Production of axial-vector mesons at e+e? collisions with double-tagging as a way to constrain the axial meson light-by-light contribution to the muon g-2 and the hyperfine splitting of muonic hydrogen

摘要

We calculate cross sections for production of axial-vector f 1 ( 1285 ) mesons for double-tagged measurements of the e + e ? → e + e ? f 1 ( 1285 ) reaction. Different γ * γ * → f 1 ( 1285 ) vertices from the literature are used. Both integrated cross section as well as differential distributions are calculated. Predictions for a potential measurement at Belle II are presented. Quite different results are obtained for the different vertices proposed in the literature. Several observables are discussed. The distribution in photon virtuality asymmetry is especially sensitive to the γ * γ * → f 1 vertex. Future measurements at e + e ? colliders could test and/or constrain the γ * γ * → f 1 ( a 1 , f 1 ′ ) vertices and associated form factors, known to be important ingredients for calculating contributions to anomalous magnetic moment of muon and hyperfine splitting of levels of muonic atoms. In addition we present helicity amplitudes as a function of both photon virtualities. Only some amplitudes are different from zero. Different models have different relative size of LT, TL, and TT amplitudes.