On the Top Quark Mass André H. Hoang

Transcription

1 On the Top Quark Mass André H. Hoang University of Vienna

2 Outline Introduction Top quark mass schemes Calibration of the Monte Carlo top mass parameter: e + e - t t (2-jettiness) Butenschön, Dehnadi, Mateu, Preisser, Stewart,AH; PRL 117 (2016) 153 MSR mass and pole mass ultimate precision Jain, Lepenik, Mateu, Preisser, Scimemi, Stewart, AHH; arxiv: Lepenik, Preisser, AHH, JHEP 1709 (2017) 099 Relation of M t Pythia 8.2 and m t pole Factorization for pp t t with and w/o jet grooming Studies for LHC top mass measurements with SoftDrop Mantry, Pathak, Stewart, AHH; arxive: Summary, future plans

3 A small history on top mass reconstruction Many individual measurements with uncertainty below 1 GeV. Some discrepancies between LHC and Tevatron Reached <500MeV range.

4 Motivation Aims: m top wanted! Reduce error in m top (MC) Clarify mass scheme m top (MC) Improve / understand better MC

5 Main Top Mass Measurements Methods LHC+Tevatron: Direct Reconstruction kinematic mass determination Determination of the best-fit value of the Monte-Carlo top quark mass parameter m MC t = ± 0.64 (Tevatron final, 2014) m MC t = ± 0.49 (CMS Run-1 final, 2015) m MC t = ± 0.70 (ATLAS Run-1 final, 2016) High top mass sensitivity Precision of MC? Meaning of m MC t? Δ m t 0.5 GeV Δ m t ~ 200 MeV (projection)

6 Top Mass Measurements Methods LHC+Tevatron Direct Reconstruction: kinematic mass determination High top mass sensitivity Precision of MC? Meaning of m MC t? Δ m t ~ 0.5 GeV Δ m t ~ 200 MeV (projection) Indirect Mass Fit: global mass dependence Future Linear Collider: Top Pair Threshold: kinematic mass determination perturbative toponium Total cross section tt+jet invariant mass pqcd calculations dominate Control of mass scheme Lower top mass sensitivity High sensitivity to norm errors Δ m t ~ 1-2 GeV High top mass sensitivity pqcd calculations dominate Control of mass scheme Available (maybe) > 2035 Δ m t ~ 100 MeV

7 Monte-Carlo Event Generators 1) Matrix elements (LO/NLO) 2) Parton shower (LL) 3) Hadronization model Full simulation of all processes (all experimental aspects accessible) QCD-inspired: partly first principles QCD partly model Description power of data better than intrinsic theory accuracy. Top quark in parton shower: treated like a real particle (m t MC m t pole +?). Top quark in splitting function/matrix elements: m t MC = m t pole BUT: parton showers sum (real & virtual!) perturbative corrections only above the shower cut and not pickup any corrections from below. Uncertainty (a): But how precise is modelling? Part of exp. Analyses Unvertainty (b): What is the meaning of MC QCD parameters? Calibration & Theory

8 Top Quark Mass Schemes MS scheme: m(µ) + Useful scheme for apple m 0 = m(µ) 1 = p m 0 (p, m 0,µ) (m 0,m 0,µ)=m 0 h s +... i s +... is pure UV-object without IR-sensitivity µ>m Far away from a kinematic mass of the quark + fin (m 0,m 0,µ) Like running strong coupling Pole scheme: m 0 = m pole apple 1 s +... fin (m pole,m pole,µ) Absorbes all self energy corrections into the mass parameter Close to the notion of the quark rest mass (kinematic mass) Renormalon problem: infrared-sensitive contributions from < 1 GeV that cancel between self-energy and all other diagrams cannot cancel. Should not be used if uncertainties are below 1 GeV! Has perturbative instabilities due to sensitivity to momenta < 1 GeV (Λ QCD )

9 Top Quark Mass Schemes MS scheme: + apple m 0 = m(µ) 1 s +... = p m 0 (p, m 0,µ) (m 0,m 0,µ)=m 0 h s +... i + fin (m 0,m 0,µ) Pole scheme: m 0 = m pole apple 1 s +... fin (m pole,m pole,µ) MSR scheme: m MSR (R) =m pole fin (R, R, µ) Jain, Lepenik, Mateu, Preisser, Scimemi, Stewart, AHH; arxive: Jain, AH, Scimemi, Stewart (2008) Like pole mass, but self-energy correction from <R are not absorbed into mass Interpolates between MSbar and pole mass scheme m MSR t (R = 0) = m pole m MSR t (R = m(m)) = m(m) More stable in perturbation theory. m MSR t (R =1GeV) close to the notion of a kinematic mass, but without renormalon problem.

