The $a_1$ factorisation coefficient in ${\overline{B}}^0\to D^{(\ast )+}{M}^{-}$ and ${\overline{B}}^0\to D^{(\ast )+}{D}_s^{(\ast )-}$ decays: measurements versus theory

Abstract

Using recent measurements of exclusive B-meson decays we extract the $a_1$ factorization parameter in ${\overline{B}}_d^0\to D^{(\ast {)}^{+}}{K}^{-}/{\pi }^{-}$ decay channels. { The values obtained in the four channels are very similar, in agreement with the theoretical expectations obtained in the $m_Q\to \infty$ limit, but the measured values differ definitely from the expected central values. } Such differences have already been observed. Using recent data, we improve the accuracy by {a factor close to two} in this comparison. We study possible interpretations for such a difference and conclude that the claimed accuracy of corrections due to soft gluon contributions and finite mass effects has to be revisited before arguing for possible "New-Physics" effects. We observe that the corrections to the $m_Q\to \infty$ limit are larger in the spectator topology than effects from exchange amplitude contributions. We discuss also the way expected ratios of $a_1$ values, involving hypotheses from theory, are used to obtain the fraction of $B_s^0$ meson production in jets at LHC and conclude that the uncertainties attached to this approach are not well established. Finally, the $a_1$ values extracted from ${\overline{B}}_d^0\to D^{(\ast )+}{D}_s^{-}$ decays are found to be similar, within uncertainties, to the ones obtained with $K^{-}$ emission, once expected penguin contributions are corrected. Using the same approach, we note that $a_1$ values measured in channels with a $D_s^{\ast -}$ emission are about two standard deviations lower than $a_1(D^{(\ast )+}{K}^{-}$).

Comments: 40 pages