Status and Research Goals for the Interpretation of the Top Mass

André H. Hoang

University of Vienna

Status and Research Goals for the

Interpretation of the Top Mass

A small history on top mass reconstruction

• 

Many individual measurements with uncertainty below 1 GeV.

• 

Some discrepancies between LHC and Tevatron

• 

Reached < 500 MeV uncertainties

Outline

•  Introduction

•  Multipurpose MCs and Top quark mass schemes

•  Calibration of the Monte Carlo top mass parameter: e

⁺

e

^-

→ t t (2-jettiness)

•  Factorization for pp → t t with and w/o jet grooming (SoftDrop)

•  MC top mass from inside MC:

Parton-shower cutoff dependence of jet masses

•  Summary, future plans

Butenschön, Dehnadi, Mateu, Preisser, Stewart,AH; PRL 117 (2016) 153

Mantry, Pathak, Stewart, AHH; arXive:1708.02586

Plätzer, Samitz, AHH; w.i.p.

⊕ High top mass sensitivity

⊖ Precision of MC ?

⊖ Meaning of m_t^MC ?

Top Mass from Reconstruction

LHC+Tevatron: Direct Reconstruction

kinematic mass determination

Δ m_t ~ 200 MeV (projection) Δ m_t ∼ 0.5 GeV

Determination of the best-fit value of

the Monte-Carlo top quark mass

parameter

m^MC_t = 174.34±0.64 (Tevatron final, 2014) m^MC_t = 172.44±0.49 (CMS Run-1 final, 2015) m^MC_t = 172.84±0.70 (ATLAS Run-1 final, 2016)

Monte-Carlo Event Generators

• 

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

Issue 1: But how precise is modelling? Part of exp. analyses (but theory) Issue 2: What is the meaning of MC QCD parameters?

BUT: parton showers sum (real & virtual !) perturbative corrections only above the shower cut and not pickup any corrections from below.

Theory

1)  Matrix elements (LO/NLO) 2)  Parton shower (NLL)

3)  Hadronization model

Alternative Top Mass Measurements Methods

Total Cross Section:

ATLAS: Eur. Phys. J., C74 (2014) 3109

m^pole_t = 172.9^+2.5_2.6 GeV

m^pole_t = 172.7^+2.4_2.7 GeV CMS: JHEP 09 (2017) 051

Theory: Czakon, Fiedler, Mitov, PRL 110 (2013) 252004

tt+jet mass distribution:

m^pole_t = 173.7^+2.3_2.1 GeV m^pole_t = 169.9^+4.5_3.7 GeV

ATLAS: JHEP 10 (2015) 121 CMS: CMS-PAS-TOP-13-006

Theory: Alioli etal. , Eur.Phys.J. D73 (2013) 2438 Fuster etal. , Eur.Phys.J. D77 (2017) 794

Kinematic endpoints (leptonic top decays):

CMS: JHEP 10 (2015) 121 Theory: Purely MC based

m^MC_t = 173.9^+1.9_2.3 GeV

Alternative Top Mass Measurements Methods

b-jet energy distribution:

CMS: CMS-PAS-TOP-15-002

Theory: Agashe etal., Eur.Phys.J. C76 (2016) 636 m^MC_t = 172.3±2.9 GeV

Leptonic observables (no kinematic mass dependence):

m^pole_t = 173.2±1.7 GeV ATLAS: Eur.Phys.J. C77 (2017) 804 CMS: CMS-PAS-TOP-13-006

m^pole_t = 171.7^+2.9_3.3 GeV

Theory: Frixione, Mitov , JHEP 09 (2014) 012

• 

Unrealistic to expect that these method ever reach precision of reconstruction

• 

More inclusive observables more sensitive to norm uncertainties

• 

Essential problem is what the top quark state is one is sensitive to remains unresolved.

