The σ and ρ coupling constants for charmed and bottom mesons from bootstrap method

초록

In this talk, we evaluate the sigma and rho coupling constants for the D(D*) and B(B*) mesons. We first calculate DDbar(D* D*bar)-> pipi amplitudes in the pseudophysical region. Combining the pipi transition amplitudes with the DDbar (D* D*bar) -> pipi amplitudes by using the Blankenbecler-Sugar equation, we construct the correlated amplitudes based on a meson-exchange model. The S- and P-channel spectral functions are derived from the two-body unitarity of S-matrix. We obtain the DD (D*D*) partial amplitudes from the dispersion integral along the unitarity cut (4 m_pi^2 \le t \le 50 m_pi^2)) which corresponds to the DDbar (D* D*bar) -> pipi reaction. Employing the zero-width approximation, we provide the sigma and rho coupling constants for DD(D* D*) as the function of the physical t. As for the sigma couplings, we examine the dependence of the sigma coupling on the mass of the sigma meson. We also compute the BB and B* B* coupling constants in a similar way. Finally, we discuss our results compared with those of other models.