Finite- and infinite-volume study of DDπ scattering

A bstract We develop a comprehensive framework for extracting the pole position and properties of the doubly-charmed tetraquark $$ {T}_{\textrm{cc}}^{+}(3875) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mi>cc</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mfenced> <mml:mn>3875</mml:mn> </mml:mfenced> </mml:math> from lattice QCD data using the relativistic three-particle formalism. This approach incorporates the effect of the one-pion exchange diagram in DDπ and DD ∗ scattering, making it applicable at energies coinciding with the left-hand cut in the partial-wave projected DD ∗ amplitude. We present an example application of this framework to existing lattice QCD data at m π = 280 MeV. We solve the integral equations describing the DDπ reaction, use LSZ reduction to determine the corresponding DD ∗ amplitude, and find the values of the infinite-volume two- and three-body K matrices that lead to agreement with lattice DD ∗ phase shifts within their uncertainties. Using these K matrices in the three-particle quantization condition, we describe the finite- volume DD ∗ spectrum and find good agreement with the lattice QCD energies. Our results suggest that, at this pion mass, the tetraquark appears as a pair of subthreshold complex poles whose precise location strongly depends on the value of the DDπ three-particle K matrix.