• 

Hadronization effects related to the top quark state unavoidable (top = color triplet)

• 

Represent cross checks of reconstruction 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

Method:

•  different tunings

•  parton showers

•  color reconnection

•  Intrinsic error, …

m^MC_t = m^MSR_t (R = 1 GeV) + _t,MC(R = 1 GeV)

t,MC(1 GeV) = ¯ + MC + pQCD + param

•  perturbative error

•  scale uncertainties

•  electroweak effects

•  strong coupling α_s

•  Non-perturbative parameters

✓

✓

✓

Monte Carlo dependence: QCD errors: Parametric errors:

Treated in our analysis Experimental

systematics

m^MSR_t (Q₀) = m^pole_t ↵_s(Q₀)

4⇡ Q₀ ⇥ 5.33

Thrust Distribution

Observable: 2-jettiness in e+e- for Q = 2p

_T

≫ m

_t

(boosted tops)

⌧ = 1 max

_~n

P

i

| ~ n · ~ p

_i

| Q

Invariant mass distribution in the resonance region of wide hemisphere jets !

⌧₂^peak = 1 s

1 4m²_t Q² Excellent mass sensitivity:

(tree level)

⌧₂!peak

⇡ M

₁²

+ M

₂²

Q

²

Boosted Top Quarks

•  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.

First simplification:

•  Enables us to be inclusive w.r. to the hard-collinear decay products

Q 2p

_T

m

_t

d

d⌧

₂

= f (m

^MSR_t

(R), ↵

_s

(M

_Z

), ⌦

₁

, ⌦

₂

, . . . , µ

_h

, µ

_j

, µ

_s

, µ

_m

, R,

_t

)

2-Jettiness for Top Production (QCD)

MSR mass

MSR mass

•  Good convergence

•  Reduction of scale

uncertainty (NLL to NNLL)

•  Control over whole distribution

•  Higher mass sensitivity for lower Q (p

_T

)

•  Finite lifetime effects included

•  Dependence on non- perturbative parameters

•  Convergence: Ω

_1,2,…

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

any scheme possible

Fit Procedure Details

▶ Tune 7 (Monash︎)

21 fit setups

(PYTHIA 8.205)

▶ Take α_S(M_Z) as input from world average.

(Sensitivity to strong coupling very weak.)

Butenschön, Dehnadi, Mateu, Preisser, Stewart,AH; PRL 117 (2016) 153

Fit Result: Pythia 8.205 vs. Theory

Γ_t=1.4 GeV, tune 7, m_t^MC = 173 GeV

Ω₁ = 0.44 GeV,

m_t^MSR(1GeV) = 172.81 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)

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

Final Result for m t MSR (1 GeV)

m

_t^MSR

(1GeV)

= m

_t^MC

- 0.18 ± 0.22 GeV

MSR Mass Tune Dependence

1 3 7

Extension to pp → t t X

Extension to pp (in principle) straightforward: (e.g. N-jettiness & X-Cone jets)

Same jet functions as e

⁺

e

^-

Extension to pp → t t X

Same jet functions as e

⁺

e

^-

Extension to pp (in principle) straightforward: (e.g. N-jettiness & X-Cone jets)

Jet Mass of Boosted Top Quarks

Grooming with SoftDrop

Larkowski, Marzani, Soyez, Thaler, 2014

•  Allows for factorization calculations

•  .

Frye, Larkowski, Schwartz, Yan, 2016

Mode separation: additional soft-collinear modes

Theory Set Up with SoftDrop

AH, Mantry, Pathak, Stewart; arXive:1708.02586

⇣` k⇣ k Q_cut

⌘₁₊¹ ⌘ Q

1 1+

cut , , µ

SoftDrop Effects

AH, Mantry, Pathak, Stewart; arXive:1708.02586

Top Mass Fits (to Pythia 8 output)

AH, Mantry, Pathak, Stewart; arXive:1708.02586

Hadronization only: MC mass and MSR mass compatible

→ Results compatible with 2-jettiness calibration for e⁺e^- annihilation.

Top Mass Fits (to Pythia 8.2 output)

AH, Mantry, Pathak, Stewart; arXive:1708.02586

Hadronization + MPI: MC mass and MSR mass compatible

→ Results compatible with 2-jettiness calibration for e⁺e^- annihilation.

Understanding m t MC from within MC’s

Understanding the interface of Parton Shower and Hadronization Model Central Task:

1)  What is the principle precision current MCs have concerning the interpretation of m_t^MC ?

ü

2)  What is the role the shower cut Q₀? (ü)

3)  What is the role of “practical multi-purpose issues” contained in the MC?

