Limits on active-sterile neutrino mixing and the primordial deuterium abundance.

Studies of limits on active-sterile neutrino mixing derived from big bang nucleosynthesis considerations are extended to consider the dependance of these constraints on the primordial deuterium abundance. This study is motivated by recent measurements of D/H in quasar absorption systems, which at present yield discordant results. Limits on active-sterile mixing are somewhat relaxed for high D/H. For low D/H ( 2 10 ), no active-sterile neutrino mixing is allowed by currently popular upper limits on the primordial He abundance Y . For such low primordial D/H values, the observational inference of active-sterile neutrino mixing by upcoming solar neutrino experiments would imply that Y has been systematically underestimated, unless there is new physics not included in standard BBN. Typeset using REVTEX 1 Upper limits on the abundance of He produced in big bang nucleosynthesis (BBN) have been used to limit mixing between active ( e, , or ) and sterile ( s, no standard model interactions) neutrinos [1]. In this paper, we point out and discuss how these constraints are dependant on the adopted primordial deuterium abundance. Previous limits on sterile neutrino mixing have assumed a value for the lower bound on the baryon-to-photon ratio derived from interstellar medium and solar system measurements of deuterium (D) and He, and models of chemical and galactic evolution. Recent measurements of D/H in quasar absorption systems (QAS) have yielded discordant values of this ratio, some higher than previously derived ranges [2], and some lower [3]. Several factors make an investigation of the primordial D/H dependance of BBN constraints on active-sterile neutrino mixing timely: the discordant QAS measurements of D/H; the fact that future solar neutrino experiments may be able to distinguish and identify e s mixing [4]; and the use of sterile neutrinos in schemes for neutrino masses and mixings that explain all available data [5]. As is well known (e.g., Ref. [6]), the abundance of He produced by BBN is essentially determined by the ratio of neutron to proton number densities (n/p) at \weak freeze-out" (WFO). WFO occurs when the reactions that interchange neutrons and protons proceed too slowly relative to the expansion rate of the universe to keep n/p at its equilibrium value of n/p exp( m=T ). Here m mn mp 1:293 MeV is the neutron-proton mass di erence, and T is the photon temperature. Mixing between active and sterile neutrinos increases (n/p)WFO, and therefore the primordial He mass fraction Y , in two ways. First, active-sterile neutrino mixing e ectively brings more degrees of freedom into thermal contact, increasing the energy density and hence the expansion rate of the universe. Second, activesterile mixing|especially e s mixing|depletes the electron neutrino and antineutrino populations, reducing the rates of the n$ p interconversion reactions. Both of these e ects cause n/p to freeze out at a lower temperature. Using a neutrino ensemble evolution formalism [1,7] that includes both neutrino oscillations (with matter e ects) and neutrino collisions, previous authors [1] have produced exclusion plots in the m-sin 2 plane for both e s and s mixing [9]. Here m 2