Abstract: We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Luscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K -> 3 pi weak decay, the isospin-breaking eta -> 3 pi QCD transition, and the electromagnetic gamma (*) -> 3 pi amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g – 2.

Abstract: The NEXT experiment aims at the sensitive search of the neutrinoless double beta decay in Xe-136, using high-pressure gas electroluminescent time projection chambers. The NEXT-White detector is the first radiopure demonstrator of this technology, operated in the Laboratorio Subterr & aacute;neo de Canfranc. Achieving an energy resolution of 1% FWHM at 2.6 MeV and further background rejection by means of the topology of the reconstructed tracks, NEXT-White has been exploited beyond its original goals in order to perform a neu-trinoless double beta decay search. The analysis considers the combination of 271.6 days of Xe-136-enriched data and 208.9 days of 136Xe-depleted data. A detailed background mod-eling and measurement has been developed, ensuring the time stability of the radiogenic and cosmogenic contributions across both data samples. Limits to the neutrinoless mode are obtained in two alternative analyses: a background-model-dependent approach and a novel direct background-subtraction technique, offering results with small dependence on the background model assumptions. With a fiducial mass of only 3.50 +/- 0.01 kg of Xe-136-enriched xenon, 90% C.L. lower limits to the neutrinoless double beta decay are found in the T-1/2(0 nu) > 5.5x10(23) -1.3x10(24) yr range, depending on the method. The presented techniques stand as a pro of-of-concept for the searches to be implemented with larger NEXT detectors.

Abstract: We study the scaling of kaon decay amplitudes with the number of colours, N-c, in a theory with four degenerate flavours, N-f = 4. In this scenario, two current-current operators, Q(+/-), mediate Delta S = 1 transitions, such as the two isospin amplitudes of non-leptonic kaon decays for K -> (pi pi)(I=0,2), A(0) and A(2.) In particular, we concentrate on the simpler K -> pi amplitudes, A(+/-), mediated by these two operators. A diagrammatic analysis of the large-N-c scaling of these observables is presented, which demonstrates the anticorrelation of the leading O(1/N-c) and O(N-f/N-c(2)) corrections in both amplitudes. Using our new N-f = 4 and previous quenched data, we confirm this expectation and show that these corrections are naturally large and may be at the origin of the Delta I = 1/2 rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, g(+/-), can be determined. A NLO estimate of the K -> (pi pi)(I=0,2) isospin amplitudes can then be derived, which is in good agreement with the experimental value.