Dispersive bounds for local form factors in ${\Lambda }_b\to \Lambda$ transitions

Abstract

We investigate the ten independent local form-factors relevant to the $b$-baryon decay ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$, combining information of lattice QCD and dispersive bounds. We propose a novel parametrization of the form factors in terms of orthonormal polynomials that diagonalizes the form factor contributions to the dispersive bounds. This is a generalization of the unitarity bounds developed for meson-to-meson form-factors. In contrast to ad-hoc parametrizations of these form factors, our parametrization provides a degree of control of the form-factor uncertainties at large hadronic recoil. This is of phenomenological interest for theoretical predictions of, e.g., ${\Lambda }_b\to \Lambda \gamma$ and ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$ decay processes.

Comments: 20 pages, 4 figures