Slide 1

2nd Workshop on Jet modification in RHIC and LHC era1Xin-Nian WangCentral China Normal University / Lawrence Berkeley Lab

Wayne State University, Aug. 20-22, 2013High-twist approach to jet quenching

1High-twist approach to multiple scattering

Loosely bound nucleus (p+, q- >> binding energy)e-Twist-expansion and gauge Invariance

Expansion in kT

One should also consider

Final matrix elements should contain:kpTMD factorizationCollinear Expansion

Collinear expansion:

Collinear Expansion (contd)

Twist-2 unintegrated quark distributionqxp

Liang & XNW06

Twist-3 unintegrated quark distribution x1pqxpTMD (unintegrated) quark distribution

Contribute to azimuthal and single spin asymmetry

Twist-two integrated quark distribution

+LO DIS cross section up to twist-47

Azimuthal asymmetry:

Liang & XNW (2007)Gao, Liang & XNW (2010)Song, Gao Liang & XNW (2011), (2013)TMD (unintegrated) quark distribution

Longitudinal gauge link

Belitsky, Ji & Yuan2003

Transverse gauge link

0y

Transport Operator

All info in terms of collinear quark-gluon matrix elementsLiang, XNW & Zhou08

Taylor expansion

Transport operator

Color Lorentz force:

Momentum Broadening

2-gluon correlation approximation

Jet transport parameterLiang, XNW & Zhou08Majumder & Muller07Kovner & Wiedemann01BDMPS96f_A^q(x,\vec k_\perp)\approx \frac{A}{\pi \Delta}\int d^2 q_\perp \exp\left[-\frac{(\vec k_\perp - \vec q_\perp)^2}{\Delta}\right]f_N^q(x,\vec q_\perp)

\Delta =\langle \Delta k_\perp^2\rangle=\int d\xi_N^- \hat q(\xi_N)11

PT Broadening

1

Nuclear dependenceof 12

13

14

DIS of large nuclei

Deng & XNW (2010)15

Drell-Yan in pA Collisions

Xing & XNW, NPA 879 (2012)77

16

17

18

Di-hadron fragmentation function

h1h2jetMajumder & XNW04DGLAP for Dihadron Fragmentation

h1h2h1h2h1h2

Medium Modified DihadronD(z1,z2)/D(z1)Triggering h1

Jet quenching at LHC22

Muller, Schukfrat & Wyslouch 2012

Majumder 2012

Elastic versus radiative e-loss23

Majumder 2008Qin and Majumder 2010

GyulassyWicks, etcDijet and gamma-jet asymmetry24

Qin and Muller (2011); Qin arXiv:1210.6610

MC simulation of jet transport25

Use the radiative Kernel in the Sudakov form factor and parton splittingNumerical simulation of mDGLAP equations:

Majumder 2013

Interplay between hard and soft probes26

Pb-Pbpp referencesoft probeshard probes

Linear Boltzmann jet transport

Li, Liu, Ma, XNW and Zhu, PRL 106 2010 012301XNW and Zhu, PRL 111 (2013) 062301

Induced radiationf_i(p_i)=\frac{1}{e^{p_i\cdot u/T}\pm 1} (i=2,4)f_i(p)=(2\pi)^3\delta^3(\vec p_i-\vec p_0)\delta^3(\vec x-\vec x_0-t\vec v_i) [i=1,3]

\frac{dN_g}{dzd^2k_\perp dt}=\frac{2\alpha_s N_c}{\pi k_\perp^4} P(z)(\hat p\cdot u) \hat q \sin^2(\frac{t-t_0}{2\tau_f})

28Jet-induced medium excitation

Jet propagation in a uniform medium

g-jets in an expanding medium29

XNW and Zhu, PRL 111 (2013) 062301

Similar results byDai, Vitev and Zhang, PRL 110 (2013) 032302Broadening of jet transv. profile30

R=0.3Medium mod. of frag function31

Energy of reconstructed jet dominated by leading particleSuppression of fragmentation functions relative to initial energy XNW and Zhu, PRL 111(2013)062301 Seen in CMS & ATLAS single jetsXNW, Huang & Sarcevic (1996)Broadening of g-hadron correlation32Li, Liu, Ma, XNW and Zhu, PRL 106 2010 012301Ma and XNW, PRL 106 (2011) 162301

g-hadron from AMPT calculation

g-jet from LBTJet azimuthal angle broadening is smaller but still finiteFuture perspective: extracting qhat

RHIC

from DISDeng & XNW PRC 81 (2010) 024902Chen, Greiner, Wang, XNW, Xu, PRC 812010064908LHC: T_0=473 MeV qhat/T^3=3.14RHIC: T_0=373 MeV qhat/T^3=3.4733Future perspective: NLO34

See talk by Hongxi Xing on Thuyrsday @ NLO meeting

SIDISDYDGLAP Eq. for Twist-4 correlation function:3536MC approach to jet medium interaction 37

