Jet Propagation in Medium - Theory groups• Jet propagation in medium leads to pt broadening and parton energy loss • Jet transport in medium can be studied through pt broadening

Hirschegg 2012

Xin-Nian Wang

CCNU & LBNL

Jet Propagation in Medium

January 15-21 2012

1

Facets of Strong-Interaction Physics

Thursday, January 26, 2012

Jets in high-energy reactions

2


Jets in pp collisions at LHC

3


Jets in Heavy-ion Collisions

4


Hard Probes of Dense Matter

Jet quenching

kT broadening


fqA(x) =

�dy−

4πeixp+y−�A|ψ̄(0)γ+ψ(y−)|A�

Deeply Inelastic Scattering

6

k=xpp

Quark distribution in collinear factorized pQCD parton model:

quarks carrying momentum fraction x of the nucleon (nucleus)


fqA(x) =

�dy−

4πeixp+y−�A|ψ̄(0)γ+L�(0, y−;�0⊥)ψ(y−)|A�

L�(0, y−;�0⊥) = P exp

�ig

� y−

0dξ−A+(ξ−,�0⊥)

�

Gauge Invariance and Multiple Interaction

7

kp

....


fqA(x,�k⊥) =

�dy−

4π

d2y⊥(2π)2

eixp+y−−i�k⊥·�y⊥�A|ψ̄(0)γ+L(0, y)ψ(y)|A�

L⊥(∞; �y⊥,�0) = P exp

�−ig

� �y⊥

�0⊥

d�ξ⊥ · �A⊥(∞, �ξ⊥)

�

L(0, y) = L†�(∞, 0;�0⊥) L�(∞, y−; �y⊥)L†

⊥(∞; �y⊥,�0⊥)

TMD parton distribution in DISBelitsky, Ji and Yuan (2002)

L�(0, y−;�0⊥) = P exp

�ig

� y−

0dξ−A+(ξ−,�0⊥)

�

kp

....


Jet Transport in Medium

Classical Lorentz force:

....

fqA(x,�k⊥) =

�dy−

4πeixp+y−�A|ψ̄(0)γ+ exp[ �W⊥(y−) · ∇k⊥ ]ψ(y−)|A�δ(2)(�k⊥)

�W⊥(y−, �y⊥) ≡ i �D⊥(y) + g

� y−

−∞dξ− �F+⊥(ξ−, y⊥)

Liang, XNW & Zhou （2008）

Jet Transport Operator

k


fqA(x,�k⊥) ≈ A

π∆

�d2q⊥ exp

�− (�k⊥ − �q⊥)2

∆

�fq

N (x, �q⊥)

Momentum Broadening

2-gluon correlation approximation


fqA(x,�k⊥) ≈ A

π∆

�d2q⊥ exp

�− (�k⊥ − �q⊥)2

∆

�fq

N (x, �q⊥)

Momentum Broadening

∆ = �∆k2⊥� =

�dξ−N q̂(ξN )

Jet transport parameter

Liang, XNW & Zhou’08Majumder & Muller’07Kovner & Wiedemann’01BDMPS’96


fq A(x

,kT)/

Af

q N(x

,kT)

kT

fqN (x, kT ) ∼ 1/(k2

T + p20)

α

PT Broadening

11

1


Jet Acoplanarity

12

p+p, s1/2=200 GeV

ET= 10 GeV

ET= 15 GeV

ET (GeV)

g pp(E

T,E T)

(1/G

eV)

0

0.05

0.1

0.15

0 5 10 15 20 25

0

0.05

0.1

0.15

0 5 10 15 20 25

EγT


∆γ(z, �2⊥) = CA1 + z2

(1− z)+2�4⊥

�dξ−q̂(ξ)[1− cos(xLp+ξ−)]

∆E

E= CA

αs

2π

�dl2Tl4T

�dz[1 + (1− z)2]

�dξ−q̂(ξ)4 sin2(xLp+ξ−/2)

Parton Energy Loss

Splitting functions in medium

kp

....

Parton Energy Loss


R =NeA

h

NeDh

q̂N ≈ 0.02 GeV2/fm

DIS of large nuclei

14

RMh

Ne

Kr(-0.05)

Xe(-0.2)

+

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8

q̂=0.016 GeV2/fmq̂=0.024 GeV2/fmq̂=0.032 GeV2/fm

z

<E>=10.742 18.358 GeV<Q2>=2.252 GeV2 2.655 GeV2

-

0.0 0.2 0.4 0.6 0.8

RMh

+

6 9 12 15 18 21

<z>=0.326 0.583<Q2>=1.889 2.595 GeV20.2

0.4

0.6

0.8

1.0

E (GeV)

NeKr

(-0.05)

Xe(-0.2)

-

6 9 12 15 18 21 24

q̂=0.016 GeV2/fmq̂=0.024 GeV2/fmq̂=0.032 GeV2/fm

Deng & XNW (2010)


Drell-Yan in pA Collisions

15

P

A

P

A

P

A

Xing & XNW arXiv:1110.1903 q̂N ≈ 0.02 GeV2/fm


Jet Quenching phenomena at RHIC

Pedestal&flow subtracted

STAR Preliminary


Jet quenching in QGP & hadronic phase

17

T [GeV]0.1 0.15 0.2 0.25 0.3 0.35

3/Tq

0

1

2

3

4

5

6

/fm2GeV+0.05-0.04=0.9

0q

30% quenching from hadronic phase

q̂N = 0.02 GeV2/fm

Chen, Greiner, Wang, XNW, Xu （2010）


Survival under the LHC sea

18

q̂ ∝ 1τ0πR2

A

dNch

dη


Jet Quenching at LHC

19


ω > ωc

ωc = 1− 2 GeV

Di-Jet Asymmetry

20Y. He, Vite, B.W. Zhang, arXiv:1105.2566


Mach-cone-like excitation

21


gamma-hadron correlation

22

Guo-liang Ma & XNW (2011)


Summary

• Jet propagation in medium leads to pt broadening and parton energy loss

• Jet transport in medium can be studied through pt broadening and jet quenching

• Jet quenching in heavy-ion collisions shows large jet transport parameter

• Jet quenching also leads to medium excitation that can be measured via correlation

23


Theoretical uncertainties

24

N. Armesto et al. arXiv:1106.1106Systematic comparisons of different approaches:

Single gluon emission

Sensitivity to maximumangle cut-off for gluonemission


collinear k2⊥ < µ2

large angle k2⊥ > µ2

Collinear approximation & NLO pQCD

25

.... ksingle jet -- LO

.... k

two jets -- NLO


Future Perspectives

26


Documents

Jet Propagation in Medium - Theory groups• Jet propagation in medium leads to pt broadening and parton energy loss • Jet transport in medium can be studied through pt broadening