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.

11 pages, 5 figures with minor corrections

References in corpus (3)

• Consistent Analysis of the $B\to \pi$ Transition Form Factor in the Whole Physical Region
• B-Meson Wavefunction in the Wandzura-Wilczek Approximation
• Transverse Momentum Dependent Light-Cone Wave Function of B-Meson and Relation to the Momentum Integrated One

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