J ET QUENCHING 101 1708.04962 jet quenching effects manifest as - - PowerPoint PPT Presentation

SUDAKOV EFFECTS IN JET QUENCHING

Konrad Tywoniuk

Strong & Electroweak Matter 2018, Barcelona, 25-29 June 2018

• K. Tywoniuk (CERN)

SEWM2018

HEAVY

• ION COLLISIONS
• studying hot & dense, dynamical nuclear matter
• bulk observables: “collectivity”
• persists across wide range of system sizes
• do we understand the mechanism of equilibration?
• can we resolve constituents of quark-gluon plasma

(quasi-particles,…)?

2

• K. Tywoniuk (CERN)

SEWM2018

HARD PROBES

• a wide array of probes
• hadronic: inclusive, quarkonia, heavy-flavor, jets
• electro-weak: photons, Z/W, Higgs…
• jets are ideal & complex probes
• calibrated from e+e-, pp (jet rates, substructure)
• probes different time & length scales
• out-of-equilibrium (softening & isotropization)

3

• K. Tywoniuk (CERN)

SEWM2018

JET QUENCHING 101

• jet quenching effects manifest as strong reduction of

yields of hadrons & jets over a large range in pT

• substructure modifications: broadening & softening
• enhancement of soft & large-angle particles

4

1708.04962 see D. Pablos Mon 15:30

• K. Tywoniuk (CERN)

SEWM2018

JET QUENCHING 101

• jet quenching effects manifest as strong reduction of

yields of hadrons & jets over a large range in pT

• substructure modifications: broadening & softening
• enhancement of soft & large-angle particles

4

1708.04962 see D. Pablos Mon 15:30

• K. Tywoniuk (CERN)

SEWM2018

MOTIVATION

• many experimental results & successful model

implementations

• modeling jet quenching phenomena realistically involves

“multi-stage” Monte Carlo approach

• competing effects in the soft sector (medium back-

reaction, color decoherence…)

• theoretical guidance at high-pT?
• what drives quenching & substructure modifications?
• developing a probabilistic picture from first principles

(including interferences)

5

see E. Iancu Mon 15:00 see D. Pablos Mon 15:30

• K. Tywoniuk (CERN)

SEWM2018

HIGH-ENERGY APPROXIMATIONS

• assume separation of scales (high temperature)
• elastic interactions: transverse
• 2D non-relativistic quantum mechanics
• dressed (retarded) propagators

6

perturbative interactions

(w/ screening)

γ(x) = g2 Z d2q (2π)2 eix·q q4

hAa

med(t, x)Ab med(t0, y) = δabn(t)δ(t t0)γ(x y)

two-point correlator

• K. Tywoniuk (CERN)

SEWM2018

RADIATION IN THE MEDIUM

7

tf = ω k2

⊥

∼ rω ˆ q modified splitting kinematics

lack of collinear singularity!

hk2

⊥i ⇠ ˆ

qt

momentum broadening

Baier, Dokshitzer, Mueller, Peigné, Schiff (1997-2000); Zakharov (1996); Arnold, Moore, Yaffe (2002)

see P . Arnold Wed 12:30

ω dI dω = αsCR π L tf = αsCR π r ˆ qL2 ω

• K. Tywoniuk (CERN)

SEWM2018

RADIATION IN THE MEDIUM

7

tf = ω k2

⊥

∼ rω ˆ q modified splitting kinematics

lack of collinear singularity!

hk2

⊥i ⇠ ˆ

qt

momentum broadening

Baier, Dokshitzer, Mueller, Peigné, Schiff (1997-2000); Zakharov (1996); Arnold, Moore, Yaffe (2002)

θbr(ωc) ∼ r 1 ˆ qL3 ≡ θc

ωc = ˆ qL2

rare, small- angle emission

ωs = ¯ α2ˆ qL2

copious, large- angle emissions

θbr(ωs) ∼ 1 ¯ α3/2 θc

see P . Arnold Wed 12:30

ω dI dω = αsCR π L tf = αsCR π r ˆ qL2 ω

• K. Tywoniuk (CERN)

