Is There a Real Difference between $|V_{qb}|_{\rm excl}$ vs. $|V_{qb}|_{\rm incl}$ from Semi-leptonic $B$ Decays?

TL;DR

This paper investigates the differences between inclusive and exclusive measurements of |V_{ub}| from semi-leptonic B decays, emphasizing the role of hadronic final states and potential duality violations near thresholds, with implications for future experiments.

Contribution

It highlights the importance of hadronic final states and resonance effects in understanding discrepancies between inclusive and exclusive |V_{ub}| determinations, proposing new experimental avenues.

Findings

Inclusive measurements may be smaller than previously thought.

Resonance effects near 1-2 GeV could affect |V_{ub}| extraction.

Future data from LHCb and Belle II could clarify the |V_{ub}| gap.

Abstract

For a long time there have been active discussions about the sizable differences between $|V_{ub}|_{\rm incl}$ \& $|V_{ub}|_{\rm excl}$. However, the real $|V_{ub}|_{\rm incl}$ might be smaller than usually stated. The connection of the worlds of hadrons and quarks (\& gluons) is subtle: we cannot ignore final states with a pair of $\bar KK$ mesons plus pions: $\left[ R (B \to l \nu \; \pi ' s) + R (B \to l \nu \; (K\bar K +\pi 's )) \right]$ $\simeq$ $R ([b\bar q] \to l \nu \, u (\bar q_i q_i + \bar q_jq_j\bar q_k q_k...) \bar q )$ with $\bar q=\bar u, \bar d$ \& $q_i = u,d,s$. It might show the limits or violations of duality close to thresholds. While inclusive FS cannot be measured, exclusive ones can be done soon by LHCb and later also by Belle II about $B^+ \to l^+ \nu K^+K^-$ \& $B^0 \to l^+ \nu K^+K^-\pi^+$. Present data have not given us the information about resonances in the region of 1 - 2 GeV that we need to understand the underlying dynamics in $\Delta S=0$. Future data for exclusive $B \to l \nu \pi \pi$ might also narrow the gap between $|V_{ub}|_{\rm incl}$ \& $|V_{ub}|_{\rm excl}$ in the opposite direction. I comment about $B_s^0 \to l^+ \nu X_u^{(s)}(\Delta S = -1)$.