Jin-Yi Pang

In the presence of a long-range force, a modified Lüscher equation is derived, which can be applied for the extraction of the two-body scattering phase shifts on the lattice. A brief comparison with the existing approaches is carried out.

A bstract: An efficient numerical algoritm is proposed for the calculation of the modified Lüscher zeta-function in the presence of a long-range force. Using the formalism developed in ref. JHEP05(2024)168 for the analysis of synthetic data on the finite-volume energy levels in a toy model, it is demonstrated that, in contrast to the standard Lüscher approach, the truncation of the higher partial waves has very little effect on the final result. Furthermore, the regularization and renormalization of the modified Lüscher zeta-function is discussed in detail, as well as the problems arising within the cutoff regularization. It is shown that, using the renormalization scheme proposed in the present paper, one obtains modified effective range expansion parameters of natural size in all partial waves.

An efficient numerical algoritm is proposed for the calculation of the modified Lüscher zeta-function in the presence of a long-range force. Using the formalism developed in Ref.~\cite{Bubna:2024izx} for the analysis of synthetic data on the finite-volume energy levels in a toy model, it is demonstrated that, in contrast to the standard Lüscher approach, the truncation of the higher partial waves has very little effect on the final result. Furthermore, the regularization and renormalization of the modified Lüscher zeta-function is discussed in detail, as well as the problems arising within the cutoff regularization. It is shown that, using the renormalization scheme proposed in the present paper, one obtains modified effective range expansion parameters of natural size in all partial waves.

We derive modified Lüscher equation that enables one to extract scattering phase shifts from the lattice energy levels even in the presence of a long-range force. The method avoids large partial-wave mixing which is a priori expected in the presence of such force, and is applicable in the region of the left-hand cut. More details can be found in the recent publication R.Bubna, H.~W.Hammer, F.Müller, J.-Y.Pang, A.Rusetsky and J.-J.Wu, JHEP 05 (2024) 168, arXiv:2402.12985 [hep-lat].

The D D K system has gained increasing attention in recent research due to its potential to contain a three-hadron bound state. This paper utilizes an extension of the nonrelativistic effective field theory and the finite volume particle-dimer framework to derive Lorentz invariant quantization conditions for the D D K three-body system. Using current model input conditions, the finite volume energy spectrum of the D D K three-body system was calculated. This new calculation incorporates relativistic kinematics, allowing it to be applicable across a broader energy range starting from the threshold. In this work, we present a comprehensive O ( p 2 ) calculation. The spurious pole is effectively subtracted within the framework of relativistic kinematics. The spectra in the moving frame are also obtained. These analyses provide a broader testing ground for future lattice simulations. Based on this framework, it is expected to reveal more detailed properties of the D D K system and other three-hadron systems, if various higher-order effects, such as the isospin I = 1 D K interactions and the coupled-channel effects are introduced. Published by the American Physical Society 2024

We derive an explicit expression for the Lellouch-Lüscher (LL) factor in the K → 3π decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the K → 3π decays on the lattice.