Weinberg Angle, Neutron Abundance in BBN, and Lifetime

Abstract

The Big-Bang nucleosynthesis (BBN) initial neutron abundance and the neutron lifetime depend on the magnitude of the Fermi coupling constant $G_F$. When allowing for radiative corrections, $G_F$ depends on the symmetry breaking Weinberg angle $s_\mathrm{W}$, a free parameter in the standard model of particle physics which could have considerable environmental (e.g. cosmological or temperature) dependence. We establish how the value of $s_\mathrm{W}$ influences BBN and neutron lifetime.

Figures (8)

• Figure S1: The normalized Fermi constant $(G_F/G_F^\mathrm{exp})^2$ as a function of the Weinberg angle $s_\mathrm{W}$ within the range $0.21<s_\mathrm{W}<0.24$. The horizontal dotted line indicates the standard-model value $G_F=G_F^\mathrm{exp}$. The two methods of treating the radiative corrections are discussed in text.
• Figure S2: Neutron lifetime with respect to vacuum reference value $\tau_n/\tau_n^0$ as a function of plasma temperature $T$ for three different values of the Weinberg angle $s_\mathrm{W}$ with range $0.21, 0.223, 0.24$.
• Figure S3: Thermal reaction rates as a function of temperature $10\geqslant T\geqslant0.01$MeV for processes shown in subscripts.
• Figure S4: The neutron concentration $X_n$ as a function of temperature. Dashed line: Result obtained under assumption that WI dominate Hubble expansion. Green dotted line: corresponds to thermal equilibrium, it is hard to see a difference but in the ratio $X^{th}_n/X^{ad}_n$ seen in the insert. Blue dotted line: Correction to dashed line arising allowing kinetic neutron abundance processes and Hubble expansion. Solid line: The concentration of neutrons in the Universe. Results obtained for standard WI reaction constant and as indicated by $\Upsilon_\nu=1$ for chemically equilibrated (free streaming) neutrino background.
• Figure S5: Top frame: The neutron concentration $X_n$ as a function of temperature $T$ with different values of Weinberg angle $s_\mathrm{W}$ and assumed chemical equilibrium of background neutrinos, $\Upsilon_\nu=1$. The cases $s_\mathrm{W}=0.1$ and $s_\mathrm{W}=0.3$ illustrate the range of the Weinberg angle for which the approximation in Eq. (\ref{['GFcorr']}) remains valid. The insert amplifies variation of neutron concentration for temperature characteristic of BBN onset and small variation of $s_\mathrm{W}$ from standard value as we considered before. There is no dependence on $s_\mathrm{W}$ in the adiabatic component (dashed line); Bottom frame: The normalized neutron concentration $X_n/X_n^{\mathrm{BBN}}$ as a function of Weinberg angle $s_\mathrm{W}$ for different temperature values with chemical equilibrium neutrino fugacity $\Upsilon_\nu=1$. We can track as a function of $s_\mathrm{W}$ the change in value $X^\mathrm{BBN}_n=0.13$ (horizontal black dotted line). The vertical black dotted line marks the adopted CODATA value $s_\mathrm{W}=0.223$. The yellow region indicates the range of the Weinberg angle for which the approximation in Eq. (\ref{['GFcorr']}) is valid.