• 

Parton shower dependence on Q₀ (role of unitarization, coherent branching vs dipole)

• 

Hadronization model dependence on Q₀ (string vs cluster)

• 

Tests of factorization

• 

Choice of renormalization scales

• 

Gluonmass, etc.

• 

Parton shower dependence on Q₀ (role of unitarization)

• 

Hadronization model dependence on Q₀

Understanding intrinsic limitations and pQCD content of MC

S. Plätzer, D. Samitz, AHH w.i.p.

Quark Mass Threshold in Coherent Branching

How precisely can MCs define the quark mass definition they use in principle?

J(k², Q, m) = (k² m²) + CF↵s

2⇡



8L_m⇣ln(k² m²) k² m²

⌘

+ 8⇣ln(k² m²) k² m²

⌘

+

+(4L²_m + 2Lm + ANLO[6= 2⇡²]) (k² m²)

LL + NLL produced by parton shower

A_NLO fixed by unitarization

Result in pole mass scheme ! Note: In the single particle threshold region all MCs use the narrow width approximation,

which is based on the factorization of on-shell production and on-shell decay.

We consider the quasi collinear limit (Q >> m).

P_QQ(↵_s,q˜², z) = P_qq(↵_s,q˜²) + ↵_sC_F 2⇡

2m² z(1 z)˜q²

Quark Mass Threshold in Coherent Branching

Peak position x₀ of function f(x): f(x) = f₀(x) + ↵(f₁(x) + f₀(x))

LO: f₀⁰(x^LO₀ ) = 0

J(k², Q, m) = (k² m²) + C_F↵_s 2⇡



8Lm

⇣ln(k² m²) k² m²

⌘

+ 8⇣ln(k² m²) k² m²

⌘

+

+(4L²_m + 2L_m + A_NLO[6= 2⇡²]) (k² m²)

NLO: f⁰(x^NLO₀ ) = 0, x^NLO₀ = x^LO₀ x₀

, f⁰(x^LO₀ x₀) = f₀⁰(x₀) f₀⁰⁰(x^LO₀ ) x₀ +↵(f₁⁰(x₀) +f₀⁰(x₀)) , x₀ = ↵ f₁⁰(x0)

f₀⁰⁰(x0)

= 0 = 0

⇒ NLL MC has full NLO precision concerning mass threshold !

LL + NLL produced by parton shower

Same form !

Quark Mass Threshold in Coherent Branching

• 

^{PS uses m}_t^{pole for Q}₀⁼⁰

• 

Realistically, PS use Q₀>0 with values small enough to be unresolved for observables: e.g. due to hadronization smearing.

• 

^{Finite Q}₀ does not affect the total cross section due to unitarization:

Z

dM J(M, Q)_Q0 = 1

J (M, Q)

Q₀=0

J(M, Q)_Q⁰₀ J(M, Q)_Q0

= m(m, Q, Q⁰₀, Q₀) ⁰(M m^pole_t ) +. . .

J (M, Q)

Q₀

, J (M, Q)

_Q⁰

0>Q0

Quark Mass Threshold in Coherent Branching

• 

Using a finite shower cut Q₀ causes a change in the threshold location from the unresolved regime (multipole expansion)

• 

This implies that for Q₀>0 the PS does not use the pole mass scheme, but a low

scale short distance mass scheme.

J (M, Q)

Q₀=0

J(M, Q)_Q⁰₀ J(M, Q)_Q0

= m(m, Q, Q⁰₀, Q₀) ⁰(M m^pole_t ) +. . .

J (M, Q)

Q₀

, J (M, Q)

_Q⁰

0>Q0

m(m, Q, Q⁰₀, Q₀) = ↵_s

⇡

⇣#Q

m + #⌘

(Q⁰₀ Q₀) soft ultrcollinear

“dead cone”

Quark Mass Threshold in Coherent Branching

0.4 0.6 0.8 1.0 1.2 1.4 1.6 Q0

0.281 0.282 0.283 0.284 τ₂

Q = 500 GeV

2-Jetiness distribution in e⁺e^- annihilation

Caveats (for those who want to attempt immediate phenomenological interpretation)

• 

Realistic MC use various phenomenological approximation and modifications that may change the result the the interpretation.

