Regularization, Renormalization, and Dimensional Analysis: Dimensional Regularization meets Freshman E&M

We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the translational symmetry. We then introduce a Minimal Subtraction (MS) and a Modified Minimal Subtraction (MS-Bar) scheme to renormalize the result. Finally, we consider dimensional transmutation as encountered in the case of compact extra-dimensions.

Heavy Quark Production in the ACOT Scheme Beyond NLO

We analyze the properties of the ACOT scheme for heavy quark production and make use of the MS-Bar massless results at NNLO and N3LO for the structure functions F2 and FL in neutral current deep-inelastic scattering to estimate the higher order corrections. The dominant heavy quark mass effects at higher orders can be taken into account using the massless Wilson coefficients together with an appropriate slow-rescaling prescription implementing the phase space constraints. Combining the exact ACOT scheme at NLO with these expressions should provide a good approximation to the full calculation in the ACOT scheme at NNLO and N3LO.

A Survey of Heavy Quark Theory for PDF Analyses

We survey some of the recent developments in the extraction and application of heavy quark Parton Distribution Functions (PDFs). We also highlight some of the key HERA measurements which have contributed to these advances.

A Review of Target Mass Corrections

With recent advances in the precision of inclusive lepton--nuclear scattering experiments, it has become apparent that comparable improvements are needed in the accuracy of the theoretical analysis tools. In particular, when extracting parton distribution functions in the large-x region, it is crucial to correct the data for effects associated with the nonzero mass of the target. We present here a comprehensive review of these target mass corrections (TMC) to structure functions data, summarizing the relevant formulas for TMCs in electromagnetic and weak processes. We include a full analysis of both hadronic and partonic masses, and trace how these effects appear in the operator product expansion and the factorized parton model formalism, as well as their limitations when applied to data in the x->1 limit. We evaluate the numerical effects of TMCs on various structure functions, and compare fits to data with and without these corrections.