Relating e+e- annihilation to high energy scattering at weak and strong coupling

1. Relating e+e- annihilation to high energy scattering at weak and strong coupling Yoshitaka Hatta (U. Tsukuba) JHEP 11 (2008) 057; arXiv:0810.0889 [hep-ph]

2. Outline • Jets in QCD • Jets and BFKL? • e+e- annihilation in AdS/CFT • Soft gluons away from jets

3. 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)

4. Fragmentation function Count how many hadrons are there inside a quark. Feynman-x First moment gives the average multiplicity

5. Timelike anomalous dimension Lowest order perturbation ~ Soft singularity Resummation angle-ordering

6. Inclusive spectrum Structure of jets well understood in pQCD DLA + QCD coherence largel-x small-x

7. Away-from-jets region Gluons emitted at large angle, insensitive to the collinear singularity Resum only the soft logarithms

8. Marchesini-Mueller equation Differential probability for the soft gluon emission large Nc

9. BFKL equation Differential probability for the dipole splitting large Nc

10. BFKL dynamics in jets The two equations become formally identical after the small angle approximation The interjet soft gluon number grows like the BFKL Pomeron ! Question : Is this just a coincidence, or is there any deep relationship between the two processes ?

11. The AdS/CFT correspondence Maldacena `98 N=4 SYM at strong coupling is dual to weakly coupled type IIB superstring theory on Gauge theory correlators calculable from string theory CFT string (anomalous) dimension mass `t Hooft parameter curvature radius number of colors string coupling constant

12. e+e- annihilation in AdS/CFT Hofman & Maldacena, 0803.1467; YH, Iancu & Mueller, 0803.2481; YH & Matsuo, 0804.4733, 0807.0098; YH, 0810.0889. Calorimeters here

13. Properties at strong coupling Energy distribution spherical, there are no jets ! In a sense, the entire solid angle is like an interjet region… Branching is so fast and efficient. The total multiplicity grows linearly with the energy Hofman & Maldacena YH, Iancu & Mueller YH & Matsuo The inclusive spectrum is ‘thermal’ YH & Matsuo

14. The Poincare coordinates as a hypersurface in 6D Introduce two Poincare coordinate systems Our universe Poincare 1 : Poincare 2 : Related via a conformal transformation on the boundary

15. Shock wave picture of e+e- annihilation Want to compute the total energy flow Treat the photon as a shock wave in Poincare 2, solve the 5D Einstein equation Energy density on the boundary Use the stereographic map to find the distribution on a sphere

16. Shock wave picture of a high energy hadron A color singlet state lives in the bulk. At high energy, it is a shock wave in Poincare 1. Energy distribution on the boundary transverse plane Gubser, Pufu & Yarom, `08

17. The stereographic map High energy, Regge Exact relationship between the final state in e+e- annihilation and the high energy hadronic Wavefunction ! e+e- annihilation

18. Revisit the weak coupling problem The same stereographic map transforms BFKL into the Marchesini-Mueller equation

19. Interjet gluon angular distribution Exact solution to the BFKL equation known. Due to conformal symmetry, it is a function only of the anharmonic ratio. The exact solution to the Marchesini-Mueller equation Angular distribution of soft gluons Related to the BFKL anomalous dimension

20. Conclusions • Novel correspondence between the final state in e+e- annihilation and the small-x hadronic wavefunction. • At strong coupling, the correspondence is exact. • At weak coupling, the correspondence is useful to study interjet observables. • Energy correlation functions are also related.