Jet tomography of hot and cold nuclear matter Xin-Nian Wang - - PowerPoint PPT Presentation

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Xin-Nian Wang

Central China Normal University Lawrence Berkeley National Laboratory

Jet tomography of hot and cold nuclear matter

Theoretical Physics Colloquium (online) 2020.7.22

QCD: Theory for strong interaction

• SU(3) gauge symmetry (non-Abelian)
• Asymptotic freedom at short distance
• Confinement at long distance
• Chiral symmetry and its spontaneous

breaking

• Goldstone boson and chiral condensate
• Scale and UA(1) anomaly
• ….

, 1

1 ( ) 2 4

f

n a QCD a a a f a

L i gA m F F

µ µ µn µ µn

l yg y

=

= ¶ -

• å

å

αs(Q2) = 4π/(11 − 2nf/3) ln(Q2/Λ2

QCD)

h ¯ ψψi 6= 0

hF µνFµνi 6= 0

3

Phase structure of QCD Matter

EOS from lattice QCD

4

✏SB =  6nf 7⇡2 120 + 16⇡2 30

• T 4

At T ~ 5Tc, e still 80% of the Stefan-Boltzmann value: quasi-particle modes at high T

3p/T4 /T4 3s/4T3 4 8 12 16 130 170 210 250 290 330 370 T [MeV]

HRG non-int. limit Tc

(HotQCD-Bielefeld-BNL-CCNU) PRD90(2014)094503

QGP in heavy-ion collisions

nucleus quark-gluon plasma (QGP) High T, µ

De-confinement confinement

5

LHC RHIC

Properties of QGP in A+A Collisions

Dynamic System:

§Hard probes: Medium response to strong interaction Jet quenching § EM emission: Medium response to EM interaction g production, J/Y suppression §Soft probes: Bulk properties of medium collective flow

Jets in high-energy collisions

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S Bethke J. Phys. G26 (2000) R27

• -tools for studying QCD and new discoveries
• Uncorrelated jet model for hadron production: De Groot and Ruijgrok (1971)
• Asymptotic freedom of QCD: Gross & Wilczek, Politzer (1973)
• Partons in QCD: Ellis, Gaillard & Ross (1976), Georgi & Machacek (1977)
• Jets in QCD: Sterman & Weinberg (1977)

Jets in heavy-ion collisions

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q q

Jet 1 Jet 2

Multiple scattering Transverse momentum broadening Parton energy loss Jet suppression

Hard and soft probes

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Pb-Pb pp reference

soft probes hard probes

EM Radiation: Single scattering

EM field carried by a fast charge particle before and after scattering v Initial rad. Final rad. EM Radiation by scattering: Interference between initial and final state radiation

! dI d! ≈ 2↵ ⇡  ln 2E2(1 − ~ vi · ~ vf) m2 − 1

• <latexit sha1_base64="X1fOqjaXVz+tbHVZ/LiJBXqPA0=">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</latexit>

! d2I d!dΩ = e2 4⇡2

• ~

k × ~ vi ~ k · ~ vi − ! − ~ k × ~ vf ~ k · ~ vf − !

• 2

Bethe Heitler

EM Radiation: multiple scattering

EM current of a charged through a scattering

Lorentz Invariant form: Classical radiation of a point charge (Jackson, p671)

i j

Jµ

i (k) =

pi−1 k · pi−1 − pi k · pi

! d2I d!dΩ = e2 4⇡2

• X

i

~ k × ~ vi ~ k · ~ vi − ! − ~ k × ~ vi+1 ~ k · ~ vi+1 − ! ! ei(!ti−~

k·~ ri)

• 2

ω d3I d3k = e2 2(2π)3 X

λ

• ελ(k) ·

X

i

Ji(k)eik·xi

• 2

Two Limits: (In)coherent radiation

single coherent scattering

Coherent Limit: Incoherent Bethe Heitler Limit:

Photon formation time: exp[ik · (xi − xj)] = exp[i∆xij/τf]

τf = 1 ω(1 − cos θ) ≈ 2 ωθ2

Jµ(k) = X

i

✓ pi−1 k · pi−1 − pi k · pi ◆ eik·xi ≈ p1 k · p1 − pN k · pN

ω d3I d3k = e2 4π2 2 4X

i,λ

|ελ · Ji|2 + 2Re X

i,λ

X

j>i,λ0

(ελ · Ji)(ελ0 · Jj)eik·(xi−xj) 3 5

τf ∆xij

τf ⌧ ∆xij

ω dI dω = L λmfp ✓ ω dI dω ◆

BH

∝ N 2α π

LPM Interference

# of scattering for a coherent radiation

Ncoh Effective spectra

Ncoh Ncoh Ncoh

Ncoh

τf = 2 ωθ2

θ2 = Ncoh q2

⊥

E2

ω dI dω = L λ ✓ ω dI dω ◆

BH

1 Ncoh / N α π r hq2

⊥i

E2 λω

Ncohλ ⇡ τf ! Ncoh = 2E p ωhq2

⊥iλ

Radiation in QCD: Colors Makes the Difference

QCD: gluons carry color: interference incomplete pi pf k a c k pf pi k Gluon multiple scattering (BDMP’96) pi pf a c y y dN/dy dN/dy QED QCD

