Solving the left-hand cut problem in lattice QCD: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>3875</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo></mml:msup></mml:math> from finite volume energy levels

Abstract

We discuss a novel effective-field-theory-based approach for extracting two-body scattering information from finite volume energies, serving as an alternative to Lüscher’s method. By explicitly incorporating one-pion exchange, we overcome the challenging left-hand cut problem in Lüscher’s method and can handle finite volume energy levels both below and above the left-hand cut. Applied to the lattice data for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi><a:msup><a:mi>D</a:mi><a:mo>*</a:mo></a:msup></a:math> scattering at a pion mass of 280 MeV, as an illustrative example, our results reveal the significant impact of the one-pion exchange on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>P</c:mi></c:math>-wave and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi></e:math>-wave phase shifts. The pole position of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>T</g:mi><g:mrow><g:mi>c</g:mi><g:mi>c</g:mi></g:mrow></g:msub><g:mo stretchy="false">(</g:mo><g:mn>3875</g:mn><g:msup><g:mo stretchy="false">)</g:mo><g:mo>+</g:mo></g:msup></g:math> state, extracted from the finite-volume energy levels at this pion mass while taking into account left-hand cut effects, range corrections and partial-wave mixing, is consistent with a near-threshold resonance. This study demonstrates, for the first time, that two-body scattering information can be reliably extracted from lattice spectra including the left-hand cut. Published by the American Physical Society 2024

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