Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven

We analyze neutrinoless double beta decay ($0\nu\beta\beta$) within the framework of the Standard Model Effective Field Theory. Apart from the dimension-five Weinberg operator, the first contributions appear at dimension seven. We classify the operators and evolve them to the electroweak scale, where we match them to effective dimension-six, -seven, and -nine operators. In the next step, after renormalization group evolution to the QCD scale, we construct the chiral Lagrangian arising from these operators. We develop a power-counting scheme and derive the two-nucleon $0\nu\beta\beta$ currents up to leading order in the power counting for each lepton-number-violating operator. We argue that the leading-order contribution to the decay rate depends on a relatively small number of nuclear matrix elements. We test our power counting by comparing nuclear matrix elements obtained by various methods and by different groups. We find that the power counting works well for nuclear matrix elements calculated from a specific method, while, as in the case of light Majorana neutrino exchange, the overall magnitude of the matrix elements can differ by factors of two to three between methods. We calculate the constraints that can be set on dimension-seven lepton-number-violating operators from $0\nu\beta\beta$ experiments and study the interplay between dimension-five and -seven operators, discussing how dimension-seven contributions affect the interpretation of $0\nu\beta\beta$ in terms of the effective Majorana mass $m_{\beta \beta}$.Comment: Matches version published in JHE

Low Energy Tests of the Weak Interaction

The study of low energy weak interactions of light quarks and leptons continues to provide important insights into both the Standard Model as well as the physics that may lie beyond it. We review the status and future prospects for low energy electroweak physics. Recent important experimental and theoretical developments are discussed and open theoretical issues are highlighted. Particular attention is paid to neutrino physics, searches for permanent electric dipole moments, neutral current tests of the running of the weak mixing angle, weak decays, and muon physics. We argue that the broad range of such studies provides an important complement to high energy collider searches for physics beyond the Standard Model. The use of low energy weak interactions to probe novel aspects of hadron structure is also discussed.Comment: 82 pages, 6 figures: published version (with some additional references and a typographical error fixed

Quantum Monte Carlo calculations of weak transitions in A A\,= \,6--10 nuclei

Ab initio calculations of the Gamow-Teller (GT) matrix elements in the $\beta$ decays of $^6$He and $^{10}$C and electron captures in $^7$Be are carried out using both variational and Green's function Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon interactions, and axial many-body currents derived from either meson-exchange phenomenology or chiral effective field theory. The agreement with experimental data is excellent for the electron captures in $^7$Be, while theory overestimates the $^6$He and $^{10}$C data by $\sim 2\%$ and $\sim 10\%$, respectively. We show that for these systems correlations in the nuclear wave functions are crucial to explain the data, while many-body currents increase by $\sim 2$--$3\%$ the one-body GT contributions. These findings suggest that the longstanding $g_A$-problem, i.e., the systematic overprediction ($\sim 20 \%$ in $A\le 18$ nuclei) of GT matrix elements in shell-model calculations, may be resolved, at least partially, by correlation effects.Comment: 6 pages, 2 figure

Low-energy neutrino physics and neutrino mass

Among the principal concerns in neutrino physics today are the questions of whether neutrinos are massive and, if so, whether the neutrinos emitted in a weak decay are pure or mixed quantum states. The concept of mixed neutrinos has been with us for more than 20 years, having first been introduced by Maki et al (1) and by Pontecorvo (2) following demonstration in 1962 that more than one type (flavor) of neutrino existed. After having been dormant for some time, the interest in these issues was reborn in recent years with the advent of grand unified theories, which predict nonvanishing neutrino mass and which can accommodate eutrino mixing, in a natural way. Controversial experiments also refueled the excitment (and consternation) of researchers in this endeavor

Inclusive neutrino scattering off deuteron at low energies in chiral effective field theory

Cross sections for inclusive neutrino scattering off deuteron induced by neutral and charge-changing weak currents are calculated from threshold up to 150 MeV energies in a chiral effective field theory including high orders in the power counting. Contributions beyond leading order (LO) in the weak current are found to be small, and increase the cross sections obtained with the LO transition operators by a couple of percent over the whole energy range (0--150) MeV. The cutoff dependence is negligible, and the predicted cross sections are within $\sim 2$\% of, albeit consistently larger than, corresponding predictions obtained in conventional meson-exchange frameworks.Comment: 16 pages, 10 figures, edits made to the text and added two figures, as suggested by Referee. References adde

Metastable GeV-scale particles as a solution to the cosmological lithium problem

The persistent discrepancy between observations of 7Li with putative primordial origin and its abundance prediction in Big Bang Nucleosynthesis (BBN) has become a challenge for the standard cosmological and astrophysical picture. We point out that the decay of GeV-scale metastable particles X may significantly reduce the BBN value down to a level at which it is reconciled with observations. The most efficient reduction occurs when the decay happens to charged pions and kaons, followed by their charge exchange reactions with protons. Similarly, if X decays to muons, secondary electron antineutrinos produce a similar effect. We consider the viability of these mechanisms in different classes of new GeV-scale sectors, and find that several minimal extensions of the Standard Model with metastable vector and/or scalar particles are capable of solving the cosmological lithium problem. Such light states can be a key to the explanation of recent cosmic ray anomalies and can be searched for in a variety of high-intensity medium-energy experiments.Comment: 50 pages, 13 figures; references added, typo correcte

Form Factors in the radiative pion decay

We perform an analysis of the form factors that rule the structure-dependent amplitude in the radiative pion decay. The resonance contributions to pion -> e nu_e gamma decays are computed through the proper construction of the vector and axial-vector form factors by setting the QCD driven asymptotic properties of the three-point Green functions VVP and VAP, and by demanding the smoothing of the form factors at high transfer of momentum. A comparison between theoretical and experimental determinations of the form factors is also carried out. We also consider and evaluate the role played by a non-standard tensor form factor. We conclude that, at present and due to the hadronic incertitudes, the search for New Physics in this process is not feasible.Comment: 14 pages, no figures. Typos corrected. Accepted for publication in The European Physical Journal