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Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... ·...

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Bottom-quark fragmentation and impact on the top mass reconstruction Gennaro Corcella INFN - Laboratori Nazionali di Frascati 1. Introduction 2. QCD calculations and Monte Carlo codes for b-fragmentation in top events 3. Hadronization models and fits to LEP and SLD data 4. B-hadron spectrum in top decay 5. Systematic error on the top mass measurement 6. Conclusions Based on work by G.C., F.Mescia, V. Drollinger, A.D. Mitov, M. Cacciari, LEP, SLD, ATLAS and CMS top/heavy-quark working groups Work in progress with F.Mescia and K.Tywoniuk – Typeset by Foil T E X 1
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Page 1: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Bottom-quark fragmentation

and impact on the top mass reconstruction

Gennaro Corcella

INFN - Laboratori Nazionali di Frascati

1. Introduction

2. QCD calculations and Monte Carlo codes for b-fragmentation in top events

3. Hadronization models and fits to LEP and SLD data

4. B-hadron spectrum in top decay

5. Systematic error on the top mass measurement

6. Conclusions

Based on work by G.C., F.Mescia, V. Drollinger, A.D. Mitov, M. Cacciari, LEP, SLD, ATLAS and CMS top/heavy-quark

working groups

Work in progress with F.Mescia and K.Tywoniuk

– Typeset by FoilTEX – 1

Page 2: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Reliable description of multiple radiation in top production and decay and ofb-quark fragmentation is fundamental in the measurements of the top properties

Monte Carlo event generators (HERWIG/PYTHIA) widely used to simulate topproduction and decay and bottom-quark hadronization

LHC and Tevatron inclusive analyses (dilepton, lepton+jets and all-hadrons)propagate the uncertainty on b-fragmentation to the systematic error due tob-jet energy scale and b-tagging efficiency:

∆mt(bfrag) ≃ 250− 430 MeV ; ∆mt(tot) ≃ 920 MeV (TOPLHCWG)

J/ψ+ lepton final states (103/year in high-luminosity phase)

t→ bW ; b→ B → J/ψ X ; J/ψ → µ+µ− ; W → ℓνℓ

A. Kharchilava, PLB 476 (2000) 73, R. Chierici and A. Dierlamm, CMS Note 2006/058

mmax3ℓ = 0.56 mt − 25.3 GeV Systematics (theo + exp): ∆mt(syst) ≃ 1.47 GeV

b-fragmentation (PYTHIA+Peterson model): ∆mt(frag) ≃ 0.51 GeV

Several calculations and tools are available for bottom fragmentation in topdecays, but not unique strategy for the systematic error: comparing two tunedcodes/computations, one program varying fragmentation parameters, etc.

Page 3: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Top production and decays at hadron colliders, e.g. in qq̄ annihilation

Perturbative QCD allows one to calculate the parton-level (b-quark) spectrum

Phenomenological hadronization models are given in terms of non-perturbativefragmentation functions

σ(t→WB) = σ(t→Wb)⊗Dnp(b→ B)

Dnp(b→ B) contains parameters to be fitted to experimental data

Narrow-width approximation:

dσhaddxB

(t→ B) ≃dΓhad

dxB(t→ B) ;

dΓhad

dxB(t→ B) =

dΓpart

dxb(t→ b)⊗Dnp(b→ B)

– Typeset by FoilTEX – 3

Page 4: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Top decay at NLO:

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t(q) → b(pb)W (pW )(

g(pg)

)

xb =1

1−m2W

/m2t

2pb·ptm2

t

1

Γ0

dxb= δ(1− xb) +

αS(µ)

[

Pqq(xb) lnm2

t

m2b

+A(xb)

]

+O

[(

mb

mt

)p]

Pqq(xb) = CF

(

1 + x2b1− xb

)

+

;

∫ 1

0

dxbf(xb)[g(xb)]+ =

∫ 1

0

dxb[f(xb)− f(1)]g(xb)

Mass logarithms and large-xb terms need resummation (soft/collinear radiation)

– Typeset by FoilTEX – 4

Page 5: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

b-quark energy spectrum in top decaymt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ = mt, µ0 = µ0F = mb, ΛMS

=200 GeV

Solid: soft and collinear resummation Dashes: only collinear resummation

Dots: massive NLO without resummation

Resummations in the NLL approximation:

Collinear: αS ln(m2t/m

2b), α

2S ln(m2

t/m2b), . . . α

nS lnn(m2

t/m2b), α

nS lnn−1(m2

t/m2b), . . .

