Abstract: In this work, we use an extension of the quantization condition, given in ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle bound states or narrow two-particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finite-volume signature for a variety of two- and three-particle interactions. We determine the spectrum for parameters such that the system contains both dimers (two-particle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the two-particle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinite-volume dimer-particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteron-nucleon scattering. All calculations presented here are restricted to the case of three identical scalar particles.

Abstract: We present a general method for deriving the energy shift of an interacting system of N spinless particles in a finite volume. To this end, we use the nonrelativistic effective field theory (NREFT), and match the pertinent low-energy constants to the scattering amplitudes. Relativistic corrections are explicitly included up to a given order in the 1/L expansion. We apply this method to obtain the ground state of N particles, and the first excited state of two and three particles to order L-6 in terms of the threshold parameters of the two- and three-particle relativistic scattering amplitudes. We use these expressions to analyze the N-particle ground state energy shift in the complex phi (4) theory.

Abstract: By combining the simplest (3,1) version of the seesaw mechanism containing a single heavy “right-handed” neutrino with the minimal scotogenic approach to dark matter, we propose a theory for neutrino oscillations. The “atmospheric” mass scale arises at tree level from the seesaw, while the “solar” oscillation scale emerges radiatively, through a loop involving the “dark sector” exchange. Such simple setup gives a clear interpretation of the neutrino oscillation lengths, has a viable WIMP dark matter candidate, and implies a lower bound on the neutrinoless double beta decay rate.

Abstract: In recent years, several observables associated to semileptonic b -> s processes have been found to depart from their predicted values in the Standard Model, including a few tantalizing hints of lepton flavor universality violation. In this work, we consider an existing model with a massive Z' boson that addresses the anomalies in b -> s transitions and extend it with a nontrivial embedding of neutrino masses. We analyze lepton flavor-violating effects, induced by the nonuniversal interaction associated to the b -> s anomalies and by the new physics associated to the neutrino mass generation, and determine the expected ranges for the most relevant observables.

Abstract: We study theoretically the resonant structure of the double Cabibbo suppressed D+ -> K-K+K+ decay. We start from an elementary production diagram, considered subleading in previous approaches, which cannot produce a final K-K+ pair at the tree level but which we show to be able to provide the strength of the decay through final meson-meson state interaction. The different meson-meson elementary productions are related through SU(3), and the final rescattering is implemented from a suitable implementation of unitary extensions of chiral perturbation theory, which generate dynamically the scalar resonances1 f(0)(980) and a(0)(980). We obtain a good agreement with recent experimental data from the LHCb Collaboration with a minimal freedom in the fit and show the dominance of the a(0)(980) contribution close to the threshold of the K-K+ spectrum.