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We present a simple scheme for solving relativistic integral equations for the partial-wave projected three-body amplitudes. Our techniques are used to solve a problem of three scalar particles with a formation of a S-wave two-body bound state. We rewrite the problem in a form suitable for numerical solution and then explore three solving strategies. In particular, we discuss different ways of incorporating the bound-state pole contribution in the integral equations. All of them lead to agreement with previous results obtained using finite-volume spectra of the same theory, providing further evidence of the validity of the existing finite- and infinite-volume formalism for studying three-particle systems. We discuss an analytic and numerical estimate of the systematic errors and provide numerical evidence that the methods presented allow for determination of amplitude above the three-body threshold as well. In conjunction with the previously derived finite-volume formalism, this work furthers the objective for extracting three-hadron scattering amplitudes directly from lattice QCD. [ABSTRACT FROM AUTHOR]

This work explores scattering amplitudes that couple two-particle systems via a single external current insertion, 2+J→2. Such amplitudes can provide structural information about the excited QCD spectrum. We derive an exact analytic representation for these reactions. From these amplitudes, we show how to rigorously define resonance and bound-state form factors. Furthermore, we explore the consequences of the narrow-width limit of the amplitudes as well as the role of the Ward-Takahashi identity for conserved vector currents. These results hold for any number of two-body channels with no intrinsic spin, and a current with arbitrary Lorentz structure and quantum numbers. This work and the existing finite-volume formalism provide a complete framework for determining this class of amplitudes from lattice QCD. [ABSTRACT FROM AUTHOR]

In recent years, different on-shell 3→3 scattering formalisms have been proposed to be applied to both lattice QCD and infinite-volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in [M. T. Hansen and S. R. Sharpe, Phys. Rev. D 92, 114509 (2015).] and subsequently Briceño et al. in [R. A. Briceño, M. T. Hansen, and S. R. Sharpe, Phys. Rev. D 95, 074510 (2017).] can be recovered from the B-matrix representation, derived on the basis of S-matrix unitarity, presented by Mai et al. in [M. Mai, B. Hu, M. Döring, A. Pilloni, and A. Szczepaniak, Eur. Phys. J. A 53, 177 (2017).] and Jackura et al. in [A. Jackura, C. Fernández-Ramírez, V. Mathieu, M. Mikhasenko, J. Nys, A. Pilloni, K. Saldaña, N. Sherrill, and A. P. Szczepaniak (JPAC Collaboration), Eur. Phys. J. C 79, 56 (2019).] Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the nonrelativistic limit of both representations. [ABSTRACT FROM AUTHOR]

Using the general formalism presented in [Phys. Rev. D 94, 013008 (2016); Phys. Rev. D 100, 034511 (2019)], we study the finite-volume effects for the 2+J→2 matrix element of an external current coupled to a two-particle state of identical scalars with perturbative interactions. Working in a finite cubic volume with periodicity L, we derive a 1/L expansion of the matrix element through O(1/L5) and find that it is governed by two universal current-dependent parameters, the scalar charge and the threshold two-particle form factor. We confirm the result through a numerical study of the general formalism and additionally through an independent perturbative calculation. We further demonstrate a consistency with the Feynman-Hellmann theorem, which can be used to relate the 1/L expansions of the ground-state energy and matrix element. The latter gives a simple insight into why the leading volume corrections to the matrix element have the same scaling as those in the energy, 1/L³, in contradiction to Phys. Rev. D 91, 074509 (2015), which found a 1/L² contribution to the matrix element. We show here that such a term arises at intermediate stages in the perturbative calculation, but cancels in the final result. [ABSTRACT FROM AUTHOR]

Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide nontrivial checks on the final results and also to explore limiting cases in which more straightforward predictions may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume independent and equal to the total charge of the two-particle state. Second, we study the implications for a two-particle bound state. We demonstrate that the infinite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. Finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuteron's scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state. [ABSTRACT FROM AUTHOR]

In the search for exotic mesons, the GlueX Collaboration will soon extract moments of the ηπ0 angular distribution. In the perspective of these results, we generalize the formalism of moment extraction to the case in which the two mesons are produced with a linearly polarized beam and build a model for the reaction →γp→ηπ0p. The model includes resonant S, P, and D waves in ηπ0, produced by natural exchanges. Moments of the ηπ0 angular distribution are computed with and without the P wave, to illustrate the sensitivity to exotic resonances. Although little sensitivity to the P wave is found in moments of even angular momentum, moments of odd angular momentum are proportional to the interference between the P wave and the dominant S and D waves. We also generalize the definition of the beam asymmetry for two mesons photoproduction and show that, when the meson momenta are perpendicular to the reaction plane, the beam asymmetry enhances the sensitivity to the exotic P wave. [ABSTRACT FROM AUTHOR]