Jet Mass Spectrum for Groomed and Ungroomed Top Jets Iain Stewart - - PowerPoint PPT Presentation

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Jet Mass Spectrum for Groomed and Ungroomed Top Jets

Iain Stewart MIT

Sante Fe Jets and Heavy Flavor W

• rkshop

January 2018 based on: Hoang, Mantry, Pathak, IS (1708.02586 + ongoing work)

Outline

• Motivation for Studying Top Jets:

Top Mass from Jet Mass measurement Quantify Soft Effects

• Factorization Theorems: Ungroomed and Groomed

Calibration of Monte Carlo and Comparisons Conclusion

172 174 176 178 180 0.002 0.004 0.006 0.008 0.010 0.012

dσ dM

M

mt

M peak model this tion corrections M 2 =

i∈J

pµ

i

2

1

H

:

t

t

The Top Quark is Special

• Largest Mass Largest Higgs Coupling

H ∝ mi i i Dominates Higgs Production

• The only quark that decays before it binds into a hadron

Top width

t → bW Γt = 1.4 GeV >

ΛQCD 0.3 GeV

confinement scale

u d u

mt = 173 GeV

1

H

:

t

t

The Top Quark is Special

• Largest Mass Largest Higgs Coupling

H ∝ mi i i Dominates Higgs Production

• The only quark that decays before it binds into a hadron

Top width

Γt = 1.4 GeV >

ΛQCD 0.3 GeV

confinement scale

u d u

mt = 173 GeV

Breit Wigner

1 q2−m2

t

mt

2 + Γ2

t

mt

t → bW

Why should I care about a precision ?

mt Stability of the Standard Model vacuum!

mt

mHiggs

uncertainty dominated by mt

Andreassen, Frost, Schwartz Butazzo, Degrassi, Giardino, Giudice, Sala

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Precision Electro-weak Measurements Indirect Global Fit Direct Measurements

Gfitter group, 2014

• t

t

measured from jets with help of Monte Carlo simulations

Heaviest known elementary particle. As heavy as 180 protons!

mt = 172.84 ± 0.70 mt = 172.44 ± 0.49 mt = 174.34 ± 0.64

Tevatron CMS ATLAS GeV GeV GeV

MC

MC MC

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Direct Reconstruction Methods (Tevatron & LHC)

t

¯ t

b-jet

b-jet

jet jet jet

jet

p

p

Kinematic Fit: m2

t = p2 t = (pJb + pJ1 + pJ2)2

t

¯ t

hadrons

Λshower = 1 GeV

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Theory (QFT) Experiment Simulation

(Monte Carlo)

mpole

t

, mt, mMSR

t

, . . .

mMC

t

Definition ?

mt = mMC

t

+ ? an additional uncertainty ∼ 1 GeV

L :

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Mass Definitions:

• Pole Mass

Mass that naturally appears in Breit Wigner. Has a (renormalon) ambiguity ∝ 1 p / − mpole

t

∆mpole

t

∼ ΛQCD

Mass

MS

• mt

Not compatible with Breit Wigner. No Ambiguity. X mpole

t

= mt + 0.4 αsmt + . . .

• 7 GeV Γt = 1.4 GeV
• MSR Mass

mMSR(R)

(Hoang, Jain, Scimemi, IS, 2008)

a mass which nicely interpolates

No Ambiguity Breit Wigner R ∼ Γt R > ΛQCD

• take R = 1 GeV

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Soft Effects in

Perturbative soft radiation Hadronization MPI / Underlying Event

t

¯ t

hadrons

t

¯ t

b-jet

jet jet

p p

pp → t¯ tX

pp → t¯ t

Soft Effects can be significant. eg. Jet Mass in Pythia

Theory Issues for

• suitable top mass scheme for jets
• initial state radiation

final state radiation jet observable underlying event/MPI color reconnection parton distributions

• sum large logs

Q mt Γt

pp → t¯ tX

Production Energy

ΛQCD

Γt 1.4 GeV

Q = 2pT ∼ 1 TeV

mt = 173 GeV

• hadronization

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First simplification:

