Uncovering multipleCP-nonconserving mechanisms of(ββ)0νdecay

Abstract

We consider the possibility of several different mechanisms contributing to the (ββ)0ν -decay amplitude in the general case of CP nonconservation: light Majorana neutrino exchange, heavy left-handed (LH) and heavy right-handed (RH) Majorana neutrino exchanges, lepton charge nonconserving couplings in SUSY theories with R-parity breaking. If the (ββ)0ν -decay is induced by, e.g., two "non-interfering" mechanisms (light Majorana neutrino and heavy RH Majorana neutrino exchanges), one can determine |ηi| 2 and |ηj | 2 , ηi and ηj being the two fundamental parameters characterising these mechanisms, from data on the half-lives of two nuclear isotopes. In the case when two "interfering" mechanisms are responsible for the (ββ)0ν -decay, |ηi| 2 and |ηj | 2 and the interference term can be uniquely determined, in principle, from data on the half-lives of three nuclei. Given the half-life of one isotope, the "positivity conditions" |ηi| 2 ≥ 0 and |ηj | 2 ≥ 0 lead to stringent constraints on the half-lives of the other (ββ)0ν -decaying isotopes. These conditions, as well as the conditions for constructive (destructive) interference are derived and their implications are analysed in two specific cases. The experimental limits on neutrino masses obtained in the 3 H β-decay experiments can constrain further the multiple mechanisms of (ββ)0ν -decay if one of the mechanisms involved is the light Majorana neutrino exchange. The measurements of the half-lives with rather high precision and the knowledge of the relevant nuclear matrix elements with relatively small uncertainties is crucial for establishing that more than one mechanisms are operative in (ββ)0ν -decay. The method considered by us can be generalised to the case of more than two (ββ)0ν -decay mechanisms. It allows to treat the cases of CP conserving and CP nonconserving couplings generating the (ββ)0ν -decay in a unique way.

Nuclear matrix elements for neutrinoless double-beta decay and double-electron capture

“…In Table II we show the calculated ranges of the nuclear matrix element M ′ 0ν evaluated within the QRPA, RQRPA [25] and SRQRPA [27] in a self-consistent way with the CCM CD-Bonn and Argonne SRC functions by assuming both the standard (g A = 1.254) and quenched (g A = 1.0) axial-vector couplings. These ranges quantify the uncertainty in the calculated 0νββ-decay NMEs of a given QRPA-like approach.…”

Analysis of mechanisms that could contribute to neutrinoless double-beta decay

“…If the η λ and η η contributions could be ruled out by the twoelectron energy and angular distributions the remaining η ν and η R NR terms have very small interference contribution (the interference term is at most 8% of the two terms in the parenthesis of Eq. 3 [25,49]), and the half-life becomes…”

“…(3). Then, the relative contribution of the η ν and η R NR terms can be identified if one measures the half-life of at least two isotopes [5,25], provided that the corresponding matrix elements M 0ν and M 0N are known with good precision. Ref.…”

“…Then, the relative contribution of the η ν and η R NR can be gauged out if one measures the half-life of at least two isotopes [5,25], provided that the corresponding matrix elements M 0ν and M 0N are known with good precision (see section V below). These matrix elements were calculated using several methods including interacting shell model (ISM) [6-8, 10-12, 17] (see Ref.…”

“…For example, considering only the competition between the light left-handed neutrino-exchange mechanism and the heavy right-handed neutrino exchange mechanism, one could identify the dominant effect using half-lives of several isotopes, such as 76 Ge and 136 Xe [25]. Some of these heavy neutrino-exchange NME for isotopes of immediate experimental relevance are shown in Fig. 14 of Ref.…”