Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875{)}^{+}$ 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 $D{D}^{\ast }$ 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.

15 pages and 12 figures

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Cited by in corpus (20)

• Near-threshold states in coupled $D{D}^{\ast }-D^{\ast }{D}^{\ast }$ scattering from lattice QCD
• Doubly charm tetraquark channel with isospin $1$ from lattice QCD
• Study of isoscalar scalar $bc\bar{u}\bar{d}$ tetraquark $T_{bc}$ from lattice QCD
• Doubly heavy tetraquark bound and resonant states
• Doubly heavy tetraquark states in a mass splitting model
• Lattice study of $cc\bar{u}\bar{s}$ tetraquark channel in $D^{(\ast )}{D}_s^{(\ast )}$ scattering
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• Towards modeling the short-range interactions of hidden/open charm pentaquark molecular states
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Charmoniumlike Channels $1^{+}$ with Isospin $1$ from Lattice and Effective Field Theory
• Effective range expansion with a long-range force
• Construction of general $N$-body lattice operators with arbitrary momenta
• Machine Learning Unveils the Power Law of Finite-Volume Energy Shifts
• Coupled-channel scattering of $DD,D{D}^{\ast }$ and $D^{\ast }{D}^{\ast }$ in isospin-$1$ from lattice QCD
• Lattice study of scattering phase shifts for $D{D}^{\ast }$ and $B{B}^{\ast }$ systems using twisted boundary conditions: Search for bound state formation
• Pion scattering in finite volume within the Inverse Amplitude Method
• Hadronic molecules and multiquark states
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$
• ${\eta }_c{\eta }_c$ and $J/\psi J/\psi$ scatterings from lattice QCD
• Low-energy $DD$ scattering in lattice QCD