Inclusive decay rate for B #-># X_d+#gamma# in next-to-leading logarithmic order and CP asymmetry in the standard model

We compute the decay rate for the Cabibbo-Kobayashi-Maskawa (CKM)-suppressed electro-magnetic penguin decay B#-># anti X_d+#gamma# (and its charge conjugate) in the next-to-leading order in QCD, including leading power corrections in 1/m_b"2 and 1/m_c"2 in the standard model. The average branching ratio left angle B(B#-># X_d + #gamma#) right angle of the decay B #-># X_d + #gamma# and its charge conjugate B#-># anti X_d + #gamma# is estimated to be in the range 6.0 x 10"-"6 #<=# left angle B(B #-># X_d + #gamma#) right angle #<=# 2.6 x 10"-"5, obtained by varying the CKM-Wolfenstein parameters #rho# and #eta# in the range -0.1#<=##rho##<=#0.4 and 0.2#<=##eta##<=#0.46 and taking into account other parametric dependence. In the NLL approximation and in the stated range of the CKM parameters, we find the ratio R(d#gamma#/s#gamma#)#ident to# left angle B(B #-># X_d#gamma#) right angle / left angle B(B #-># X_s#gamma#) to lie in the range 0.017#<=#R(d#gamma#/s#gamma#)#<=#0.074. Theoretical uncertainties in this ratio are estimated and found to be small. Hence, this ratio is well suited to provide independent constraints on the CKM parameters. The CP-asymmetry in the decay rates, defined as a_C_P(B #-># X_d#gamma#) #ident to# (#GAMMA#(B #-># X_d#gamma#) - #GAMMA#(anti B #-># anti X_d#gamma#))/(#GAMMA#(B #-># X_d#gamma#) + #GAMMA#(anti B #-># anti X_d#gamma#)), is found to be in the range (7-35)%. Both the decay rates and CP asymmetry are measurable in forthcoming experiments at B factories and possibly at HERA-B. (orig.)Available from TIB Hannover: RA 2999(97-255) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman