Virtual and bremsstrahlung corrections to b→dl+l- in the standard model -: art. no. 074007

We present the calculation of the virtual and bremsstrahlung corrections of O(alpha(s)) to the matrix elements <dl(+)l(-)\O-i\b>. This is the missing piece in the full next-to-next-to-leading logarithmic (NNLL) results for various observables associated with the process B-->X(d)l(+)l(-), such as the branching ratio, the CP-rate asymmetry, and the forward-backward asymmetry. This paper is an extension of analogous calculations done by some of us for the process B-->X(s)l(+)l(-). As the contributions of the diagrams induced by the four-quark operators O-1(u) and O-2(u) with a u quark running in the quark loop are strongly Cabibbo-Kobayashi-Maskawa suppressed, they were omitted in the analysis of B-->X(s)l(+)l(-). This is no longer possible for B-->X(d)l(+)l(-), as the corresponding contributions are not suppressed. The main new work therefore consists of calculating the O(alpha(s)) corrections to <dl(+)l(-)\O-1,2(u)\b>. In this paper we restrict ourselves to the range 0.05less than or equal tos/m(b)(2)less than or equal to0.25 (s is the invariant mass of the lepton pair), which lies above the rho and omega resonances and below the J/psi resonance. We present the analytic results for the mentioned observables related to the process B-->X(d)l(+)l(-) as expansions in the small parameters s=s/m(b)(2), z=m(c)(2)/m(b)(2), and s/(4m(c)(2)). In the phenomenological analysis at the end of the paper we discuss the impact of the NNLL corrections on the observables mentioned above.