Effective Hamiltonian forB→Xse+

Abstract

We calculate the next-to-leading QCD corrections to the effective Hamiltonian for B → X s e + e − in the NDR and HV schemes. We give for the first time analytic expressions for the Wilson Coefficient of the operator Q 9 = (sb) V −A (ēe) V in the NDR and HV schemes. Calculating the relevant matrix elements of local operators in the spectator model we demonstrate the scheme independence of the resulting short distance contribution to the physical amplitude. Keeping consistently only leading and next-to-leading terms, we find an analytic formula for the differential dilepton invariant mass distribution in the spectator model. Numerical analysis of the m t , Λ MS and µ ≈ O(m b ) dependences of this formula is presented. We compare our results with those given in the literature. * Supported by the German Bundesministerium für Forschung und Technologie under contract 06 TM 743 and the CEC Science project SC1-CT91-0729.

A model independent determination of |Vub|

“…Of these, i) and ii) are expected to be small unless q 2 is very close to m 2 B . The effects of iii) have also been estimated to be at the few percent level [20], although these uncertainties are very hard to quantify and could be comparable to the ±8% scale dependence [29] of theB → X s + − rate. Integrating over a large enough range of q 2 , q 2 0 < q 2 < m 2 B with m 2 ψ(2S) < q 2 0 < ∼ 17 GeV 2 , the result implied by Eq.…”

Large hadronic power corrections or new physics in the rare decay B → K ∗ μ + μ −?

“…The one-loop contributions of the four-quark operators can be described through the matrix element of O 9 and hence are usually taken into account in the form of corrections to C 9 via the effective Wilson coefficient C eff 9 (= C 9 + Y (q 2 )) [38][39][40]. There are other contributions from H had eff such as weak annihilation and soft gluon exchange [41] which are more complicated to estimate and cannot be factorised into form factors and leptonic currents.…”

The effects of the fourth generation on the double-lepton polarization in theB→Kℓ+ℓ−decay

“…(1). The explicit forms of the C new i can be obtained from the corresponding expression of the Wilson coefficients in the SM by substituting m t → m t ′ (see [37,38]). If theŝ quark mass is neglected, the above effective Hamiltonian leads to the following matrix element for the b → sℓ + ℓ − decay…”