Relativistic flux tube model calculation of the Isgur-Wise function

Abstract

The relativistic flux tube model is used to calculate the Isgur-Wise (IW) functions describing the exclusive semileptonic decays of B\ifmmode\bar\else\textasciimacron\fi{} and B${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{s}}$ mesons. The light quark mass dependence is investigated and the predicted universal function agrees well with the results of lattice simulations, and with the experimental data. Recent experimental measurements of the B\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\rightarrow}${\mathit{D}}^{\mathrm{*}}$l\ensuremath{\nu}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{l}}$ decay distribution yield the Cabibbo-Kobayashi-Maskawa element ${\mathit{V}}_{\mathit{b}\mathit{c}}$=0.035\ifmmode\pm\else\textpm\fi{}0.001. The IW function slope and second derivative at the zero recoil point are predicted to be \ensuremath{\xi}'(1)=-0.93\ifmmode\pm\else\textpm\fi{}0.04 and \ensuremath{\xi}''(1)=1.7\ifmmode\pm\else\textpm\fi{}0.1 for a range of light quark masses. The importance of including higher derivatives in analyses of experiment is emphasized.