High energy collisions in AdS

1. High energy collisions in AdS Yoshitaka Hatta U. Tsukuba Asian triangle heavy-ion conference 2008/10/13

2. Outline • Motivation • Gluon saturation in QCD • DIS and e+e- annihilation in sSYM • Jets at strong coupling? • Jet decay at finite temperature

3. Jet quenching at RHIC Is the strong suppression entirely of perturbative origin ?

4. The soft Pomeron 2 1.08 Note: The data are also consistent with the log behavior

5. Thermal hadron spectrum Identified particle yields are well described by a thermal model The model works in e+e- annihilation, hadron collisions, and heavy-ion collisions Becattini; Chliapnikov; Braun-Munzinger et al.

6. Motivation Why N=4 SYM? • There are many phenomena at collider experiment which defy weak coupling approaches. • Study N=4 SYM as a toy model of QCD. (Interesting in its own right…) One can solve strong coupling problems using AdS/CFT. Think how it may (or may not?) be related to QCD later… • Possible applications to jet quenching at RHIC and LHC. • Lots of works on DIS. e+e- annihilation is a cross channel of DIS. Why study jets ?

7. Regge limit of QCD One of the most challenging problems of QCD is the high energy limit. Can we compute the total cross section ? What are the properties of the final states ?

8. Deep inelastic scattering Two independent kinematic variables • Photon virtuality • Bjorken- Physical meaning : momentum fraction of the constituents (`partons’) High energy = small-

9. Gluons at HERA The gluon distribution rises very fast at small-x

10. Small- resummation Ordinary perturbation theory At small- such that

11. The BKFL Pomeron The ladder diagrams sum up to a Pomeron—like behavior More precisely, solve the bootstrap equation + = Eigenvalue of :

12. Gluon saturation Without interaction With interaction (BK-JIMWLK) Rapid growth of the gluon number tamed, leading to a Bose condensate of gluons, or the Color Glass Condensate.

13. `Phase diagram’ of QCD Saturation BFKL DGLAP

14. Recent progress on saturation Complete NLO BK equation Running coupling effects for gluon production Balitsky & Chirilli Kovchegov & Weigert A proof of factorization for inclusive gluon production in AA Gelis, Lappi & Venugopalan Two gluon production and correlation in pA production in pA production in pA and AA Evolution of glasma flux tubes Saturation in Mueller-Navelet jets Fukushima & Hidaka Fillion-Gourdean & Jeon Kharzeev, Levin & Tuchin Fujii & Itakura; Iwazaki Iancu, Kugeratski & Triantafyllopoulos

15. Gluon correlation in impact parameter space YH & Mueller (2007) Avsar & YH (2008) BK equation The mean field approximation OK for a large nucleus, but notOK for a small target (e.g., a proton). Factorization violated due to the power-law correlation in impact parameter space from BFKL

16. N=4 Super Yang-Mills • The ‘t Hooft coupling doesn’t run: • Global SU(4) R-symmetry  choose a U(1) subgroup and gauge it. N=4 SYM QCD

17. Type IIB superstring • Consistent superstring theory in D=10 • Supergravity sector admits the black 3-brane solution which is asymptotically Our universe 5th dimension

18. The correspondence Maldacena (1997) • Take the limits and • N=4 SYM at strong coupling is dual to weak coupling type IIB on • Spectrums of the two theories match CFT string (anomalous) dimension mass `t Hooft parameter curvature radius number of colors string coupling constant

19. What one would expect at strong coupling… • Rapid fragmentation. Most interesting physics is at small-x. • String S-matrix dominated by J=2 singularity. Pomeron graviton in AdS. • There are no jets. Final states look spherical. Polchinski & Strassler (2002) cf. Kotikov et al. (2005); Brower et al (2006) Hofman & Maldacena (2008); YH, Iancu & Mueller (2008); YH & Matsuo (2008)

20. Shock wave picture Weak coupling Strong coupling Large nucleus (CGC)  random color sources non-abelian Weiszacker-Williams field (boosted color-Coulomb field) ‘Hadron’  closed string state in cutoff AdS gravitational shock wave (boosted Schwartzschild metric) Characteristic size wavefunction localized at figure from Gubser, Pufu & Yarom (2008)

21. DIS at strong coupling Polchinski & Strassler (2002) R-charge current excites metric fluctuations in the bulk, which then scatters off a dilaton We are here Photon localized at Dilaton localized at Cut off the space at (mimic confinement)

22. String S-matrix dilaton gauge boson vertex op. vertex op. Insert t-channel string states dual to twist-2 operators AdS version of the graviton Regge trajectory

23. Phase diagram at strong coupling YH, Iancu & Mueller (2007)

24. DIS vs. e+e- annihilation crossing Parton distribution function Fragmentation function Bjorken variable Feynman variable

25. The reciprocity relation DGRAP equation The two anomalous dimensions derive from a single function Dokshitzer, Marchesini & Salam (2006) Nontrivial check up to three loops (!) in QCD Mitov, Moch & Vogt (2006) Application to AdS/CFT Basso & Korchemsky (2007) Assume this is valid at strong coupling and see where it leads to.

26. Average multiplicity at strong coupling crossing spacelike anomalous dimension timelike anomalous dimension YH & Matsuo (2008) c.f. in perturbation theory, c.f. heuristic argument YH, Iancu & Mueller (2008)

27. Jets at strong coupling? in the supergravity limit The inclusive distribution is peaked at the kinematic lower limit Rapidly decaying function for 1 Branching is so fast. Nothing remains at large-x ! All the particles have the minimal four momentum There are no jets at strong coupling !

28. Matrix element between a photon and particles. Thermal hadron production from gauge/string duality YH& Matsuo (2008) ~ complex saddle point in the z-integral

29. Finite temperature AdS/CFT Witten (1999) AdS　Schwartzschild AdS Our universe Hawking temperature = gauge theory temperature Event horizon

30. Evolution of jets in a N=4 plasma Solve the 5D Maxwell equation in the background of Schwarzschild AdS_5 Event horizon

31. Time-dependent Schrödinger equation YH, Iancu & Mueller (2008) To study time-evolution, add a weak t-dependence and keep only the 1st t-derivative t=0 Solutions available only piecewise. A new characteristic scale Minkowski boundary plasma saturation momentum horizon

32. (naive) Gauge theory interpretation Use the correspondence disappear into the plasma breakup into a “ pair”

33. Relation to other works The scale is the meson screening length Liu, Rajagopal & Wiedemann (2006) WKP solution after the breakup features the trailing string solution Herzog, et al, Gubser (2006) Time to reach the horizon (penetration length) cf. damping time of a gluon Gubser, Gulotta & Pufu (2008) cf. weak coupling result (BDMPS)

34. Branching picture at strong coupling Final state cannot be just a pair of partons. Energy and virtuality of partons in the n-th generation At strong coupling, branching is as fast as allowed by the uncertainty principle (vacuum) (medium) Trajectory of the parton pair  Enveloping curve of the parton shower.

35. Conclusions • Various aspects of high energy scattering at strong coupling—including some details of the final state—are accessible from gauge/string duality techniques. • Going to phenomenology, it is important to think when AdS-based approaches may be a good starting point and when it is not. e.g., Mueller (2008) • If the initial hard scattering were described by a strongly coupled theory, there would be no jets to begin with. • pp or AA collisions not fully explored yet. Sin, Shuryak & Zahed (2005); Albacete, Kovchegov & Taliotis (2008)