Analyticity, shapes of semileptonic form factors, andB¯→πlν¯

We give a pedagogical discussion of the physics underlying dispersion relation-derived parametrizations of form factors describing $B\to \pi l\overline{\nu }$ and $B\to \mathrm{Dl}\overline{\nu }$. Moments of the dispersion relations are shown to provide substantially tighter constraints on the $f_{+}\mathrm{}\left(t\right)\mathrm{}$ form factor describing $\overline{B}\to \pi l\overline{\nu }$ than the unweighted dispersion relation alone. Heavy quark spin symmetry relations between the $B\to \pi l\overline{\nu }$ and $B^{*}\to \pi l\overline{\nu }$ form factors enable such constraints to be tightened even further.