Evolution of Efimov states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

Electroweak three-body decays in the presence of two- and three-body bound states

Briceño,

Jackura,

Pefkou

et al. 2024

Incorporating DDπ effects and left-hand cuts in lattice QCD studies of the Tcc(3875)+

Hansen,

Romero-López,

Sharpe

2024

We generalize the relativistic field-theoretic three-particle finite-volume scattering formalism to describe generic DDπ systems in the charm C = 2 sector. This includes the isospin-0 channel, in which the recently discovered doubly-charmed tetraquark Tcc(3875)+ is expected to manifest as a pole in the DDπ → DDπ scattering amplitude. The formalism presented here can also be applied to lattice QCD settings in which the D* is bound and, in particular, remains valid below the left-hand cut in DD* scattering, thus resolving an issue in previous analyses of lattice-determined finite-volume energies.

Finite-volume scattering on the left-hand cut

Baião Raposo,

Hansen

2024

The two-particle finite-volume scattering formalism derived by Lüscher and generalized in many subsequent works does not hold for energies far enough below the two-particle threshold to reach the nearest left-hand cut. The breakdown of the formalism is signaled by the fact that a real scattering amplitude is predicted in a regime where it should be complex. In this work, we address this limitation by deriving an extended formalism that includes the nearest branch cut, arising from single particle exchange. We focus on two-nucleon (NN → NN) scattering, for which the cut arises from pion exchange, but give expressions for any system with a single channel of identical particles. The new result takes the form of a modified quantization condition that can be used to constrain an intermediate K-matrix in which the cut is removed. In a second step, integral equations, also derived in this work, must be used to convert the K-matrix to the physical scattering amplitude. We also show how the new formalism reduces to the standard approach when the N → Nπ coupling is set to zero.