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

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

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

Note: The data are also consistent with the log behavior The soft Pomeron

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.

 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. Motivation Why N=4 SYM? Why study jets ?

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 ?

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

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

Small- resummation Ordinary perturbation theory At small- such that

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

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.

`Phase diagram ’ of QCD Saturation BFKL DGLAP

Recent progress on saturation 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 Fujii & Itakura; Iwazaki Complete NLO BK equation Running coupling effects for gluon production Balitsky & Chirilli Kharzeev, Levin & Tuchin Iancu, Kugeratski & Triantafyllopoulos Kovchegov & Weigert

Gluon correlation in impact parameter space BK equation The mean field approximation OK for a large nucleus, but not OK for a small target (e.g., a proton). Factorization violated due to the power-law correlation in impact parameter space from BFKL YH & Mueller (2007) Avsar & YH (2008)

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

Type IIB superstring Consistent superstring theory in D=10 Supergravity sector admits the black 3- brane solution which is asymptotically Our universe5 th dimension

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

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. cf. Polchinski & Strassler (2002) Kotikov et al. (2005); Brower et al (2006) Hofman & Maldacena (2008); YH, Iancu & Mueller (2008); YH & Matsuo (2008)

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

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

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

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

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

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

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

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

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

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

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

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

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

The scale is the meson screening length Relation to other works 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)

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

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)