Spin-dependent polarizabilities of heavy vector mesons

Abstract

We investigate the spin-dependent electromagnetic polarizabilities of the heavy vector mesons \(D^*\) and \(B^*\) in heavy meson chiral perturbation theory up to \(\mathcal O(p^3)\). Using a twelve-element tensor basis for the real-photon Compton scattering on a spin-1 target, we determine two scalar, four vector and six tensor polarizabilities. We take the charm- and bottom-sector axial couplings from the measured \(D^*\) width and lattice-QCD calculations, respectively, and estimate the magnetic couplings in the nonrelativistic constituent-quark model. In the charm sector, the proximity of the charged \(D\pi\) thresholds generates strongly nonanalytic \(P\phi\)-loop contributions, producing large real contributions to several \(\bar D^{*0}\) polarizabilities and sizable imaginary parts for \(D^{*-}\), whose charged \(D\pi\) channel is open. The \(E1E1\)-type polarizabilities are enhanced much more strongly than their \(M1M1\)-type counterparts, consistent with the velocity suppression of the pion-cloud magnetic coupling. No analogous enhancement occurs for \(B^*\): the Born terms govern the magnetic polarizabilities, and the anomaly poles dominate the vector polarizabilities that receive no Born contribution. These results resolve the spin dependence of the \(D\pi\) threshold effect and provide benchmarks for future lattice-QCD studies.