Precision Jet Substructure using Soft Collinear Effective Theory

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Precision Jet Substructure using Soft Collinear Effective Theory

Yang-Ting Chien

LHC Theory Initiative Fellow, MIT Center for Theoretical Physics

November 9, 2017

Workshop of Recent Developments in QCD and QFTs, NTU

with Ivan Vitev (PRL 119, 112301 (2017)) and Iain Stewart (to appear soon)

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Outline

I

Jets

I

hard probes of quark-gluon plasma

I

precision jet substructure and grooming

I

Soft Collinear Effective Theory (SCET)

I

Hard and soft jet substructure

I

splitting function and subjet distribution

I

groomed jet mass with small jet radius

I

Conclusion

Y.-T. Chien Precision jet physics 2 / 29

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The creation of the Quark Gluon Plasma (QGP)

I A hot and dense medium is created during heavy ion collisions

I The medium quickly thermalizes and allows a hydrodynamic description of its spacetime evolution, eventually turning into soft hadrons

I Energetic jets are also produced abundantly in the medium

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Jets and QCD

I Jets are collimated particles observed at high energy colliders

I They are manifestations of underlying partons and defined using jet algorithms with radius R I Jet physics gets the richest in heavy ion

collisions

I Thousands of particles are produced and the underlying event backgrounds are enormous

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Jet algorithm

kT anti kT

β = 1: kT β = 0, C/A β = −1, anti-kT I Jet clustering algorithms merge pairs of closest particles until the angular resolution R I The distance dijbetween particles i and j is defined as dij= min(p^2β_ti , p^2β_tj )∆R²_ij/R²

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Jets are quenched and modified in heavy ion collisions

I Jets are not only embedded in an enormous underlying event background but also significantly modified

I Because of the huge background, one needs to do both background subtraction and jet grooming and measure jets with small radii (0.2 < R < 0.4)

I Dramatic suppression of jets and momentum imbalance is observed

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Hadron and jet cross section suppression

I R_AA< 1 is the ratio of the cross sections in AA and pp collisions

ATLAS s_NN = 2.76 TeV

R = 0.4, È Η È < 2

50 100 150 200 250 300 350 400

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

p_T R_AA

g = 2.0 H± 0.2L centrality 0-10%

centrality 30-50%

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Jet spectroscopy of the QGP

ΨJ(r) = P

ri<rE_{T i} P

ri<RE_{T i} hΨi = 1

N_J

NJ

X

J

ΨJ(r, R)

ρ(r) =dhΨi dr

I Jets have become essential tools to probe the quark-gluon plasma produced in heavy ion collisions

I One typically evaluates the observable modification by the ratio of the curves in AA and pp collisions^O_O^AApp

I With detailed understanding of jets and their structures we can relate their modifications to the medium properties: the need of precise jet substructure studies

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Jet substructure calculation and resummation

I Jet shapes probe the averaged energy distribution inside a jet I The infrared structure of QCD induces Sudakov logarithms I Fixed order calculation breaks down at small r

I Large logarithms of the form αⁿ_slog^mr/R (m ≤ 2n), n = 1, ..., ∞ need to be resummed I Sensitive to the partonic origin of jets and the quark/gluon jet fraction

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QCD and effective field theory

Systematically decompose QCD radiations

I Resolve jets at different energy scales

I A jet is not simply a parton but with sequential branching and splitting

I Substructure measurements allow us to study the jet formation mechanism at various energy scales

I The dominant contributions to jet observables come from radiations which are

I Energetic, collinear

I Soft, ubiquitous (not necessarily collinear)

I Power counting by systematically defining collinearity and softness

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Resummation and effective field theory

THE BASIC IDEA

I Logarithms of scale ratios appear in perturbative calculations

I Logarithms become large when scales become hierarchical log r

R= logscale 1 scale 2

I In effective field theories, logarithms are resummed using renormalization group evolution between characteristic scales

I To resum all the logarithms we need to identify all the relevant scales in EFT

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Resummation using Soft-Collinear Effective Theory (SCET)

I Effective field theory techniques are most useful when there is hierarchy between characteristic energy scales

I SCET factorizes physical degrees of freedom in QCD by a systematic expansion in power counting

