1 / 37

Jets in N=4 SYM from AdS/CFT

Jets in N=4 SYM from AdS/CFT. Yoshitaka Hatta U. Tsukuba. Y.H., E. Iancu, A. Mueller, arXiv:0803.2481 [hep-th] (JHEP) Y.H., T. Matsuo, arXiv:0804.4733 [hep-th]. Contents. Introduction e^+e^- annihilation and Jets in QCD Jet structure at strong coupling Jet evolution at finite temperature.

geoffrey-lancaster
Download Presentation

Jets in N=4 SYM from AdS/CFT

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Jets in N=4 SYM from AdS/CFT Yoshitaka Hatta U. Tsukuba Y.H., E. Iancu, A. Mueller, arXiv:0803.2481 [hep-th] (JHEP) Y.H., T. Matsuo, arXiv:0804.4733 [hep-th]

  2. Contents • Introduction • e^+e^- annihilation and Jets in QCD • Jet structure at strong coupling • Jet evolution at finite temperature

  3. Strongly interacting matter at RHIC Observed jet quenching of high-pt hadrons is stronger than pQCD predictions.

  4. Strongly interacting matter at RHIC Ideal hydro simulation works, suggesting short mean free path. low viscosity, strong jet quenching

  5. The Regge limit of QCD Hadron-hadron total cross section grows with energy (‘soft Pomeron’) or ? c.f., pQCD prediction (BFKL, ‘hard Pomeron’)

  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, or in the `unparticle’ sector at the LHC? • Lots of works on DIS. e^+e^- annihilation is a cross channel of DIS. Why study jets ? Strassler, arXiv:0801.0629 [hep-ph]

  7. Deep inelastic scattering in QCD Two independent kinematic variables • Photon virtuality • Bjorken- Momentum fraction of a parton : Parton distribution function Count how many partons are there inside a proton. DGLAP equation

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

  9. Jets in QCD Observation of jets in `75 provides one of the most striking confirmations of QCD Average angular distribution reflecting fermionic degrees of freedom (quarks)

  10. Fragmentation function Count how many hadrons are there inside a quark. Feynman-x First moment average multiplicity Second moment energy conservation

  11. Evolution equation The fragmentation functions satisfy a DGLAP-type equation Take a Mellin transform Timelike anomalous dimension (assume )

  12. Anomalous dimension in QCD Lowest order perturbation ~ Soft singularity Resummation Angle-ordering Mueller, `81

  13. Inclusive spectrum roughly an inverse Gaussian peaked at largel-x small-x

  14. N=4 Super Yang-Mills • SU(Nc) local gauge symmetry • Conformal symmetry SO(4,2) The ‘t Hooft coupling doesn’t run. • Global SU(4) R-symmetry  choose a U(1) subgroup and gauge it.

  15. Type IIB superstring • Consistent superstring theory in D=10 • Supergravity sector admits the black 3-brane solution which is asymptotically AdS `radius’ coordinate Our universe

  16. The correspondence Maldacena, `97 • 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

  17. DIS at strong coupling Polchinski, Strassler, `02 Y.H. Iancu, Mueller, `07 R-charge current excites metric fluctuations in the bulk, which then scatters off a dilaton (`glueball’) We are here Photon localized at large Dilaton localized at small Cut off the space at (mimic confinement)

  18. e^+e^- annihilation at strong coupling Hofman, Maldacena Y.H., Iancu, Mueller, Y.H. Matsuo arXiv:0803.1467 [hep-th] arXiv:0803.2481 [hep-th] arXiv:0804.4733 [hep-th] 5D Maxwell equation Dual to the 4D R-current

  19. A reciprocity relation DGRAP equation The two anomalous dimensions derive from a single function Dokshitzer, Marchesini, Salam, ‘06 Confirmed up to three loops (!) in QCD Mitov, Moch, Vogt, `06 Application to AdS/CFT Basso, Korchemsky, ‘07 Assume this is valid at strong coupling and see where it leads to.

  20. Anomalous dimension in N=4 SYM Leading Regge trajectory Twist—two operators lowest mass state for given j lowest dimension operator for given j Gubser, Klebanov, Polyakov, `02 The `cusp’ anomalous dimension Kotikov, Lipatov, Onishchenko, Velizhanin `05 Brower, Polchinski, Strassler, Tan, `06

  21. Average multiplicity crossing Y.H., Matsuo ‘08 c.f. in perturbation theory, Y.H., Iancu, Mueller ‘08 c.f. heuristic argument

  22. Jets at strong coupling? in the supergravity limit The inclusive distribution is peaked at the kinematic lower limit Rapidly decaying function for 1 At strong coupling, branching is so fast and efficient. There are no partons at large-x !

  23. Energy correlation function Hofman, Maldacena `08 Energy distribution is spherical for any Correlations disappear as weak coupling strong coupling All the particles have the minimal four momentum~ and are spherically emitted. There are no jets at strong coupling !

  24. Evolution of jets in a N=4 plasma Y.H., Iancu, Mueller `08 Solve the Maxwell equation in the background of Schwarzschild AdS_5 Event horizon To compute correlation functions :

  25. Time-dependent Schrödinger equation To study time-evolution, add a weak t-dependence and keep only the 1st t-derivative Solutions available only piecewise. Qualitative difference between t=0 ‘low energy’ and ‘high energy’ 2 Minkowski boundary : plasma saturation momentum horizon

  26. low-energy, Early time diffusion solution with This represents diffusion up to time

  27. Gauge theory interpretation is the formation time of a parton pair (a.k.a., the coherence time in the spacelike case) IR/UV correspondence c.f., general argument from pQCD Farrar, Liu, Strikman, Frankfurt ‘88

  28. low-energyIntermediate free streaming region solution with constant (group-) velocity motion

  29. Gauge theory interpretation is the transverse velocity IR/UV correspondence Linear expansion of the pair

  30. low-energyFalling down the potential solution with A classical particle with mass falling down the potential

  31. Gauge theory interpretation In-medium acceleration start to `feel’ the plasma disappear into the plasma

  32. The high energy case No difference between the timelike/spacelike cases A new characteristic time

  33. Energy loss, meson screening length, and all that breakup The scale is the meson screening length Liu, Rajagopal, Wiedemann, `06 WKP solution after the breakup features the trailing string solution Herzog, et al, ‘06, Gubser, ‘06

  34. Energy loss, meson screening length,and all that Rate of enery flow towards the horizon Identical to the motion of our wavepacket Time to reach the horizon c.f., damping time of a gluon Gubser, Gulotta, Pufu, Rocha, 0803.1470 [hep-th]

  35. Branching picture at strong coupling Final state cannot be just a pair of partons Energy and virtuality of partons in n-th generation At strong coupling, branching is as fast as allowed by the uncertainty principle or

  36. Medium-induced branching at finite-T Mach cone? where time-dependent drag force

  37. Conclusion • Various aspects of jets at strong coupling—including the details of the final state—are accessible from gauge/string duality techniques. • Photon evolution problem sheds new light on the physics of energy loss, etc. in a strongly coupled plasma.

More Related