Constraints from nucleosynthesis and SN 1987A on Majoron-emitting double beta decay.

We examine whether observable majoron emission in double beta decay can be compatible with the big-bang nucleosynthesis (NS) and the observed neutrino flux from SN1987A. It is found that the NS upper bound on He abundance implies that the majoron-neutrino Yukawa coupling constant g ≤ 9 × 10 and its maximal value is allowed only when the scalar quartic coupling constant λ is extremely small, λ ≤ 100g. It is also observed that, although quite less restrictive, SN1987A also provides independent constraints on coupling constants. Majoron is the massless Goldstone boson associated with spontaneous lepton number violation [1]. If exists, it would lead to many interesting phenomenological consequences. Amongst them, one particularly interesting phenomenon is “majoron emitting neutrinoless double beta decay” (ββJ) [2]. Recently it was pointed out that the potential anomaly in the double beta decay spectra of several elements may be explained by ββJ [3]. The desired value of the Yukawa coupling constant is roughly gee ≃ 10. Regardless of this observation, if gee is not very small, e.g. not less than 10, one may be able to observe ββJ in the near future. As was shown in ref. [4], it is not difficult to construct majoron models which provides such a value of gee while satisfying all known experimental constraints. However in view of the strong cosmological and astrophysical implications of majoron [5], it is desirable to examine whether observable ββJ can be compatible with the big-bang cosmology and also with astrophysical observations. In this paper, we consider possible constraints from the big-bang nucleosynthesis and the supernova SN1987A on majoron models in which observable ββJ is possible. If the lepton number symmetry L is spontaneously broken at an energy scale v, majoron-neutrino Yukawa coupling matrix gαβ (α,β=e, μ, τ) is related to the neutrino mass matrix mαβ as gαβ = mαβ/v. Current data on ν-less ββ decay implies mee ≤ 1 eV and gee ≤ few× 10 with uncertainties arising from nuclear matrix elements [2]. For ββJ to be observable in the near future, we may need gee ≥ 10. This implies that L-breaking scale is very small compared to the Fermi scale, v ≤ 100 keV, (1) leading to a fine tuning problem in general [6]. Here we will not concern this theoretical difficulty. We rather concentrate on models with such a low L-breaking scale to see whether observable ββJ can be compatible with the standard nucleosynthesis model [7] and the observed neutrino flux from SN1987A [8].