Soft [1/(1− xb)+ → lnN ]: αS ln2N,αS lnN, . . . αnS lnn+1N,αn

S lnnN, . . .

– Typeset by FoilTEX – 5

Page 6: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Monte Carlo generators for high-energy colliders

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Figure by Frank Krauss

Hard 2 → 2 subprocess: leading-order (LO) matrix element

Parton showers in the soft or collinear approximation

Matrix-element corrections for hard and large-angle parton radiation

Models for hadronization and underlying event

Page 7: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Parton shower algorithms

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θp(E)

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k(ω)

- p2(E2), z = ω/EdP = αS

2π P̂ (z)dz dQ2

Q2 ∆S(Q2max, Q

2)

Q2: ordering variable

∆S(Q2max, Q

2) Sudakov form factor: no radiation in [Q2, Q2max]

∆S(Q2max, Q

2) = exp

−αS

∫ Q2max

Q2

dQ′2

Q′2

∫ zmax

zmin

dzP̂ (z)

HERWIG : Q2 = E2(1− cos θ) ≃ E2θ2/2 Soft approximation: angular ordering

PYTHIA (up to 6.2 version): Q2 = p2

It includes angular ordering only by an additional veto

PYTHIA 6.3 and 8: Q2 = k2T

Showers are equivalent to LO+LL resummation, with the inclusion of some NLLs(ΛMS → ΛMC = ΛMS exp(4Kβ0))

– Typeset by FoilTEX – 7

Page 8: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Hadronization: NP fragmentation functions and Monte Carlo models

DK(x, α) = (1 + α)(2 + α)x(1− x)α ; DP(x, ǫ) =NP

x [1− 1/x− ǫ/(1− x)]HERWIG: cluster model

Perturbative evolution ends at Q2 = Q20

Angular ordering ⇒ colour preconfinement

Forced gluon splitting (g → qq̄)

Colour-singlet clusters decay into the observed hadrons

PYTHIA: string model

q and q̄ move in opposite directions

The colour field collapses into a string with uniform energy density

qq̄ pairs are produced

The string breaks into the observed hadrons

Possible interface with NP fragmentation functions

Tuning involves hadronic and perturbative parameters: Q0, ΛMC, mg, etc. and relieson precise e+e− data (LHC data in future?)

– Typeset by FoilTEX – 8

Page 9: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Bottom-quark fragmentation at the Z0 pole

0

100

200

300

0

100

200

300

0

100

200

300

0

100

200

0.2 0.6 1.0

SLD JETSET+Braaten et al. χ2= 83/16

JETSET+Collins, Spiller χ2= 103/16

JETSET+Lund χ2= 17/15

HERWIG χ2= 94/17

UCLA χ2= 25/17

JETSET+Peterson et al. χ2= 62/16

JETSET+Kartvelishvili et al. χ2= 34/16

JETSET+Bowler χ2= 17/15

En

trie

s

x Brec

x Brec

0.2 0.6 1.0

12-99 8515A1

0

1

2

3

0 0.2 0.4 0.6 0.8 1

xwd

B

1/N

dN

/dxw

d

B

Data

Peterson

0

1

2

3

0 0.2 0.4 0.6 0.8 1

xL

B

1/N

dN

/dxL B

Data

Peterson

ALEPH

0

1

2

3

0 0.2 0.4 0.6 0.8 1

xwd

B

1/N

dN

/dxw

d

B

Data

Kartvelishvili

0

1

2

3

0 0.2 0.4 0.6 0.8 1

xL

B

1/N

dN

/dxL B

Data

Kartvelishvili

0

1

2

3

0 0.2 0.4 0.6 0.8 1

xwd

B

1/N

dN

/dxw

d

B

Data

Collins

0

1

2

3

0 0.2 0.4 0.6 0.8 1

xL

B

1/N

dN

/dxL B

Data

Collins

LEP tuning of PYTHIA+Peterson used in J/ψ + ℓ analysis

Best-fit parameters not the same, e.g. ǫb = 0.0033 (ALEPH), 0.0055 (SLD);αK = 11.9 (OPAL), 13.7 (ALEPH), 10.0 (SLD)

– Typeset by FoilTEX – 9

Page 10: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

G. C. and V. Drollinger, NPB (2005): weakly-decaying B-hadron data from OPAL(mesons and baryons), ALEPH (only mesons) and SLD (mesons and baryons)

