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

High Energy Physics - Phenomenology 2015-09-23 v3

Abstract

For a long time there have been active discussions about the sizable differences between Vubincl|V_{ub}|_{\rm incl} \& Vubexcl|V_{ub}|_{\rm excl}. However, the real Vubincl|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 KˉK\bar KK mesons plus pions: [R(Blν  πs)+R(Blν  (KKˉ+πs))]\left[ R (B \to l \nu \; \pi ' s) + R (B \to l \nu \; (K\bar K +\pi 's )) \right] \simeq R([bqˉ]lνu(qˉiqi+qˉjqjqˉkqk...)qˉ)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 qˉ=uˉ,dˉ\bar q=\bar u, \bar d \& qi=u,d,sq_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+l+νK+KB^+ \to l^+ \nu K^+K^- \& B0l+νK+Kπ+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 ΔS=0\Delta S=0. Future data for exclusive BlνππB \to l \nu \pi \pi might also narrow the gap between Vubincl|V_{ub}|_{\rm incl} \& Vubexcl|V_{ub}|_{\rm excl} in the opposite direction. I comment about Bs0l+νXu(s)(ΔS=1)B_s^0 \to l^+ \nu X_u^{(s)}(\Delta S = -1).

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Cite

@article{arxiv.1507.01842,
  title  = {Is There a Real Difference between $|V_{qb}|_{\rm excl}$ vs. $|V_{qb}|_{\rm incl}$ from Semi-leptonic $B$ Decays?},
  author = {Ikaros I. Bigi},
  journal= {arXiv preprint arXiv:1507.01842},
  year   = {2015}
}

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11 pages