Pseudoscalar decay constants in the relativized quark model and measuring the CKM matrix elements

Abstract

We have calculated the pseudoscalar decay constants using the relativized quark model. We find $f_D\simeq 240\pm 20$ MeV, ${f_D}_s\simeq 290\pm 20$ MeV, $f_B\simeq 155\pm 15$ MeV, ${f_B}_s\simeq 210\pm 20$ MeV, and ${f_B}_c\simeq 410\pm 40$ MeV where the "errors" are our estimates of the reliability of the results. We used these values to study the Cabibbo-Kobayashi-Maskawa matrix elements. In particular, we combined our theoretical estimate of $f_B$ with the ARGUS/CLEO result for $B^0-{\overline{B}}^0$ mixing to study the relation between $\left|V_{\mathrm{td}}\right|$ and the $t$-quark mass. Recent measurements of $\left|V_{\mathrm{bc}}\right|$ and $\left|V_{\mathrm{bu}}\right|$ constrain $m_t\gtrsim 70$ GeV.