A novel method of reconstructing semileptonic $B$ decays

Semileptonic decays of charged and neutral $B$ mesons play a critical role in the determination of the magnitudes of the CKM-matrix elements $V_{cb}$ and $V_{ub}$, and in the test of the lepton universality which is a basic assumption of the Standard Model. Due to the missing neutrino in the semileptonic decays, the measurements depend strongly on the tag efficiency of the $B$ meson in the recoil side which is at a few per mille to a few per cent level, and this values a limiting factor for high precision measurement and high sensitivity test mentioned above. We develop a novel method of reconstructing semileptonic decays of the $B$ mesons by introducing the $B$ momentum information calculated from the $B$ decay vertex and the interaction point, as well as the kinematic information of $e^{+}e^{-}\to B\overline{B}$ at the $B$-factories such as BaBar, Belle, and Belle II. As this method does not depend on the reconstruction of the $B$ meson in the recoil side, the gain in the efficiency could be as large as two orders of magnitudes. This makes high precision measurement of CKM-matrix elements $|V_{cb}|$ and $|V_{ub}|$ and high precision test of lepton universality at $B$-factories more promising. We present the algorithms for the semileptonic decays of neutral and charged $B$ mesons separately, as they are affected by the magnetic field in the detector differently.