arXiv subjects

Christian J. Shultz

Publications and source records attributed to Christian J. Shultz.

3 recordsLinked to original sources

arXiv2016

The $ππ\toπγ^\star$ amplitude and the resonant $ρ\toπγ^\star$ transition from lattice QCD

We present a determination of the $P$-wave $ππ\toπγ^\star$ 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 $ρ\to πγ^\star$ transition form factor. This calculation, at $m_π\approx 400$ MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.

hep-ph↗

arXiv2015

The resonant $π^+γ\toπ^+π^0$ amplitude from Quantum Chromodynamics

We present the first ab initio calculation of a radiative transition of a hadronic resonance within quantum chromodynamics (QCD). We compute the amplitude for $ππ\to πγ^\star$, 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 $m_π\approx 400$~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 $ρ\to πγ^\star$ form factor.

hep-ph↗

arXiv2015

Excited meson radiative transitions from lattice QCD using variationally optimized operators

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.

hep-lat↗