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标题：A study of the radiative transition $\pi \pi \to \pi \gamma^{\ast}$ with lattice QCD
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作者：L.Leskovec ; C.Alexandrou ; G.Koutsou 等
期刊名称：PoS - Proceedings of Science
印刷版ISSN：1824-8039
出版年度：2016
卷号：256
DOI：10.22323/1.256.0159
语种：English
出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：Lattice QCD calculations of radiative transitions between hadrons have in the past been limited to processes of hadrons stable under the strong interaction. Recently developed methods for $1\to2$ transition matrix elements in a finite volume now enable the determination of radiative decay rates of strongly unstable particles. Our lattice QCD study focuses on the process $\pi \pi \to \pi \gamma^{\ast}$, where the $\rho$ meson is present as an enhancement in the cross-section. We use $2+1$ flavors of clover fermions at a pion mass of approximately $320$ MeV and a lattice size of approximately $3.6$ fm. The required $2$-point and $3$-point correlation functions are constructed from a set of forward, sequential and stochastic light quark propagators. In addition to determining the $\rho$ meson resonance parameters via the Lüscher method, the scattering phase shift is used in conjunction with the $1\to2$ transition matrix element formalism of Brice\~no, Hansen and Walker-Loud \cite{Briceno:2014uqa} to compute the $\pi\pi\to\pi\gamma^{\ast}$ amplitude at several values of the momentum transfer and $\pi\pi$ invariant mass.