Scheming in Dimensional Regularization

Abstract

We consider the most general loop integral that appears in non-relativistic effective field theories with no light particles. The divergences of this integral are in correspondence with simple poles in the space of complex space-time dimensions. Integrals related to the original integral by subtraction of one or more poles in dimensions other than D=4 lead to nonminimal subtraction schemes. Subtraction of all poles in correspondence with ultraviolet divergences of the loop integral leads naturally to a regularization scheme which is precisely equivalent to cutoff regularization. We therefore recover cutoff regularization from dimensional regularization with a nonminimal subtraction scheme. We then discuss the power-counting for non-relativistic effective field theories which arises in these alternative schemes.

12 pages, additional text in opening section, version to be published in J. Phys. A

References in corpus (10)

• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Effective Field Theory for Short-Range Forces
• The potential of effective field theory in NN scattering
• Low Energy Theorems For Nucleon-Nucleon Scattering
• Effective theory for the two-nucleon system
• A momentum subtraction scheme for two--nucleon effective field theory
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• Low-momentum effective theory for nucleons
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• Lattice QCD and Three-particle Decays of Resonances
• Improving the Convergence of NN Effective Field Theory
• Gravity localization on thick branes: a numerical approach
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• An effective field theory for coupled-channel scattering
• Deuteron electromagnetic properties and the viability of effective field theory methods in the two-nucleon system
• Chiral symmetry breaking in dimensionally regularized nonperturbative quenched QED
• Narrow resonances and short-range interactions
• The renormalisation group and nuclear forces
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• More about the Wilsonian analysis on the pionless NEFT
• Effective field theory for shallow P-wave states
• Dynamical symmetry breaking of $\lambda {\varphi }^4$ in two loop effective potential
• Effective range expansion in various scenarios of EFT($\notpi$)
• Nucleon-nucleon scattering with perturbative pions: The uncoupled $P$-wave channels