- Published 1997

We calculate the decay rate Γ(B → Xsγγ) via intermediate psuedoscalar charmonium ηc. This process is thought to be the main long-distance contribution which dominates the corresponding inclusive rare B decay. We point out that once the momentum dependence of ηc → γγ conversion strength, due to off-shellness of the intermediate ηc, is taken into account, the rate of this decay mode is reduced. The change in differential decay rate in region of spectrum immediately below mηc is more significant. On the other hand, we point out that the unexpectedly large branching ratio for B → Xsη which is recently observed by CLEO could indicate a potentially larger long-distance contribution via η resonance. Email: ahmady@riken.go.jp Email: kou@fs.cc.ocha.ac.jp Email:sugamoto@phys.ocha.ac.jp 1 The rare decays of B meson are quite interesting since, among other reasons, their measurement could point to some clues on physics beyond Standard Model. For this purpose, however, it is essential to isolate the short-distance(SD) contributions from the longdistance(LD) background as only the former is sensitive to virtual exotic particles from ”new physics”. For example, the rare dileptonic B decay B → Xsll(l = μ, e) in which the total decay rate is dominated by the LD resonance contribution from intermediate ψ and ψ vector mesons, much theoretical attentions have been focused on searching for observables and regions of various decay distributions where one can probe SD physics without significant LD interference [1,2]. Therefore, for the purpose of extracting reliable conclusions on parameters of Standard Model and beyond from rare B decays, careful consideration of LD effects is of utmost importance. In this paper, we examine the pure LD contribution to B → Xsγγ via intermediate psuedoscalar ηc. This is expected to be the main process dominating the corresponding flavor changing neutral current (FCNC) decay channel [3]. However, we show that a careful consideration of the off-shellness of the intermediate ηc could reduce the contribution of this LD mode. In fact, a model calculation of ηc-photon-photon coupling reveals a drastic suppression of this vertex form factor f(q) when q, the invariant mass of the two photons, is small as compared to when q ≈ m2ηc . Indeed, similar suppression of ψ-γ conversion strength on photon mass shell as compared to when ψ is on its mass-shell was shown to be responsible for significant reduction of resonance to non-resonance interference in dileptonic rare decays B → Xsll [2]. Inclusion of this form factor for ηc → γγ in the evaluation of B → Xsγγ via ηc is our main point in this paper. We also comment on the possibility that the recent CLEO measurement of a large B → Xsη decay rate could indicate a potentially larger LD contribution to B → Xsγγ via η. We start by writing the effective Hamiltonian for LD B → Xsγγ via ηc which is approximated by quark level decay b → sηc → sγγ. The ηc → γγ transition is modeled by a triangle quark loop (Fig. 1) where the coupling of the psuedoscalar meson ηc to charm quarks is taken to be a constant: 2 T (ηc → γγ) = Nf(q)ǫp1αp2β , (1) where p1 and p2 are the four-momenta of the photons and q = p1 + p2. The form factor f(q) is obtained from the quark loop calculation: f(q) = ∫ 1 0 dx ∫ 1−x 0 dy 1 mc − q2xy

@inproceedings{Ahmady1997347V,
title={34 7 v 1 1 4 A ug 1 99 7 RIKEN - AF - NP - 265 Intermediate psuedoscalar resonance contributions to B → X s γγ},
author={Mohammad R. Ahmady and Akio Sugamoto},
year={1997}
}