πγ→ππ transition and the ρ radiative decay width from lattice QCD

Abstract

We report a lattice QCD determination of the πγ → ππ transition amplitude for the P -wave, I = 1 two-pion final state, as a function of the photon virtuality and ππ invariant mass. The calculation was performed with 2 + 1 flavors of clover fermions at a pion mass of approximately 320 MeV, on a 32 3 × 96 lattice with L ≈ 3.6 fm. We construct the necessary correlation functions using a combination of smeared forward, sequential and stochastic propagators, and determine the finite-volume matrix elements for all ππ momenta up to | P | = √ 3 2π L and all associated irreducible representations. In the mapping of the finite-volume to infinite-volume matrix elements using the Lellouch-Lüscher factor, we consider two different parametrizations of the ππ scattering phase shift. We fit the q 2 and s dependence of the infinite-volume transition amplitude in a model-independent way using series expansions, and compare multiple different truncations of this series. Through analytic continuation to the ρ resonance pole, we also determine the πγ → ρ resonant transition form factor and the ρ meson photocoupling, and obtain |Gρπγ| = 0.0802(32)(20). arXiv:1807.08357v3 [hep-lat]

Lattice QCD and neutrino-nucleus scattering

“…The applications have largely focused on the meson sector. To cite an example bearing some similarity to W * n → ∆ in neutrino scattering, the γ * π → ρ transition has been computed in lattice QCD [143,144], providing the first rigorous calculation of the transition form factor to an unstable hadron, illustrated in Fig. 6 In addition, methods to extract resonance-to-resonance transitions, for example, γ * ρ → ρ, via lattice calculations of two-to-two transition amplitudes, in this case γ * ππ → ππ, have been developed [145,146].…”

Scattering amplitudes from finite-volume spectral functions

“…The former matrix elements are exactly those determined in existing lattice QCD calculations of the form factor [36,44], while the latter somewhat resemble the finite-volume matrix elements calculated for the process π + γ * → ππ (where γ * denotes a virtual photon) in Refs. [61,62] but with an arbitrary pion interpolator in place of the electromagnetic current.…”

“…Calculations of transition amplitudes involving external currents are presented in Refs. [36,44,61,62] and scattering involving vector bosons is treated in Refs. [37,63].…”

Opportunities for Lattice QCD in quark and lepton flavor physics

“…The theoretical challenge is to relate these two types of matrix element. This has been achieved for processes involving multiple two-particle channels [91,[115][116][117][118][119][120][121][122], based on the seminal work of Lüscher [123,124] and Lellouch [125], and has been implemented in several lattice calculations [126][127][128][129][130][131][132].…”