Light-cone Wilson loop in classical lattice gauge theory

The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity.

Towards understanding thermal jet quenching via lattice simulations

After reviewing how simulations employing classical lattice gauge theory permit to test a conjectured Euclideanization property of a light-cone Wilson loop in a thermal non-Abelian plasma, we show how Euclidean data can in turn be used to estimate the transverse collision kernel, C(k⊥), characterizing the broadening of a high-energy jet. First results, based on data produced recently by Panero et al, suggest that C(k⊥) is enhanced over the known NLO result in a soft regime k⊥ < a few T. The shape of k3⊥ C(k⊥) is consistent with a Gaussian at small k⊥.

A relation between screening masses and real-time rates

Thermal screening masses related to the conserved vector current are determined for the case that the current carries a non-zero Matsubara frequency, both in a weak-coupling approach and through lattice QCD. We point out that such screening masses are sensitive to the same infrared physics as light-cone real-time rates. In particular, on the perturbative side, the inhomogeneous Schrödinger equation determining screening correlators is shown to have the same general form as the equation implementing LPM resummation for the soft-dilepton and photon production rates from a hot QCD plasma. The static potential appearing in the equation is identical to that whose soft part has been determined up to NLO and on the lattice in the context of jet quenching. Numerical results based on this potential suggest that screening masses overshoot the free results (multiples of 2πT) more strongly than at zero Matsubara frequency. Four-dimensional lattice simulations in two-flavour QCD at temperatures of 250 and 340 MeV confirm the non-static screening masses at the 10% level. Overall our results lend support to studies of jet quenching based on the same potential at T ≳ 250 MeV.

Parton energy loss and momentum broadening at NLO in high temperature QCD plasmas

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 ↔ 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.

Dispersion relation for hadronic light-by-light scattering: theoretical foundations

In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to (g − 2) μ . We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coefficient functions are free of kinematic singularities and zeros, and thus fulfill a Mandelstam double-dispersive representation; and the explicit relation for the HLbL contribution to (g − 2) μ in terms of the coefficient functions simplifies substantially. We demonstrate explicitly that the dispersive approach defines both the pion-pole and the pion-loop contribution unambiguously and in a model-independent way. The pion loop, dispersively defined as pion-box topology, is proven to coincide exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.

Hadronic light-by-light scattering and the muon g−2

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g − 2)μ come from hadronic contributions. In particular, it can be expected that in a few years the subleading hadronic light-by-light (HLbL) contribution will dominate the theory uncertainty. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. Such a model-independent Approach opens up an avenue towards a data-driven determination of the HLbL contribution to the (g − 2)μ.