Lattice spectra of $DDK$ three-body system with Lorentz covariant kinematic

TL;DR

This paper develops a Lorentz-invariant approach to calculate the energy spectrum of the three-hadron $DDK$ system, incorporating relativistic effects to enhance the analysis of three-body bound states and aid future lattice studies.

Contribution

It extends non-relativistic effective field theory with Lorentz covariant kinematics to derive quantization conditions for the $DDK$ system, broadening the applicability of three-body spectrum calculations.

Findings

Calculated finite volume energy spectrum for $DDK$ system.

Incorporated relativistic kinematics into three-body spectrum analysis.

Provided spectra in moving frames for lattice simulation testing.

Abstract

The $DDK$ system has gain increasing attention in recent research due to its potential to contain a three-hadron bound state. This article utilizes an extension of the Non-Relativistic Effective Field Theory (NREFT) and the finite volume particle-dimer framework to derive Lorentz-invariant quantization conditions for the $DDK$ three-body system. Using current model input conditions, the finite volume energy spectrum of the $DDK$ 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. They are expected to reveal more detailed properties of the $DDK$ system and other three-hadron systems.