We present a determination of the P -wave ππ → πγ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite-volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-Lüscher formalism. We determine the amplitude for a range of discrete values of the ππ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the ρ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue at the ρ pole extract the ρ → πγ transition form factor. This calculation, at mπ ≈ 400 MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.

We present the first ab initio calculation of a radiative transition of a hadronic resonance within Quantum Chromodynamics (QCD). We compute the amplitude for ππ → πγ , as a function of the energy of the ππ pair and the virtuality of the photon, in the kinematic regime where ππ couples strongly to the unstable ρ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to mπ ≈ 400 MeV. We obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the ρ pole and identify from its residue the ρ → πγ form-factor. Introduction:The electromagnetic transitions of the nucleon into unstable resonant N excitations is a primary tool in the experimental study of nucleon structure and spectroscopy [1]. These processes give us insight into the mechanisms that lead to the formation of the low-lying and excited hadrons from the basic quark and gluon building blocks of Quantum Chromodynamics (QCD). It is crucial to have a complimentary theoretical program that connects physically observed transitions to QCD. One major challenge in studying these transitions is their resonant nature, where the N excitation decays rapidly to asymptotic scattering states composed of two or more stable hadrons. To investigate these processes within QCD, one needs a non-perturbative framework that can accommodate resonant behavior, and presently, lattice QCD is the only available tool to evaluate such observables while making only controlled approximations. Its implementation for the determination of properties of hadron resonances is still at an exploratory stage, and in this work we will extend the exploration into a new area with the first calculation of a radiative production amplitude of an unstable hadronic resonance from QCD.

We explore the use of 'optimized' operators, designed to interpolate only a single meson eigenstate, in three-point correlation functions with a vector-current insertion. These operators are constructed as linear combinations in a large basis of meson interpolating fields using a variational analysis of matrices of two-point correlation functions. After performing such a determination at both zero and non-zero momentum, we compute three-point functions and are able to study radiative transition matrix elements featuring excited state mesons. The required two-and three-point correlation functions are efficiently computed using the distillation framework in which there is a factorization between quark propagation and operator construction, allowing for a large number of meson operators of definite momentum to be considered. We illustrate the method with a calculation using anisotopic lattices having three flavors of dynamical quark all tuned to the physical strange quark mass, considering form-factors and transitions of pseudoscalar and vector meson excitations. The dependence on photon virtuality for a number of form-factors and transitions is extracted and some discussion of excited-state phenomenology is presented.

No abstract

No abstract