Towards a precision calculation of N eff in the Standard Model IV: Estimating the impact of positronium formation

Le résumé fourni par la source

Abstract We present a first assessment of how the previously unexplored effect of positronium formation can impact on the value of the effective number of neutrino species in the Standard Model, N eff SM. Adopting a Yukawa form for the electrostatic potential, we discuss two possible scenarios that differ primarily in their assumptions about entropy evolution. The first, out-of-equilibrium scenario assumes that thermal corrections to the potential such as Debye screening prevent positronium from appearing until the temperature drops below a threshold. Once the threshold is reached, entropy generated in the QED sector from the equilibration process, if instantaneous, leads to a variation in N eff SM of at most |ΔN eff| ∼ 10-4, comparable to other uncertainties in the current benchmark value for N eff SM. A more gradual formation could however yield a larger change. The second, equilibrium scenario assumes the QED sector to stay in equilibrium at all times. In this case, we show that cancellations between the first, s-wave bound- and scattering-states contributions ensure that it is possible to evolve the system across the bound-state formation threshold without generating entropy in the QED sector. The corresponding change in N eff SM then closely matches the 𝒪(e 2) perturbative result derived in previous works and the 𝒪(e 2) contribution is capped at |ΔN eff| ≲ 10-6. We also comment on the impact of deviations from a pure Yukawa potential due to the presence of a thermal width.

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