Hot axions, thermally produced in the Early Universe, would contribute to dark radiation and are thus subject to present and future constraints from . In this paper we quantify the contribution to and its uncertainty in models with axion-gluon couplings from thermal dynamics above the QCD transition. In more detail, we determine the leading-order thermal axion production rate for axion momenta of the order of the temperature adopting three different schemes for the incorporation of the collective dynamics of soft gluons. We show how these three schemes extrapolate differently into the regime of softer axion production, thus giving us a first quantitative handle on the theory uncertainty of the rate. Upon solving the Boltzmann equation, we find that this theory uncertainty translates to an uncertainty of order 0.002 for the contribution to prior to the QCD crossover. The uncertainty from common momentum-averaged approximations to the Boltzmann equation is smaller. We also discuss how QCD transition dynamics would need to be integrated into our results and we show how existing rate determinations in the literature based on gauge-dependent resummations are problematic.

France

Killian Bouzoud

Jacopo Ghiglieri

Thermal axion production at hard and soft momenta

High-energy particles traversing the Quark-Gluon plasma experience modified (massive) dispersion, although their vacuum mass is negligible compared to the kinetic energy. Due to poor convergence of the perturbative series in the regime of soft loop momenta, a more precise determination of this effective mass is needed. This paper continues our investigation on the factorisation between strongly-coupled infrared classical and perturbative ultraviolet behavior. The former has been studied non-perturbatively within EQCD by determining a non-local operator on the lattice. By computing the temperature-scale contribution to the same operator in 4D QCD at next-to-leading order (NLO), we remove the ultraviolet divergence of the EQCD calculation with an opposite infrared divergence from the hard thermal scale. The result is a consistent, regulator-independent determination of the classical contribution where the emergence of new divergences signals sensitivities to new regions of phase space. We address the numerical impact of the classical and NLO thermal corrections on the convergence of the factorised approach and on the partial applicability of our results to calculations of transport coefficients.

Germany

Philipp Schicho

Switzerland

Niels Schlusser

Eamonn Weitz

The force-force correlator at the hard thermal scale of hot QCD

The thermal plasma in the early Universe produced a stochastic gravitational wave (GW) background, which peaks today in the microwave regime and was dubbed the cosmic gravitational microwave background (CGMB). In previous works, only single graviton production processes that contribute to the CGMB have been considered. Here, we also investigate graviton pair production processes and show that these can lead to a significant contribution if the ratio between the maximum temperature and the Planck mass, <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>max</mi></mrow></msub><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></math>, divided by the internal coupling in the heat bath is large enough. As the dark matter freeze-in production mechanism is conceptually very similar to the GW production mechanism from the primordial thermal plasma, we refer to the latter as “GW freeze-in production.” We show that quantum gravity effects appear in single graviton production and are smaller by a factor <math><mo>(</mo><msub><mi>T</mi><mi>max</mi></msub><mo>/</mo><msub><mi>m</mi><mi>p</mi></msub><msup><mo>)</mo><mn>2</mn></msup></math> than the leading order contribution. In our work, we explicitly compute the CGMB spectrum within a scalar model with quartic interaction.

United States

Jan Schütte-Engel

Enrico Speranza

Freezing-in gravitational waves

The transverse momentum broadening coefficient   <math> <mover> <mi>q</mi> <mo>̂</mo> </mover> </math>  $$ \hat{q} $$  receives both soft, classical and radiative, quantum corrections. The former are responsible for a large   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (g) correction, whereas the latter enter at relative order α  s , but are enhanced by a double logarithm of the length of the medium over the thermal wavelength. We analyze radiative corrections for a weakly-coupled quark-gluon plasma. We find that a thermal population of dynamical gluons changes the boundaries and reduces the size of the double-logarithmic phase space. It also provides new subdominant logarithmic corrections. We also show how the quantum, double-logarithmic and classical, soft phase spaces are smoothly connected once the radiated gluon becomes soft enough. Finally, we discuss a pathway to a determination of radiative corrections beyond the harmonic-oscillator approximation.

