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Register a new userHeavy physics contributions to neutrinoless double beta decay from QCD
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Observation of neutrinoless double beta decay, a lepton number violating process that has been proposed to clarify the nature of neutrino masses, has spawned an enormous world-wide experimental effort. Relating nuclear decay rates to high-energy, beyond the Standard Model (BSM) physics requires detailed knowledge of non-perturbative QCD effects. Using lattice QCD, we compute the necessary matrix elements of short-range operators, which arise due to heavy BSM mediators, that contribute to this decay via the leading order $pi^- to pi^+$ exchange diagrams. Utilizing our result and taking advantage of effective field theory methods will allow for model-independent calculations of the relevant two-nucleon decay, which may then be used as input for nuclear many-body calculations of the relevant experimental decays. Contributions from short-range operators may prove to be equally important to, or even more important than, those from long-range Majorana neutrino exchange.
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We present the first ab initio calculations of neutrinoless double beta decay matrix elements in $A=6$-$12$ nuclei using Variational Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon potential and Illinois-7 three-nucleon interaction. We study both light Majorana neutrino exchange and potentials arising from a large class of multi-TeV mechanisms of lepton number violation. Our results provide benchmarks to be used in testing many-body methods that can be extended to the heavy nuclei of experimental interest. In light nuclei we have also studied the impact of two-body short range correlations and the use of different forms for the transition operators, such as those corresponding to different orders in chiral effective theory.
Second order beta-decay processes with and without neutrinos in the final state are key probes of nuclear physics and of the nature of neutrinos. Neutrinoful double-beta decay is the rarest Standard Model process that has been observed and provides a unique test of the understanding of weak nuclear interactions. Observation of neutrinoless double-beta decay would reveal that neutrinos are Majorana fermions and that lepton number conservation is violated in nature. While significant progress has been made in phenomenological approaches to understanding these processes, establishing a connection between these processes and the physics of the Standard Model and beyond is a critical task as it will provide input into the design and interpretation of future experiments. The strong-interaction contributions to double-beta decay processes are non-perturbative and can only be addressed systematically through a combination of lattice Quantum Chromoodynamics (LQCD) and nuclear many-body calculations. In this review, current efforts to establish the LQCD connection are discussed for both neutrinoful and neutrinoless double-beta decay. LQCD calculations of the hadronic contributions to the neutrinoful process $nnto pp e^- e^- bar u_ebar u_e$ and to various neutrinoless pionic transitions are reviewed, and the connections of these calculations to the phenomenology of double-beta decay through the use of effective field theory (EFTs) is highlighted. At present, LQCD calculations are limited to small nuclear systems, and to pionic subsystems, and require matching to appropriate EFTs to have direct phenomenological impact. However, these calculations have already revealed qualitatively that there are terms in the EFTs that can only be constrained from double-beta decay processes themselves or using inputs from LQCD. Future prospects for direct calculations in larger nuclei are also discussed.
We present a method to determine the leading-order (LO) contact term contributing to the $nn to pp e^-e^-$ amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude $n(p_1) n(p_2) W^+ (k) to p(p_1^prime) p(p_2^prime) W^- (k)$, in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon ($N! N$) scattering in the $^1S_0$ channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing the analog $I = 2$ $N! N$ contact term and by reproducing, within uncertainties, the charge-independence-breaking contribution to the $^1S_0$ $N! N$ scattering lengths. While our analysis is performed in the $overline{rm MS}$ scheme, we express our final result in terms of the scheme-independent renormalized amplitude ${cal A}_ u(|{bf p}|,|{bf p}^prime|)$ at a set of kinematic points near threshold. We illustrate for two cutoff schemes how, using our synthetic data for ${cal A}_ u$, one can determine the contact-term contribution in any regularization scheme, in particular the ones employed in nuclear-structure calculations for isotopes of experimental interest.
The process at the heart of neutrinoless double-beta decay, $nn rightarrow p p, e^- e^-$ induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-number-violating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet $S$-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-leading corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-beta decay and nuclear charge-independence breaking induced by electromagnetism. Data on the latter confirm the need for a leading-order short-range operator, but do not allow for a full determination of the corresponding lepton-number-violating coupling. Using a crude estimate of this coupling, we perform ab initio calculations of the matrix elements for neutrinoless double-beta decay for $^6$He and $^{12}$Be. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.
Neutrinoless double beta decay is a hypothetical radioactive process which, if observed, would prove the neutrino to be a Majorana fermion: a particle that is its own antiparticle. In this lecture mini-series I discuss the physics of Majorana fermions and the connection between the nature of neutrino mass and neutrinoless double beta decay. We review Dirac and Majorana spinors, discuss methods of distinguishing between Majorana and Dirac fermions, and derive in outline the connection between neutrino mass and double beta decay rates. We conclude by briefly summarizing the experimental landscape and the challenges associated with searches for this elusive process.
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