• boosted top quarks,

Q = 2pT mt

enables us to be inclusive over decay products t

ΛQCD

Γt 1.4 GeV

Q = 2pT ∼ 1 TeV

mt = 173 GeV

Soft-Collinear EFT (SCET) Heavy Quark EFT (HQET) Use EFT tools:

factorization, logs, non-perturbative effects

Jets with Substructure

t → Wb → (u ¯ d )(b) = 3 prong jet

pp → t¯ t

Theory Issues for

• suitable top mass for jets
• initial state radiation

final state radiation jet observable underlying event/MPI color reconnection parton distributions

• sum large logs

Q mt Γt

pp → t¯ tX

First

e+e− → t¯ tX

and the issues

• hadronization

Answer

Hard Functions

Evolution and decay of top quark close to mass shell Perturbative Cross talk

(boosted HQET) Jet Functions Soft Function

Fleming, Hoang, Mantry, IS

Factorization for double jet-mass:

(2007)

control over mass scheme

QCD SCET HQET

• d2σ

dM 2

t dM 2 ¯ t

• hemi

= σ0HQ(Q, µm)Hm

• m, Q

m, µm, µ

• ×JB
• ˆ

st − Q m , Γ, m, µ

• JB
• ˆ

s¯

t − Q

m , Γ, m, µ

• Shemi(−k, −k, µ)F(k, k)

Hadronization

dominant effect is from first moment

Ω1 =

• dkdk k F(k, k)

ˆ st ⇥ M 2

t m2

m ⇤ Γ ⌅ m

d d

usoft particles n-collinear jet n-collinear jet

Answer

172 174 176 178 180 0.002 0.004 0.006 0.008 0.010 0.012

dσ dM

M

mt

M peak

measure this extract this

• d2σ

dM 2

t dM 2 ¯ t

• hemi

= σ0HQ(Q, µm)Hm

• m, Q

m, µm, µ

• ×JB
• ˆ

st − Q m , Γ, m, µ

• JB
• ˆ

s¯

t − Q

m , Γ, m, µ

• Shemi(−k, −k, µ)F(k, k)

Factorization for double jet-mass:

Fleming, Hoang, Mantry, IS (2007)

M peak mt + Γt(αs + α2

s + . . .) + QΩ1

mt

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Theory (QFT) Experiment Simulation

(Monte Carlo)

One application: Top Mass Calibration

Butenschoen, Dehnadi, Hoang, Mateu, Preisser, IS PRL 2016

mpole

t

, mt, mMSR

t

, . . .

mMC

t

e+e− = ⇒ pp

mt = mMC

t

+ . . .

• determined by fit to common observable

calibration

e+e− → t¯ t

2

boosted

τ2 ∼ M 2

t + M 2 ¯ t

Example from Fit to Pythia8 Simulation: Results:

• Depend on which QFT based

theory mass is used for fit.

• Provides uncertainties:

input: mMC

t

= 173 GeV mpole

t

= 172.43 ± 0.28 GeV mMSR

t

= 172.82 ± 0.22 GeV

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Calculate pp → t¯

t

boosted top:

pT mt

jet mass

MJ

t

¯ t

b-jet

b-jet

jet jet jet jet

p

p

Theory Issues for

• suitable top mass for jets
• initial state radiation

final state radiation jet observable underlying event/MPI color reconnection parton distributions

• sum large logs

Q mt Γt

pp → t¯ tX

can handle with SCET/HQET

• Jet veto

Jet Mass in Jet of radius R multiple channels

“contamination”

• hadronization

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IS, Tackmann, Waalewijn (2010)

