We derive simple expressions to regularise functional determinants from fluctuations of fields with spin 0, 1/2, and 1. These are important for the precise dimensionful determination of false vacuum decay rates. We work in $\textit{D}$ = 4 Euclidean dimensions and use familiar Feynman diagrammatic techniques with a double expansion in interactions and masses, together with dimensional regularisation in momentum space. We Fourier transform to coordinate space and end up with a simple regularisation prescription in terms of single integrals over the Euclidean radius of field-dependent masses and their derivatives. Our results apply to models with an arbitrary scalar potential and with any number of scalars, fermions, gauge bosons and associated ghosts. We exemplify this approach on the Standard Model with a streamlined calculation of the renormalisation and isolation of divergences in fluctuation determinants.

Slovenia

Pietro Baratella

Miha Nemevšek

Yutaro Shoji

Katarina Trailović

Lorenzo Ubaldi

Functional determinants for false vacuum decay

We consider a single real scalar field in flat spacetime with a polynomial potential up to $\textit{ϕ}$ , that has a local minimum, the false vacuum, and a deeper global minimum, the true vacuum. When the vacua are almost degenerate we are in the thin wall regime, while as their difference in potential energy increases, we approach the thick wall regime. We give explicit simple formulae for the decay rate of the false vacuum in 3 and 4 spacetime dimensions. Our results include a careful treatment both of the bounce action, which enters at the exponent of the decay rate, and of the functional determinant at one loop, which determines the prefactor. The bounce action is computed analytically as an expansion in the thin wall parameter in generic $\textit{D}$ dimensions. We find that truncating such an expansion at second order we obtain a remarkably accurate bounce action also deep into thick wall regimes. We calculate the functional determinant numerically in 3 and 4 dimensions and fit the results with simple polynomials of the same thin wall parameter. This allows us to write the complete one-loop decay rate as a compact expression, which works accurately from thin to thick wall regimes.

Marco Matteini

False vacuum decay rate from thin to thick walls

We revisit the decay rate of the electroweak vacuum in the standard model with the full one-loop prefactor. We focus on the gauge degrees of freedom and derive the degeneracy factors appearing in the functional determinant using group theoretical arguments. Our treatment shows that the transverse modes were previously overcounted, so we revise the calculation of that part of the prefactor. The new result modifies the gauge fields’ contribution by 6% and slightly decreases the previously predicted lifetime of the electroweak vacuum, which remains much longer than the age of the Universe. Our discussion of the transverse mode degeneracy applies to any calculation of functional determinants involving gauge fields in four dimensions.

Revising the Full One-Loop Gauge Prefactor in Electroweak Vacuum Stability

We consider a simple setup with a dark sector containing dark electrons charged under an Abelian <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>D</mi></msub></math> gauge symmetry. We show that, if the massless dark photon associated to the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>D</mi></msub></math> is produced during inflation in such a way as to form a classical dark electric field, then dark electron-positron pairs are also produced close to the end of inflation via the Schwinger effect even if they are very massive. For large enough dark electric force, dark electrons with masses larger than the Hubble scale can be produced which are nonrelativistic at production and throughout their cosmic evolution. They can account for the dark matter abundance today for masses in the range <math><mo>∼</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> to <math><msup><mn>10</mn><mn>17</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and up to 6 orders of magnitude larger than the Hubble scale at the end of inflation where purely gravitational production is exponentially suppressed. We examine the regime where the dark electrons do not thermalize with the dark photons throughout their cosmic history and assume negligible kinetic mixing with the visible <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> so they remain decoupled from the Standard Model thermal bath as well. Thus, the final dark matter relic abundance is determined only by the initial inflationary Schwinger production and redshifting after reheating.

Spain

Mar Bastero-Gil

Portugal

Paulo B. Ferraz

Italy

Roberto Vega-Morales

Super heavy dark matter from inflationary Schwinger production

Aleksandar Ivanov

Erratum to: Analytic thin wall false vacuum decay rate

We derive a closed-form false vacuum decay rate at one loop in the thin wall limit, where the true and false vacua are nearly degenerate. We obtain the bounce configuration in D dimensions, together with the Euclidean action with a higher order correction, counter-terms and renormalization group running. We extract the functional determinant via the Gel’fand-Yaglom theorem for low and generic orbital multipoles. The negative and zero eigenvalues appear for low multipoles and the translational zeroes are removed. We compute the fluctuations for generic multipoles, multiply and regulate the orbital modes. We find an explicit finite renormalized decay rate in D = 3, 4 and give a closed-form expression for the finite functional determinant in any dimension.

Analytic thin wall false vacuum decay rate

A kinetic mixing between the axion and the inflaton allows for a production of axion dark matter even if the inflationary Hubble scale is smaller than the zero-temperature axion mass. We analyze the axion dynamics in this recently discovered “inflaxion” frame- work, and present a new cosmological scenario where the axion drifts away from its vacuum during the reheating epoch, giving rise to the observed dark matter abundance. We discuss the implications for both the QCD axion and axion-like particles.

Japan

Takeshi Kobayashi

Reheating-induced axion dark matter after low scale inflation

A new mechanism for producing axion dark matter is proposed. By invoking low-scale inflation and a kinetic mixing between the axion and the inflaton, it is shown that the axion is driven to a field point slightly displaced from the potential minimum, which can give rise to the observed dark matter abundance. In this framework, different combinations of the axion and inflaton fields play various cosmological roles, including generating the cosmological perturbations, reheating the universe, and serving as dark matter. The kinetic mixing also relates the dark matter lifetime with the reheating temperature. The mechanism tames axions that would otherwise overdominate the universe, and thus opens up new windows in the axion parameter space, including decay constants at the GUT scale and higher.

Inflaxion dark matter

We propose a complete <math><mi>R</mi></math>-parity violating supersymmetric model with baryon triality that contains a Dine-Fischler-Srednicki-Zhitnitsky axion chiral superfield. We parametrize supersymmetry breaking with soft terms and determine under which conditions the model is cosmologically viable. As expected we always find a region of parameter space in which the axion is a cold dark matter candidate. The mass of the axino, the fermionic partner of the axion, is controlled by a Yukawa coupling. When heavy [<math><mrow><mi>O</mi><mo>(</mo><mi>TeV</mi><mo>)</mo></mrow></math>], the axino decays early and poses no cosmological problems. When light [<math><mi>O</mi><mo>(</mo><mi>keV</mi><mo>)</mo></math>], it can be long lived and a warm dark matter candidate. We concentrate on the latter case and study in detail the decay modes of the axino. We find that constraints from astrophysical x rays and gamma rays on the decay into photon and neutrino can set new bounds on some trilinear supersymmetric <math><mi>R</mi></math>-parity violating Yukawa couplings. In some corners of the parameter space the decays of a relic axino can also explain a putative 3.5 keV line.