SEWM2018

QUENCHING WEIGHTS PARADIGM

8

Strong quenching: energy loss dominated by typical emitted energy

Baier, Dokshitzer, Mueller, Schiff (2001); Salgado, Wiedemann (2003)

• resummation necessary when the number of induced

gluons become large

• quasi-instantaneous medium-induced emissions
• generically: QW for any energy loss
• no a priori dependence on jet scales

P(✏) = r!s ✏3 e− ⇡!s

✏

• K. Tywoniuk (CERN)

SEWM2018

WHAT DO JETS LOOK LIKE?

9

proton-proton two-jet event heavy-ion two-jet event

• K. Tywoniuk (CERN)

SEWM2018

JET SPACE-TIME EVOLUTION

10

• jets are multi-particle objects

with interesting space-time pattern

• double-logarithmic regime
• strong energy ordering
• strong angular ordering
• formation time

hadronization

∼ 10 fm

Bassetto, Ciafaloni, Marchesini (1983); Dokshitzer, Troyan, Khoze, Mueller (1991)

• K. Tywoniuk (CERN)

SEWM2018

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ ln 1/θ

dP ∼ 2αsCR π

zEθ > Q0

JET SPACE-TIME EVOLUTION

10

• jets are multi-particle objects

with interesting space-time pattern

• double-logarithmic regime
• strong energy ordering
• strong angular ordering
• formation time

hadronization

∼ 10 fm

Bassetto, Ciafaloni, Marchesini (1983); Dokshitzer, Troyan, Khoze, Mueller (1991)

• K. Tywoniuk (CERN)

SEWM2018

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ ln 1/θ

dP ∼ 2αsCR π

zEθ > Q0

JET SPACE-TIME EVOLUTION

10

• jets are multi-particle objects

with interesting space-time pattern

• double-logarithmic regime
• strong energy ordering
• strong angular ordering
• formation time

1

tf,1

tf,1

hadronization

∼ 10 fm

Bassetto, Ciafaloni, Marchesini (1983); Dokshitzer, Troyan, Khoze, Mueller (1991)

• K. Tywoniuk (CERN)

SEWM2018

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ ln 1/θ

dP ∼ 2αsCR π

zEθ > Q0

JET SPACE-TIME EVOLUTION

10

• jets are multi-particle objects

with interesting space-time pattern

• double-logarithmic regime
• strong energy ordering
• strong angular ordering
• formation time

1

tf,1

tf,1

2

tf,2

tf,2

hadronization

∼ 10 fm

Bassetto, Ciafaloni, Marchesini (1983); Dokshitzer, Troyan, Khoze, Mueller (1991)

• K. Tywoniuk (CERN)

SEWM2018

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ ln 1/θ

dP ∼ 2αsCR π

zEθ > Q0

JET SPACE-TIME EVOLUTION

10

• jets are multi-particle objects

with interesting space-time pattern

• double-logarithmic regime
• strong energy ordering
• strong angular ordering
• formation time

1

tf,1

tf,1

2

tf,2

tf,2

3

tf,3

tf,3

hadronization

∼ 10 fm

Bassetto, Ciafaloni, Marchesini (1983); Dokshitzer, Troyan, Khoze, Mueller (1991)

• K. Tywoniuk (CERN)

SEWM2018

PHASE SPACE FOR MEDIUM EFFECTS

11

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ

tf > L

tf < L

QW paradigm applies only to ~50% of the full diagram!

Casalderrey, Milhano, Quiroga-Arias PLB 710 (2010) 175

At high-pT, many collinear particles can be resolved inside the medium.

