1. Collisional energy loss in a finite size QCD medium revisited Alejandro Ayala Instituto de Ciencias Nucleares, UNAM

2. Radiative and collisional energy losses

3. Mass and color charge effects…

4. 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

5. 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

6. 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 medium needs to travel some distance before losing energy at the highest rate. Conclusion: finite size reduces the rate of energy loss. Conserved current

7. M. Djordjevic, PRC 74, 064907 (2006) Condition for interaction between jet and medium parton to occur inside finite QCD medium of size L. Conclusion: finite size does not affect the rate of energy loss. Perturbative collisional energy loss, 2  2 processes in a finite QCD medium Particle source

8. Scattering diagram Source: J (t, x )

9. Classical, conserved current Simple model: Color singlet dipole, i.e., two partons in color singlet state traveling with velocities v 1 and v 2 In Fourier space, this is: + (retarded prescription)

10. But suppose    ( finite) Current life-time: In Fourier space:

11. Parton should travel length of plasma Interaction rate involves ratio of currents after and without collision Explicit dependence on current life-time

12. Scattering diagram Source: J (t, x )

13. Modified matrix element Current life-time Interaction within the plasma

14. Modified matrix element 

15. Modified matrix element squared

16. Differential rate

17. Elementary scattering process

18. Auxiliary functions for average over velocity directions

19. 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.