Parton Energy Loss. At Strong Coupling. Hard Probes 2010 Eilat, Israel: October Berndt Müller

Transcription

1 Parton Energy Loss At Strong Coupling Berndt Müller Hard Probes 2010 Eilat, Israel: October 2010

2 Overview Reminder: Jet quenching at weak coupling Micro-Primer: Strongly coupled AdS/CFT duality Jet quenching in strongly coupled AdS/CFT Phenomenological comparisons Final thoughts Some references: Gubser, hep-th/ Gubser, Gulotta, Pufu & Rocha, Chesler, Jensen, Karch & Yaffe, Marquet & Renk, Casalderrey-Solana, Fernandez & Mateos, Arnold & Vaman,

3 Jet production & quenching 3

4 Jet production & quenching Itʼs NOT about this (the hard scattering) 3

5 Jet production & quenching Itʼs NOT about this (the hard scattering) Itʼs ALL about this (medium interaction) 3

6 pqcd approach Treat energetic parton dynamics (radiation) perturbatively Treat medium dynamics (gluon content) non-perturbatively Medium properties encoded in transport coefficients ˆq = p2 T L L Transverse momemtum diffusion rate ê = E L L Elastic energy loss rate 4

7 Z-BDMPS formalism Zakharovʼs path integral for in-medium gluon radiation DGLAP splitting kernel eikonal propagator of the parton-gluon dipole A typical diagram 5

8 pqcd scenarios Jet quenching scenarios landscape S. Caron-Huot & C. Gale LPM effect interference of vacuum and medium radiation QGP brick at T = 400 MeV screened 1-gluon exchange 6

9 pqcd scenarios Assumes weakly coupled QGP Jet quenching scenarios landscape S. Caron-Huot & C. Gale LPM effect interference of vacuum and medium radiation QGP brick at T = 400 MeV screened 1-gluon exchange 6

10 Weak vs. strong coupling (P vs. NP) medium structure: P or NP gluon propagation: P or NP gluon quark P = perturbative (weakly coupled) NP = non-perturbative (strongly coupled) hard vertex: always P radiation vertex: P or NP quark propagation: P or NP pqcd only allows for NP medium structure (via qhat, ehat) Rigorous AdS/CFT calculation treats all components NP Hybrid approaches treat some aspects P and some NP 7

11 5 th dimension AdS5 S5 / N = 4 SYM duality Quark-gluon plasma Our world (χ=0) Black hole / brane (χ0) 10-dim. metric: Strong coupling λ = g 2 Nc >> 1 classical gravity limit 8

12 Jets in N=4 SYM? Jets are not naturally formed at strong coupling! Why?? Democratic splitting prevents formation of jets. democratic splitting Splitting time: ts = E/Q 2, the final transverse size is: Lf ~ 1/Qf. To discuss jet-like phenomena, we must select special (high E/Q 2 ) initial states or assume that strong coupling somehow only sets in after a parton has reached virtuality Q 2 ~ T 2! 9

13 Heavy quark energy loss Quark-gluon plasma Deposited energy and momentum Trailing string (flux tube) Black hole Heavy quark = endpoint of a string attached to a D7-brane at χm = λ / mq << χ0 10

14 Heavy quark = trailing string χh = χm comoving field v Upper and lower parts of the training string are causally disconnected radiated field χ0 = Energy radiated by quark (described by string below χh) thermalizes almost instantly: medium response well described by hydrodynamics. same formula as in QCD, but with 11

15 pqcd vs. SC N=4 SYM pqcd: Gluons are liberated by (multiple) scattering in the medium radiation is governed by transverse momentum diffusion: Strongly coupled N=4 SYM: Gluons are liberated in (multiple) branching cascade; kept off-shell by thermal force from the medium 12

16 Dual picture Parton cascade holographic image of trailing string envelope of the parton cascade hydro regime hydro regime parton cascade Dynamics beyond 1/T is hydrodynamics! r 3 r trailing string 13