• 

Still lot of work left to do.

m

^P.Sh._t

(Q

₀

) = m

^pole_t

↵

_s

(Q

₀

)

⇡ Q

₀

c

NLO corrections calculable

Summary and Outlook

• 

MC top mass calibration:

• 

Theory for the MC top quark mass:

▶︎ m_t^Pythia = m_t^MSR(1GeV) +0.18 ± 0.22 GeV

• 

Public code for calibration (CALIPER)

• 

Extend to other e⁺e^- eventshapes (C-parameter, HJM)

• 

NNNLL for e⁺e^- 2-jettiness

• 

Application to bottom production → 2-loop SCET massive quark jet function

• 

Electroweak corrections → log summation, tadpoles, more differential

• 

pp with SoftDrop (at NNLL) → precision tests with LEP data / of MC

• 

Parton shower (cutoff-dependence)

• 

Hadronisation model

• 

Tests of factorization

• 

Extension of matching

• 

Finite lifetime effects

Introducing Herwig 7

Herwig Herwig++

HERWI G

The Herwig family is one of three multipurpose event generators.

Herwig++ has seen a ten-year development to meet a

milestone intended to succeed the FORTRAN HERWIG program.

This milestone evolved over time as the experimental and phenomenological needs did.

On top of its first definition (= at least as good as HERWIG), precision has become the key goal

Herwig++ 3.0 → Herwig 7.0

[Herwig collaboration – Eur.Phys.J. C76 (2016) 665]

Simon Plätzer

Herwig (related) activities

Development centered around two shower algorithms.

Automated NLO QCD matching and merging is key working horse for precision.

Matching systematics, (shower) uncertainties and tops are main focus recently.

Phenomenological effort centred around VBF and VBS. → VBFSCan (CA 16108)

Improvements to hadronization models and colour reconnection underway.

Subleading-N corrections and theoretical frameworks under development.

[Gieseke, Stephens, Webber – JHEP 0312 (2003) 045] [Plätzer, Gieseke – JHEP 1101 (2011) 024]

[Plätzer, Gieseke – EPJ C72 (2012) 2187] [Bellm, Gieseke, Plätzer – arXiv:1705.06700]

[Bellm, Nail, Plätzer, Schichtel, Siodmok – EPJ C76 (2016) 665] & work in progress

[Campanario, Figy, Plätzer, Sjödahl – PRL 111 (2013) 211802]

[Plätzer, Rauch –EPJ C77 (2017) 293] & work in progress

[Gieseke, Kirchgaesser, Plätzer – EPJ C78 (2018) 99] & work in progress

[Plätzer, Sjödahl – JHEP 1207 (2012) 042]

[Angeles Martinez, DeAngelis, Forshaw, Plätzer, Seymour – arXiv:1802.xxxx]

Simon Plätzer

Backup Slides

Multipurpose Event Generators

Indispensable tools

for experiments & phenomenology.

Realistic, fully detailed simulation spanning orders of magnitude in relevant energy scales.

Factorization dictates work flow.

Hard process calculation Parton shower algorithms Multiple interaction models Hadronization models

Simon Plätzer

• 

Very strong sensitivity to m_t

• 

Low sensitivity to strong coupling

• 

Take PDF strong coupling as input: α_S(M_Z) = 0.1181(13)

(error irrelevant for m_t^MSR, m_t^pole)

• 

^𝝌2_min ^{and δm}_t^{stat do} not have any physical meaning

• 

PDF rescaling method:

(𝝌²_min)^rescale = 1

can be used to define an

Peak Fits Parameter Sensitivity

●

●

●

● ● ● ● ● ●

●

●

167 168 169 170 171 172 0

2500 5000 7500 10000 12500 15000 17500

●

● ●

●

●

●

●

●

●

●

●

0.113 0.114 0.115 0.116 0.117 108.5

109.0 109.5 110.0 110.5 111.0

α χ²

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)%

2

2 m^MSR_t (5 GeV)

↵s(MZ)

𝝌²_min ~ O(100)

MSR/MS Parametric Dependence on α S

m^MSR_t (1 GeV)

m_t(m_t)

Signal ttbar vs full ee→WWbb

MadGraph 5 study:

