apple =.97-3 CMS Preliminary Data t t (signal t t (other Single Top W + jets Z/γ* + jets CMS-PAS-TOP-3-5 Event probability using LO uncorrelated ME Event probability using LO correlated ME Correlated - 9.7 fb (8 TeV - -2lnλ event Uncorrelated 2

Matrix element method results CMS-PAS-TOP-3-5 Fit 2ln event distribution using correlated and uncorrelated templates Q2 and JES dominant systematics Events / (.4 x 9 8 7 6 5 4 3 3 CMS Preliminary - 9.7 fb (8 TeV Data total fit corr. (SM tt uncorr. tt background event = P uncor P cor 2.6.4.2.2.4.6.8.2-2lnλ event f SM =.72 ±.9 (stat +.5 -.3 (syst 5/9/5 22

Spin correlations summary Summary of most precise f SM measurements Variable Channel Collaboration fsm ϕ dilepton ATLAS (8 TeV.2 ±.4 ME-based dilepton ATLAS (7 TeV.87 ±.8 (S-ratio ϕ lepton+jets ATLAS (7 TeV.2 ±.25 * All consistent with f SM = f SM = strongly disfavoured 5/9/5 ϕ dilepton CMS (8 TeV.6 ±.5 D dilepton CMS (8 TeV.9 ±.6 ME-based lepton+jets CMS (8 TeV.72 ±.7 Proof top really behaves like a bare quark * ATLAS 7 TeV dilepton ϕ measurement has lower relative uncertainty (fsm=.9±.2, improved on by 8 TeV result (above 23

Summary and Outlook 5/9/5 24

Summary Top quark spin variables are an excellent test of the SM and probe for NP So far the results are very consistent with SM expectations Inclusive measurements systematics limited both experimental and theory systematics Differential results mostly still statistics limited 5/9/5 25

Outlook 4 Top quark pairs per hour at peak inst. luminosity 3 2 4, 2,5 7, Tevatron LHC@7TeV LHC@8TeV LHC@3TeV cross sections from arxiv:33.6254: Tevatron ~7pb, LHC@7TeV ~72pb, LHC@8TeV ~246pb, LHC@3TeV ~86pb peak inst. luminosity: Tevatron: ~4x 32 cm -2 s -, LHC@7TeV: ~4x 33 cm -2 s -, LHC@8TeV: ~8x 33 cm -2 s -, LHC@3TeV: ~.3x 34 cm -2 s - In Run 2 we have another order of magnitude increase for pair production Improvements in systematic and theoretical uncertainties essential to keep pace Could new physics show up first in top spin variables in Run 2? t t 5/9/5 26

Backup 5/9/5 27

ATLAS spin correlations (l+2l, 7 TeV Phys. Rev. D. 9, 26 (24 ATLAS 7 TeV analysis measured large suite of variables in l and 2l channels template fit using simulated correlated and uncorrelated t t dilepton ϕ and S-ratio most precise Standard 8.4.6 ATLAS - Ldt = 4.6 fb, φ (dilepton.9 ±.9 ±.8 φ (l+jets.2 ±. ±.22 S-ratio.87 ±. ±.4 cos(θ + cos(θ - helicity basis cos(θ + cos(θ - maximal basis s = 7 TeV tt spin correlation measurements f SM ± (stat ± (syst.75 ±.9 ±.23.83 ±.4 ±.8.5.5 2 model fraction π Events /. 2 5 ATLAS - L dt = 4.6 fb s = 7 TeV dilepton fit result tt (SM tt (no corr. data background Events /.2 2 ATLAS - L dt = 4.6 fb s = 7 TeV dilepton fit result tt (SM tt (no corr. data background 5 Ratio 5/9/5.2.8.5.5 2 2.5 3 φ [rad].2.8.2.4.6.8.2.4.6.8 2 Ratio S-Ratio 28

Top quark properties Why are top properties interesting? top quark decays before it can form bound states unique opportunity to study a bare quark (using the decay products heaviest elementary particle known (m t ~ 73 GeV large coupling to Higgs boson suggests special role in EWSB top properties measurements test SM and probe new physics Δm H 2 = H y t y t + 5/9/5 29

Top quark spin and helicity The measurements rely on an understanding of the helicities of the top quarks we produce reminder: helicity is the particle s spin component along its momentum direction I ll denote particle momenta and spin directions with solid and open arrows: Right-handed top quark Left-handed top quark tr tl 5/9/5 3

SM spin correlations Same helicity contribution is dominant near threshold Opposite helicity becomes dominant when E t >> m t helicity conservation Net spin correlation strength of ~3% (LHC.3.2. M tt dependence of contributions to total strength of spin correlations 4 6 8 2 4 change of sign M tt (GeV arxiv:3.3926 5/9/5 3

SM spin correlations Initial state and invariant mass dependence of spin correlations makes them a rich process to test our understanding of perturbative QCD future very high precision measurements sensitive to proton quark and gluon content 5/9/5 32

Measuring spin correlations Direct measurement of spin correlations requires full reconstruction of t and t t Can we try something more simple? Choose dilepton final state (charged leptons best spin analysers Preferred lepton directions in the top rest frames given by top spins: t l+ R g R g R l ± angular distributions: ( ± cos /2 (parity violating weak decay t R l - t θ l Same helicity gluons Positive spin correlations 5/9/5 33

/σ dσ/d( φ l + l - t t ϕ interpretation Can reinterpret measured ϕ distribution in terms of new physics that affects spin correlations In general, new physics in production due to heavy particle exchange manifests as a colour dipole coupling of top to gluons modifies the expected spin correlations Supersymmetry top quarks and antiquarks produced from decay of scalar (spin particles have no way of being correlated Data/Simulation.5.45.4.35.3.25.5.95 CMS Preliminary W. Bernreuther & Z.-G.Si (SM, µ = m t W. Bernreuther & Z.-G.Si (uncorrelated, µ = m t - 9.5 fb Data (stat. unc. Syst. uncertainty (8 TeV MC@NLO parton level π /6 π /3 π /2 2 π/3 5π/6 π φ l + l - 5/9/5 34

Anomalous top CMDM results /σ dσ/d φ l +l-.42.4.38.36.34.32 CMS.3.28.26.24.22 Data it NLO W m A value of Re(µ t outside the range -.5 < Re(µ t <.76 is excluded at 95% CL competitive with existing limits ( µ t = g s ˆµ t m t uncertainty dominated by scale variations in the theoretical predictions 5/9/5.2.5.5 2 2.5 3 ^ ^ φ l +l- 35

5/9/5 Direct measurement of spin correlations Spin correlation quantified by relative numbers of same and opposite helicity pairs: Lepton direction favours top spin direction, with distribution ± cos ` the measured is a proxy for the top helicity (diluted by a factor of 2 Measure ± cos ` for both tops in each event, and take the product ( c c 2 t t C σ(t R t R + t L t L σ(t R t L + t L t R σ(t R t R + t L t L +σ(t R t L + t L t R tt CM frame t q q t boost to top rest frame = -C/4 spin correlation coefficient top CM frame θ * l l factor /4 because our helicity measurement is diluted by a factor of 2 for each top ( ± cos ` /2 36