3+1D hydro +Jet transport +HadronizationBerkeley-Wuhan Hybrid MC3+1D hydro + Linear Boltzmann Jet TransportJet-induced medium excitation & anisotropic flowJet quenching in an anisotropic/expanding medumHydro description of A+A CollisionsHydrodynamic:

a low-momentum effective theoryInputs from first principle QCD (lattice QCD)EoS p(e), transport coefficients x(T), z(T) (??)Initial condition: parton prod. & thermalization38

T^{\mu\nu}=(\epsilon + P)u^\mu u^\nu - P g^{\mu\nu} +\Delta T^{\mu\nu}

\Delta T^{\mu\nu}=\eta (\Delta^\mu u^\nu+\Delta^\nu u^\mu) + (\frac{2}{3}\eta-\zeta)H^{\mu\nu}\partial_\rho u^\rho

\partial_\mu T^{\mu\nu}=0

38Initial conditions for hydro392D fluctuating geometry: MC- Glauber, MC-KLN2D fluctuating geometry + QM: IP-Glasma3D fluctuating geometry +QM: HIJING, AMPT, NeXus, UrQMD

hxxy(3+1)D ideal hydro with AMPT initial condition Nonlinear interaction expansion in both transverse and longitudinal directions39Effects of tran. & long. fluctuations40

Pang , Wang and XNW PRC 81 (2012) 031903No fluctTrans. onlyFull fluctAnisotropic flow & relics of minijets41

Pang, Wang & XNW 2013 (preliminary)Anisotropic flow & relics of minijets42

Pang, Wang & XNW 2013 (preliminary)

Summary43

Bluhm, Kampfer & Redlich 2010

Majumder, Muller & XNW 2007AdS/CFTHard probes and anisotropic flows provide unprecedented constraints on the transport properties of the sQGP in A+A

Future: mapping out T-dependence at RHIC & LHC

RHIC

from DIS\frac{\eta}{s} \ge \frac{3T^3}{2\hat q}43

Jet Quenching phenomena at RHIC

Zhang, Owns, Wang, XNW, PRL 98 (2007) 212301Zhang, Owns, Wang, XNW, PRL 103 (2009) 032302RHIC experiments marked a milestone for jet quenching, from a theoretical concept to a reality.444546Hydro dynamics of dense matter47cS EOS of QGP

47QGP in p+p & p+A collisions?48

p+p @ 7 TeVCollective flow in high multiplicity events of p+p & pA?Werner et al 12, Bozek & Broniowski13 Maybe from initial state: glasma? But no jet quenching!Venugapalan & Dusling et al, 12But large values of v3!See talks by Roland (G1)Transport properties of QCD matter

Bluhm, Kampfer & Redlich 2010Lattice QCD: Nakamura & Sakai 2005; Meyer 2007 pion gasPrakash93AdS/CFT

Arnold, Moore & Yaffe 2003\eta=\lim_{\omega\rightarrow 0}\frac{1}{2\omega}\int dtdx e^{i\omega t}\langle \left[T^{ij}(x,t),T^{ij}(0,0)\right]\rangle

49Viscosity of QGP in A+A collisions 50

Fluctuation + viscous hydro required to fit all vnViscosity at LHC is larger than at RHICSee talk by Schenke ( Wednesday, IUPAP prize)Gale, Jeon, Schenke, Tribedy & Venugopalan 2013Heinz & Song 2010

51

Phase structure of QCD matter

Fluctuation and Tc

T_c=175 \; {\rm MeV} \approx 2\times 10^{14} \;{\rm K}

51Quark number scaling of v2

Anisotropic flow52

STAR: Phys. Rev. Lett. 92, 052302(04)

n: valence quark

RHIC QGP52

Hard probes of dense matter53

Jet quenching via parton energy loss

RHICQGP

53Running coupling in jet quenching54

2013Gamma-jet asymmetry55

1.0

XNW & Zhu13ATLASLBTRapid expansion & recoiled partonx=p_T^{jet}/p_T^\gamma

55Dijet asymmetry at LHC56

He, Vitev & Zhang 2012Young, Schenke, Jeon & Gale, 2012

Qin & Muller 2012Multiple scattering & angular ordering

57

Formation time

Color coherence is rapidly lost in medium, independent emission is enhanced by L/tf Blaizot, Dominguez, Iancu, Mehtar-Tani 12Mehta-Tani,Salgado,Tywoniuk10Multi-scatteringMany-body int.Hydrodynamics

\frac{1}{\tau_f}\sim \frac{k_T^2}{2\omega}

\tau_f(\omega)\sim \sqrt{\frac{2\omega}{\hat q}}57Hard QCD Physics @ CCNUJet physics:W2Z2: Enke Wang, XNW, Benwei Zhang, Hanzhong Zhang High-twist approach to parton energy lossBowen Xiao hard processes at small xGuangyou Qin AMY jet quenching, and flowDefu Hou jet quenching in AdS/CFTChunbin Yang Oregon-Wuhan (Hwa-Yang) recombination Fuming Liu -- Direct photons Experiments:ALICE@LHC, STAR@RHICLattice QCDHengtong Ding58