Charm mass effects in bulk channel correlations

The bulk viscosity of thermalized QCD matter at temperatures above a few hundred MeV could be significantly influenced by charm quarks because their contribution arises four perturbative orders before purely gluonic effects. In an attempt to clarify the challenges of a lattice study, we determine the relevant imaginary-time correlator (of massive scalar densities) up to NLO in perturbation theory, and compare with existing data. We find discrepancies much larger than in the vector channel; this may hint, apart from the importance of taking a continuum limit, to larger non-perturbative effects in the scalar channel. We also recall how a transport peak related to the scalar density spectral function encodes non-perturbative information concerning the charm quark chemical equilibration rate close to equilibrium.

Thermal right-handed neutrino production rate in the relativistic regime

The production rate of right-handed neutrinos from a Standard Model plasma at a temperature above a hundred GeV is evaluated up to NLO in Standard Model couplings. The results apply in the so-called relativistic regime, referring parametrically to a mass M ~ πT, generalizing thereby previous NLO results which only apply in the non-relativistic regime M ≫ πT. The non-relativistic expansion is observed to converge for M ≳ 15T, but the smallness of any loop corrections allows it to be used in practice already for M ≳ 4T. In the latter regime any non-covariant dependence of the differential rate on the spatial momentum is shown to be mild. The loop expansion breaks down in the ultrarelativistic regime M ≪ πT, but after a simple mass resummation it nevertheless extrapolates reasonably well towards a result obtained previously through complete LPM resummation, apparently confirming a strong enhancement of the rate at high temperatures (which facilitates chemical equilibration). When combined with other ingredients the results may help to improve upon the accuracy of leptogenesis computations operating above the electroweak scale.

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.

Thermal 2-loop master spectral function at finite momentum

When considering NLO corrections to thermal particle production in the “relativistic” regime, in which the invariant mass squared of the produced particle is K2 ~ (πT)2, then the production rate can be expressed as a sum of a few universal “master” spectral functions. Taking the most complicated 2-loop master as an example, a general strategy for obtaining a convergent 2-dimensional integral representation is suggested. The analysis applies both to bosonic and fermionic statistics, and shows that for this master the non-relativistic approximation is only accurate for K2 ~(8πT)2, whereas the zero-momentum approximation works surprisingly well. Once the simpler masters have been similarly resolved, NLO results for quantities such as the right-handed neutrino production rate from a Standard Model plasma or the dilepton production rate from a QCD plasma can be assembled for K2 ~ (πT)2.

Lattice study of an electroweak phase transition at mh ~ 126 GeV

We carry out lattice simulations of a cosmological electroweak phase transition for a Higgs mass mh 126 GeV. The analysis is based on a dimensionally reduced effective theory for an MSSM-like scenario including a relatively light coloured SU(2)-singlet scalar, referred to as a right-handed stop. The non-perturbative transition is stronger than in 2-loop perturbation theory, and may offer a window for electroweak baryogenesis. The main remaining uncertainties concern the physical value of the right-handed stop mass which according to our analysis could be as high as mR 155 GeV; a more precise effective theory derivation and vacuum renormalization than available at present are needed for confirming this value.

Sommerfeld effect in heavy quark chemical equilibration

The chemical equilibration of heavy quarks in a quark-gluon plasma proceeds via annihilation or pair creation. For temperatures T much below the heavy quark mass M, when kinetically equilibrated heavy quarks move very slowly, the annihilation in the colour singlet channel is enhanced because the quark and antiquark attract each other which increases their probability to meet, whereas the octet contribution is suppressed. This is the so-called Sommerfeld effect. It has not been taken into account in previous calculations of the chemical equilibration rate, which are therefore incomplete for T ≲ α2sM . We compute the leading-order equilibration rate in this regime; there is a large enhancement in the singlet channel, but the rate is dominated by the octet channel, and therefore the total effect is small. In the course of the computation we demonstrate how operators that represent the annihilation of heavy quarks in non-relativistic QCD can be incorporated into the imaginary-time formalism.

Hot QCD vs cosmology

It is a long-standing dream to “simulate” cosmology in laboratory through heavy ion collision experiments. Although the QCD epoch itself may not leave major cosmological signatures, theoretical methods developed and tested in the context of heavy ion collision experiments could indeed find applications at other energy scales. Here recent progress in this spirit is reviewed.