∆E =⇡ αsNc 4 hq2

⊥i

λ L2

R(1)

S

≈ ig 2~ ✏⊥ · ~ k⊥ k2

⊥

[TaTc − TcTa]

R(2)

S

≈ ig 2~ ✏⊥ · (~ q⊥ − ~ k⊥) (~ q⊥ − ~ k⊥)2 [Ta, Tc]

Parton propagation in nuclear medium

p k e e

dNg dl2

⊥dz =

Z ∞

y− dy− 1

" ⇢A(y−

1 , ~

y⊥)2⇡↵s Nc ⇡ Z dk2

⊥

(2⇡)2 N(0,~ k⊥) k2

⊥

# ⇡ ↵s 2⇡ Pqg(z)CA l2

⊥

Ng(~ l⊥,~ k⊥)

N static+soft

g

= Z d' 2⇡ 2~ k⊥ ·~ l⊥ (~ l⊥ − ~ k⊥)2 1 − cos[ (~ l⊥ − ~ k⊥)2 2q−z(1 − z)y−

1 ]

!

q l Nucleon TMD gluon distr. Formation time of the gluon emission

y−

1 /τf

τf

Zhang, Qin and XNW arXiv:1905.12699

GLV

Parton energy loss and jet transport

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Extract jet transport coefficient from parton energy loss

(High-twist approach)

Jet transport coefficient:

ˆ q(y) = 4π2αsCR N 2

c − 1 ρ(y)xG(x)|x≈0

pQCD (BDMPS’96) AdS/CFT (Liu,Rajagopal &Wideman’06) lattice QCD (Majumder’12)

Elastic energy loss

dEel dx = Z d3k (2π)3 dq2

⊥f(k)q2 ⊥

2k dσ dq2

⊥

⇡ h 1 2ω iˆ q

= hq2

⊥i

λ

dErad dx ≈ E 2CA↵s ⇡ ˆ q(x) Z dz d`2

⊥

`4

⊥

zP(z) sin2 `2

⊥(x − x0)

4z(1 − z)E

Jet tomography via leading hadrons

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Parton energy loss leads to suppression of leading hadrons

jet parton Energy loss distribution or medium induced splitting function Modified frag function & hadron spectra:

dσh = X

a,b,c

fa ⊗ fb ⊗ dσab→c+X ⊗ e Dc/h

z 1-z

∆ e Pa→ag(z) ≈ 2CA↵s ⇡ Z dxˆ q(x) Z d`2

⊥

`4

⊥

P(z) sin2 `2

⊥(x − x0)

4z(1 − z)E

e Dc/h(zh) ≈ [Pa→ag(z) + ∆ e Pa→ag(z)] ⊗ Da/h(zh)

Jet Quenching phenomena at RHIC

Pedestal&flow subtracted

STAR Preliminary

Jet quenching phenomenology

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6 8 10 12 14 16 18 20 0.2 0.4 0.6 0.8 1

AA

R

(GeV)

T

p

PHENIX 2008 (0-5%) PHENIX 2012 (0-5%)

GLV-CUJET MARTINI-AMY (0-10%) McGill-AMY HT-BW HT-M

10 20 30 40 50 60 70 80 90 100 0.2 0.4 0.6 0.8 1

AA

R (GeV)

T

p

CMS (0-5%) Alice (0-5%)

GLV-CUJET MARTINI-AMY McGill-AMY HT-BW HT-M

RHIC LHC

Suppression of single hadron spectra at RHIC and LHC Best c2 fits with different model calculations :

Jet transport coefficient

JET Collaboration: arXiv:1312.5003

ˆ q ≈ ⇢ 1.2 ± 0.3 1.9 ± 0.7 GeV2/fm at T=370 MeV, T=470 MeV, RHIC LHC

Dijet asymmetry at LHC

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AJ = ET 1 − ET 2 ET 1 + ET 2

Jet energy and background subtraction

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Jet energy as defined in the jet reconstruction algorithm Uncorrelated background should be subtracted Jet-induced medium response is correlated with jet: not background Some of the energy lost by leading partons remain inside jet-cone

Mach-cone of medium excitation

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Chesler and Yaffe (0712.0050) Nuefeld, Muller and Ruppert 0802.2254)

Casalderrey-Solana, Shuryak; Stoecker, 2005

LBT: Linear Boltzmann Transport

Li, Liu, Ma, XNW and Zhu, PRL 106 （2010） 012301 XNW and Zhu, PRL 111 (2013) 062301; He, Luo, XNW & Zhu, PRC91 (2015) 054908;