10 MSR Mass Jain, Lepenik, Mateu, Preisser, Scimemi, Stewart, AHH; arxiv: MS Scheme: MSR Scheme: (R <m(m)) ( m b = m c = 0 ) See Lepenik, Preisser, AHH; arxiv: for treatment of finite m b, m c Short-distance mass that smoothly interpolates all R scales pole mass subtraction for momentum scales larger than R Precision in relation to any other short-distance mass: 20 O(α S4 )

11 Top Quark Mass Schemes R/ Lepenik, Preisser, AHH; arxiv: n t +1=6 >m t m t t t t n t =5 m b b b RG evolution: R-evolution n b =4 n c =3 m c QCD Renormalon c pole m t m t MSR (R) m c <R<m b m t (R) m t (m t ) m t ( ) m b <R<m t m( )>m t

12 Pole Mass Renormalon Problem Asymptotic series Bad convergence Scale dependence underestimates higher order corrections Flat region defines best estimated for pole mass m pole t from m t (m t ) Scale variation: m t (m t )/2 < μ < 2 m t (m t ) m b = m c = 0, m t (m t ) = 163 GeV m t pole [GeV] minimal term Beneke, Marquard, Nason, Steinhauser arxiv: Claim: Minimal term determines best estimate and ambiguity m pole t = 70 MeV (m b = m c = 0) m pole t = 110 MeV (finite m b,m c ) calculated Lepenik, Preisser, AHH; arxiv: extrapolated Order

13 Pole Mass Renormalon Problem Our approach: Lepenik, Preisser, AHH; arxiv: Method respects heavy quark symmetry Ambiguity independent of value of top quark mass (R values) Summation of logarithms of m t, m b, m c Flat region accounted for Low scale determination approach pole mass at much lower orders. m pole t = 180 MeV (m b = m c = 0) m pole t = 250 MeV (finite m b,m c )

14 MC Top Quark Mass (for reconstruction) Jain, Lepenik, Mateu, Preisser, Scimemi, Stewart, AHH; arxiv: linear+log evolution R-evolution (low energy) log evolution (high energy) MSR mass is the extension of the MS mass for scales below the mass.

15 MC Top Quark Mass (for reconstruction) 1) Matrix elements (LO/NLO) 2) Parton shower (LL) 3) Hadronization model m MC t = m MSR t (R = 1 GeV) + t,mc (R =1GeV) t,mc(1 GeV) O(1 GeV) Stewart, AHH, 2008 AHH, 2014 small size of Δ t,mc Renormalon-free little parametric dependence on other parameters

16 Method: Calibration of the MC Top Mass 1) Strongly mass-sensitive hadron level observable (as closely as possible related to reconstructed invariant mass distribution!) 2) Accurate hadron level QCD predictions at NLL/NLO with full control over the quark mass scheme dependence. 3) QCD masses as function of m t MC from fits of observable. 4) Cross check observable independence / universality m MC t = m MSR t (R = 1 GeV) + t,mc (R =1GeV) t,mc(1 GeV) = + MC + pqcd + param Experimental systematics Monte Carlo dependence: QCD errors: Parametric errors: different tunings parton showers color reconnection Intrinsic error, perturbative error scale uncertainties electroweak effects strong coupling α s Non-perturbative parameters Treated in our analysis

17 Boosted Top Quarks First simplification: Q 2p T m t Enables us to be inclusive w.r. to the hard-collinear decay products Top mass from reconstruction of boosted tops consistent with low p T results. More precise studies possible with more statistics from Run-2. Meaning of m t MC for boosted tops and slow top quarks consistent.

18 Theory Issues for pp t t X

19 Theory Issues for pp t t X ( ) Only final-final state color reconnection

20 Thrust Distribution Observable: 2-jettiness in e+e- for Q = 2p T m t =1 max ~n P i ~n ~p i Q (boosted tops) 2!peak M M 2 2 Q 2 Invariant mass distribution in the resonance region of wide hemisphere jets! Excellent mass sensitivity: s peak 4m 2 t 2 =1 1 Q 2 (tree level)

21 Factorization: EFT Treatment n f = n` +1

22 Factorization: EFT Treatment Jain, Lepenik, Mateu, Preisser, Scimemi, Stewart, AHH : NNLL + NLO + non-singular + hadronization + renormalon-subtraction + top quark decay Good convergence Reduction of scale variation (NLL vs. NNLL)

23 Why the Observed Pole is not at the Pole Mass Jet function: perturbative, any mass scheme depends on Breit-Wigner at tree level Gauge-invariant off-shell top quark dynamics Singular functions encode information about where the physical pole is located Fleming, AHH, Mantry, Stewart 2007

