Light-front Wave Functions of Vector Mesons in an Algebraic Model
B. Almeida-Zamora🇲🇽 · J.J. Cobos-Martínez🇲🇽 · A. Bashir🇲🇽 · K. Raya🇪🇸 · J. Rodríguez-Quintero🇪🇸 · J. Segovia🇪🇸
Inspired by the recent development of an algebraic model which provides an adequate and unified description of the internal structure of the lowest-lying pseudo-scalar mesons, belonging both to the light quarks sector and to the one of heavy quarks, we perform its first extension to the vector-meson case. The algebraic model describes meson's structure in terms of the spectral density function that appears in a Nakanishi integral representation of the covariant quark-antiquark bound-state amplitude, \emph{i.e.}, the Bethe-Salpeter amplitude. We compute the leading-twist light-front wave functions of the , , and mesons through their connection with the parton distribution amplitudes. Among the results we present, the following are of particular interest: (i) transverse light-front wave functions can be obtained algebraically from the corresponding parton distribution amplitudes, whereas that is not the case for longitudinal light-front wave functions, which requires an intermediate step where a spectral density function must be derived from the particular parton distribution amplitude; (ii) the derived spectral density functions show marked differences between light and heavy vector mesons, the latter being narrower as compared to the former; these are also non-positive definite, although the integral over the entire curve is larger than zero as expected; and (iii) the longitudinal and transverse light-front wave functions of vector mesons with light quark content exhibit steep - and -dependence, while those of the and mesons are characterized by narrow distributions in the -range but, comparatively, much more gradual fall-offs with respect to the -range depicted.