N-jettiness event shapes for hadron colliders

XCone is a particularly nice choice for jet and T2 = min

nt,n¯

t

X

i

min{ρjet(pi, nt), ρjet(pi, n¯

t), ρbeam(pi)}

= T t

2 + T ¯ t 2 + T beam 2

,

t

¯ t

beam jet jet

gives jet-mass T t

2 = M 2 J1

Qt Ungroomed Factorization Formula:

d2σ dM 2

J1dM 2 J2dT beam 2

= tr ˆ HQm ˆ S(T beam

2

, R, . . .)⊗F

• ⊗JB ⊗ JB⊗II ⊗ ff

hard

• pert. soft

hadronization same Jet functions! initial state radiation PDFs

T beam

2

gives jet-veto

Hoang, Mantry, Pathak, IS (to appear soon)

generalizes ee result to LHC

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Hadronization effects

Ω1

first moment dominates , …

x2 = Ω2 − Ω2

1

Ω2

1

Ω2

MPI / UE effects:

higher moments give smaller effects jet mass from massless quarks & gluons, known that using a larger accurately captures MPI effects

ΩMPI

1

> Ω1

(IS, Tackmann, Waalewijn 2015)

ΩMPI

1

pp → t¯ t

Issue is that MPI contamination is significant (Pythia), so uncertainty from this modeling may be too large for a precision measurement.

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Soft Drop

Larkoski, Marzani, Soyez, Thaler 2014

Grooms soft radiation from the jet

z > zcut θβ

two grooming parameters

min(pT i, pT j) pT i + pT j > zcut ∆Rij R0 β

Can still carry out calculations:

Larkoski, Marzani, Soyez, Thaler 2014 Fri, Larkoski, Schwartz, Yan 2016

ie.

To derive

• fact. theorem:

Remove soft contamination. Decouples top-jet from rest of the event!

Light Soft Drop for tops

zcut ∼ 0.01

Q = 2 pT cosh(ηJ)

top decay products & radiation leftover “collinear-soft” radiation

R

soft radiation groomed

Γt 4mt ⇣ Q 4mt ⌘β > ⇠ zcut

, z

1 2+β

cut 1

2 ✓ Γt mt 4m2

t

Q2 ◆

1 2+β

Hoang, Mantry, Pathak, IS (2017)

To derive

• fact. theorem:

Remove soft contamination. Decouples top-jet from rest of the event!

Light Soft Drop for tops

zcut ∼ 0.01

Q = 2 pT cosh(ηJ)

top decay products & radiation leftover “collinear-soft” radiation

R

soft radiation groomed

Γt 4mt ⇣ Q 4mt ⌘β > ⇠ zcut

, z

1 2+β

cut 1

2 ✓ Γt mt 4m2

t

Q2 ◆

1 2+β

Modes:

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MPI contamination reduced by factor of 5 with Light Soft Drop (eg. 4.5 GeV to 0.9 GeV):

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Factorization with Soft Drop on one jet:

Hoang, Mantry, Pathak, IS (2017) d(ΦJ) dMJ = N(ΦJ, zcut, , µ) Z dˆ s0 dΦd Dt(ˆ s0, Φd, m/Q) Z d` JB ⇣M2

J − m2 t − Q`

mt − ˆ s0, m, µ ⌘

⇣ × Z dk SC h⇣ ` − mk Q h

• Φd, m

Q ⌘ (2βQzcut)

1 1+β , , µ

i FC(k, 1)

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Factorization with Soft Drop on one jet:

d(ΦJ) dMJ = N(ΦJ, zcut, , µ) Z dˆ s0 dΦd Dt(ˆ s0, Φd, m/Q) Z d` JB ⇣M2

J − m2 t − Q`

mt − ˆ s0, m, µ ⌘

⇣ × Z dk SC h⇣ ` − mk Q h

• Φd, m

Q ⌘ (2βQzcut)

1 1+β , , µ

i FC(k, 1)

Norm (rest of the event) dynamics of top & its decay products left over perturbative collinear-soft radiation non-perturbative soft radiation

Ω1, x2

0.5 1.0 1.5 2.0 0.2 0.4 0.6 0.8 1.0

k (GeV)

F(k)

Ω1

control of mass scheme

Hoang, Mantry, Pathak, IS (2017)

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Factorization with Soft Drop on one jet:

d(ΦJ) dMJ = N(ΦJ, zcut, , µ) Z dˆ s0 dΦd Dt(ˆ s0, Φd, m/Q) Z d` JB ⇣M2

J − m2 t − Q`

mt − ˆ s0, m, µ ⌘

⇣ × Z dk SC h⇣ ` − mk Q h

• Φd, m

Q ⌘ (2βQzcut)

1 1+β , , µ

i FC(k, 1)

i

tion formula:

Dt(ˆ s0, Φd, m/Q) = Γt ⇡(ˆ s0 2 + Γ2

t ) dt(Φd, m/Q)

t t t t t t t t

b q q

‘

Φd = 5 phase space variables for decay

“decay” fact. thm.

