A theoretical reappraisal of branching ratios and CP asymmetries in the decays $B \to (X_d,X_s) \ell^+ \ell^-$ and determination of the CKM parameters

A. Ali; G. Hiller

doi:doi:10.1007/s100520050497

2021 Impact factor 4.991

Particles and Fields

Eur. Phys. J. C 8, 619-629
DOI 10.1007/s100529901111

A theoretical reappraisal of branching ratios and CP asymmetries in the decays $B \to (X_d,X_s) \ell^+ \ell^-$ and determination of the CKM parameters

A. Ali¹ - G. Hiller²

¹ Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
² INFN, Laboratori Nazionali di Frascati, I-00044 Frascati, Italy

Received: 30 December 1998 / Published online: 27 April 1999

Abstract
We present a theoretical reappraisal of the branching ratios and CP asymmetries for the decays $B \to X_q \ell^+ \ell^-$ , with q=d,s, taking into account current theoretical uncertainties in the description of the inclusive decay amplitudes from the long-distance contributions, an improved treatment of the renormalization scale dependence, and other parametric dependencies. Concentrating on the partial branching ratios $\Delta {\cal B}(B \to X_q \ell^+ \ell^-)$ , integrated over the invariant dilepton mass region $1~\mbox{GeV}^2 \leq s \leq 6~\mbox{GeV}^2$ , we calculate theoretical precision on the charge-conjugate averaged partial branching ratios $\langle \Delta{\cal B}_q \rangle= (\Delta {\cal B}(B \to X_q \ell^+ \ell^-) + \Delta {\cal B}(\bar{B} \to \bar{X}_q \ell^+ \ell^-))/2$ ,CP asymmetries in partial decay rates $(a_{CP})_q=(\Delta {\cal B}(B \to X_q \ell^+ \ell^-) - \Delta {\cal B}(\bar{B} \to \bar{X}_q \ell^+ \ell^-))/(2 \langle \Delta{\cal B}_q \rangle)$ , and the ratio of the branching ratios $\Delta {\cal R} = \langle \Delta{\cal B}_d \rangle/\langle \Delta{\cal B}_s \rangle$ . For the central values of the CKM parameters, we find $\langle \Delta {\cal B}_s \rangle =(2.22^{+0.29}_{-0.30}) \times 10^{-6}$ , $\langle \Delta {\cal B}_d \rangle =(9.61^{+1.32}_{-1.47}) \times 10^{-8}$ , $(a_{CP})_s =-(0.19^{+0.17}_{-0.19})\%$ , $(a_{CP})_d =(4.40^{+3.87}_{-4.46})\%$ , and $\Delta {\cal R} =(4.32 \pm 0.03)\%$ .The dependence of $\langle \Delta{\cal B}_d \rangle$ and $\Delta {\cal R}$ on the CKM parameters is worked out and the resulting constraints on the unitarity triangle from an eventual measurement of $\Delta {\cal R}$ are illustrated.