Efficient numerical integration of thermal interaction rates

Abstract

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 suppressed. 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.

48 pages, programs as ancillary files. v2: clarifications added

References in corpus (27)

• FORM version 4.0
• micrOMEGAs5.0 : freeze-in
• Thermal Gravitino Production and Collider Tests of Leptogenesis
• Thermal production of gravitinos
• Thermal axion production
• DarkSUSY 6 : An Advanced Tool to Compute Dark Matter Properties Numerically
• O(g) plasma effects in jet quenching
• Next-to-leading order thermal photon production in a weakly coupled quark-gluon plasma
• Thermal production of ultrarelativistic right-handed neutrinos: Complete leading-order results
• Thermal production of relativistic Majorana neutrinos: Strong enhancement by multiple soft scattering
• Gravitational wave background from Standard Model physics: Complete leading order
• Jet-Medium Interactions at NLO in a Weakly-Coupled Quark-Gluon Plasma
• Towards leptogenesis at NLO: the right-handed neutrino interaction rate
• Thermal right-handed neutrino production rate in the relativistic regime
• GeV-scale hot sterile neutrino oscillations: a derivation of evolution equations
• Right-handed neutrino production rate at T > 160 GeV
• Gravitino thermal production revisited
• Low Mass Thermal Dilepton Production at NLO in a Weakly Coupled Quark-Gluon Plasma
• Thermal 2-loop master spectral function at finite momentum
• Equilibration, particle production, and self-energy
• Freeze-in produced dark matter in the ultra-relativistic regime
• Sterile neutrino dark matter via GeV-scale leptogenesis?
• Two-loop thermal spectral functions with general kinematics
• The ultraviolet limit and sum rule for the shear correlator in hot Yang-Mills theory
• Transverse momentum broadening and collinear radiation at NLO in the $\mathcal{N}=4$ SYM plasma
• Kinetic equations for sterile neutrinos from thermal fluctuations
• A thermal neutrino interaction rate at NLO

Cited by in corpus (10)

• Lyman-$\alpha$ constraints on freeze-in and superWIMPs
• Freezing-in a hot bath: resonances, medium effects and phase transitions
• Gravitational wave background from non-Abelian reheating after axion-like inflation
• Dilepton production at next-to-leading order and intermediate invariant-mass observables
• Smooth interpolation between thermal Born and LPM rates
• Resonant $s$-channel dark matter annihilation at NLO
• Dark Matter abundance via thermal decays and leptoquark mediators
• QED corrections to the thermal neutrino interaction rate
• Shedding light on thermal photon and dilepton production
• Sterile neutrino rates for general $M$, $T$, $\mu$, $k$: review of a theoretical framework