Casalderrey et al. JHEP 1703 (2017) 135 Milhano, Zapp EPJC 76 (2016) 288

• K. Tywoniuk (CERN)

SEWM2018

PHASE SPACE FOR MEDIUM EFFECTS

11

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ

tf > L

tf < L

QW paradigm applies only to ~50% of the full diagram!

Casalderrey, Milhano, Quiroga-Arias PLB 710 (2010) 175

At high-pT, many collinear particles can be resolved inside the medium.

Casalderrey et al. JHEP 1703 (2017) 135 Milhano, Zapp EPJC 76 (2016) 288 Salgado, Mehtar-Tani, KT (2010-2012) Iancu, Casalderrey (2011) Casalderrey, Salgado, Mehtar-Tani, KT (2013)

Blue region corresponds to unresolved splittings.

• K. Tywoniuk (CERN)

SEWM2018

ENERGY LOSS OF TWO PARTICLES

• resums multiple, soft emissions at large angles
• assume hard splitting (short formation time)
• no vertex modification

12

…

Psing(ω, t) ≡ 1 Nc δi¯

iδj¯ jMij¯ j¯ i kl¯ l¯ k(ω, t)δklδ ¯ l¯ k ,

Psing(, tL) tL 1 2 ¯ 2 ¯ 1

Psing(ω, t)

• Y. Mehtar-Tani, KT arXiv:1706.06047 [hep-ph]

• K. Tywoniuk (CERN)

SEWM2018

QUENCHING EVOLUTION EQUATION

13

γ(ν, t) = Z ∞ dω

• e−νω − 1

dI dωdt

Regularized rates in Laplace space:

∂ ∂tP(ν, t) = γdir(ν, t)P(ν, t)

Rate equation for one charge

∂ ∂tPsing(ν, t) = γdir(ν, t)Psing(ν, t) + γint(ν, t)S2(t)

Rate equation for two charges

S2(t) = exp  −1 4 Z t ds ˆ q(x12, t)x2

12(s)

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decoherence parameter

• K. Tywoniuk (CERN)

SEWM2018

DECOHERENCE

14

S2(t) = δ(ω)

• S1(t)
• 2

large-Nc limit:

S1(tL, 0) = S(0)

1 (tL, 0) +

Z tL dt S(0)

1 (tL, t)Σ12(t)S1(t, 0) ,

→

1 2

× 1

Nc S1(tL)

× 1

Nc S1(t) t t′ t′ tL

• K. Tywoniuk (CERN)

SEWM2018

DECOHERENCE

14

S2(t) = δ(ω)

• S1(t)
• 2

large-Nc limit:

S1(tL, 0) = S(0)

1 (tL, 0) +

Z tL dt S(0)

1 (tL, t)Σ12(t)S1(t, 0) ,

→

1 2

× 1

Nc S1(tL)

× 1

Nc S1(t) t t′ t′ tL

∆ˆ qF (x12, t) = αsCF π Z τmax

τ0

dτ τ Z x−2

12

ˆ qτ

dq2 q2 ˆ q

Radiative correction to the jet quenching parameter

Liou, Mueller, Wu (2013); Blaizot, Mehtar-Tani (2014); Wu (2014); Iancu (2014)

universal correction ( )

τmax ∼ td

• K. Tywoniuk (CERN)

SEWM2018

QUENCHING WEIGHTS 2.0

• energy loss off dipole created by collinear splitting
• highlights important role of interferences
• two-prong QW in the large-Nc limit convolution of

quenching of total charge & resolved color singlet dipole

15

• Y. Mehtar-Tani, KT arXiv:1706.06047 [hep-ph]

Pqg = Pq ⊗ Psing

• K. Tywoniuk (CERN)

SEWM2018

QUENCHING WEIGHTS 2.0

• energy loss off dipole created by collinear splitting
• highlights important role of interferences
• two-prong QW in the large-Nc limit convolution of

quenching of total charge & resolved color singlet dipole

15

• Y. Mehtar-Tani, KT arXiv:1706.06047 [hep-ph]

