Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in finite-volume

Abstract

Whether one is interested in accessing the excited spectrum of hadrons or testing the standard model of particle physics, electroweak transition processes involving multi-hadron channels in the final state play an important role in a variety of experiments. Presently the primary theoretical tool with which one can study such reactions is lattice QCD, which is defined in a finite spacetime volume. In this work, we investigate the feasibility of implementing existing finite-volume formalism in realistic lattice QCD calculation of reactions in which a stable hadron can transition to one of several two-hadron channels under the action of an external current. We provide a conceptual description of the coupled-channel transition formalism, a practical roadmap for carrying out a calculation, and an illustration of the approach using synthetic data for two non-trivial resonant toy models. The results provide a proof-of-principle that such reactions can indeed be constrained using modern-day lattice QCD calculations, motivating explicit computation in the near future.

References in corpus (18)

• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• A relativistic, model-independent, three-particle quantization condition
• Charmonium excited state spectrum in lattice QCD
• Resonances in coupled πK,ηK scattering from quantum chromodynamics
• Three-body Unitarity in the Finite Volume
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• Coupled-Channel $D\pi$, $D\eta$ and $D_s\bar{K}$ Scattering from Lattice QCD
• Multichannel one-to-two transition amplitudes in a finite volume
• Exotic and excited-state radiative transitions in charmonium from lattice QCD
• Decays of an exotic $1^{-+}$ hybrid meson resonance in QCD
• The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD
• Solving relativistic three-body integral equations in the presence of bound states
• Decay amplitudes to three hadrons from finite-volume matrix elements
• Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states
• On the three-particle analog of the Lellouch-Lüscher formula
• Lattice QCD estimate of the ${\eta }_c(2S)\to J/\psi \gamma$ decay rate
• On-shell representations of two-body transition amplitudes: single external current

Cited by in corpus (9)

• Precision Studies of QCD in the Low Energy Domain of the EIC
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• $1^{-+}$ Hybrid in $J/\psi$ Radiative Decays from Lattice QCD
• Scalar and tensor charmonium resonances in coupled-channel scattering from QCD
• Radiative decay of the resonant $K^{\ast }$ and the $\gamma K\to K\pi$ amplitude from lattice QCD
• $B\to \rho \ell \bar{\nu }$ resonance form factors from $B\to \pi \pi \ell \bar{\nu }$ in lattice QCD
• Two-current transition amplitudes with two-body final states
• Exploring Baryon Resonances with Transition Generalized Parton Distributions: Status and Perspectives
• Prospects for ${\gamma }^{\star }{\gamma }^{\star }\to \pi \pi$ via lattice QCD