I Match SCET with QCD at the hard scale by integrating out thehardmodes

I Integrating out the off-shell modes givescollinear Wilson lines which describe the collinear radiation

I The soft sector is described bysoft Wilson linesalong the jet directions

QCD

SCET

Soft cross talk

n ¯n

R r

µ_j_R≈ EJ× R

µ_j_r≈ EJ× r

µ Renormalization group evolution

between µjrand µjRresums log µjr/µjR= log r/R (Chien et al 1405.4293)

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Power counting in SCET

I The scaling of modes in lightcone coordinates (¯n· p, n · p, p⊥) where n = (1, 0, 0, 1) and ¯n= (1, 0, 0, −1):

p_h: EJ(1, 1, 1), pc: EJ(1, λ², λ) and ps: Es(1, R², R)

I E_Jis thehardscale which is the energy of the jet

I λis thepower counting parameter (λ < R)

I EJλis thejetscale which is significantly lower than EJ I The relevantsoftscales depend on observables I QCD =O(λ⁰)+ O(λ¹) + · · ·in SCET

I Leading-power contribution in SCET is a very good approximation

p⁺ p⁻

soft

collinear hard

ultrasoft SCET_II SCETI

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Multiple scattering in a medium and QCD bremsstrahlung

I Coherent multiple scattering and induced bremsstrahlung are the qualitatively new ingredients in the medium parton shower

I Interplay between multiple characteristic scales:

I Debye screening scale µ

I Parton mean free path λ

I Radiation formation time τ

µ

∆Z L

I Jet-medium interaction using SCET with background Glauber gluon fields SCETG(Glauber-collinear: Majumder et al, Vitev et al. Glauber-soft: work in progress)

I Leading-order medium induced splitting functions P_i→jl^med(x, k⊥)were calculated using SCETG(Vitev et al)

∆z

x, k⊥

q_⊥ 1− x, − k⊥

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First quantitative understanding of jet shape modification

I Cold nuclear matter effect is negligible I Jet quenching increases the quark jet fraction I Jet-by-jet the shape is broadened

I Chien et al 1509.07257 and CMS data 1310.0878

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How do we isolate physics and distinguish jet quenching models?

I Jets are multi-scaled objects with rich information about the physics across the entire energy spectrum

I Jet observables have different sensitivities to physics at different energy scales I Through a series of jet measurements we can map out the whole jet formation history I Whether the model relies on the low scale physics corresponds to two rough pictures of jet

quenching

I Yes. Parton showers are not affected much until the later stages. The medium depletes the partons out of the jet

I No. The medium effects open up more channels in the jet formation process, all the way from the hard process through hadronization

I Can we test the two pictures and the role of medium response?

I We are able to dissect radiations and pick out the components of interest

I The idea: come up with an observable as insensitive to low scale physics as possible

I The tool: jet grooming

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Jet grooming is actually artificial jet quenching

I It is a controlled way to remove soft radiation

I How does a jet quenching model confront with jet grooming?

I Do they add up or interfere?

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Groomed momentum fraction z

g

dropped

θ

z

I Soft Drop: a tree-based procedure to drop soft radiation (Larkoski et al 1402.2657)

I Recluster a jet using C/A algorithm: angular ordered

I For each branching, consider the pTof each branch and the angle θ

I Drop the soft branch if z < zcutθ^β, where z =^min(p_p ^T,1^,p^T,2⁾

T,1+p_T,2

I CMS used β = 0, zcut= 0.1, R = 0.4, ∆R12> ∆ = 0.1 and measured zg I z_g: the momentum fraction of the soft branch. rg: the angle between the branches

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z

_g

and splitting functions

x, k⊥

1− x, − k⊥

P (x, k⊥)∝x k¹_⊥ ∆z

x, k⊥

q⊥ 1− x, − k⊥

I In vacuum, the soft branch kinematics is closely related to the Altarelli-Parisi splitting function

I In the medium, the bremsstrahlung component modifies the soft branch kinematics

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Analysis of z

g

0 1/2 1 x

k_⊥

θ = R

θ = ∆ x = z_cut x = 1− zcut

x 1− x

θ x, k_⊥ k_⊥= ω tan^θ₂x(1− x)

