Related papers: Smooth Threshold Effects from Dimensional Regulari…
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…
We examine several zero-range potentials in non-relativistic quantum mechanics. The study of such potentials requires regularization and renormalization. We contrast physical results obtained using dimensional regularization and cutoff…
We consider a version of dimensional regularization (reduction) in which the dimensionful regularization parameter $\Lambda$ is in general different from the renormalization scale $\mu$. Then in the scheme analogous to the minimal…
The absence of the quadratic divergence in the Higgs sector of the Standard Model in the dimensional regularization is usually regarded to be an exceptional property of a specific regularization. To understand what is going on in the…
The minimal renormalon subtraction (MRS) [arXiv:1802.04248; arXiv:1712.04983; arXiv:1701.00347; arXiv:2310.15137] technique is summarized. A new result is a study of the scale dependence of the pole-mass--$\overline{\rm MS}$-mass ratio in…
The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We re-examine some technical aspects of the subtractive renormalization, in particular, the mass…
Starting from a well defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare…
We compute the relation between the pole quark mass and the minimally subtracted quark mass in the framework of QCD applying dimensional reduction as a regularization scheme. Special emphasis is put on the evanescent couplings and the…
New equations governing the scale transformation behaviors of a QFT with underlying structures are derived. These equations, with their several equivalent versions, can yield some new and significant insights and results that are difficult…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
It has been shown recently that the introduction of an unphysical $\epsilon$-scalar mass $\tilde{m}$ is necessary for the proper renormalization of softly broken supersymmetric theories by dimensional reduction ($\drbar$). In these…
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…
We discuss the dependence of running couplings on the choice of regularization method in a general softly-broken N=1 supersymmetric theory. Regularization by dimensional reduction respects supersymmetry, but standard dimensional…
We describe in detail how a sliding scale is introduced in the renormalization of a QFT according to integer-dimensional implicit regularization scheme. We show that since no regulator needs to be specified at intermediate steps of the…
We introduce an on shell renormalization scheme in which the mass parameter of minimal MS scheme is replaced with the pole mass obtained from the loop order expansion of the pole mass in the MS scheme. As a consequence, the quartic coupling…
The hierarchy problem is associated with renormalization and decoupling. We can account for the smallness of the scalar mass against loop corrections and its insensitivity to ultraviolet physics through the decoupling of heavy fields. It is…
Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to…
We demonstrate that in the mass independent renormalization scheme. the renormalization group equations associated with the unphysical parameters that characterize the renormalization scheme and the mass scale leads to summation that…
For theories with multiple couplings we construct simple expressions for the four-dimensional (or, in general, integer-dimensional) renormalization constants assuming that all divergences are logarithmical. These expressions allow relating…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…