In this review article, we discuss the current status and future prospects of perturbation theory as a means of studying the equilibrium thermodynamic and near-equilibrium transport properties of deconfined QCD matter. We begin with a brief introduct
ion to the general topic, after which we review in some detail the foundations and modern techniques of the real- and imaginary-time formalisms of thermal field theory, covering e.g. the different bases used in the real-time formalism and the resummations required to deal with soft and collinear contributions. After this, we discuss the current status of applications of these techniques, including topics such as electromagnetic rates, transport coefficients, jet quenching, heavy quarks and quarkonia, and the Equations of State of hot quark-gluon plasma as well as cold and dense quark matter. Finally, we conclude with our view of the future directions of the field, i.e. how we anticipate perturbative calculations to contribute to our collective understanding of strongly interacting matter in the coming years.
Brambilla, Escobedo, Soto, and Vairo have derived an effective description of quarkonium with two parameters; a momentum diffusion term and a real self-energy term. We point out that there is a similar real self-energy term for a single open heavy fl
avor and that it can be expressed directly in terms of Euclidean electric field correlators along a Polyakov line. This quantity can be directly studied on the lattice without the need for analytical continuation. We show that Minkowski-space calculations of this correlator correspond with the known NLO Euclidean value of the relevant electric field two-point function and that it differs from the real self-energy term for quarkonium.
Following Caron-Huot and combining results for the thermal dependence of spectral functions at large time-like momenta, we write an explicit expression for the thermal width of the Higgs boson to $mathcal{O}(alpha_mathrm{s})$ for $T ll M_H$. It is an
$mathcal{O}( alpha_mathrm{s} (T/M_H)^4 )$ correction for $Hto gg$ and $Hto qbar{q}$. We also compile corresponding results for the thermal width of the $Z$-boson, and we recall which generic structures of the field theory, accessible via the operator product expansion, fix the $T/M$-dependence of the decay of heavy particles.
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.
We compute the hydrodynamic relaxation times $tau_pi$ and $tau_j$ for hot QCD at next-to-leading order in the coupling with kinetic theory. We show that certain dimensionless ratios of second-order to first-order transport coefficients obey bounds wh
ich apply whenever a kinetic theory description is possible; the computed values lie somewhat above these bounds. Strongly coupled theories with holographic duals strongly violate these bounds, highlighting their distance from a quasiparticle description.
We compute the shear viscosity of QCD with matter, including almost all next-to-leading order corrections -- that is, corrections suppressed by one power of $g$ relative to leading order. We argue that the still missing terms are small. The next-to-l
eading order corrections are large and bring $eta/s$ down by more than a factor of 3 at physically relevant couplings. The perturbative expansion is problematic even at $T simeq 100$ GeV. The largest next-to-leading order correction to $eta/s$ arises from modifications to the qhat parameter, which determines the rate of transverse momentum diffusion. We also explore quark number diffusion, and shear viscosity in pure-glue QCD and in QED.
We present an extension of the Arnold-Moore-Yaffe kinetic equations for jet energy loss to NLO in the strong coupling constant. A novel aspect of the NLO analysis is a consistent description of wider-angle bremsstrahlung (semi-collinear emissions), w
hich smoothly interpolates between 2<->2 scattering and collinear bremsstrahlung. We describe how many of the ingredients of the NLO transport equations (such as the drag coefficient) can be expressed in terms of Wilson line operators and can be computed using a Euclidean formalism or sum rules, both motivated by the analytic properties of amplitudes at light-like separations. We conclude with an outlook on the computation of the shear viscosity at NLO.
We report on a recent next-to-leading order perturbative determination of the dilepton rate from a hot QCD plasma for frequency and momentum of the order of the temperature and for much smaller invariant mass $Msim gT$. We briefly review the calculat
ion, which generalizes the previous one for the photon case ($M=0$). We then analyze the consequences of the new calculation for the extraction of the photon rate from the small mass dilepton measurements. We then review a recent NLO determination at large $M$ and we show how to match and merge its results with the low-mass ones, resulting in a single rate which is NLO-accurate over the phenomenologically relevant region.
We present an extension to next-to-leading order in the strong coupling constant $g$ of the AMY effective kinetic approach to the energy loss of high momentum particles in the quark-gluon plasma. At leading order, the transport of jet-like particles
is determined by elastic scattering with the thermal constituents, and by inelastic collinear splittings induced by the medium. We reorganize this description into collinear splittings, high-momentum-transfer scatterings, drag and diffusion, and particle
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.
