Toward Complete Leading-Order Predictions for Neutrinoless Double β Decay

Ab Initio Uncertainty Quantification of Neutrinoless Double-Beta Decay in ^{76}Ge

The observation of neutrinoless double-beta (0νββ) decay would offer proof of lepton number violation, demonstrating that neutrinos are Majorana particles, while also helping us understand why there is more matter than antimatter in the Universe. If the decay is driven by the exchange of the three known light neutrinos, a discovery would, in addition, link the observed decay rate to the neutrino mass scale through a theoretical quantity known as the nuclear matrix element (NME). Accurate values of the NMEs for all nuclei considered for use in 0νββ experiments are therefore crucial for designing and interpreting those experiments. Here, we report the first comprehensive ab initio uncertainty quantification of the 0νββ-decay NME, in the key nucleus ^{76}Ge. Our method employs nuclear strong and weak interactions derived within chiral effective field theory and recently developed many-body emulators. Our result, with a conservative treatment of uncertainty, is an NME of 2.60_{-1.36}^{+1.28}, which, together with the best-existing half-life sensitivity and phase-space factor, sets an upper limit for effective neutrino mass of 187_{-62}^{+205}  meV. The result is important for designing next-generation germanium detectors aiming to cover the entire inverted hierarchy region of neutrino masses.

Kaon electromagnetic form factors in dispersion theory

The electromagnetic form factors of charged and neutral kaons are strongly constrained by their low-energy singularities, in the isovector part from two-pion intermediate states and in the isoscalar contribution in terms of ω and ϕ residues. The former can be predicted using the respective π π → K ¯ K partial-wave amplitude and the pion electromagnetic form factor, while the latter parameters need to be determined from electromagnetic reactions involving kaons. We present a global analysis of time- and spacelike data that implements all of these constraints. The results enable manifold applications: kaon charge radii, elastic contributions to the kaon electromagnetic self energies and corrections to Dashen's theorem, kaon boxes in hadronic light-by-light (HLbL) scattering, and the ϕ region in hadronic vacuum polarization (HVP). Our main results are:⟨ r 2 ⟩ c = 0.359 ( 3 ) fm 2 ,⟨ r 2 ⟩ n = - 0.060 ( 4 ) fm 2 for the charged and neutral radii, ϵ = 0.63 ( 40 ) for the elastic contribution to the violation of Dashen's theorem,a μ K -box = - 0.48 ( 1 ) × 10 - 11 for the charged kaon box in HLbL scattering, anda μ HVP [ K + K - , ≤ 1.05 GeV ] = 184.5 ( 2.0 ) × 10 - 11 ,a μ HVP [ K S K L , ≤ 1.05 GeV ] = 118.3 ( 1.5 ) × 10 - 11 for the HVP integrals around the ϕ resonance. The global fit toK ¯ K givesM ¯ ϕ = 1019.479 ( 5 ) MeV ,Γ ¯ ϕ = 4.207 ( 8 ) MeV for the ϕ resonance parameters including vacuum-polarization effects.

Ab Initio Calculation of the Contact Operator Contribution in the Standard Mechanism for Neutrinoless Double Beta Decay

Starting from chiral nuclear interactions, we evaluate the contribution of the leading-order contact transition operator to the nuclear matrix element (NME) of neutrinoless double-beta decay, assuming a light Majorana neutrino-exchange mechanism. The corresponding low-energy constant (LEC) is determined by fitting the transition amplitude of the nn→ppe^{-}e^{-} process to a recently proposed synthetic datum. We examine the dependence of the amplitude on similarity renormalization group scale and chiral expansion order of the nuclear interaction, finding that both dependences can be compensated to a large extent by readjusting the LEC. We evaluate the contribution of both the leading-order contact operator and standard long-range operator to the neutrinoless double-beta decays in the light nuclei ^{6,8}He and the candidate nucleus ^{48}Ca. Our results provide the first clear demonstration that the contact term enhances the NME in calculations with commonly used chiral two- plus three-nucleon interactions. In the case of ^{48}Ca, for example, the NME obtained with the EM(1.8/2.0) interaction is enhanced from 0.61 to 0.87(4), where the uncertainty is propagated from the synthetic datum.