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Martinez Torres, A., Oset, E., Prelovsek, S., & Ramos, A. (2015). Reanalysis of lattice QCD spectra leading to the Ds0*(2317) and Ds1*(2460). J. High Energy Phys., 05(5), 153–22pp.
Abstract: We perform a reanalysis of the energy levels obtained in a recent lattice QCD simulation, from where the existence of bound states of KD and KD* are induced and identified with the narrow D-s0*(2317) and D-s1*(2460) resonances. The reanalysis is done in terms of an auxiliary potential, employing a single-channel basis KD(*()), and a two-channel basis KD(*()), eta D-s(()*()). By means of an extended Luscher method we determine poles of the continuum t-matrix, bound by about 40 MeV with respect to the KD and KD* thresholds, which we identify with the D-s0*(2317) and D-s1*(2460) resonances. Using a sum rule that reformulates Weinberg compositeness condition we can determine that the state D-s0*(2317) contains a KD component in an amount of about 70%, while the state D-s1*(2460) contains a similar amount of KD*. We argue that the present lattice simulation results do not still allow us to determine which are the missing channels in the bound state wave functions and we discuss the necessary information that can lead to answer this question.
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Blanton, T. D., Romero-Lopez, F., & Sharpe, S. R. (2019). Implementing the three-particle quantization condition including higher partial waves. J. High Energy Phys., 03(3), 106–56pp.
Abstract: We present an implementation of the relativistic three-particle quantization condition including both s- and d-wave two-particle channels. For this, we develop a systematic expansion of the three-particle K matrix, K-df,K-3, about threshold, which is the generalization of the effective range expansion of the two-particle K matrix, K-2. Relativistic invariance plays an important role in this expansion. We find that d-wave two-particle channels enter first at quadratic order. We explain how to implement the resulting multichannel quantization condition, and present several examples of its application. We derive the leading dependence of the threshold three-particle state on the two-particle d-wave scattering amplitude, and use this to test our implementation. We show how strong two-particle d-wave interactions can lead to significant effects on the finite-volume three-particle spectrum, including the possibility of a generalized three-particle Efimov-like bound state. We also explore the application to the 3 pi(+) system, which is accessible to lattice QCD simulations, where we study the sensitivity of the spectrum to the components of K-df,K-3. Finally, we investigate the circumstances under which the quantization condition has unphysical solutions.
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Romero-Lopez, F., Rusetsky, A., Schlage, N., & Urbach, C. (2021). Relativistic N-particle energy shift in finite volume. J. High Energy Phys., 02(2), 060–52pp.
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.
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Blanton, T. D., Romero-Lopez, F., & Sharpe, S. R. (2022). Implementing the three-particle quantization condition for pi(+)pi K-+(+) and related systems. J. High Energy Phys., 02(2), 098–49pp.
Abstract: Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K-df,K-3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O(1/L-5); and we calculate the leading-order predictions in chiral perturbation theory for K-df,K-3 in the pi(+)pi K-+(+) and pi+K+K+ systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of pi(+)pi K-+(+) levels using the two- and three-particle interactions predicted by chiral perturbation theory.
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Hansen, M. T., Romero-Lopez, F., & Sharpe, S. R. (2021). Decay amplitudes to three hadrons from finite-volume matrix elements. J. High Energy Phys., 04(4), 113–44pp.
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.
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