Constraints from primordial nucleosynthesis on the mass of the τ neutrino

Abstract

The familiar nucleosynthesis constraint on the number of neutrino species, 7V V < 3.4, applies to massless neutrino species. An MeV-mass neutrino can have even greater impact, and we show that primordial nucleosynthesis excludes a r-neutrino mass from 0.3 to 25 MeV (Dirac) and 0.5 to 25 MeV (Majorana) provided that its lifetime r v^ 1 sec, and from 0.3 to 30 MeV (Dirac) and 0.5 to 32 MeV (Majorana) for r v^ 10 3 sec. A modest improvement in the laboratory mass limit-from 35 to 25 MeV-would imply that the r-neutrino mass must be less than 0.5 MeV (provided T V^ 1 sec).PACS numbers: 98.80.Ft, 12.15.Ff, 14.60.Gh, 98.80.Cq The agreement of the predictions of primordial nucleosynthesis for the abundances of the light isotopes D, 3 He, 4 He, with 7 Li with their measured abundances is one of the great triumphs of the hot big-bang cosmology. Because of this success primordial nucleosynthesis has been used as a probe of both cosmology and particle physics [1]. In particular, primordial nucleosynthesis provides a stringent limit to the number of "light" (mass <3CMeV) degrees of freedom, which, expressed in terms of the equivalent number of light neutrino species, is AV:<3.4 [2]. Recent precision measurements of the properties of the Z° have confirmed this in spectacular fashion:In the context of nucleosynthesis, "light" refers to neutrinos of mass much less than 1 MeV, while "heavy" refers to neutrinos of mass of an MeV or greater, a division that traces to the temperature of the Universe when the weak interactions freeze out: 7>~ 1 MeV. The present laboratory limit to the mass of the r neutrino is m v < 35 MeV [4]; if the r-neutrino mass is greater than order 1 MeV, it will not be a light degree of freedom during nucleosynthesis and the above limit does not apply. Since the equilibrium energy density of a massive neutrino species is less than that of a "massless" neutrino species it would seem that the nucleosynthesis limit is irrelevant for the r neutrino.Neutrinos do not stay in thermal equilibrium; they decouple at temperature of order a few MeV [5]. After a massive neutrino species decouples and becomes nonrelativistic, its energy density grows relative to a massless neutrino species:= 7;r 2 r 4 /120, r is the ratio of the number density of massive neutrinos to massless neutrinos after freeze-out, and T v is the neutrino temperature. For an MeV-mass neutrino species r is order unity, and when the neutron-to-proton ratio freezes out (7>~ 1 MeV) its energy density is comparable to or even greater than a massless species. Since the 4 He yield is very sensitive to the value at which the neutron-to-proton ratio freezes out, which depends upon the energy density of the Universe, an MeV-mass neutrino species can have a significant effect on 4 He production.Later, when T<&\ MeV, the energy density of a massive r neutrino is even more significant: When the actual synthesis of the light elements begins in earnest (/ -200 sec, 7 1 -0.1 MeV), it can be 10 times that of a massless species, comparable to the total energy densit...

Primordial nucleosynthesis: theory and observations

“…Many other constraints on particle properties can be related to the limit on N ν . For example, neutrinos with MeV masses would also change the early expansion rate, and the effect of such a neutrino can be related to that of an equivalent number of light neutrinos [87,88,89,90]. A toy model which nicely contains ways to both increase and decrease 4 He production relative to standard BBN is the case of a massive ν τ [88].…”

Neutrinos and physics beyond the standard model

“…The breaking of this symmetry generates the cosmologically required decay of the ν τ with lifetime τ ντ ∼ 10 2 − 10 4 seconds, as well as the masses and oscillations of the three light neutrinos ν e , ν µ and ν s required in order to account for the solar and atmospheric neutrino data. One can verify that the big-bang nucleosynthesis constraints [51,52] can be satisfied in this model.…”

“…This bound can be expressed through an effective number of massless neutrino species (N ν ). Using N ν < 3.4 − 3.6, the following range of ν τ mass has been ruled out [51,52] 0.5 M eV < m ντ < 35 M eV (10)…”

Nucleosynthesis limits on the mass of long lived tau and muon neutrinos

“…Again, the physical reason for this is simple: for moderately light tau neutrinos the freeze-out temperature is close to the mass scale, so that 's annihilate while semirelativistic. Due to the chirality of the interaction, positive and negative helicity states interact with dierent strengths at freeze out, and therefore can have dierent freeze-out number densities compared to what one nds when assuming averaged interaction strengths and a total equilibrium between helicity populations [2,5,7]. Somewhat surprisingly, while each has a large eect on N , they compensate each other quite accurately, s o a s t o g i v e nal total abundance in good accordance with the helicity a v eraged approach.…”

“…One of the quantities already studied in the context of nucleosynthesis is the mass of a stable neutrino [2]- [7]. Nucleosynthesis is sensitive to neutrino masses in the interval m ' 0:1 50 MeV, and the actual values of the bounds depend on the particular value adopted for the nucleosynthesis bound on the eective n umber of neutrino degrees of freedom N .…”