Resonantπ+γ→π+π0Amplitude from Quantum Chromodynamics

Abstract

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.

Baryons as relativistic three-quark bound states

“…[276][277][278] and references therein), the baryon sector still waits to be explored. One reason is the worse signal to noise ratio as compared to the baryon sector.…”

Meson Spectroscopy from Lattice QCD

“…There are also good prospects here with the recent appearance of the first lattice QCD calculation of a transition form factor involving a resonance [10,12].…”

“…Going beyond the resonance mass and width, recently the form factor of an unstable hadron has been calculated for the first time in lattice QCD [10,12]. From computations of the ππ → πγ * transition amplitude, the resonant ρ → πγ * transition form factor and the radiative decay width were extracted.…”

Hadron Resonances from QCD

“…The development of the distillation technology needed to efficiently calculate the required threepoint correlation functions in the case of the vector current relevant to electromagnetic amplitudes was presented in [27], and the first calculation of an electromagnetic scattering amplitude, πγ → ππ, has very recently appeared [28]. In this paper, the Hadron Spectrum Collaboration determined matrix elements of the type π ψ γ µ ψ ππ on a lattice of volume ∼ (2.4 fm) 3 with m π = 391 MeV and from these extract the scattering amplitude illustrated in Figure 6.…”