Collisional energy loss in a finite size QCD medium revisited

Alejandro AyalaInstituto de Ciencias Nucleares, UNAM

Radiative and collisional energy losses

Mass and color charge effects…

Energy loss issues

Collisional vs radiative energy losses Mass and color charge effects Running of s

Non-perturbative calculations using AdS/CFT and duality arguments

... Finite size effects

A

A

B

B

Particle production region

Q: How does the size of the interaction region play a role in the description of parton energy losses?

Finite size effects

S. Peigné, P.B. Gossiaux and T. Gousset, JHEP04, 011 (2006)

Energy loss computed by slowing down of parton induced by medium produced chromoelectric field in Abelian approximation

Retardation effects: A fast parton produced in the mediumneeds to travel some distance before losing energy at thehighest rate.Conclusion: finite size reduces the rate of energy loss.

Conserved current

M. Djordjevic, PRC 74, 064907 (2006)

Condition for interaction between jet and medium parton to occur inside finite QCDmedium of size L.Conclusion: finite size does not affect the rateof energy loss.

Perturbative collisional energy loss, 2 2 processesin a finite QCD medium

Particle source

Scattering diagram

Source: J (t, x )

Classical, conserved current

Simple model: Color singlet dipole, i.e., two partonsin color singlet state traveling with velocities v1 and v2

In Fourier space, this is:

+ (retarded prescription)

But suppose ( finite)

Current life-time:

In Fourier space:

Parton should travel length of plasma

Interaction rate involves ratio of currents after and without collision

Explicit dependence on current life-time

Scattering diagram

Source: J (t, x )

Modified matrix elementCurrent life-time

Interaction within the plasma

Modified matrix element

Modified matrix element squared

Differential rate

Elementary scattering process

Auxiliary functions for average over velocity directions

Summary

Incorporate an explicit conserved current into the description of collisional energy loss

The above requires considering the time the current spends within the plasma

Predictions?... Not yet, working on them.