Kubo relations and radiative corrections for lepton number washout

The rates for lepton number washout in extensions of the Standard Model containing right-handed neutrinos are key ingredients in scenarios for baryogenesis through leptogenesis. We relate these rates to real-time correlation functions at finite temperature, without making use of any particle approximations. The relations are valid to quadratic order in neutrino Yukawa couplings and to all orders in Standard Model couplings. They take into account all spectator processes, and apply both in the symmetric and in the Higgs phase of the electroweak theory. We use the relations to compute washout rates at next-to-leading order in g, where g denotes a Standard Model gauge or Yukawa coupling, both in the non-relativistic and in the relativistic regime. Even in the non-relativistic regime the parametrically dominant radiative corrections are only suppressed by a single power of g. In the non-relativistic regime radiative corrections increase the washout rate by a few percent at high temperatures, but they are of order unity around the weak scale and in the relativistic regime.

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.

Interpolation of hard and soft dilepton rates

Strict next-to-leading order (NLO) results for the dilepton production rate from a QCD plasma at temperatures above a few hundred MeV suffer from a breakdown of the loop expansion in the regime of soft invariant masses M 2 ≪ (πT)2. In this regime an LPM resummation is needed for obtaining the correct leading-order result. We show how to construct an interpolation between the hard NLO and the leading-order LPM expression, which is theoretically consistent in both regimes and free from double counting. The final numerical results are presented in a tabulated form, suitable for insertion into hydrodynamical codes.

First order thermal phase transition with 126 GeV Higgs mass

We study the strength of the electroweak phase transition in models with two light Higgs doublets and a light SU(3)c triplet by means of lattice simulations in a dimensionally reduced effective theory. In the parameter region considered the transition on the lattice is significantly stronger than indicated by a 2-loop perturbative analysis. Within some ultraviolet uncertainties, the finding applies to MSSM with a Higgs mass mh ≈ 126 GeV and shows that the parameter region useful for electroweak baryogenesis is enlarged. In particular (even though only dedicated analyses can quantify the issue), the tension between LHC constraints after the 7 TeV and 8 TeV runs and frameworks where the electroweak phase transition is driven by light stops, seems to be relaxed.

Towards the continuum limit in transport coefficient computations

The analytic continuation needed for the extraction of transport coefficients necessitates in principle a continuous function of the Euclidean time variable. We report on progress towards achieving the continuum limit for 2-point correlator measurements in thermal SU(3) gauge theory, with specific attention paid to scale setting. In particular, we improve upon the determination of the critical lattice coupling and the critical temperature of pure SU(3) gauge theory, estimating r0Tc ≃ 0.7470(7) after a continuum extrapolation. As an application the determination of the heavy quark momentum diffusion coefficient from a correlator of colour-electric fields attached to a Polyakov loop is discussed.

Temporal mesonic correlators at NLO for any quark mass

We present NLO results for thermal imaginary-time correlators in the vector and scalar channels as a function of the quark mass. The range of quark masses for which a non-relativistic approximation works in the temperature range considered is estimated, and charm quarks turn out to be a borderline case. Comparing with simulation data from fine lattices, we find good agreement in the vector channel but a substantial discrepancy in the scalar one. An explanation for the discrepancy is suggested in terms of physics of the quark-antiquark threshold region. Perturbative predictions for the bottom scalar spectral function around the threshold are also briefly reviewed.

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⊥.

Right-handed neutrino production rate at T > 160 GeV

The production rate of right-handed neutrinos from a Standard Model plasma at a temperature above a hundred GeV has previously been evaluated up to NLO in Standard Model couplings (g ~ 2/3) in relativistic (M ~ πT) and non-relativistic regimes (M ≫ πT), and up to LO in an ultrarelativistic regime (M ≲ gT). The last result necessitates an all-orders resummation of the loop expansion, accounting for multiple soft scatterings of the nearly light-like particles participating in 1↔2 reactions. In this paper we suggest how the regimes can be interpolated into a result applicable for any right-handed neutrino mass and at all temperatures above 160GeV. The results can also be used for determining the lepton number washout rate in models containing right-handed neutrinos. Numerical results are given in a tabulated form permitting for their incorporation into leptogenesis codes. We note that due to effects from soft Higgs bosons there is a narrow intermediate regime around M ~g 1/2 T in which our interpolation is phenomenological and a more precise study would be welcome.