On the chromomagnetic expectation value μ_G² and higher power corrections in heavy flavor mesons

The important parameter \mu_G^2 of the heavy quark expansion is analyzed including perturbative and power corrections. It is found that \mu_G^2(2GeV) is known with a few percent accuracy. The perturbative corrections are computed and found small. A nonperturbative relation is suggested which allows to control the power corrections. We conclude that \mu_G^2(1GeV)=(0.35+0.03- 0.02)GeV^2. The two-loop expression for the effective `ME' radiation coupling alpha_s^(me)(\omega) is given which improves reliability of the perturbative evolution of \mu_G^2 towards the low momentum scale. On the nonperturbative side, we advocate the utility of combining the heavy quark expansion with expanding around the `BPS'-type approximation for the meson wavefunction, which implies relations \mu_\pi^2 \approx \mu_G^2 and -\rho_{LS}^3 \approx \rho_D^3 as well as similar ones for the nonlocal correlators.