24 Why the Observed Pole is not at the Pole Mass Is the pole mass determining the top single particle pole? NO! pole mass peak Invisible for Γ t > 0.5 GeV observable peak pole mass and observable peak separated by non-converging series pole mass peak (residue) decreases with order MSR mass close to observable peak complex ŝ-plane

25 2-Jettiness for Top Production (QCD) d d 2 = f(m MSR t (R), s (M Z ), 1, 2,...,µ h,µ j,µ s,µ m,r, t) any scheme possible Non-perturbative renorm. scales finite lifetime Q=700 GeV (p T = 350 GeV) Q=1400 GeV (p T = 700 GeV) Q=700 GeV Q=1400 GeV MSR mass MSR mass Higher mass sensitivity for lower Q (p T ) Finite lifetime effects included Dependence on nonperturbative parameters Convergence: Ω 1,2, Good convergence Reduction of scale uncertainty (NLL to NNLL) Control over whole distribution

26 MadGraph 5 study: Signal ttbar vs full ee WWbb

27 Pythia Study: Hemisphere Mass Cuts

28 Fit Procedure Details Butenschön, Dehnadi, Mateu, Preisser, Stewart,AH; PRL 117 (2016) 153 (PYTHIA 8.205) Tune 7 (Monash ) Take α S (M Z ) as input from world average. (Sensitivity to strong coupling very weak.) 21 fit setups

29 Fit Result: Pythia vs. Theory Γ t =1.4 GeV, tune 7, m t MC = 173 GeV Ω 1 = 0.44 GeV, m t MSR (1GeV) = GeV Good agreement of PYTHIA with NNLL/NLO theory predictions Perturbative uncertainties of theory predictions based on scale uncertainties (profiles) MC uncertainties: Vertical: rescaled statistical error (PDF rescaling method) independent on statistics Horizontal: fit coverage from 21 fit setups (incompatiblity uncertainty)

30 Convergence & Stability: MSR vs. Pole Mass Good convergence & stability for MSR mass Mass m t MSR (1GeV) mass definition closest to the MC top mass m t MC. Pole mass shows worse convergence. Pole mass not compatible with MC mass within errors 1100/700 MeV difference at NLL/NNLL m t pole M t Pythia 8.2 Similar analyses from the 20 other Q-set and n-range setups. t,mc

31 MSR Mass Tune Dependence Tune dependence partially cancels in the calibration procedure to the extent they affect the observable(s) used for the calibration.

32 Final Result for m t MSR (1 GeV) Spread of results from 21 fit setups m t MSR (1GeV) = ± 0.22 GeV

33 1) Pole mass implemented in code: Pole Mass Determination Δm tp 600 MeV Pole mass smaller than MSR mass Δm tp 700 MeV Pole mass larger than MSR mass 2) Pole mass determined from MSR mass: m pole t m MSR t O( s ) O( 2 s) O( 3 s) O( 4 s) (1 GeV) = GeV GeV s (M Z )=0.118 n f =5 Calibration in terms of the pole mass involves large + higher-order perturbative GeV corrections Additional uncertainty on pole mass: (m pole t ) NLL = ± 0.52 GeV, (added quadratically) (m pole t ) NNLL = ± 0.41 GeV Theoretical ambiguity of the top quark pole mass: 250 MeV Pole mass should be abandoned once uncertainties reach 0.5 GeV. Lepenik, Preisser, AHH; arxiv:

34 Conversion to the Top MS Mass 1) Approach: m t MC ~ m t MSR (1 GeV) m pmsr t (1 GeV) = ± 0.022, GeV m pmsr t (1 GeV) m pmsr t ( GeV) = =9.802 ± GeV m t (m t ) = ± GeV 2) Approach: m t MC ~ m t Pole m pole t m pole t = ± GeV = ± GeV m nmsr t (163 GeV) = m t (m t ) 2loop = ± GeV m t (m t ) 3loop = ± GeV m t (m t ) 4loop = ± GeV No detailed analysis! No electroweak corrections! Can be improved by next order GeV Proper interpretation hard due to renormalon problem. m t (m t ) 8loop = ± GeV

35 Theory Issues for pp t t X

36 Theory Issues for pp t t X

37 Jet Mass of Boosted Top Quarks

38 Theory Issues for pp t t X Extension to pp (in principle) straightforward: (e.g. N-jettiness & X-Cone jets) Same jet functions as e + e -

39 Theory Issues for pp t t X Extension to pp (in principle) straightforward: (e.g. N-jettiness & X-Cone jets) Same jet functions as e + e -

40 Grooming with SoftDrop. Larkowski, Marzani, Soyez, Thaler, 2014 Allows for factorization calculations Frye, Larkowski, Schwartz, Yan, 2016 Mode separation: additional soft-collinear modes

