Related papers: Why Are Renormalons Always In The Same Place ?
Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the…
In ${\cal N}=1$ supersymmetric QCD-like theories we derive the (all-order) exact equations relating the renormalization group behaviour of the strong and electromagnetic couplings and prove that they are valid in the HD+MSL renormalization…
Recovering a signal from auto-correlations or, equivalently, retrieving the phase linked to a given Fourier modulus, is a wide-spread problem in imaging. This problem has been tackled in a number of experimental situations, from optical…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
Bidirectional transformation, also called lens, has played important roles in maintaining consistency in many fields of applications. A lens is specified by a pair of forward and backward functions which relate to each other in a consistent…
We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
The QCD one-loop renormalization is restudied in a mass-dependent subtraction scheme in which the quark mass is not set to vanish and the renormalization point is chosen to be an arbitrary timelike momentum. The correctness of the…
Motivated by Dunkl operators theory, we consider a generating series involving a modified Bessel function and a Gegenbauer polynomial, that generalizes a known series already considered by L. Gegenbauer. We actually use inversion formulas…
New properties of the quark correlator are found via equations of motion. As a first result, approximate relations can be established among the "soft" functions; one such relation may help in determining the quark transversity in a nucleon.…
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…
The singular behavior of conformal interactions is examined within a comparative analysis of renormalization frameworks. The effective approach--inspired by the effective-field theory program--and its connection with the core framework are…
It is shown that the commonly accepted relationship between the Landau singularity in the running coupling constant of QED or QCD and the renormalon singularities in the Borel sums of perturbation theory expansions is only a particular…
I summarize what we know of renormalons from the 1970s and 80s: their uses and theoretical status. It is emphasized that renormalons in QCD are closely related to the Wilsonean operator product expansion (OPE) - a setup ideally suited for…
In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…
This paper investigates the use of different transformations for improving the randomness of sequences. In particular, convolutional codes are used for increasing the size of a given sequence and then a random mapping function is used for…
We show how to convert divergent series, which typically occur in many applications in physics, into rapidly convergent inverse factorial series. This can be interpreted physically as a novel resummation of perturbative series. Being…