Induced radiation

• pQCD elastic and radiative

processes (high-twist)

• Transport of medium recoil

partons ( and back-reaction)

• CLVisc 3+1D hydro bulk evolution

jet parton recoil parton Back-reaction

p1 · ∂f1 = − Z dp2dp3dp4(f1f2 − f3f4)|M12→34|2(2π)4δ4( X

i

pi) + inelastic

dNg dzd2k⊥dt ≈ 2CAαs πk4

⊥

P(z)ˆ q(ˆ p · u) sin2 k2

⊥(t − t0)

4z(1 − z)E

CoLBT-hydro (Coupled Linear Boltzmann Transport hydro)

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∂µT µν(x) = jν(x)

p · ∂f(p) = −C(p) (p · u > p0

cut)

jν(x) = X

i

pν

i δ(4)(x − xi)θ(p0 cut − p · u)

• LBT for energetic partons (jet shower and recoil)
• Hydrodynamic model for bulk and soft partons: CLVisc

CLVisc: (3+1)D viscous hydro parallelized on GPU using OpenCL

Chen, Cao, Luo, Pang & XNW, PLB777(2018)86

g-jet propagation within CoLBT-hydro

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Jet energy loss and g(Z0)-jet asymmetry

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Luo, Cao, He & XNW, PLB782(18)707

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Ös=5.02TeV

Z(ll)+jet

p

Z T>60 GeV/c

anti-KT jet R=0.3 p

T jet>30 GeV/c

|h

jet|<1.6

DfjZ>7p/8

CMS pp CMS Pb-Pb 0-30% Sherpa pp Z+jets Pb-Pb Z+jets Sherpa pp Z+1jet Pb-Pb Z+1jet Sherpa pp Z+(³2)jets Pb-Pb Z+(³2)jets 1/NZdN

jZ/dXjZ

XjZ=p

jet T /p Z T

Zhang, Luo, XNW, Zhang, arXiv:1804.11041

Medium response reduces jet energy loss

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Recoil partons within the jet cone reduce the net jet energy loss –change pt dependence Diffusion wake (backreaction) reduces the thermal background, if taken into account, increase the net jet Energy loss with given cone- size Depend on jet cone-size R Sensitive to radial flow

He, Cao, Chen, Luo, Pang & XNW 1809.02525

Energy and pT dependence

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Weak pT dependence: initial jet spectra and pT dependence of energy loss DE Week energy dependence: increase of jet energy loss and the slope of initial spectra preliminary He, Cao, Chen, Luo, Pang & XNW 1809.02525

Single jet anisotropy

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Df2=fjet-Y2

∆φ

jet

Correlation btw jet and bulk anisotropy

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vjet

n = hcos[n(φjet Ψn)]i

vjet

n = hhvn cos[n(φjet Ψn)]ii

p hv2

ni

He, Cao, Chen, Luo, Pang & XNW to be published

Medium response in gamma-jet profile

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Luo, Cao, He & XNW, arXiv:1803.06785

Enhancement of jet shape at larger r

With recoil w/o recoil r

ρ(r) = 1 ET dET dr

Medium response in jet frag func

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Wei Chen et all, 2005.09678 Particle distribution inside the jet

ξγ = log(pγ

T /ph T )

Jet tomography of nuclei at EIC

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R = N eA

h

N eD

h

Deng & XNW (2010) Chang, Deng & XNW (2015)

ˆ qN ≈ 0.02 GeV2/fm

nuclear modification of dijet at EIC

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p k v l lq=v+k-l

dˆ D dxBdQ2dzd2l⊥d2lq⊥ = 0 1 + z2 1 − z ↵2

s

Nc Z dy−

1 ⇢(y− 1 , ~

yN⊥)

⊗ Z d2~ v⊥ Z d2~ k⊥ (2⇡)2 f A

q (xB,~

v⊥)(0,~ k⊥) k2

⊥

Ng(~ l⊥,~ lq⊥,~ k⊥,~ v⊥)

~ l⊥ +~ lq⊥ = ~ k⊥ + ~ v⊥

d∆σe+Au/Aσe+p

Quadratic nuclear-size dependence due to LPM interference

d∆σe+A Aσe+p ∝ A2/3

Yuanyuan Zhang & XNW to be published

Summary

• Jet quenching has been used successfully to

study properties of QGP

• Extraction of jet transport coefficient
• Jet suppression is influenced by many

competing efforts

– Parton energy loss & medium response – Medium response leads to modification of jet shape, jet frag function

• Jet quenching and modification of dijet can

provide information about nuclear TMD parton distributions

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Acknowledgement

• Collaborators: Shanshan Cao, Wei Chen, Yayun

He, Tan Luo, Longgang Pang, Yuanyuan Zhang

• Funding: DOE, NSF (JET, JETSCAPE), NSFC

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