Lattice spectra of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mi>D</mml:mi><mml:mi>K</mml:mi></mml:math> three-body system with Lorentz covariant kinematic

The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi><a:mi>D</a:mi><a:mi>K</a:mi></a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>D</c:mi><c:mi>D</c:mi><c:mi>K</c:mi></c:math> three-body system. Using current model input conditions, the finite volume energy spectrum of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>D</e:mi><e:mi>D</e:mi><e:mi>K</e:mi></e:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>O</g:mi><g:mo stretchy="false">(</g:mo><g:msup><g:mi>p</g:mi><g:mn>2</g:mn></g:msup><g:mo stretchy="false">)</g:mo></g:math> 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 <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>D</k:mi><k:mi>D</k:mi><k:mi>K</k:mi></k:math> system and other three-hadron systems, if various higher-order effects, such as the isospin <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>I</m:mi><m:mo>=</m:mo><m:mn>1</m:mn></m:math> <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>D</o:mi><o:mi>K</o:mi></o:math> interactions and the coupled-channel effects are introduced. Published by the American Physical Society 2024