17 QGP structure QGP energy density can be expressed in terms of the parton structure function: F2(x,Q 2 ) describes the area density of gluons in the QGP which are encountered by a fast traveling parton over the coherence length lc = 2E/Q 2. Weakly coupled QGP: most of the energy density is carried by partons with x ~ 1, i.e. by quasi-particulate gluons. Strongly coupled QGP: most of the energy density resides in partons with x ~ T/Q, i.e. by wee, or field-like (but not necessarily coherent) gluons. Whether these partons are considered as part of the jet, or as part of the QGP, is a matter of interpretation (ref. frame, gauge, etc.). 14

18 Light parton energy loss χ = 0 Light partons (gluons) can be modeled as doubled strings connected to the black hole horizon, and not anchored to a brane near the boundary. Δx 4E α s N c ˆq χe χh Total distance traveled by perturbation: Splitting time: dt = E/Q(t) 2 Compare with pqcd expression: virtuality due to work on parton: Q(t) ~ (T t) 2 15

19 Light parton energy loss P. Chesler Gluon string 16

20 Light parton energy loss P. Chesler de dt Bragg peak t Gluon string 16

21 Light parton energy loss P. Chesler de dt Bragg peak t Gluon string Same phenomenon in pqcd + hydro Neufeld & BM Qin, Majumder, Song & Heinz 16

22 pqcd vs. AdS/CFT Jet fragmentation controlled by: virtuality evolution Q 2 (t) splitting functions P(z) Virtuality evolution Q 2 (t) differs both in vacuum and in medium. collinear divergence (pqcd) vs. democratic splitting (AdS/CFT) Vacuum Medium AdS/CFT pqcd 17

23 Virtuality evolution Example: E = 30 GeV, Q0 = 5 GeV, T0 = 300 MeV at t0 = 1 fm/c. 5 4 Qt GeV AdS/CFT pqcd t fmc 18

24 Virtuality evolution Example: E = 30 GeV, Q0 = 5 GeV, T0 = 300 MeV at t0 = 1 fm/c. 5 4 Qt GeV AdS/CFT pqcd t fmc 18

25 Splitting functions Include LPM effect: z(1-z)e/k 2 t > 1 and IR cut-off: k 2 > 0.5 GeV 2 Effective fragmentation pattern at time t (without cascading). Democratic splitting (αs = 1) Collinear splitting (αs = 0.3) t = 1.0 fm/c t = 0.3 fm/c t = 0.1 fm/c Dz z 19

26 Phenomenology Main difference between weak and strong coupling (besides overall strength of e-loss) is the length dependence: de/dx ~ L (pqcd) de/dx ~ L 2 (N=4 SYM) 20

27 Phenomenology Main difference between weak and strong coupling (besides overall strength of e-loss) is the length dependence: de/dx ~ L (pqcd) de/dx ~ L 2 (N=4 SYM) Marquet & Renk 20

28 Phenomenology Main difference between weak and strong coupling (besides overall strength of e-loss) is the length dependence: de/dx ~ L (pqcd) de/dx ~ L 2 (N=4 SYM) Marquet & Renk IAA Marquet & Renk 20

29 Summary: Relevant questions Are jets formed in QGP medium? YES Coupling is weak before virtuality reaches medium scale Is the QGP strongly coupled? Probably YES: jet quenching is stronger than expected from a perturbative QGP (and shear viscosity is smaller) This is not a problem for pqcd jet quenching theory Is the parent parton strongly coupled after reaching the medium virtuality? We don t know. Study cone structure of in-medium radiation for triggered jets Are the radiated gluons strongly coupled? We don t know. Study cone structure and degree of thermalization of rad. energy 21

30 What s needed? Establish length dependence of energy loss. Establish energy dependence of energy loss. Measure medium modification of angular and momentum distribution of radiated energy. Measure quark mass dependence of energy loss. Many opportunities at RHIC and LHC: Tagged jets (energy, flavor) Angle dependence System size dependence Fully reconstructed jets A world-class jet detector at RHIC is needed 22