ω

I The partonic phase space is constrained by R (jet algorithm), ∆ (jet selection) and zcut(jet grooming)

I At leading order, the 1 → 2 branching probability directly affects the subjet distribution P_i→jl(x, k⊥) = P_i→jl^vac (x, k⊥) + P_i→jl^med(x, k⊥)

I The distributions of zgand rgare calculated (P(x) = P(x) + P(1 − x))

p_i(zg) = RkR

k_∆dk⊥P_i(zg, k⊥) R1/2

zcut dxRkR

k_∆dk⊥Pi(x, k⊥)

, p_i(rg) = R1/2

zcut dx p_Tx(1 − x)Pi(x, k⊥(rg, x)) R1/2

zcut dxRkR

k_∆dk⊥Pi(x, k⊥)

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Theory calculation of z

g

I The medium enhances the small zgand suppresses the large zgregions, and the effect becomes smaller for higher pTjets

I Cutting on the angle between branches selects a special subset of the jet sample

I Jets with a two prong structure not typical for QCD jets

I The scale of this subjet branching is high: hard jet substructure

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Theory calculation of z

g

zg

0.1 0.2 0.3 0.4 0.5

PbPb/pp

0.4 0.6 0.8 1 1.2 1.4 1.6

Data

JEWEL Coherent antenna BDMPS

, L = 5 fm = 1 GeV/fm2

q

, L = 5 fm = 2 GeV/fm2

q

CMS Centrality: 0-10%

< 160 GeV

T,jet

140 < p

zg

0.1 0.2 0.3 0.4 0.5

PbPb/pp

0.4 0.6 0.8 1 1.2 1.4 1.6

< 250 GeV

T,jet

200 < p

zg

0.1 0.2 0.3 0.4 0.5

PbPb/pp

0.4 0.6 0.8 1 1.2 1.4

1.6 anti-k_T R = 0.4, |ηjet^{| < 1.3}

< 180 GeV

T,jet

160 < p

zg

0.1 0.2 0.3 0.4 0.5

PbPb/pp

0.4 0.6 0.8 1 1.2 1.4 1.6

SCETChien-Vitev g = 1.8 g = 2.2

= 4 GeV/fm2 q0 HT

Coherent Incoherent

< 300 GeV

T,jet

250 < p

zg

0.1 0.2 0.3 0.4 0.5

PbPb/pp

0.4 0.6 0.8 1 1.2 1.4

1.6 = 0.1, ∆R12^{> 0.1}

= 0, zcut

β Soft Drop

< 200 GeV

T,jet

180 < p

zg

0.1 0.2 0.3 0.4 0.5

PbPb/pp

0.4 0.6 0.8 1 1.2 1.4 1.6

< 500 GeV

T,jet

300 < p b-1

µ , PbPb 404 = 5.02 TeV, pp 27.4 pb-1

sNN

I Quantitatively agreeing with the CMS data

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Theory prediction for r

g

I The subjet angular distribution will reveal the nature of QCD bremsstrahlung I It will be a direct probe of the medium scale

I The next step is the groomed jet mass

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Groomed jet mass

I Invariant mass of soft-dropped jet: m²= (P pi)² I Factorization in SCET

0 1/2 1 x

k

_⊥

θ = R

θ = ∆

x = z

cut

x = 1 − z

cut

θ x, k

_⊥

k

_⊥

= ω tan

^θ₂

x(1 − x)

ω m

²

=

_x(1^k_−x)²^⊥

µ_h≈ EJ

µ_hc≈ EJR µ_s≈ EJR z_cut

µ_c≈ m µsc≈ m√zcut

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Power counting of modes

I Factorization and resummation:

I In-jet soft mode

p_s= EJz_cut(1, R², R), with µs= EJRz_cut I Collinear mode

p_c= (EJ,m²

E_J, m), with µj= m

I Soft-collinear mode respecting the measurement xθ²∼ m²/E²_Jand jet grooming z_cut∼ x(θ/R)^−β

p_sc= (EJz_cut

m

E_JR√ z_cut

^2β

2+β,m² E_J, m√

z_cut

m

E_JR√ z_cut

^β

2+β), with µsc= m√ z_cut

m

E_JR√ z_cut

^β

2+β

I Hard collinear mode from pure jet reconstruction

p_j_R= EJ(1, R², R), with µjR= EJR

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Groomed jet mass function

I The process-independent groomed jet mass function J_M^/^s(m², µ)captures all the soft-collinear radiation inside jets (i = q, g)

