QCD Corrections to Inclusive B Going to S Processes in the Standard Model.

The quark-level decays b to sgamma and b to se^+e^- are loop-induced processes in the Standard Model. They are therefore potentially sensitive to the presence of the (as yet unobserved) top quark, as well as to many kinds of "new physics" beyond the Standard Model. At lowest order in the electroweak interaction, the inclusive branching ratios are predicted to be in the ranges BR(b to sgamma) ~ (2 to 10) times 10^{-5} and BR(b to se^+e^ -) ~ (2 to 8) times 10^{-6} for m_{rm t} in the range 60 to 180 GeV. Present (conservative) experimental upper bounds are BR(b to s gamma) < 2 times 10^{-3} and BR(b to se^+e ^-) < 1 times 10^{-3}. Because these are GIM-suppressed processes, the effect of short-distance strong-interaction (QCD) corrections can be large. In this thesis, a calculation of these leading -logarithmic corrections is presented. In particular, three issues of theoretical interest are considered in detail. First, several authors in the past have applied the equations of motion to certain effective operators at an early stage, in order to reduce the size of the operator basis. We examine the validity of this procedure, and demonstrate that the equations of motion are indeed commutative with renormalization group scaling. Second, other authors have ignored certain contributions to the process b to sgamma which arise from the process b to sg (where g means gluon) via operator mixing. We perform a full computation including all such effects, and find that they are indeed negligible. As a corollary, we find that the process b to sg is strongly suppressed by QCD. Third, the use of naive dimensional regularization may be unjustified in applications of this type, due to the presence of spin-helicity projection operators. A variant of this technique, called dimensional reduction, has been proposed as an alternative. We calculate the QCD corrections using both techniques, and find that the results differ. A four-dimensional method is discovered by which the discrepancy is resolved in favour of dimensional regularization. The inclusive branching ratio for b to sgamma is strongly enhanced by QCD, to BR(b to sgamma ) ~ (2 to 4) times 10^{-4}, while that for b to se^+ e^- is only slightly enhanced, to BR(b to se^+e ^-) ~ (3 to 9) times 10^ {-6}, for m_{rm t} in the range 60 to 180 GeV.