BBN and the CMB constrain neutrino coupled light WIMPs

In the presence of a light weakly interacting massive particle (WIMP) with mass ${m}_{\ensuremath{\chi}}\ensuremath{\lesssim}30\text{ }\text{ }\mathrm{MeV}$, there are degeneracies among the nature of the WIMP (fermion or boson), its couplings to the standard model particles (to electrons, positrons, and photons, or only to neutrinos), its mass ${m}_{\ensuremath{\chi}}$, and the number of equivalent (additional) neutrinos, $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}$. These degeneracies cannot be broken by the cosmic microwave background (CMB) constraint on the effective number of neutrinos, ${\mathrm{N}}_{\text{eff}}$. However, since big bang nucleosynthesis (BBN) is also affected by the presence of a light WIMP and equivalent neutrinos, complementary BBN and CMB constraints can help to break some of these degeneracies. In a previous paper [K. M. Nollett and G. Steigman, Phys. Rev. D 89, 083508 (2014)] the combined BBN and Planck [P. A. R. Ade et al. (Planck Collaboration), Astron. Astrophys. 571, A16 (2014)] CMB constraints were used to explore the allowed ranges for ${m}_{\ensuremath{\chi}}$, $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}$, and ${\mathrm{N}}_{\text{eff}}$ in the case where the light WIMPs annihilate electromagnetically (EM) to photons and/or ${e}^{\ifmmode\pm\else\textpm\fi{}}$ pairs. In this paper the BBN predictions for the primordial abundances of deuterium and $^{4}\mathrm{He}$ (along with $^{3}\mathrm{He}$ and $^{7}\mathrm{Li}$) in the presence of a light WIMP that only couples (annihilates) to neutrinos [either standard model (SM) only or both SM and equivalent] are calculated. Recent observational estimates of the relic abundances of D and $^{4}\mathrm{He}$ are used to limit the light WIMP mass, the number of equivalent neutrinos, the effective number of neutrinos, and the present Universe baryon density (${\mathrm{\ensuremath{\Omega}}}_{\mathrm{B}}{h}^{2}$). Allowing for a neutrino coupled light WIMP and $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}$ equivalent neutrinos, the combined BBN and CMB data provide lower limits to the WIMP mass that depend very little on the nature of the WIMP (Majorana or Dirac fermion, real or complex scalar boson), with a best fit ${m}_{\ensuremath{\chi}}\ensuremath{\gtrsim}35\text{ }\text{ }\mathrm{MeV}$, equivalent to no light WIMP at all. The analysis here excludes all neutrino coupled WIMPs with masses below a few MeV, with specific limits varying from 4 to 9 MeV depending on the nature of the WIMP. In the absence of a light WIMP (either EM or neutrino coupled), BBN alone prefers $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=0.50\ifmmode\pm\else\textpm\fi{}0.23$, favoring neither the absence of equivalent neutrinos ($\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=0$), nor the presence of a fully thermalized sterile neutrino ($\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=1$). This result is consistent with the CMB constraint, ${\mathrm{N}}_{\text{eff}}=3.30\ifmmode\pm\else\textpm\fi{}0.27$ [1], constraining ``new physics'' between BBN and recombination. Combining the BBN and CMB constraints gives $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=0.35\ifmmode\pm\else\textpm\fi{}0.16$ and ${\mathrm{N}}_{\text{eff}}=3.40\ifmmode\pm\else\textpm\fi{}0.16$. As a result, while BBN and the CMB combined require $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}\ensuremath{\ge}0$ at $\ensuremath{\sim}98%$ confidence, they disfavor $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}\ensuremath{\ge}1$ at $g99%$ confidence. Adding the possibility of a neutrino-coupled light WIMP extends the allowed range slightly downward for $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}$ and slightly upward for ${\mathrm{N}}_{\text{eff}}$ simultaneously, while leaving the best-fit values unchanged.