J^i/_M^s(m², µ) = Z

dp²dkJ_i(p², µ)S^/_i^s(k, R, zcut, µ)δ(m²− p²− 2EJk)

where S^/_i^s(k, R, zcut, µ) = S^C_i(k, R, zcut, µ)S^IN_i (R, zcut, µ)

I Medium-induced splitting functions are used to calculate the modification of J^/_M^s(m², µ). At O(α_s),

J_M^i/^s(m², µ) =X

j,k

Z

PS

dxdk_⊥Pi→jk(x, k⊥)δ(m²− M²(x, k⊥))Θalg.Θ_/s

M²(x, k⊥) = ^k

2⊥

x(1−x), Θ_k_T= Θ(EJRx(1 − x) − k⊥), Θ_/_s = Θ(EJRx(1 − x)

x zcut

1/β

− k⊥).

I The full jet mass distribution can be calculated by weighing the groomed jet mass functions with jet cross sections

dσ dm² = X

i=q,g

Z

PS

dp_Tdy dσⁱ

dpTdyP^/_i^s(m², µ), where P^/_i^s(m², µ) =J^i/_M^s(m², µ) J_unⁱ (µ)

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Resummed groomed jet mass function

I Each function is calculated at 1-loop and depends on a single scale

I P^/_i^s(m², µ)is manifestly renormalization group invariant. Logs are resummed using the RG evolution of each function.

P^/_i^s(m², µ)

= exp h

22 + β

1 + βC_iS(µsc, µs) − 4CiS(µj, µs) + 2CiS(µjR, µs) + 2AJi(µj, µjR) + 2ASi(µsc, µjR) i

× µ²_jz

1 1+β cut

µ

2+β 1+β

sc (2EJtan^R₂)^1+β^β

2CiA_Γ(µs,µsc)2EJtan^R₂ µjR

2CiA_Γ(µs,µ_jR) S^IN_i (µs) m²Jⁱ_un(µjR)

˜Ji(∂η, µj)˜S^C_i(∂η + ln µ²_jz

1 1+β cut

µ

2+β 1+β

sc (2EJtan^R₂)^1+β^β

, µsc)m² µ²_j

ηe^−γ^E^η Γ(η)

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Preliminary results

pp

sNN =5.02 TeV R = 0.4,È Η È < 1.3 140 GeV < p_T<160 GeV

Β=0, zcut=0.1, DR12>0.1

PRELIMINARY

NLO NLL PYTHIA8 parton PYTHIA8 hadron

0 10 20 30 40

0.00 0.02 0.04 0.06 0.08 0.10

m 1

Σ dΣ dm

NLO

R = 0.4, pT=150 GeV Β=0, zcut=0.1, DR12>0.1

PRELIMINARY

medium gluon vacuum gluon medium quark vacuum quark

5 10 15 20 25 30 35

0.00 0.01 0.02 0.03 0.04 0.05 0.06

m dΣ

dm

I The ∆R12> 0.1 cut cuts out the Sudakov peak and eliminates the quark/gluon difference I The lower and upper limits of jet mass are essentially dictated by kinematics. rgand jet

mass are highly correlated

I The medium lowest-order perturbative contribution enhances the small mass region I Hard splitting can "shield" inner soft radiations from being soft-dropped

I Soft contributions (anything softer: modification of subjets, pp smearing, etc) and hadronization effects are still under examination

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Conclusion

I What we have learned: flavor dependence of jet quenching and the role of quark/gluon jet fraction in jet substructures

I Subjet distribution provides an opportunity to test the modification of hard splitting within jets I Groomed jet mass is resummed with small radius, and the medium lowest-order

perturbative contribution enhances the small mass region (preliminary)

I Effective field theory techniques allow systematically improvable jet quenching studies