Multi-isotope degeneracy of neutrinoless double-βdecay mechanisms in the quasiparticle random-phase approximation

Abstract

We calculate nuclear matrix elements (NME) of neutrinoless double beta decay (0νββ) in four different candidate nuclei ( 76 Ge, 82 Se, 100 Mo, 130 Te) within the quasiparticle random phase approximation (QRPA) and its uncertainties. We assume (up to) four coexisting mechanisms for 0ν2β decay, mediated by light Majorana neutrino exchange (ν), heavy Majorana neutrino exchange (N ), R-parity breaking supersymmetry ( / R), and squark-neutrino (q), interfering either constructively or destructively with each other. We find that, unfortunately, current NME uncertainties appear to prevent a robust determination of the relative contribution of each mechanism to the decay amplitude, even assuming accurate measurements of decay lifetimes. The near-degeneracy of 0νββ mechanisms is analyzed with simple algebraic techniques, which do not involve assumptions about the statistical distribution of errors. We discuss implications of such degeneracy on prospective searches for absolute neutrino masses.

Neutrinoless double-beta decay and physics beyond the standard model

“…For comparison, from 136 Xe data [32] one gets currently λ ′ 111 ≤ 2.7 · 10 −4 . Note, that recently [25] published sets of matrix elements for R P violating double beta decay for the pion-exchange mechanism, which are, depending on the choice of nucleonnucleon interaction, model space and value of G A , between a factor of x ∼ (2 − 3) larger than the matrix elements of Table 5. These would lead to limits on λ ′ 111 which are stronger by a corresponding factor of √ x.…”

“…One noticeable difference is that in [28,29] it was argued that the effect of short range correlations had been overestimated in earlier calculations. A recalculation of the nuclear matrix elements in [30], using the method proposed in [28], indeed led to an increase of (25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40) % in the numerical values of the nuclear matrix elements. The latest calculation [25] also has short range matrix elements which are larger than those in [22] by similar factors.…”

“…A recalculation of the nuclear matrix elements in [30], using the method proposed in [28], indeed led to an increase of (25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40) % in the numerical values of the nuclear matrix elements. The latest calculation [25] also has short range matrix elements which are larger than those in [22] by similar factors. Despite these more recent calculations we will stick to the matrix elements presented in [7,21,22,24], since (a) no other complete calculation of matrix elements exist and (b) newer matrix elements in existing cases tend to be larger than those of the above publications, i.e.…”

“…Unfortunately, despite all the efforts devoted to the improvement of the matrix element calculations, the latest QRPA matrix elements from the Tübingen group [25] differ from the shell model results revisited, for example, in [26] in many cases by factors of ∼ (2 − 3) in case of the mass mechanism 2 . Moreover, shell model matrix elements are up to now available only for the mass mechanism.…”

Constraining new physics with a positive or negative signal of neutrino-less double beta decay

“…In particular, since there is only a finite set of operators, it allows to efficiently compare different underlying models in what regards their interaction strengths. Very recent works covering different explicit 0νββ mechanisms and in particular their interplay with the standard light neutrino exchange [40,41] appeared nearly simultaneously to this paper. All the mechanisms treated there can be translated into our effective language.…”