The effects of the soft gluon emission in hard scattering processes at the phase boundary are resummed in the soft-collinear effective theory (SCET). In SCET, the soft gluon emission is decoupled from the energetic collinear part, and is obtained by the vacuum expectation value of the soft Wilson-line operator. The form of the soft Wilson lines is universal in deep inelastic scattering, in the Drell-Yan process, in the jet production from e + e − collisions, and in the γ * γ * → π 0 process, but its analytic structure is slightly different in each process. The anomalous dimensions of the soft Wilson-line operators for these processes are computed along the light-like path at leading order in SCET and to first order in α s , and the renormalization group behavior of the soft Wilson lines is discussed.Here the integration path C is determined by the kinematics of the processes, T orders gauge fields A a µ (z) in time, and P orders the generators T a of the SU(N) gauge group along the path C. The difference between W (C) and W T (C) is that the gluon fields in W (C) are ordered along the path C, but not according to time. Therefore on different parts of the path C, the gluon fields are time or anti-time ordered. The minute difference in the definitions of W T (C) and W (C) affects the analytic structure of the soft Wilson lines.The main theme of the paper is to study the analytic structure of the Wilson lines, especially the soft Wilson lines in SCET near the boundary of the phase space. We show that the soft Wilson lines appear universally in deep inelastic scattering, in the Drell-Yan process and in the jet production from e + e − collisions, in which the Wilson lines appear in the matrix elements squared or the discontinuity of the forward scattering amplitude. They

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We consider the upward-going muon flux due to the WIMP annihilations in the cores of the sun and the earth, including the upper bound on the branching ratio for B s → µ + µ − decay. We find that the constraint from B s → µ + µ − is very strong in most parameter space, and exclude the supergravity parameter space regions where the expected upward-going muon fluxes are within the expected reach of AMANDA II.

Since the CP violation in the B system has been investigated up to now only through processes related to the B-B mixing, urgently required is new way of study for the CP violation and establishing its origin in the B system independent of the mixing process. In this work, we explore the exclusive B 0 → ρ 0 γ decay to obtain the time-dependent CP asymmetry in b → d decay process in the standard model and the supersymmetric model. We find that the complex RL and RR mass insertion to the squark sector in the MSSM can lead to a large CP asymmetry in b → dγ decay through the gluino-squark diagrams, which is not predicted in the Standard Model induced by the B-B mixing.