HERWIG PYTHIA

CLSMR(1) = 0.4 (0.0)CLSMR(2) = 0.3 (0.0) PARJ(41) = 0.85 (0.30)DECWT = 0.7 (1.0) PARJ(42) = 1.03 (0.58)CLPOW = 2.1 (2.0) PARJ(46) = 0.85 (1.00)

PSPLT(2) = 0.33 (1.00)

χ2/dof = 222.4/61 (739.4/61) χ2/dof = 45.7/61 (467.9/61)

Lund/Bowler fragmentation function (PYTHIA):

fB(z) ∝1

z1+brm2b

(1− z)a exp(−bm2T/z)

HERWIG tuned parameters describe hadron gaussian smearing (CLSMR),baryon/meson (CLPOW) and decuplet/octet (DECWT) ratios, mass spectrum ofb-like clusters (PSPLT)

Our PYTHIA tuning in ATLAS jet-energy measurement (EPJ C73 (2013) 2304) and asa cross-check for top analyses

– Typeset by FoilTEX – 10

Page 11: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Comparing tuned HERWIG and PYTHIA and resummed calculations

NLO+NLL: M.Cacciari and S.Catani, NPB617 (2001) 253-290

Best fit (0.18 ≤ xB ≤ 0.94): α = 17.178± 0.303, χ2/dof = 46.2/53

– Typeset by FoilTEX – 11

Page 12: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

B-hadron spectrum in top decays:

Mild dependence on the top mass in both HERWIG and PYTHIA:

Discussion with CMS/ATLAS folks: xB hard to measure experimentally

– Typeset by FoilTEX – 12

Page 13: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

B-lepton invariant mass according to tuned HERWIG and PYTHIA

– Typeset by FoilTEX – 13

Page 14: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Linear fits to extract mt from mBℓ

HERWIG: 〈mBℓ〉H ≃ −25.31 GeV + 0.61 mt ; δ = 0.043 GeV

PYTHIA: 〈mBℓ〉P ≃ −24.11 GeV + 0.59 mt ; δ = 0.022 GeV

NLO: 〈mBℓ〉NLO ≃ −26.7 GeV + 0.60 mt ; δ = 0.004 GeV

S.Biswas, K.Melnikov and M.Schulze, JHEP 1008 (2010) 048: mBℓ at NLO

∆〈mBℓ〉H,P ≃ 1.2 GeV ; ∆〈mBℓ〉H,NLO ≃ 2.2 GeV ; ∆〈mBℓ〉P,NLO ≃ 1.1 GeV

NLO+showers for top decays or C++ codes may shed light on this discrepancy

– Typeset by FoilTEX – 14

Page 15: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

HERWIG++ : improved fragmentation model and mass-dependent splitting functions

Pqq(z) = CF

[

1 + z2

1− z−

2m2

Q2z(1− z)

]

+

0 0.2 0.4 0.6 0.8 1

xE(B Hadrons)

-0.2-0.1

00.10.2

0

0.5

1

1.5

2

2.5

3

3.5no ME correctionδ = 1.7 GeVδ = 2.3 GeVδ = 3.2 GeVSLD 02

Left: HERWIG++ vs. SLD data on B-hadron energy fraction (δ: shower cutoff)

Right: tuning PYTHIA 8 (C++) to LEP and SLD data (K.Tywoniuk, preliminary)

– Typeset by FoilTEX – 15

Page 16: Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... · b-quark energy spectrum in top decay mt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ

Conclusions and outlook

Bottom fragmentation in top decays is a source of uncertainty on the measurementof the top properties in inclusive (b-tagging and b-energy scale) and exclusive analyses(J/ψ + ℓ)

LO+shower codes and NLO+NLL calculations for b-fragmentation, tuning hadronizationmodels to e+e− data

Predictions for top decays yielded by the different codes exhibit some discrepancies,mostly driven by unsatisfactory tunings

Preliminary results with object-oriented codes exhibit a better description of b-quarkfragmentation in e+e− collisions after the tuning

Perspectives:

Comparing tuned PYTHIA and HERWIG++ can be a valuable way to estimate b-hadronization systematics

Extending the analysis to NLO+showers tools (POWHEG and aMC@NLO with off-shelleffects) and ultimately NNLO calculations

Tuning fragmentation parameters directly to LHC data (tt̄, bb̄, Z/γ+ b) and comparisonwith e+e− fits to test factorization and quality of hadronization models

– Typeset by FoilTEX – 16


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