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Double-beta processes play a key role in the exploration of neutrino and weak interaction properties, and in the searches for effects beyond the Standard Model. During the last half century many attempts were undertaken to search for double-beta decay with emission of two electrons, especially for its neutrinoless mode ($0 u2beta^-$), the latter being still not observed. Double-electron capture (2EC) was not in focus so far because of its in general lower transition probability. However, the rate of neutrinoless double-electron capture ($0 u2$EC) can experience a resonance enhancement by many orders of magnitude in case the initial and final states are energetically degenerate. In the resonant case, the sensitivity of the $0 u2$EC process can approach the sensitivity of the $0 u2beta^-$ decay in the search for the Majorana mass of neutrinos, right-handed currents, and other new physics. We present an overview of the main experimental and theoretical results obtained during the last decade in this field. The experimental part outlines search results of 2EC processes and measurements of the decay energies for possible resonant $0 u$2EC transitions. An unprecedented precision in the determination of decay energies with Penning traps has allowed one to refine the values of the degeneracy parameter for all previously known near-resonant decays and has reduced the rather large uncertainties in the estimate of the $0 u2$EC half-lives. The theoretical part contains an updated analysis of the electron shell effects and an overview of the nuclear structure models, in which the nuclear matrix elements of the $0 u2$EC decays are calculated. One can conclude that the decay probability of $0 u$2EC can experience a significant enhancement in several nuclides.
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Neutrinoless double beta decay, which is a very old and yet elusive process, is reviewed. Its observation will signal that lepton number is not conserved and the neutrinos are Majorana particles. More importantly it is our best hope for determining the absolute neutrino mass scale at the level of a few tens of meV. To achieve the last goal certain hurdles have to be overcome involving particle, nuclear and experimental physics. Nuclear physics is important for extracting the useful information from the data. One must accurately evaluate the relevant nuclear matrix elements, a formidable task. To this end, we review the sophisticated nuclear structure approaches recently been developed, which give confidence that the needed nuclear matrix elements can be reliably calculated. From an experimental point of view it is challenging, since the life times are long and one has to fight against formidable backgrounds. If a signal is found, it will be a tremendous accomplishment. Then, of course, the real task is going to be the extraction of the neutrino mass from the observations. This is not trivial, since current particle models predict the presence of many mechanisms other than the neutrino mass, which may contribute or even dominate this process. We will, in particular, consider the following processes: (i)The neutrino induced, but neutrino mass independent contribution. (ii)Heavy left and/or right handed neutrino mass contributions. (iii)Intermediate scalars (doubly charged etc). (iv)Supersymmetric (SUSY) contributions. We will show that it is possible to disentangle the various mechanisms and unambiguously extract the important neutrino mass scale, if all the signatures of the reaction are searched in a sufficient number of nuclear isotopes.
Study of the neutrinoless double beta decay and searches for the manifestation of the neutrino mass in ordinary beta decay are the main sources of information about the absolute neutrino mass scale, and the only practical source of information about the charge conjugation properties of the neutrinos. Thus, these studies have a unique role in the plans for better understanding of the whole fast expanding field of neutrino physics.
We investigate neutrinoless double beta decay ($0 ubetabeta$) in the presence of sterile neutrinos with Majorana mass terms. These gauge-singlet fields are allowed to interact with Standard-Model (SM) fields via renormalizable Yukawa couplings as well as higher-dimensional gauge-invariant operators up to dimension seven in the Standard Model Effective Field Theory extended with sterile neutrinos. At the GeV scale, we use Chiral effective field theory involving sterile neutrinos to connect the operators at the level of quarks and gluons to hadronic interactions involving pions and nucleons. This allows us to derive an expression for $0 ubetabeta$ rates for various isotopes in terms of phase-space factors, hadronic low-energy constants, nuclear matrix elements, the neutrino masses, and the Wilson coefficients of higher-dimensional operators. The needed hadronic low-energy constants and nuclear matrix elements depend on the neutrino masses, for which we obtain interpolation formulae grounded in QCD and chiral perturbation theory that improve existing formulae that are only valid in a small regime of neutrino masses. The resulting framework can be used directly to assess the impact of $0 ubetabeta$ experiments on scenarios with light sterile neutrinos and should prove useful in global analyses of sterile-neutrino searches. We perform several phenomenological studies of $0 ubetabeta$ in the presence of sterile neutrinos with and without higher-dimensional operators. We find that non-standard interactions involving sterile neutrinos have a dramatic impact on $0 ubetabeta$ phenomenology, and next-generation experiments can probe such interactions up to scales of $mathcal O(100)$ TeV.
We present a master formula describing the neutrinoless-double-beta decay ($0 ubetabeta$) rate induced by lepton-number-violating (LNV) operators up to dimension nine in the Standard Model Effective Field Theory. We provide an end-to-end framework connecting the possibly very high LNV scale to the nuclear scale, through a chain of effective field theories. Starting at the electroweak scale, we integrate out the heavy Standard Model degrees of freedom and we match to an $SU(3)_cotimes U(1)_{mathrm{em}}$ effective theory. After evolving the resulting effective Lagrangian to the QCD scale, we use chiral perturbation theory to derive the lepton-number-violating chiral Lagrangian. The chiral Lagrangian is used to derive the two-nucleon $0 ubetabeta$ transition operators to leading order in the chiral power counting. Based on renormalization arguments we show that in various cases short-range two-nucleon operators need to be enhanced to leading order. We show that all required nuclear matrix elements can be taken from existing calculations. Our final result is a master formula that describes the $0 ubetabeta$ rate in terms of phase-space factors, nuclear matrix elements, hadronic low-energy constants, QCD evolution factors, and high-energy LNV Wilson coefficients, including all the interference terms. Our master formula can be easily matched to any model where LNV originates at energy scales above the electroweak scale. As an explicit example, we match our formula to the minimal left-right-symmetric model in which contributions of operators of different dimension compete, and we discuss the resulting phenomenology.
We study the impact of the mixing (LR mixing) between the standard model $W$ boson and its hypothetical, heavier right-handed parter $W_R$ on the neutrinoless double beta decay ($0 ubetabeta$-decay) rate. Our study is done in the minimal left-right symmetric model assuming type-II dominance scenario with charge conjugation as the left-right symmetry. We then show that the $0 ubetabeta$-decay rate may be dominated by the contribution proportional to this LR mixing, which at the hadronic level induces the leading-order contribution to the interaction between two pions and two charged leptons. The resulting long-range pion exchange contribution can significantly enhance the decay rate compared to previously considered short-range contributions. Finally, we find that even if future cosmological experiments rule out the inverted hierarchy for neutrino masses, there are still good prospects for a positive signal in the next generation of $0 ubetabeta$-decay experiments.
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