41 Theory Set Up with SoftDrop AH, Mantry, Pathak, Stewart; arxive:

42 Theory Set Up with SoftDrop Modes: massless quarks: top quarks: Frye, Larkowski, Schwartz, Yan, 2016 Mantry, Pathak, Stewart, AHH; arxive:

43 Theory Set Up with SoftDrop AH, Mantry, Pathak, Stewart; arxive: ` k 1 1+ k Q 1 1+ cut,,µ Q cut ( high-p T factorization )

44 Preliminary Studies of SoftDrop Effects AH, Mantry, Pathak, Stewart; arxive:

45 Preliminary Studies of SoftDrop Effects AH, Mantry, Pathak, Stewart; arxive:

46 Preliminary Studies of SoftDrop Effects AH, Mantry, Pathak, Stewart; arxive:

47 Preliminary Studies of SoftDrop Effects AH, Mantry, Pathak, Stewart; arxive:

48 Top Mass Fits (to Pythia 8 output) AH, Mantry, Pathak, Stewart; arxive: Hadronization only: MC mass and MSR mass compatible

49 Top Mass Fits (to Pythia 8 output) AH, Mantry, Pathak, Stewart; arxive: Hadronization only: MC mass and pole mass have larger discrepancy

50 Top Mass Fits (to Pythia 8.2 output) AH, Mantry, Pathak, Stewart; arxive: Hadronization + MPI: MC mass and MSR mass compatible

51 Top Mass Fits (to Pythia 8.2 output) AH, Mantry, Pathak, Stewart; arxive: Hadronization + MPI: MC mass and pole mass have larger discrepancy

52 Summary First systematic MC top quark mass calibration based on e + e - 2-jettiness (large p T ): related to observables dominating the reconstruction method m t Pythia8.2 = 173 GeV m t MSR (1GeV) = ± 0.22 GeV (m t pole ) NLO = ± 0.41 GeV NNLL+NLO QCD calculations based on an extension of the SCET approach concerning massive quark effects (all large logs incl. Ln(m) s summed systematically) describing boosted top quarks. Future: consolidation & extension to pp collisions & MC studies Extension to pp collisions looks very promising with SoftDrop grooming to suppress MPI effects (boosted top quarks essential as well). Provides new ways to test and improve MC event generators. Plans: Public code for calibration (CALIPER) Other e + e - eventshapes (C-parameter, HJM) NNNLL for e + e - pp with SoftDrop (at NNLL) Electroweak corrections Theory of the MC top quark mass: parton shower, hadronization model, NLO matching

53 Backup Slides

54 Peak Fits Parameter Sensitivity m MSR χ α t (5 GeV) s (M Z ) Default renormalization scales; Γ t =1.4 GeV, tune 7, Ω 1,smear =2.5 GeV, m t Pythia =171 GeV, Q={700, 1000, 1400} GeV, peak fit (60/80)% χ 2 min ~ O(100) Very strong sensitivity to m t Low sensitivity to strong coupling Take PDF strong coupling as input: α S (M Z ) = (13) (error irrelevant for m t MSR, m t pole ) χ 2 min and δm t stat do not have any physical meaning PDF rescaling method: (χ 2 min) rescale = 1 can be used to define an incompatibility uncertainty

55 MSR/MS Parametric Dependence on α S m MSR t (1 GeV) m t (m t )

56 Top Mass Reconstruction Error Budget m MC t = ± 0.49 (CMS Run-1 final, 2015) arxiv: NLO ME corrections

57 MSR Mass Definition m MC t = m MSR t ( GeV) = mmsr t (3 GeV) AH, Stewart: arxive: Good choice for R: 1S, PS, mas ses Of order of the typical scale of the observable used to measure the top mass. Peak of invariant mass distribution, endpoints Top-antitop threshold at the ILC Total cross section, e.w.precsion obs., Unification, MSbar mass

58 Masses Loop-Theorists Like to use Total cross section (LHC/Tev): m MSR t (R = m t )=m t (m t ) M t = M (O) t + M t (0) s +... more inclusive sensitive to top production mechanism (pdf, hard scale) indirect top mass sensitivity large scale radiative corrections Langenfeld, Moch, Uwer Threshold cross section (ILC): m MSR t (R 20 GeV),m 1S t,m PS t (R) M t = M (O) t + hp Bohr i s +... hp Bohr i = 20 GeV Inv. mass reconstruction (ILC/LHC): Mass schemes related to different computational methods Relations computable in perturbation theory Beneke, AH, Melnikov, Nagano, Penin, Pivovarov, Teubner, Signer, Smirnov, Sumino, Yakovlev, Yeklkovski Fleming, AH, Mantry, Stewart m MSR t (R t ),m jet t (R) M t = M (O) t + t s +... t = 1.3 GeV more exclusive sensitive to top final state interactions (low scale) direct top mass sensitivity small scale radiative corrections