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]

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Presentation transcript:

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

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

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

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

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

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

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

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

BFKL equation large Nc Differential probability for the dipole splitting

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 ?

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

e+e- annihilation in AdS/CFT Hofman & Maldacena, ; YH, Iancu & Mueller, ; YH & Matsuo, , ; YH, Calorimeters here

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 YH, Iancu & Mueller YH & Matsuo Hofman & Maldacena The inclusive spectrum is ‘ thermal ’ YH & Matsuo

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

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

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

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

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

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

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.