Here we present results for the "brick" problem using exactly the methodology of
Energy loss of leading hadrons and direct photon production in evolving quark-gluon plasma
by Turbide et al, hep-ph/0502248 (inelastic energy loss using the AMY method) and
Radiative and collisional jet energy loss in the quark-gluon plasma at RHIC
by Qin et al, arXiv:0710.0605(hep-ph) (inelastic plus elastic).
The procedure developed in these papers allows the evolution of a probability distribution with energy for quarks+gluons to evolve through a slab of medium; hydrodynamics is treated by evolving through a series of slabs. The physics which is included is:
- Parton splitting due to scattering in the medium; the treatment includes
- treatment of the medium as dynamical scattering, with HTL screening
- solution of integral equation which treats the LPM effect as an O(1) effect, smoothly interpolating between Bethe-Heitler for low emission energy and strong LPM effect for high emission energy
- Bose stimulation factors at low energies and inverse Bremsstrahlung absorption from the medium
- medium induced dispersion corrections
- inclusion of all subsequent evolution of all daughters of a splitting process (above a cutoff energy)
- Compton-type QCD scattering, qq to gg and qg to gq
- Elastic energy loss
- all processes explicitly obey detailed balance.
The most important physical effect which is neglected is interference between vacuum and thermal bremsstrahlung. Similarly interference between regions of the medium with significantly different densities (and hence scattering rates) is not treated completely correctly.
As discussed in the Wednesday, July 2, 2008 phone conference, we discard partons below some energy cutoff. To clarify, this does NOT mean that we discard the possibility of low energy gluon bremsstrahlung emission. We do allow such gluons to be emitted; but we do not keep track of the subsequent evolution of such emitted low-energy gluons, as we do for higher-energy emitted gluons.
The following plots give the energy probability distribution for a quark to leave the "brick" of medium if it enters the brick at 10 GeV: to use these to compare an inclusive final state hadron spectrum with the vacuum (pp) spectrum, one compares the hadronization products of quarks with this final energy distribution with the hadronization products of a 10 GeV quark using the same hadronization procedure.
We used a thermalized medium with 3 quark flavors, and . The temperature then fixes the density of scatterers and the screening of scattering interactions. The scatterers are treated as dynamical.
For the original brick problem:
AMY plots, original brick
AMY plots, 100 GeV original brick
Note that in these plots we cut off the presented particle momenta below about 2.5 GeV. This is because in our code we do not keep track of the lowest energy partons (in solving the brick problem we threw out partons below 2 GeV). This is partly for technical reasons within the calculation, but it is also motivated by the difficulty in distinguishing such particles from thermal particles. The fraction of quarks which are "lost," quoted in the figure, arises mostly from quarks falling below this lower cutoff.
Also note the nonzero probability to have higher final energy than 10 GeV, even when elastic processes are ignored. This is because we include inverse bremsstrahlung with thermal gluons in the medium, which can raise a quark's energy.
These plots are intended to address issues or questions which arose in
the Wednesday, July 2, 2008 phone conference.
Brick problem but starting with a gluon rather than a quark:
AMY plots, gluon
Brick problem, setting N_f=0 (glue only bath) and dropping Compton processes:
AMY plots, nf=0
Effect of modifying low-energy cutoff (including discussion):
AMY plots, E-cutoff
Curves with different T and L which give the same fractional energy loss:
AMY plots, TL plane
For the Wiedemann modifiction:
AMY plots, Widemann brick
Here we fixed the medium length to be 2 Fermi and controlled the energy loss rate by varying the temperature. Note that, as shown on these figures, getting 10 percent average energy loss required an unphysically low temperature.
For comparison, WHDG find a higher temperature is needed to achieve the same energy loss. There are several systematic differences in the treatments: physics present in our treatment but missing in theirs includes
- Quarks as well as gluons in the medium
- Dynamical rather than static medium
- Compton scattering processes (numerically the most important in this case)
- Sequential emission rather than convolution
Together these differences account for just under half the difference. The physics present in their treatment but absent in ours is
- Inclusion of destructive interference between medium and vacuum emission
and this accounts for a little more than half of the difference in temperature.
Therefore in this case destructive interference may be somewhat more important than the other differences in the treatment. This should be less the case for a thicker medium; it would be interesting to compare medium temperatures to achieve 40% energy loss for a 5 Fermi brick.
AMY comparison with Bethe-Heitler
which we include out of curiosity.
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