Effective valence quark model and a possible dip in $d\, {\rm Br}(B\to K\ell\bar{\ell})/dq^2$

<jats:p> In rare B meson decays B → Kℓ<jats:sup>+</jats:sup>ℓ<jats:sup>-</jats:sup>, a possible contribution of ℓ<jats:sup>+</jats:sup>ℓ<jats:sup>-</jats:sup> emission via photon from the "spectator" quark q(q = u, d) in the B meson [Formula: see text] is investigated in addition to the conventional one [Formula: see text]. If such a contribution is sizable compared with the standard estimation of B → Kℓ<jats:sup>+</jats:sup>ℓ<jats:sup>-</jats:sup>, we will observe visible difference between dΓ(B<jats:sup>0</jats:sup> → K<jats:sup>0</jats:sup>ℓ<jats:sup>+</jats:sup>ℓ<jats:sup>-</jats:sup>)/dq<jats:sup>2</jats:sup> and dΓ(B<jats:sup>+</jats:sup> → K<jats:sup>+</jats:sup>ℓ<jats:sup>+</jats:sup>ℓ<jats:sup>-</jats:sup>)/dq<jats:sup>2</jats:sup> in q<jats:sup>2</jats:sup> dependence [Formula: see text]. Besides, as a result of the interference between the conventional one and a new one, a dip appears in dΓ(B → Kℓ<jats:sup>+</jats:sup>ℓ<jats:sup>-</jats:sup>)/dq<jats:sup>2</jats:sup> at a small region of q<jats:sup>2</jats:sup>. The interference effect in the B<jats:sup>0</jats:sup> decay will also be observed differently from that in the B<jats:sup>+</jats:sup> decay. The calculation is done based on a semiclassical approach, a valence quark model. In the present model, the photon emission from the spectator quark q, d → d+γ(u → u+γ) is independent of the b–s transition mechanism, and the characteristic results are due to a straightforward estimate of the quark propagator which cannot be incorporated into the factorization method. The model is not a valence quark "dominant" model, so that, for example, the valence quarks in the final state carry only 24% of the energy–momentum of the kaon. </jats:p>