The non-linear evolution of jet quenching

Abstract

We construct a generalization of the JIMWLK Hamiltonian, going beyond the eikonal approximation, which governs the high-energy evolution of the scattering between a dilute projectile and a dense target with an arbitrary longitudinal extent (a nucleus, or a slice of quark-gluon plasma). Different physical regimes refer to the ratio $L/\tau$ between the longitudinal size $L$ of the target and the lifetime $\tau$ of the gluon fluctuations. When $L/\tau \ll 1$, meaning that the target can be effectively treated as a shockwave, we recover the JIMWLK Hamiltonian, as expected. When $L/\tau \gg 1$, meaning that the fluctuations live inside the target, the new Hamiltonian governs phenomena like the transverse momentum broadening and the radiative energy loss, which accompany the propagation of an energetic parton through a dense QCD medium. Using this Hamiltonian, we derive a non-linear equation for the dipole amplitude (a generalization of the BK equation), which describes the high-energy evolution of jet quenching. As compared to the original BK-JIMWLK evolution, the new evolution is remarkably different: the plasma saturation momentum evolves much faster with increasing energy (or decreasing Bjorken's $x$) than the corresponding scale for a shockwave (nucleus). This widely opens the transverse phase-space for the evolution and implies the existence of large radiative corrections, enhanced by the double logarithm ${\ln }^2(LT)$, with $T$ the temperature of the medium. This confirms and explains from a physical perspective a recent result by Liou, Mueller, and Wu (arXiv:1304.7677). The dominant corrections are smooth enough to be absorbed into a renormalization of the jet quenching parameter $\hat{q}$. This renormalization is controlled by a linear equation supplemented with a saturation boundary, which emerges via controlled approximations from the generalized BK equation alluded to above.

54 pages plus 4 appendices, 6 figures

References in corpus (8)

• The Color Glass Condensate
• The theory and phenomenology of perturbative QCD based jet quenching
• Jet physics in heavy-ion collisions
• Antiangular Ordering of Gluon Radiation in QCD Media
• Gluon energy loss in the gauge-string duality
• Comparing energy loss and $p_{\perp }$-broadening in perturbative QCD with strong coupling $\mathcal{N}=4$ SYM theory
• Deep inelastic scattering off a N=4 SYM plasma at strong coupling
• pT-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order

Cited by in corpus (8)

• Non-linear evolution in QCD at high-energy beyond leading order
• Medium Induced Transverse Momentum Broadening in Hard Processes
• Radiative energy loss and radiative p_T-broadening of high-energy partons in QCD matter
• Classical vs quantum corrections to jet broadening in a weakly-coupled Quark-Gluon Plasma
• The LPM effect in sequential bremsstrahlung: 4-gluon vertices
• Nuclear $p_{\perp }$-broadening of Drell-Yan and quarkonium production from SPS to LHC
• Multi-particle correlations and KNO scaling in the medium-induced jet evolution
• Higher-twist contributions to the transverse momentum broadening in semi-inclusive deep inelastic scattering off large nuclei