B meson wave function from the $B\to\gamma l\nu$ decay

Abstract

We show that the leading-power $B$ meson wave function can be extracted reliably from the photon energy spectrum of the $B\to\gamma l\nu$ decay up to $O(1/m_b^2)$ and $O(\alpha_s^2)$ uncertainty, $m_b$ being the $b$ quark mass and $\alpha_s$ the strong coupling constant. The $O(1/m_b)$ corrections from heavy-quark expansion can be absorbed into a redefined leading-power $B$ meson wave function. The two-parton $O(1/m_b)$ corrections cancel exactly, and the three-parton $B$ meson wave functions turn out to contribute at $O(1/m_b^2)$. The constructive long-distance contribution through the $B\to V\to\gamma$ transition, $V$ being a vector meson, almost cancels the destructive $O(\alpha_s)$ radiative correction. Using models of the leading-power $B$ meson wave function available in the literature, we obtain the photon energy spectrum in the perturbative QCD framework, which is then compared with those from other approaches.