v 3 3 1 M ay 1 99 4 OITS - 538 Hadronic Penguin B Decays In The Standard And The Two - Higgs - Doublet Models ∗

We study in next-to-leading order QCD hadronic penguin B decays in the Standard and two-Higgs-doublet models. Although the gluonic penguin dominates, we find the electroweak contribution non-negligible. In the Standard Model, the branching ratio for B → Xsφ is predicted to be in the range (0.6 ∼ 2) × 10−4. The ranges of branching ratios for B → Kφ, B → Kφ, and Bs → φφ are (0.4 ∼ 2)× 10−5, (0.2 ∼ 1)× 10−5, and (0.15 ∼ 0.5)× 10−5, respectively. The contribution from the charged Higgs boson in two Higgs doublet models depend on cotβ, and can be as large as 40%. Typeset using REVTEX Work supported in part by the Department of Energy Grant No. DE-FG06-85ER40224. 1 Rare B decays, particularly pure penguin decays, have been subject of considerable theoretical and experimental interest recently [1]. The photonic penguin induced process B → Kγ has been observed by CLEO collaboration [2] and is consistent with the Standard Model (SM) prediction [3]. The gluonic penguin induced B decays are expected to be observed very soon. A large number of gluonic penguin induced B decay channels were studied in Ref. [4] using ∆B = 1 effective Hamiltonian H∆B=1 in the lowest nonvanishing order. In Ref. [5] the next-to-leading order QCD corrected pure gluonic penguin H∆B=1 was used with top quark mass mt fixed at 150 GeV. In this paper we study the next-to-leading order QCD corrected Hamiltonian H∆B=1 in the SM and in two Higgs doublet models, taking particular care to include the full electroweak contributions and find the dependence on mt and αs. Using this Hamiltonian we study the cleanest signature of hadronic penguin processes: B → Xsφ, B → Kφ(Kφ), and Bs → φφ. The process B → Xsφ is particularly recommended because it is free from form factor uncertainties. We find not only that the QCD correction in next-to-leading order are large, but also inclusion of the full electroweak contributions have significant effect on the branching ratio which could reduce the pure gluonic penguin contribution by 30% at the upper range of allowed top quark mass. Our results which have been derived independently, agree with Ref. [6] where only the SM is considered. ∆B = 1 gluonic penguin Hamiltonian The QCD corrected H∆B=1 relevant to us can be written as follows [7]: H∆B=1 = GF √ 2 [VubV ∗ us(c1O u 1 + c2O u 2 ) + VcbV ∗ cs(c1O c 1 + c2O c 2)− VtbV ∗ ts ∑ ciOi] +H.C. , (1) where the Wilson coefficients (WCs) ci are defined at the scale of μ ≈ mb; and Oi are defined as O 1 = s̄αγμ(1− γ5)bβ q̄βγ(1− γ5)qα , O 2 = s̄γμ(1− γ5)bq̄γ(1− γ5)q , O3 = s̄γμ(1− γ5)b ∑ q q̄γμ(1− γ5)q′ , Q4 = s̄αγμ(1− γ5)bβ ∑ q q̄′ βγμ(1− γ5)q′ α , O5 = s̄γμ(1− γ5)b ∑ q q̄γ(1 + γ5)q ′ , Q6 = s̄αγμ(1− γ5)bβ ∑ q q̄′ βγμ(1 + γ5)q ′ α , (2)