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arXiv · 2312.01930

Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875)^+$ from finite volume energy levels

Lu Meng·Vadim Baru·Evgeny Epelbaum·Arseniy A. Filin·Ashot M. Gasparyan
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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 L\"uscher's method. By explicitly incorporating one-pion exchange, we overcome the challenging left-hand cut problem in L\"uscher's method and can handle finite volume energy levels both below and above the left-hand cut. Applied to the lattice data for $DD^*$ scattering at a pion mass of 280 MeV, as an illustrative example, our results reveal the significant impact of the one-pion exchange on P-wave and S-wave phase shifts. The pole position of the $T_{cc}(3875)^+$ 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.

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Lu Meng, Vadim Baru, Evgeny Epelbaum, Arseniy A. Filin, Ashot M. Gasparyan. 2023-12-04. Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875)^+$ from finite volume energy levels. https://doi.org/10.1103/physrevd.109.l071506

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