Decay constants, mass formulas, and mixings with radially excited states of the light and heavy ground-state pseudoscalar mesons

In the absence of mixings with radially excited states and/or no exotic states, asymptotic flavor symmetry predicts, for the ground-state pseudoscalar mesons, f/sub K/ = f/sub π/, f/sub +//sup K//sup π/(0) = 1, and m/sub F/2-m/sub D/2 = m/sub K/2-m/sub π/2, etc. In this paper, we assume that the observed small deviations from these predictions originate mainly from the mixing between the ground states and the first radially excited states. Then, new sum rules f/sub +//sup a//sup b/(0) = cos(θ/sub a/-θ/sub b/) and f/sub b//f/sub a/ = cos(θ/sub b/-phi)/cos(θ/sub a/-phi) are derived, where θ/sub a/ (a = π,K,D,F,. . . ) is the mixing angle between the ground-state meson a and its radially excited counterpart a' and phi is a flavor-independent constant with chemical bondphichemical bond≤π/4. The experimentally indicated and theoretically plausible value f/sub +//sup K//sup π/(0)≅0.973 leads to θ/sub K/-θ/sub π/≅130 (for convenience, θ/sub K/>θ/sub π/ is assumed) and f/sub K//f/sub π/≅1.163 to θ/sub π/-phi≅-400. This value of θ/sub π/-phi imposes an interesting restriction on the decay constant f/sub P/, f/sub P//f/sub π/approx. <1.4, for any pseudoscalar meson P (P = π,K,D,F,. . . )