Radiative B-decay as a test of CKM unitarity

We point out that R ≡ Br(b → dγ)/Br(b → sγ) is a sensitive probe of possible violation of CKM unitarity. We compute R in a minimal extension of the Standard Model containing an additional isosinglet charge (−1/3) quark, which leads to a deviation from CKM unitarity. CERN-TH. 7294/94 June 1994 ♥) [email protected] ♣) [email protected] ♦) [email protected] *) On leave of absence from: Departamento de Fisica and CFIF/UTL, Instituto Superior Técnico, Avenida Rovisco Pais, 1096 Lisboa Cedex, Portugal. The study of radiative B-decays provides an important test of the Standard Model (SM) and is indeed a sensitive probe of physics beyond the SM. The recent discovery, by the CLEO collaboration, [1] of the decay B → Kγ with a branching ratio Br(B → Kγ) = (4.5 ± 1.5 ± 0.9) × 10 provides further motivation for this study. Within the framework of the SM, the rare decays b → dγ and b → sγ provide independent measurements of the Cabibbo-Kobayashi-Maskawa (CKM) elements Vtd and Vts, respectively, which can be tested against the ones measured from Bd-B̄d and Bs-B̄s mixings [2]. In this note we will point out that the decay amplitudes b → qγ (q = d, s) have a crucial dependence on the unitarity of the (3× 3) CKM matrix. Thus the magnitude of such rare decays provides an excellent testing ground for new physics leading to the violation of the CKM unitarity. For definiteness, we will analyse the above radiative decays in the framework of a minimal extension of the SM where a charge (−1/3) SU(2) singlet quark is introduced. Although we treat this extension beyond the SM from a phenomenological viewpoint, there are theoretically appealing motivations behind its consideration, including E6 grand-unified theories and some superstring-inspired models [3]. Furthermore, isosinglet quarks provide a simple solution [4] to the strong CP problem [5]. We will show that the branching fraction b → dγ can change significantly due to lack of GIM cancellation resulting from unitarity violation in the new CKM matrix. However, the branching fraction b → sγ is not affected to any level of significance. Therefore, the most important impact of the violation of CKM unitarity would be a change in the ratio R ≡ Br(b → dγ)/Br(b → sγ) which, in the SM, provides a reliable measure of |Vtd/Vts|. Before describing the model in some detail, let us first recall the general structure of the radiative b-decay and fix our notation. To the leading order, the quark-level branching ratio b → qγ (q = d, s) is given in units of the semileptonic b-decay branching ratio, as Br(b → qγ) Br(b → ceν) = 6α πρλ ∣∣∣∣ VtbV ∗ tq Vcb ∣∣∣∣ 2 [ ηAγ + 8 3 (η − η)Ag + C ]2 , (1) where η ≡ αS(MZ)/αS(mb) = 0.548, ρ = (1−8r2+8r6−r8−24r4lnr) with r = mc/mb, λ = 1 − 1.61 αS(mb)/π, and C(= −0.1766) is a term emanating from a complete calculation of the leading-logarithmic QCD corrections [6]; V is the standard CKM matrix. It may be noted that the mb 5 dependence in the partial decay widths of the b quark cancels out in eq. (1). An O(mq/mb) part in the branching ratio has been neglected. We use Br(b → ceν) = 0.107. Aγ and Ag are the coefficients of the effective operators for the magnetic and chromomagnetic moment couplings for b → q