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

Abstract

In rare B meson decays B → Kℓ+ℓ-, a possible contribution of ℓ+ℓ- 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+ℓ-, we will observe visible difference between dΓ(B0 → K0ℓ+ℓ-)/dq2 and dΓ(B+ → K+ℓ+ℓ-)/dq2 in q2 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+ℓ-)/dq2 at a small region of q2. The interference effect in the B0 decay will also be observed differently from that in the B+ 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.