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Radiative Energy Loss

Radiative Energy Loss. Radiative Energy Loss. Radiative Energy Loss. Radiative Energy Loss. Radiative Energy Loss. Radiative Energy Loss. Radiative Energy Loss. Radiative Energy Loss. Radiative Energy Loss. at all orders in opacity. Simon Wicks, Yale-Columbia fest, May 2008

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Radiative Energy Loss

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  1. Radiative Energy Loss Radiative Energy Loss Radiative Energy Loss Radiative Energy Loss Radiative Energy Loss Radiative Energy Loss Radiative Energy Loss Radiative Energy Loss Radiative Energy Loss at all orders in opacity Simon Wicks, Yale-Columbia fest, May 2008 Reference: arXiv:0804.4704

  2. Radiative energy loss An opacity expansion ... ...the hard way

  3. The Hard Way I 13 diagrams

  4. The Hard Way II 135 diagrams

  5. The Hard Way III ??? diagrams

  6. An opacity expansion ... ... the clever way (once someone has done the hard way, and check with comparison to the hard way)‏ Radiative energy loss

  7. An opacity expansion ... ... the clever way (once someone has done the hard way, and check with comparison to the hard way)‏ Find an operator recursion from order to order The 'reaction operator' Radiative energy loss

  8. The Recursion Classical cascade Quantum source term(s)‏

  9. The Quantum Source Term Sum over all opacities:

  10. The Quantum Source Term

  11. An opacity expansion is ... An opacity expansion is a Dyson expansion ... ... of an operator equation, similar to a Schrodinger equation ... ... that gives a nice form in impact parameter space.

  12. Spot the difference GLV is equivalent to: BDMPS, at an intermediate stage, is:

  13. Spot the difference II In q-space, BDMPS can be expressed as: AMY is:

  14. Energy loss formalisms differ in:

  15. Provides: 1) A method of derivation of the Schrodinger-like equation 2) A method of solution of the Schrodinger-like equation The opacity expansion To almost arbitrary precision!

  16. Results – Orders in opacity (x/L) dN/dxdk Lambda = 1fm, mu = 0.5 GeV Bertsch-Gunion incoherent 'limit', L/x

  17. Results - Length dependence

  18. Results – dN/dx, dI/dx

  19. Conclusion • Future work: • Different V(q) (Djodjevic's `dynamical medium'?)‏ • Connection with 'thick medium' approximation in BDMPS • Variable density along path length • Effect on RAA • Multiple emission convolution • Convolution with collisional energy loss • Geometry integration

  20. Q: Will the opacity expansion converge quickly? Naïve expectation: largest term is the L/lambda'th. BUT: Strong imaginary potential: strongly absorbing Hence, higher orders << lower orders

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