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Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven
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abstract
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 $m_{\beta \beta}$.
Forward citations
Cited by 6 Pith papers
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Chiral Effective Field Theories for Strong and Weak Dynamics
The paper constructs complete and minimal relativistic operator bases for nucleon-nucleon, pion-nucleon-nucleon, and three-nucleon sectors up to p6, and a spurion-based leptonic sector up to p4, using Hilbert series a...
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Neutrinoless Double-Beta Decays from Operator Mixing
Renormalization-group mixing lets heavy-quark dimension-seven operators feed neutrinoless double-beta decay, giving some of the strongest current bounds on these new-physics operators.
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Challenging Majorana neutrino effects in $B\to K^{(\ast)}\nu\nu$ and $K\to \pi\nu\nu$ decays
Belle-II's B→Kνν excess cannot be explained by dimension-7 lepton-number-violating SMEFT operators without fine-tuning neutrino masses, while a light sterile-neutrino extension can, with testable decay spectra.
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Systematic Spurion Matching between Low Energy EFT and Chiral Lagrangian
A single SU(3)_V spurion can organize both LEFT and chiral Lagrangian operators up to dimension 9, enabling systematic operator-level matching between quark and hadron levels.
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Beyond Half-Life Limits: Robust Operator-Level Interpretation of Multi-Isotope Neutrinoless Double-Beta Decay
Among tested operators, light-Majorana exchange gives the most stable multi-isotope coefficient limits and half-life ratios; selected dim-6 operators are intermediate; short-range dim-9 examples can be highly NME- and...
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Positron-Emitting and Electron-Capturing Double-Beta Processes in the Standard Model and Beyond
Nuclear matrix elements and phase-space factors are computed for 2ν and 0ν positron-emitting double-beta modes in three isotopes, yielding sensitivity to SMEFT lepton-number-violating operators at 1-100 TeV and showin...
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