Pqg = Pq ⊗ Psing

• K. Tywoniuk (CERN)

SEWM2018

QUENCHING WEIGHTS 2.0

• energy loss off dipole created by collinear splitting
• highlights important role of interferences
• two-prong QW in the large-Nc limit convolution of

quenching of total charge & resolved color singlet dipole

15

td ∼ (ˆ qθ12)−1/3

tf td

• Y. Mehtar-Tani, KT arXiv:1706.06047 [hep-ph]

Pqg = Pq ⊗ Psing

HOW TO APPLY WHAT WE

LEARNED TO OBSERVABLES?

• K. Tywoniuk (CERN)

SEWM2018

JET SPECTRUM IN HEAVY-ION COLLISIONS

17

quenching weight: probability distribution of losing energy quenching factor = nuclear modification factor

Rjet = ✓dσmed dp2

Tdy

◆ . ✓ dσvac dp2

Tdy

◆

dmed dp2

Tdy =

Z ∞ d✏ P(✏)dvac(pT + ✏) dp2

Tdy

Rjet ∼ ˜ P

• n/pT
• ≡ Q(pT)

⇓

product of probabilities (Laplace space) from quenching of resolved color

Qq(pT) = e−2√

nπωs/pT

total color charge

• K. Tywoniuk (CERN)

SEWM2018

HIGHER-ORDER CONTRIBUTIONS

• leading term corresponds to quenching of the total charge
• common factor at all 𝛽s (large-Nc)
• enhanced higher-order correction
• the mismatch is largest at short formation times

18

Rjet = Q(0)(pT) + Q(1)(pT) + O(α2

s)

+

sensitive to two prongs sensitive to one prong

Q(1)(pT ) = αs π Z 1 dzPgq(z) Z R dθ θ h Qqg(pT ) − Qq(pT ) i

• K. Tywoniuk (CERN)

SEWM2018

REDRAWING PHASE SPACE

19

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ

∼ 2¯ α log R θc log pT ωc ⇥ Q2

q(pT) − 1

⇤

Leading-logs count the number of collinear modes resolved by the medium Enhancement from jet scales ⇒ resummation

tf > L

tf < td < L

ln 1/θ

Dominance of virtual term (Sudakov effect)

• K. Tywoniuk (CERN)

SEWM2018

SUDAKOV SUPPRESSION FACTOR

• jet loses energy through total charge & resolved

substructure fluctuations

• qualitatively different quenching mechanism

compared to leading hadrons

• Sudakov resummation of medium logs via non-linear

equation

20

Rjet = Qq(pT) × C(pT, R)

C(1, pT, R) = 1 + Z 1 dz Z R

θc

dθ θ αs(k⊥) π Pgq(z)Θ(tf < td) × ⇥ C(z, pT, θ)C(1 − z, pT, θ)Q2

q(pT) − C(1, pT, θ)

⇤

• Y. Mehtar-Tani, KT arXiv:1707.07361 [hep-ph]

• K. Tywoniuk (CERN)

SEWM2018

JET SUPPRESSION: NUMERICS

21

100 1000 p 0.2 0.4 0.6 0.8 1 1.2

R

Quark energy loss Jet energy loss (incoherent approx.) Jet energy loss - R=0.4

T

jet

[GeV]

Quantitative difference for incoherent scenario: log Cincoh ∼ αs log2 pT

“hadron” jet w/coherence jet w/o coherence

R = 0.4

• K. Tywoniuk (CERN)

SEWM2018

CONCLUSIONS

• jet quenching at high-pT
• quenching of total charge (+mass effects)
• novel Sudakov suppression factor (collimator)
• relating quenching to jet scales
• analytic understanding
• sensitivity to opening angle
• general features from hard scale analysis
• assumptions about medium modifications leads to

redrawing of phase space

• guidance for (a large class of) MC modeling
• importance of data scanning pT & R

22

THANK YOU!