8 v 2 1 2 N ov 1 99 9 BIHEP - Th / 98 - 9 A New Estimate of B → ( ρ , ω ) + γ In The Light - Cone QCD Sum Rule

We propose a new estimate of the process B → (ρ, ω) + γ by using the light-cone QCD sum rule. The aim is to choose the chiral quark current operators in order to eliminate the uncertainty arising from the chiral-even operators in the correlator. In the case of neglecting the corrections from ρ-meson mass, the sum rules for form factors are obtained, which are valid to the twist-three accuracy. The resulting branching ratios are consistent with the experimental data. Email: [email protected], [email protected], [email protected] Mailing address The rare decays of B mesons have been studied for years for a precise understanding of the physics of CP-Violation related to the structure of the CKM mixing matrix elements and testing of standard model to search for new physics. At present, only upper bounds on the exclusive modes B → (ρ, ω) + γ are available from CLEO∐, namely Br(B → ργ) ≤ 3.9×10−5, Br(B → ωγ) ≤ 1.3×10−5, and Br(B → ργ) ≤ 1.1×10−5 in Ref.[1]. The rare decay modes B → (ρ, ω) + γ are very suitable for study with the light-cone QCD sum rule method, which is developed in Ref.[2,3] recently, and have been investigated in Refs.[4,5]. The points of the light-cone QCD sum rule are combining the traditional QCD sum rule method with the hadronic wavefunction descriptions of the hard exclusive process. However, instead of the small distance x ≃ 0 in the traditional QCD sum rule method, the operator product expansion (OPE) in the light-cone sum rule is carried out in terms of nonlocal operators near the light cone x ≃ 0; and instead of the vacuum condensate, the nonperturbative dynamics is parametrized as so-called light-cone wavefunctions classified by their twist. Using the lightcone QCD sum rule, the authors in Ref.[4] found the form factor F(0) = 0.285 ± 15% with the b-quark pole mass mb = 4.8GeV and a threshold s0 = 33.5 ± 0.5GeV . However, g ⊥ and g a ⊥, the nonleading twist distribution wavefunctions of ρ meson used in Ref.[4,5], are not known well with a drastic effect on the resulting precision. In addition, there are the uncertainties in the b-quark pole mass and condensate parameters, which is an important input parameter in the light-cone sum rule for the form factor F(0). Therefore, a further precision investigation of this rare process is valuable and necessary. Ref.[6] has made a new estimate of the process B → Kγ by choosing the chiral current operators in the correlator. Similarly, through the choices of the chiral current operators in the correlation function, the uncertain nonperturbative quantities can be eliminated effectively from the respective sum rules for the form factor F(0) and decay constant fB, and thus a more precise prediction for the rare process can be made. Following the procedure in Ref.[6], we calculate the rare decay B → ργ which is induced by the effective Hamiltonian Heff = −4GF √ 2 ξt 8