Hard processes in AdS/CFT Yoshitaka Hatta (Tsukuba U) Based on works done in collaboration with E. Iancu, T. Matsuo, A.H. Mueller, D. Triantafyllopoulos
Outline Motivation High energy CD with a virtual photon Deep inelastic scattering in gauge/string duality Jets in the vacuum Jets at finite temperature
Why AdS/CFT? Perturbative CD very successful for hard processes. Why bother AdS? Regge (small-x) scattering historically important for strings. New perspectives from AdS/CFT? Possible applications to strongly coupled GP at RHIC, and hidden conformal sectors at the LHC (Strassler)
Spacelike photon Deep inelastic scattering Photon virtuality e P X q = > 0 Bjorken-x x = (spacelike) P q ¼ s (x 1) Probing partons with energy Z 1 ¼ Im i d 4 ye iqy hp jt fj ¹ (y)j º (0)jP i µ ¹º = + q¹ q º F 1 (x; ) + q xp + and transverse size 1= µ P ¹ P q q q¹ µ P º P q F (x; ) q qº P q
Parton distribution function
Hard (BFKL) Pomeron Anomalous dim. of the twist-two operators j 1 F (x; ) Z µ dj (j) µ j 1 1» ¼i ¹ x µ 0:5 1»» s 0:5 x
`Phase diagram of CD 1 ln s ln Saturation x 1 3 ( x) A x 1 s 4.9 s F (x; )» ln s(x)= in the saturation region BFKL DGLAP ln 7
Timelike photon Jets in CD In e+e- annihilation, some of the most stringent tests of pcd have been done. High pt jets at the LHC could be an important discovery channel of BSM
Number distribution inside a jet Fragmentation function d dx D T ( x, ) x E Feynman-x E e e peak at 1 x = s ¹
Jets in heavy-ion collisions Nuclear modification factor R AA = dn AA dp T N coll dn pp dp T High energy particles are a diagnostic tool of the strongly coupled quark gluon plasma
DIS at strong coupling Polchinski, Strassler; Brower, Tan; YH, Iancu, Mueller; Cornalba, Costa; Ballon Bayona, Braga, Nelson; Our universe ( z 0) Photon localized at small z 1 Target localized at large z Cut off the space at z 1 (mimic confinement) z
Large-x:No partons! At large-x, a hadron scatters as a whole. OPE SUGRA SUGRA ' SUGRA Double trace operators dominate the OPE at large-x. Twist-two operators : (j)» 1=4,, contribution strongly suppressed.
Small-x : Regge scattering Large-x region does not contribute to the energy-momentum sum rule. R 1 0 dxf (x; )» ³ ¹ () = const: Small x small j The anomalous dimension remains small in the vicinity of j = The Pomeron vertex operator V j ~ z ( j) j X X j j Brower, Polchinski, Strassler, Tan
Spacelike anomalous dimension in N=4 Energy-momentum operator (twist-two) relevant at exponentially small-x x» 1 s» e p j F 1 (x; )» 1 x F (x; )» 1 N c µ 1 x j0
`Phase diagram at strong coupling YH, Iancu, Mueller
Fits to the HERA F data F (x; )» µ ²( 1 ) x Cornalba & Costa Brower, Djuric, Sarcevic & Tan
e+e- annihilation in N=4 SYM
Energy correlation function Hofman, Maldacena (008) Energy distribution is spherical for any Correlations disappear as 1 (3) = O( ) 1 weak coupling 1 4 strong coupling heei! 0 There are no jets!
Energy distribution at strong coupling ), ( ~ IR T x D dx d ), ( ) ( ), ( ln j D j j D T T T Timelike anomalous dimension Fragmentation function 1, ) ( ), ( ln z x D z P z dz x D T T x T satisfies the Altarelli-Parisi equation Mellin transform
Timelike anomalous dimension in N=4 (j) = weak coupling strong coupling 4¼ (Ã(1) Ã(j 1)) (j) = 1 µj j 0 j p Lipatov, et al. YH, Matsuo x D(x; =¹ IR) = Z dj µ j µ 1 (j) x ¹ IR Dominant value of x where the energy is concentrated µ =1 µ ¹ x weak» >> ¹ x strong» 1 = p
Time-evolution in the final state x +» y +» D µx; ; ¹ = xq+ ~ q Measurement time» xq+ ¹» q+ x Typical size of `partons x» 1 xq +» ; x?» 1 ¹» The same as the size of the whole system. No pointlike structure at strong coupling.
Jets at finite-t : Jet quenching in N=4
Jet quenching at weak coupling Energy loss by coherent Bremsstrahlung (LPM effect) E! E» Z E!dI d!dz d!dz» s p^qe L L max» E 1=
Jet quenching at strong coupling Solve the Maxwell equation in the background of Schwarzschild AdS_5 z 0 Event horizon z z 0 1 T H
Effective Schrodinger equation A ietiqx ( t, x, z) e ( t, z) weak, residual t-dependence i @Ã @t = µ 1 q @ @z + V (z) Ã Potential qualitatively different between V (z) low energy 3 ET V (z) high energy 3 ET
Stopping distance and spacetime evolution Low energy 3 ET `meson screening length Liu, Rajagopal, Wiedemann 1 ( 1 v T 4 ) 1/ 1 T L max E 1 4 High energy YH, Iancu, Mueller, Arnold, Vaman L max E 1 3 ET À 3 1 ( ET 3 ) 1 1 T Gubser, Gulotta, Pufu, Rocha YH, Iancu, Mueller Chesler, Jensen, Karch, Yaffe
Recent developments Arnold, Vaman (011); 103.6658 [hep-th] ³ L max / E 1=3 1 + # 3= +! 1 L max E 1 1
Conclusions AdS/CFT offers an interesting framework to study nonperturbative aspects of high energy processes. Beware, some features are completely different from CD. At strong coupling, all the interesting physics is at small-x due to the strong fragmentation.