A New Formalism for Soft Collinear Effective Theory with Applications

In this thesis a new formalism for Soft Collinear Effective Theory (SCET) is developed and a new calculation relevant to high-precision studies of Quantum Chromodynamics (QCD) involving the summation of Sudakov double logarithms is presented. The new formalism of SCET possesses certain desirable properties not manifest in the standard SCET formalism and is constructed in a framework consistent with the traditional effective field theory perspective. In particular, effective theory operators are organized in an expansion of inverse powers of the matching scale such that operator power counting is determined solely by dimensional analysis rather than requiring the introduction of an abstract power-counting parameter. In contrast to the standard formalism, the infrared degrees of freedom in the effective theory are not subdivided into separate modes determined by relative momentum scaling. The lack of separate collinear and ultrasoft modes is combined with a new subtraction prescription which plays the role of the zero-bin subtraction in the standard formalism. The distinction between different sources of subleading corrections in the effective theory is clarified in this formalism, allowing for a simpler organization of the calculation of these subleading corrections. This formalism is first demonstrated by applying it to the study of Deep Inelastic Scattering (DIS) in the endpoint limit, a process which has been treated several times using SCET. The result and intermediate steps of this calculation are contrasted with previous treatments to demonstrate the relevant features of the new formalism. Next, the calculation of subleading corrections to event shape distributions is addressed. An original calculation of operator anomalous dimensions is presented which will form the basis of future work addressing the current discrepancy in global determinations of the strong coupling constant.Ph.D