The decay constants of pseudoscalar mesons in a relativistic quark model

Abstract

The decay constants of pseudoscalar mesons are calculated in a relativistic quark model which assumes that mesons are made of a valence quark antiquark pair and of an effective vacuum like component. The results are given in terms of quark masses and of some free parameters entering the expression of the internal wave functions of the mesons. By using the pion and kaon decay constants $F_{{\pi }^{+}}=130.7MeV,F_{K^{+}}=159.8MeV$ to fix the parameters of the model one gets $60MeV\le F_{D^{+}}\le 185MeV,95MeV\le F_{D_s}\le 230MeV,80MeV\le F_{B^{+}}\le 205MeV$ for the light quark masses $m_u=5.1MeV,m_d=9.3MeV,m_s=175MeV$ and the heavy quark masses in the range: $1.GeV\le m_c\le 1.6GeV,4.1GeV\le m_b\le 4.5GeV$. In the case of light neutral mesons one obtains with the same set of parameters $F_{{\pi }^0}\approx 138MeV,F_{\eta }\approx 130MeV,F_{{\eta }^{\prime }}\approx 78MeV$. The values are in agreement with the experimental data and other theoretical results.

Comments: 11 pages, LaTex