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Romero-Lopez, F., Sharpe, S. R., Blanton, T. D., Briceno, R. A., & Hansen, M. T. (2019). Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states. J. High Energy Phys., 10(10), 007–43pp.
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.
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Romero-Lopez, F., Rusetsky, A., & Urbach, C. (2018). Two- and three-body interactions in phi 4 theory from lattice simulations. Eur. Phys. J. C, 78(10), 846–15pp.
Abstract: We calculate the one-, two- and three-particle energy levels for different lattice volumes in the complex phi(4) theory on the lattice. We argue that the exponentially suppressed finite-volume corrections for the two- and three-particle energy shifts can be reduced significantly by using the single particle mass, which includes the finite-size effects. We show numerically that, for a set of bare parameters, corresponding to the weak repulsive interaction, one can reliably extract the two- and three-particle energy shifts. From those, we extract the scattering length, the effective range and the effective three-body coupling. We show that the parameters, extracted from the two- and three-particle energy shifts, are consistent. Moreover, the effective three-body coupling is significantly different from zero.
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Donini, A., Hernandez, P., Pena, C., & Romero-Lopez, F. (2016). Nonleptonic kaon decays at large N-c. Phys. Rev. D, 94(11), 114511–6pp.
Abstract: We study the scaling with the number of colors, N-c, of the weak amplitudes mediating kaon mixing and decay. We evaluate the amplitudes of the two relevant current-current operators on the lattice for N-c = 3-7. We conclude that the subleading 1/N-c corrections in B-k, are small, but those in the K -> pi pi amplitudes are large and fully anticoirelated in the I = 0, 2 isospin channels. We briefly comment on the implications for the Delta I = 1/2 rule.
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