Pythia Study: Hemisphere Mass Cuts

Pole Mass Determination

m^pole_t m^MSR_t (1 GeV) = 0.173 + 0.138 + 0.159 + 0.23 GeV + 0.53 + 1.43 + 4.54 + 16.6 GeV + 68.6 + 317.7 + 1629 + 9158 GeV

↵

s

(M

Z

) = 0.118 n

f

= 5

• 

Calibration in terms of the pole mass involves large higher-order perturbative corrections

• 

Additional uncertainty on pole mass: (m_t^pole)_NLL = 172.45 ± 0.52 GeV, (added quadratically) (m_t^pole)_NNLL= 172.72 ± 0.41 GeV

• 

Theoretical ambiguity of the top quark pole mass: 250 MeV

Pole mass should be abandoned once uncertainties reach 0.5 GeV.

O(↵s) O(↵²_s) O(↵³_s) O(↵⁴_s)

1) Pole mass implemented in code:

2) Pole mass determined from MSR mass:

Δm_t^p ≈ 700 MeV Δm_t^p ≈ 600 MeV

Lepenik, Preisser, AHH; arXiv:1706.08526

Pole mass smaller than MSR mass

Pole mass larger than MSR mass

Conversion to the Top MS Mass

m

^pMSR_t

(1 GeV) m

^pMSR_t

(163.018 GeV) =

= 8.913 + 0.906 + 0.052 0.070 ± 0.035 GeV

= 9.802 ± 0.035 GeV m

^pMSR_t

(1 GeV) = 172.82 ± 0.022, GeV

m

_t

(m

_t

) = 163.020 ± 0.230 GeV 1) Approach: m

_t^MC

~ m

_t^MSR

(1 GeV)

2) Approach: m

_t^MC

~ m

_t^Pole

m

^pole_t

= 172.72 ± 0.410 GeV

m

^pole_t

m

^nMSR_t

(163 GeV) = 7.505 + 1.581 + 0.481 + 0.193

+ 0.111 + 0.079 + 0.066 + 0.064 + 0.071 + . . . GeV m

_t

(m

_t

)

_2loop

= 163.634 ± 0.890 GeV

m

_t

(m

_t

)

_3loop

= 163.153 ± 0.475 GeV

No detailed analysis!

No electroweak corrections!

Can be improved by next order

Proper interpretation hard due to renormalon problem.

Preliminary Studies of SoftDrop Effects

AH, Mantry, Pathak, Stewart; arXive:1708.02586

Proposal for VCES Cost Support 2019

A short history :

•  First meeting in 1978

•  Started as joint Vienna-Bratislava seminars

Walter Thirring (U Vienna), Milan Petráš (Comenius U), Mikuláš Blažek (SAS)

•  Approximately covering countries within former Austro- Hungarian Empire

Triangle = (Vienna, Bratislava, Budapest)

GP3 activity !!

Proposal for VCES Cost Support

1)  Nov 25-28, 2004:

2)  Nov 25-27, 2005:

3)  Dec 1-3, 2006:

4)  Nov 30-Dec 2, 2007:

5)  Nov 28-30, 2008:

6)  Nov 27-20, 2009:

7)  Nov 26-28, 2010:

8)  Nov 25-27, 2011:

9)  Nov 30-Dec 2, 2012:

10)  Nov 28-29, 2014:

11)  Nov 27-28: 2015:

Advances in Quantum Field Theory Frontiers in Astroparticle Physics

Challenges in Particle Physics Phenomenology Commutative and Noncommutative Quantum Fields Highlights in Computational Quantum Field Theory Effective Field Theories

Complex Stochastic Dynamics Particle Physics and the LHC

Dark Matter, Dark Energy, Black Holes – Quantum Aspects of the Universe Inflation and Cosmology

Quantum and Gravity

→ Prior to 2004: Vienna Triangle Seminar

Proposal for VCES Cost Support

•  2-3 day conference

•  Approx. 100 participants

•  Venue: somewhere in Vienna (likely University Vienna location)

•  COST support aimed to support (in particular young) researchers from ITCs:

500 Euros lumpsum per capita → 16 x EUR 500 = EUR 8000

•  Talks by invitation, participation bu registration

•  50 Euros registration fee (except for local (→DKPI support) and supported participants)

•  Local organizers: Simon Plätzer, Massimiliano Procura, André Hoang

•  External organizers welcome, organization starts fall 2018