Q < ⇠ 4mt

• 2mtzcut/ΛQCD

1/β

Soft drop stops when comparing energetic top decay products

Hoang, Mantry, Pathak, IS (2017)

t

W

b q q

‘

pt pb p p

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Factorization with Soft Drop on one jet:

d(ΦJ) dMJ = N(ΦJ, zcut, , µ) Z dˆ s0 dΦd Dt(ˆ s0, Φd, m/Q) Z d` JB ⇣M2

J − m2 t − Q`

mt − ˆ s0, m, µ ⌘

⇣ × Z dk SC h⇣ ` − mk Q h

• Φd, m

Q ⌘ (2βQzcut)

1 1+β , , µ

i FC(k, 1)

“decay” fact. thm.

tan(θd/2) = m Q h

• Φd, m

Q

• θd is angle to jet-axis of last

decay product reclustered by soft-drop

Hoang, Mantry, Pathak, IS (2017)

Q < ⇠ 4mt

• 2mtzcut/ΛQCD

1/β

Soft drop stops when comparing energetic top decay products

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Factorization with Soft Drop on one jet:

Hoang, Mantry, Pathak, IS (2017)

Q 4mt(2mtzcut/ΛQCD)1/β

“high-pT”

d(ΦJ) dMJ = N(ΦJ, zcut, , µ)

• d JB

M 2

J − m2 t − Q

mt , Γt, m, µ

• decay products well

inside groomed jet

×

• dk SC
• − k
• k

2βQzcut

• 1

1+β

(2βQzcut)

1 1+β , , µ

• FC(k, )

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Groomed Factorization Results (NLL + Hadronization)

36

Groomed Factorization Results

sensitive to top mass:

37

Hadronization effects (smaller than ungroomed): Ω1 dominates

x2 = Ω2 − Ω2

1

Ω2

1

smaller

Groomed Factorization Results

38

Groomed Factorization Results

pT dependence (smaller than ungroomed): Ungroomed Soft Drop groomed

39

Test Theory Predictions with Simulations

Predict: independent of Jet Radius

• Without

Soft Drop (huge): R

41

zcut dependence (simulation)

Predict transition for “light Soft Drop” most contamination is removed

42

Fit Factorization to Simulations (Calibration)

43

Simultaneous fit to different pTs

pT ≥ 750 GeV

pT ≥ 1000 GeV

no MPI with MPI

Pythia Simulation vs. Factorization (with SoftDrop)

without Contamination:

mMC

t

= 173.1 GeV

mMSR

t

= 172.8 GeV

with Contamination:

mMC

t

= 173.1 GeV

unchanged!

dominant change is as expected:

mMSR

t

= 173.1 GeV

• Ω1

Pythia Simulation vs. Factorization (with SoftDrop)

46

MSR Mass versus Pole Mass

equally good fit (an order dependent shift) pole mass comes out smaller, just like MSR pole

e+e−

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Retain agreement when we vary other knobs:

zcut = 0.02

48

Retain agreement when we vary other knobs:

β = 1

49

But smaller pT fails for Soft Drop:

not unexpected since in pinch of validity region

50

Could still use ungroomed factorization for smaller pT Fit works, gives a larger as expected

ΩMPI

1

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Theory (QFT) Experiment Simulation

(Monte Carlo)

pp Calibration (soft drop) Direct Analysis (ungroomed)

Promising new techniques to answer “what mass is it?”

Summary

• Answers from connecting theory (QFT) to Monte Carlo or Data
• A dominant uncertainty in the top mass is “what mass is it?”

Discussed a promising new method for Top Jet Mass predictions in pp with/without a light Soft Drop

• Can Calibrate MC to determine relation:
• mMC

t

= mt + . . .

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The End

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