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

Abstract

Meson Green's functions and decay constants $f_{\Gamma }$ in different channels $\Gamma$ are calculated using the Field Correlator Method. Both, spectrum and $f_{\Gamma }$, appear to be expressed only through universal constants: the string tension $\sigma$, ${\alpha }_s$, and the pole quark masses. For the $S$-wave states the calculated masses agree with the experimental numbers within $\pm 5$ MeV. For the $D$ and $D_s$ mesons the values of $f_{\mathrm{P}}(1S)$ are equal to 210(10) and 260(10) MeV, respectively, and their ratio $f_{D_s}/f_D$=1.24(3) agrees with 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.

Comments: 37 pages, 10 tables, RevTeX4