Improving the kinematics for low-x QCD evolution equations in coordinate space

High-energy evolution equations, such as the BFKL, BK or JIMWLK equations, aim at resumming the high-energy (next-to-)leading logarithms appearing in QCD perturbative series. However, the standard derivations of those equations are performed in a strict high-energy limit, whereas such equations are then applied to scattering processes at large but finite energies. For that reason, there is typically a slight mismatch between the leading logs resummed by those evolution equations without finite-energy corrections and the leading logs actually present in the perturbative expansion of any observable. That mismatch is one of the sources of large corrections at NLO and NLL accuracy. In the case of the BFKL equation in momentum space, that problem is solved by including a kinematical constraint in the kernel, which is the most important finite-energy correction. In this paper, such an improvement of kinematics is performed in mixed-space (transverse positions and $k^+$) and with a factorization scheme in the light-cone momentum $k^+$ (in a frame in which the projectile is right-moving and the target left-moving). This is the usual choice of variables and factorization scheme for the the BK equation. A kinematically improved version of the BK equation is provided, consistent at finite energies. The results presented here are also a necessary step towards having the high energy limit of QCD (including gluon saturation) quantitatively under control beyond strict leading logarithmic accuracy.Comment: 42 pages, 4 figure

Dipole factorization for DIS at NLO: Combining the qqˉq\bar{q} and qqˉgq\bar{q}g contributions

The NLO corrections to the DIS structure functions $F_2$ and $F_L$ (or equivalently the photon-target cross sections $\sigma^{\gamma^*}_{T}$ and $\sigma^{\gamma^*}_{L}$) at low $x_{Bj}$ are obtained, as a generalization of the dipole factorization formula. For the first time, the contributions of both the $q\bar{q}$ and the $q\bar{q}g$ Fock states in the photon are directly calculated, using earlier results for the $q\bar{q}$ light-front wave-functions at one loop inside a dressed virtual photon. Both the $q\bar{q}$ and the $q\bar{q}g$ contributions have UV divergences, which are shown to cancel each other, using conventional dimensional regularization as UV regulator. Finally, the resummation of high-energy logarithms on top of the NLO results for $\sigma^{\gamma^*}_{T}$ and $\sigma^{\gamma^*}_{L}$ is discussed.Comment: 37 pages, 1 figur

Energy loss and thermalization of heavy quarks in a strongly-coupled plasma

Using the AdS/CFT correspondence, we compute the medium-induced energy loss of a decelerating heavy quark moving through a strongly-coupled supersymmetric Yang Mills plasma. In the regime where the deceleration is small, a perturbative calculation is possible and we obtain the first two corrections to the energy-loss rate of a heavy quark with constant velocity. The thermalization of the heavy quark is also discussed.Comment: 4 pages, no figures, Proceedings of the 21st International Conference on Ultra-Relativistic Nucleus Nucleus Collisions (QM09), Knoxville, USA, March 30-April 4 200

Heavy-quark energy loss and thermalization in a strongly coupled SYM plasma

Using the AdS/CFT correspondence, we compute the radiative energy loss of a slowly decelerating heavy quark with mass M moving through a supersymmetric Yang Mills (SYM) plasma at temperature T at large t'Hooft coupling \lambda. The calculation is carried out in terms of perturbation in \sqrt{\lambda}T/M, and the rate of the energy loss is computed up to second order. We explain the physical meaning of each correction and estimate the thermalization time of a heavy quark moving in a strongly-coupled plasma.Comment: 14 pages, 1 figur