No Arabic abstract
We compute O(g) NLO corrections to the transverse scattering kernel and transverse momentum broadening coefficient $hat{q}$ of weakly-coupled $mathcal{N}=4$ SYM. Based on this, we also compute NLO correction to the collinear splitting rates. For $hat{q}$ we find that the NLO/LO ratio is similar to the QCD one, with large NLO corrections. This is contrasted by our findings for the collinear splitting rate, which show a much better convergence in SYM than in QCD, providing further support to earlier expectations that NLO corrections have signs and relative magnitudes controlled by the specifics of the theory. We also compare the ratio of $hat{q}$ in QCD and in $mathcal{N}=4$ theory to strong coupling expectations.
Quark-gluon plasma produced at the early stage of ultrarelativistic heavy ion collisions is unstable, if weakly coupled, due to the anisotropy of its momentum distribution. Chromomagnetic fields are spontaneously generated and can reach magnitudes much exceeding typical values of the fields in equilibrated plasma. We consider a high energy test parton traversing an unstable plasma that is populated with strong fields. We study the momentum broadening parameter $hat q$ which determines the radiative energy loss of the test parton. We develop a formalism which gives $hat q$ as the solution of an initial value problem, and we focus on extremely oblate plasmas which are physically relevant for relativistic heavy ion collisions. The parameter $hat q$ is found to be strongly dependent on time. For short times it is of the order of the equilibrium value, but at later times $hat q$ grows exponentially due to the interaction of the test parton with unstable modes and becomes much bigger than the value in equilibrium. The momentum broadening is also strongly directionally dependent and is largest when the test parton velocity is transverse to the beam axis. Consequences of our findings for the phenomenology of jet quenching in relativistic heavy ion collisions are briefly discussed.
We present numerical results for the nonplanar lightlike cusp and collinear anomalous dimension at four loops in ${mathcal N} = 4$ SYM theory, which we infer from a calculation of the Sudakov form factor. The latter is expressed as a rational linear combination of uniformly transcendental integrals for arbitrary colour factor. Numerical integration in the nonplanar sector reveals explicitly the breakdown of quadratic Casimir scaling at the four-loop order. A thorough analysis of the reported numerical uncertainties is carried out.
We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which we term the rapidity identity operators, that will generically appear at subleading power in problems involving both rapidity and virtuality scales. To illustrate our formalism, we analytically solve these equations to resum the power suppressed logarithms appearing in the back-to-back (double light cone) limit of the Energy-Energy Correlator (EEC) in $mathcal{N}$=4 super-Yang-Mills. These logarithms can also be extracted to $mathcal{O}(alpha_s^3)$ from a recent perturbative calculation, and we find perfect agreement to this order. Instead of the standard Sudakov exponential, our resummed result for the subleading power logarithms is expressed in terms of Dawsons integral, with an argument related to the cusp anomalous dimension. We call this functional form Dawsons Sudakov. Our formalism is widely applicable for the resummation of subleading power rapidity logarithms in other more phenomenologically relevant observables, such as the EEC in QCD, the $p_T$ spectrum for color singlet boson production at hadron colliders, and the resummation of power suppressed logarithms in the Regge limit.
We present an overview of a perturbative-kinetic approach to jet propagation, energy loss, and momentum broadening in a high temperature quark-gluon plasma. The leading-order kinetic equations describe the interactions between energetic jet-particles and a non-abelian plasma, consisting of on-shell thermal excitations and soft gluonic fields. These interactions include 2<->2 scatterings, collinear bremsstrahlung, and drag and momentum diffusion. We show how the contribution from the soft gluonic fields can be factorized into a set of Wilson line correlators on the light cone. We review recent field-theoretical developments, rooted in the causal properties of these correlators, which simplify the calculation of the appropriate Wilson lines in thermal field theory. With these simplifications lattice measurements of transverse momentum broadening have become possible, and the kinetic equations describing parton transport have been extended to next-to-leading order in the coupling g.
In this letter, we present the NNLL-NNLO transverse momentum Higgs distribution arising from gluon fusion. In the regime $p_perpll m_H$ we include the resummation of the large logs at next to next-to leading order and then match on to the $alpha_s^2$ fixed order result near $p_perp sim m_h$. By utilizing the rapidity renormalization group (RRG) we are able to smoothly match between the resummed, small $p_perp$ regime and the fixed order regime. We give a detailed discussion of the scale dependence of the result including an analysis of the rapidity scale dependence. Our central value differs from previous results, in the transition region as well as the tail, by an amount which is outside the error band. This difference is due to the fact that the RRG profile allows us to smoothly turn off the resummation.