Unitarity Constraints on the B and B^* Form Factors from QCD Analyticity and Heavy Meson Spin Symmetry

A method of deriving bounds on the weak meson form factors, based on perturbative QCD, analyticity and unitarity, is generalized in order to fully exploit heavy quark spin symmetry in the ground state $(L=0)$ doublet of pseudoscalar $(B)$ and vector $(B^*)$ mesons. All the relevant form factors of these mesons are taken into account in the unitarity sum. They are treated as independent functions along the timelike axis, being related by spin symmetry only near the zero recoil point. Heavy quark vacuum polarisation up to three loops in perturbative QCD and the experimental cross sections $\sigma(e^+e^- \rightarrow \Upsilon)$ are used as input. We obtain bounds on the charge radius of the elastic form factor of the $B$ meson, which considerably improve previous results derived in the same framework.