In many problems in particle cosmology, interaction rates are dominated by ${2}leftrightarrow{2}$ scatterings, or get a substantial contribution from them, given that ${1}leftrightarrow{2}$ and ${1}leftrightarrow{3}$ reactions are phase-space suppres
sed. We describe an algorithm to represent, regularize, and evaluate a class of thermal ${2}leftrightarrow{2}$ and ${1}leftrightarrow{3}$ interaction rates for general momenta, masses, chemical potentials, and helicity projections. A key ingredient is an automated inclusion of virtual corrections to ${1}leftrightarrow{2}$ scatterings, which eliminate logarithmic and double-logarithmic IR divergences from the real ${2}leftrightarrow{2}$ and ${1}leftrightarrow{3}$ processes. We also review thermal and chemical potential induced contributions that require resummation if plasma particles are ultrarelativistic.
Studying the diffusion and kinetic equilibration of heavy quarks within a hot QCD medium profits from the knowledge of a coloured Lorentz force that acts on them. Starting from the spatial components of the vector current, and carrying out two matchi
ng computations, one for the heavy quark mass scale ($M$) and another for thermal scales ($sqrt{MT}$, $T$), we determine 1-loop matching coefficients for the electric and magnetic parts of a Lorentz force. The magnetic part has a non-zero anomalous dimension, which agrees with that extracted from two other considerations, one thermal and the other in vacuum. The matching coefficient could enable a lattice study of a colour-magnetic 2-point correlator.
If a homogeneous field evolves within a medium, with the latter gradually picking up a temperature, then the friction felt by the field depends on how its evolution rate compares with medium time scales. We suggest a framework which permits to incorp
orate the contributions from all medium time scales. As an example, we illustrate how warm axion inflation can be described by inputting the retarded pseudoscalar correlator of a thermal Yang-Mills plasma. Adopting a semi-realistic model for the latter, and starting the evolution at almost vanishing temperature, we show how the system heats up and then enters the weak or strong regime of warm inflation. Previous approximate treatments are scrutinized.
A magnon Bose-Einstein condensate in superfluid $^3$He is a fine instrument for studying the surrounding macroscopic quantum system. At zero temperature, the BEC is subject to a few, distinct forms of decay into other collective excitations, owing to
momentum and energy conservation in a quantum vacuum. We study the vortex-Higgs mechanism: the vortices relax the requirement for momentum conservation, allowing the optical magnons of the BEC to transform into light Higgs quasiparticles. This observation expands the spectrum of possible interactions between magnetic quasiparticles in $^3$He-B, opens pathways for hunting down elusive phenomena such as the Kelvin wave cascade or bound Majorana fermions, and lays groundwork for building magnon-based quantum devices.
Many lattice studies of heavy quark diffusion originate from a colour-electric correlator, obtained as a leading term after an expansion in the inverse of the heavy-quark mass. In view of the fact that the charm quark is not particularly heavy, we co
nsider subleading terms in the expansion. Working out correlators up to $O(1/M^2)$, we argue that the leading corrections are suppressed by $O(T/M)$, and one of them can be extracted from a colour-magnetic correlator. The corresponding transport coefficient is non-perturbative already at leading order in the weak-coupling expansion, and therefore requires a non-perturbative determination.
We compute the production rate of the energy density carried by gravitational waves emitted by a Standard Model plasma in thermal equilibrium, consistently to leading order in coupling constants for momenta $ksim pi T$. Summing up the contributions f
rom the full history of the universe, the highest temperature of the radiation epoch can be constrained by the so-called $N_{rm eff}$ parameter. The current theoretical uncertainty $Delta N_{rm eff} le 10^{-3}$ corresponds to $T_{rm max} le 2times 10^{17}$ GeV. In the course of the computation, we show how a subpart of the production rate can be determined with the help of standard packages, even if subsequently an IR subtraction and thermal resummation need to be implemented.
It has been proposed that two resonances could coincide in the early universe at temperatures $T sim 0.2 ... 0.5$ GeV: one between two nearly degenerate GeV-scale sterile neutrinos, producing a large lepton asymmetry through freeze-out and decays; an
other between medium-modified active neutrinos and keV-scale sterile neutrinos, converting the lepton asymmetry into dark matter. Making use of a framework which tracks three sterile neutrinos of both helicities as well as three separate lepton asymmetries, and scanning the parameter space of the GeV-scale species, we establish the degree of fine-tuning that is needed for realizing this scenario.
The Debye mass sets a scale for the screening of static charges and the scattering of fast charges within a gauge plasma. Inspired by its potential cosmological applications, we determine a QCD Debye mass at 2-loop order in a broad temperature range
(1 GeV ... 10 TeV), demonstrating how quark mass thresholds get smoothly crossed. Along the way, integration-by-parts identities pertinent to massive loops at finite temperature are illuminated.
The interaction rate of an ultrarelativistic active neutrino at a temperature below the electroweak crossover plays a role in leptogenesis scenarios based on oscillations between active neutrinos and GeV-scale sterile neutrinos. By making use of a Eu
clideanization property of a thermal light-cone correlator, we determine the $O(g)$ correction to such an interaction rate in the high-temperature limit $pi T gg m_W$, finding a $sim 15 ... 40%$ reduction. For a benchmark point, this NLO correction decreases the lepton asymmetries produced by $sim 1%$.
We confront the thermal NLO vector spectral function (both the transverse and longitudinal channel with respect to spatial momentum, both above and below the light cone) with continuum-extrapolated lattice data (both quenched and with $N_{rm f} = 2$,
at $T sim 1.2 T_{rm c}$). The perturbative side incorporates new results, whose main features are summarized. The resolution of the lattice data is good enough to constrain the scale choice of $alpha_{rm s}$ on the perturbative side. The comparison supports the previous indication that the true spectral function falls below the resummed NLO one in a substantial frequency domain. Our results may help to scrutinize direct spectral reconstruction attempts from lattice QCD.
