Holographic Calculation of Semileptonic Form Factors and the Isgur--Wise Function for $B_{(s)}\to D_{(s)}$ Decays

Abstract

We present a holographic analysis of the semileptonic decays $B \to D \ell \barν_\ell$ and $B_s \to D_s \ell \barν_\ell$ within the Softwall Model (SWM) and the Non-Quadratic Softwall Model (NQSWM). We extract the Isgur-Wise function from the overlap integral of bulk wavefunctions, with model parameters fixed by the heavy-light meson spectra. We impose Heavy Quark Symmetry (HQS) at zero recoil and address the apparent paradox of a non-conserved electroweak current dual to a massless bulk vector field. We argue that the non-conservation, arising from explicit flavor-- symmetry breaking by quark masses, does not generate an anomalous dimension. Hence the bulk field remains massless, and the non-conservation is \emph{encoded} in the independent boundary couplings $g_+$ and $g_-$. Our predictions for the branching fractions are in good agreement with LHCb data for $B_s \to D_s$ decays. The lepton-flavor universality ratios $R(D)$ and $R(D_s)$ are consistent with Standard Model and lattice QCD predictions. We find that the holographic models reproduce the universality of the Isgur-Wise function near zero recoil, while discrepancies at maximum recoil suggest that a more complete treatment of higher-order $1/m_Q$ corrections is needed.