Classical vs quantum corrections to jet broadening in a weakly-coupled Quark-Gluon Plasma

We provide the first next-to-leading-order (NLO) weak-coupling description of the thermalization process of far-from-equilibrium systems in non-Abelian gauge theory. We study isotropic systems starting from either over- or underoccupied initial conditions and follow their time evolution toward thermal equilibrium by numerically solving the QCD effective kinetic theory at NLO accuracy. We find that the NLO corrections remain well under control for a wide range of couplings and that the overall effect of NLO corrections is to reduce the time needed to reach thermal equilibrium in the systems considered.

China

Yu Fu

Shahin Iqbal

Norway

Aleksi Kurkela

Thermalization of non-Abelian gauge theories at next-to-leading order

High-energy particles traversing a medium experience modified dispersion. In the Quark-Gluon Plasma, such dispersion affects jet propagation and transport properties and should be determined better. Above ~ 2T  c  we expect strongly coupled infrared behavior and perturbative ultraviolet behavior, allowing a perturbative matching to an effective theory called EQCD, which can be studied non-perturbatively. We study the relevant non-local operator in EQCD at next-to-leading order which allows for a complete EQCD-to-lattice match and prepares the groundwork for a matching between EQCD and full QCD. Our results in EQCD show remarkable agreement between perturbation theory and the lattice in the expected regime.

Guy Moore

Finland

The force-force-correlator in hot QCD perturbatively and from the lattice

We compute   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (g) NLO corrections to the transverse scattering kernel and transverse momentum broadening coefficient   <math> <mover> <mi>q</mi> <mo>^</mo> </mover> </math>  $$ \widehat{q} $$  of weakly-coupled   <math> <mi>N</mi> <mo>=</mo> <mn>4</mn> </math>  $$ \mathcal{N}=4 $$  SYM. Based on this, we also compute NLO correction to the collinear splitting rates. For   <math> <mover> <mi>q</mi> <mo>^</mo> </mover> </math>  $$ \widehat{q} $$  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   <math> <mover> <mi>q</mi> <mo>^</mo> </mover> </math>  $$ \widehat{q} $$  in QCD and in   <math> <mi>N</mi> <mo>=</mo> <mn>4</mn> </math>  $$ \mathcal{N}=4 $$  theory to strong coupling expectations.

CERN

South Korea

HyungJoo Kim

Transverse momentum broadening and collinear radiation at NLO in the   <math> <mi>N</mi> <mo>=</mo> <mn>4</mn> </math>  $$ \mathcal{N}=4 $$  SYM plasma

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 the real self-energy term 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 existing Minkowski-space calculations of this correlator correspond with the known NLO Euclidean value of the relevant electric-field two-point function.

Alexander M. Eller

Guy D. Moore

Thermal quarkonium mass shift from Euclidean correlators

Following Caron-Huot and combining results for the thermal dependence of spectral functions at large timelike momenta, we write an explicit expression for the thermal width of the Higgs boson to <math><mrow><mi>O</mi><mo>(</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></mrow></math> for <math><mi>T</mi><mo>≪</mo><msub><mi>M</mi><mi>H</mi></msub></math>. It is an <math><mrow><mi>O</mi><mrow><mo>(</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub><msup><mrow><mo>(</mo><mfrac><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>H</mi></mrow></msub></mrow></mfrac><mo>)</mo></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></mrow></mrow></math> correction for <math><mi>H</mi><mo>→</mo><mi>g</mi><mi>g</mi></math> and <math><mi>H</mi><mo>→</mo><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover></math>. We also compile corresponding results for the thermal width of the <math><mi>Z</mi></math>-boson, and we recall which generic structures of the field theory, accessible via the operator product expansion, fix the <math><mfrac><mi>T</mi><mi>M</mi></mfrac></math>-dependence of the decay of heavy particles.

Urs Achim Wiedemann

Thermal width of the Higgs boson in hot QCD matter

We compute the hydrodynamic relaxation times <math><msub><mi>τ</mi><mi>π</mi></msub></math> and <math><msub><mi>τ</mi><mi>j</mi></msub></math> 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 which 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.