Anomalous dimension of transverse momentum broadening in planar $\mathcal{N}=4$ SYM

Abstract

The typical transverse momentum $Q_s(t)$ (or "saturation" momentum) acquired by a hard particle propagating through a $\mathcal{N}=4$ SYM plasma increases over time like $t^{\gamma }$, with an anomalous exponent $\gamma >1/2$ characteristic of super-diffusion. This anomalous exponent is a function of the 't Hooft coupling $\lambda =g^2{N}_c$. Recently, a method has been proposed to systematically compute the perturbative series of $\gamma (\lambda )$ at weak coupling. This method relies on the traveling wave interpretation of the time evolution of $Q_s(t)$ and on the dominance of soft-collinear radiative corrections at large times. In this paper, we compute $\gamma (\lambda )$ up to $\mathcal{O}({\lambda }^2)$ using the double logarithmic behaviour of the BFKL equation in planar $\mathcal{N}=4$ SYM at three loops. This calculation allows us to discuss the transition towards the strong coupling regime where AdS/CFT calculations predict $\gamma \to 1$.

arXiv comment8 pages, 1 figure, contribution to the proceedings of the "XVth International Conference on Quark Confinement and the Hadron Spectrum"

References in corpus (32)

• Front propagation into unstable states
• The Pomeron and Gauge/String Duality
• Conformal Regge theory
• The Energy Dependence of the Saturation Momentum
• Jet quenching in high-energy heavy-ion collisions
• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
• A resummation of large sub-leading corrections at small x
• NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories
• Geometric scaling as traveling waves
• Photon and dilepton production in supersymmetric Yang-Mills plasma
• Medium-Induced QCD Cascade: Democratic Branching and Wave Turbulence
• Jet evolution in the N=4 SYM plasma at strong coupling
• A simple sum rule for the thermal gluon spectral function and applications
• Radiative pT-broadening of high-energy quarks and gluons in QCD matter
• Renormalization of the jet-quenching parameter
• Probabilistic picture for medium-induced jet evolution
• Non-linear evolution in QCD at high-energy beyond leading order
• Perturbatively Stable Resummed Small x Evolution Kernels
• Comparing energy loss and $p_{\perp }$-broadening in perturbative QCD with strong coupling $\mathcal{N}=4$ SYM theory
• NNLO BFKL Pomeron eigenvalue in N=4 SYM
• Deep inelastic scattering off a N=4 SYM plasma at strong coupling
• Deciphering the $z_g$ distribution in ultrarelativistic heavy ion collisions
• The non-linear evolution of jet quenching
• Cone size dependence of jet suppression in heavy-ion collisions
• Pomeron in the N=4 supersymmetric gauge model at strong couplings
• BFKL at Next-to-Next-to-Leading Order
• Medium-induced fragmentation and equilibration of highly energetic partons
• Quantum chromodynamics at high energy and statistical physics
• Running coupling effects in the evolution of jet quenching
• Transverse momentum broadening and collinear radiation at NLO in the $\mathcal{N}=4$ SYM plasma
• Classical vs quantum corrections to jet broadening in a weakly-coupled Quark-Gluon Plasma
• Universality (beyond leading log) of soft radiative corrections to $\hat{q}$ in $p_{\perp }$ broadening and energy loss