Heavy- to light-meson transition form factors

Semileptonic heav$\overrightarrow{\mathrm{y}}$heavy and heav$\overrightarrow{\mathrm{y}}$light meson transitions are studied as a phenomenological application of a heavy-quark limit of Dyson-Schwinger equations. Employing two parameters, $E$, the difference between the mass of the heavy meson and the effective mass of the heavy quark, and $\Lambda$, the width of the heavy-meson Bethe-Salpeter amplitude, we calculate $f_{+}\mathrm{}\left(t\right)\mathrm{}$ for all decays on their entire kinematically accessible $t$ domain. Our study favors $f_B$ in the range $0.135$–$0.17$ GeV and with $E=0.44\mathrm{}$ GeV and $1/\Lambda =0.14\mathrm{}$ fm we obtain $f_{+}^{B\pi }\mathrm{}\left(0\right)=0.46\mathrm{}$. As a result of neglecting ${1/m}_c$ corrections, we estimate that our calculated values of ${\rho }^2=0.87\mathrm{}$ and $f_{+}^{\mathrm{DK}}\mathrm{}\left(0\right)=0.62\mathrm{}$ are too low by approximately 15%. However, the bulk of these corrections should cancel in our calculated values of Br$\left(\overrightarrow{D}\pi \mathcal{l}\nu \right)/\mathrm{Br}\left(\overrightarrow{D}K\mathcal{l}\nu \right)=0.13\mathrm{}$ and $f_{+}^{D\pi }{\mathrm{}\left(0\right)/f}_{+}^{\mathrm{DK}}\mathrm{}\left(0\right)=1.16\mathrm{}$.