Decay constants of the heavy-light mesons from the field correlator method

Abstract

Meson Green's functions and decay constants ${f}_{\ensuremath{\Gamma}}$ in different channels $\ensuremath{\Gamma}$ are calculated using the field correlator method. Both, spectrum and ${f}_{\ensuremath{\Gamma}}$, appear to be expressed only through universal constants: the string tension $\ensuremath{\sigma}$, ${\ensuremath{\alpha}}_{s}$, and the pole quark masses. For the $S$-wave states the calculated masses agree with the experimental numbers within $\ifmmode\pm\else\textpm\fi{}5\text{ }\text{ }\mathrm{MeV}$. For the $D$ and ${D}_{s}$ mesons the values of ${f}_{\mathrm{P}}(1S)$ are equal to 210(10) and $260(10)\text{ }\text{ }\mathrm{MeV}$, respectively, and their ratio ${f}_{{D}_{s}}/{f}_{D}=1.24(3)$, agrees with a recent CLEO experiment. The values ${f}_{\mathrm{P}}(1S)=182$, 216, 438 MeV are obtained for the $B$, ${B}_{s}$, and ${B}_{c}$ mesons with the ratio ${f}_{{B}_{s}}/{f}_{B}=1.19(2)$ and ${f}_{D}/{f}_{B}=1.14(2)$. The decay constants ${f}_{\mathrm{P}}(2S)$ for the first radial excitations as well as the decay constants ${f}_{\mathrm{V}}(1S)$ in the vector channel are also calculated. The difference of about 20% between ${f}_{{D}_{s}}$ and ${f}_{D}$, ${f}_{{B}_{s}}$ and ${f}_{B}$ directly follows from our analytical formulas.