Combined Constraints on Majorana Masses from Neutrinoless Double Beta Decay Experiments

Abstract

Combined bounds on the Majorana neutrino mass for light and heavy neutrino exchange mechanisms are derived from current neutrinoless double beta decay (0νββ) search results for a variety of nuclear matrix element (NME) models. The approach requires self-consistency of a given model to predict NMEs across different isotopes. The derived bounds are notably stronger than those from any single experiment and show less model-to-model variation, highlighting the advantages of using multiple isotopes in such searches. Projections indicate that the combination of near-term experiments should be able to probe well into the inverted neutrino mass hierarchy region. A method to visually represent 0νββ experimental results is also suggested to more transparently compare across different isotopes and explicitly track model dependencies.

The unfinished fabric of the three neutrino paradigm

“…See e.g. [61] for a recent discussion. We describe below our approach to these issues, in order to build first a probability distribution for half-lives T i and then, including NME's, for the effective mass m ββ .…”

“…For each experiment we need not only a limit (T 90 ) but the probability distribution of T i or, equivalently, a function ∆χ 2 (S i ). Unfortunately, such detailed information is not provided by current experiments in an explicit or user-friendly way; see [61,68] for recent attempts to parametric reconstructions.…”

“…We adopt a ∆χ 2 (S i ) parametrization inspired by [68] and based on the following considerations. In 0νββ searches with zero background and nearly null results, the likelihood L of a signal S > 0 should be a poissonian with a scaling coefficient µ (L ∼ exp(−µS)), leading to a linear dependence on S (∆χ 2 ∼ ln L ∝ S) [61]. In 0νββ searches with nonnegligible background subtraction, the dependence is expected to be nearly gaussian (∆χ 2 ∝ (S − S 0 ) 2 ), where the best-fit signal S 0 may fall either in the physical region (S 0 ≥ 0) or in the unphysical one (S 0 < 0).…”

“…In order to assess the coefficients (a i , b i , c i ), we have carefully sifted the information contained in the experimental publications [62][63][64][65][66][67] and in available PhD theses conducted within EXO-200 [69,70], KamLAND-Zen 400 [71] and KamLAND-Zen 800 (preliminary) [72]. We find that the linear approximation advocated in [61] for GERDA, can be roughly applied also to MAJORANA (up to subleading corrections at small S i , neglected herein). The other experimental bounds on T i can be reasonably approximated by parabolic ∆χ 2 curves, setting the various coefficients (a i , b i , c i ).…”

“…the recent reviews in [60,[75][76][77][78][79][80][81]. It is common practice to select a set of published values {M i } in order to obtain a set of upper bounds {m ββ }, whose spread may be taken as indicative of the theoretical uncertainties; see [61] for a very recent application. However, this procedure overlooks significant correlations among the NME uncertainties of different nuclides [82][83][84][85] that, as shown below, are as important as the uncertainties themselves in obtaining conservative bounds.…”