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

TL;DR

This paper introduces a new effective-field-theory approach to extract two-body scattering information from lattice QCD data, explicitly addressing the left-hand cut problem and successfully analyzing the $T_{cc}(3875)^+$ resonance.

Contribution

It develops an alternative to L"uscher's method that incorporates one-pion exchange, enabling reliable extraction of scattering parameters including left-hand cut effects from lattice spectra.

Findings

The method accurately determines the $T_{cc}(3875)^+$ pole position.

One-pion exchange significantly affects phase shifts in $DD^*$ scattering.

The approach works for energies both below and above the left-hand cut.

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.