Abstract
Neutrinoless double beta decay can significantly help to shed light on the issue of non-zero neutrino mass, as observation of this lepton number violating process would imply neutrinos are Majorana particles. However, the underlying interaction does not have to be as simple as the standard neutrino mass mechanism. The entire variety of neutrinoless double beta decay mechanisms can be approached effectively. In this work we focus on a theoretical description of short-range effective contributions to neutrinoless double beta decay, which are equivalent to 9-dimensional effective operators incorporating the appropriate field content. We give a detailed derivation of the nuclear matrix elements and phase space factors corresponding to individual terms of the effective Lagrangian. Using these, we provide general formulae for the neutrinoless double beta decay half-life and angular correlation of the outgoing electrons.
Highlights
While the Standard Model (SM) gauge group SUð3ÞC × SUð2ÞL × Uð1ÞY perfectly explains the interactions we observe, its breaking provides masses to the charged fermions via the Higgs mechanism
We have developed a general formalism for short-range mechanisms contributing to neutrinoless double beta decay in an effective operator approach
Such contributions will arise when the lepton number is broken at a new physics scale ΛNP much larger than the typical energy scale of 0νββ decay q ≈ 100 MeV
Summary
While the Standard Model (SM) gauge group SUð3ÞC × SUð2ÞL × Uð1ÞY perfectly explains the interactions we observe, its breaking provides masses to the charged fermions via the Higgs mechanism. Besides the light and heavy neutrino exchange, exotic long-range mechanisms have received the most attention so far [46–50] This is reasonable, as the underlying SM invariant operators already occur at dimension 7, and, as mentioned above, 0νββ decay is sensitive to high scales of the order of ΛO7 ≈ 105 GeV. In the left-right symmetry example, the short-range contribution originates from two right-handed charged currents with Oð1Þ gauge strength interactions In both long- and short-range contributions, the half-life triggered by a single mechanism may be generically expressed to Eq (3): jεI j2 GI jMI j2 ; ð4Þ where GI is the nuclear PSF and MI the NME, both generally depending on the Lorentz structure of the effective operator in question.
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