Related papers: Higher Order Renormalons
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
A method is described to probe high-scale physics in lower-energy experiments by employing sum rules in terms of renormalisation group invariants. The method is worked out in detail for the study of supersymmetry-breaking mechanisms in the…
We give an expression of polynomials for higher sums of powers of integers via the higher order Bernoulli numbers.
I discuss the resummation of soft gluon contributions to direct photon and W + jet production and I present some results for the next-to-next-to-leading order expansions of the resummed cross sections for these processes near threshold.
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…
Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the…
There are two sources of the factorial large-order behavior of a typical perturbative series. First, the number of the different Feynman diagrams may be large; second, there are abnormally large diagrams known as renormalons. It is well…
We resum Sudakov threshold enhancements in heavy quark hadroproduction for single-heavy quark inclusive and pair-inclusive kinematics. We expand these resummed results and derive analytical finite-order cross sections through…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
Although old, this may be of interest. In particular, I have had inquiries concerning the renormalization group calculations in Sec. 6.4. This is a Latex transcription. A scanned version of the original typed manuscript is available at…
In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry…
Higher-order diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman diagrams. The…
We present a systematic procedure for analyzing cumulants to arbitrary order in the context of heavy-ion collisions. It generalizes and improves existing procedures in many respects. In particular, particles which are correlated are allowed…
We obtain solutions to the recursive sequences of the form $$x_{n + 1} = \frac{x_{n - 3}x_{n }}{x_{n - 2}(a_n + b_nx_{n -3}x_{n})}$$ where $a_n$ and $b_n$ are arbitrary sequences of real numbers, and the initial values are gives as;…
We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the…
Power corrections to exclusive processes are usually calculated using models for twist-four distribution amplitudes (DA) which are based on the leading-order terms in the conformal expansion. In this work we develop a different approach…
This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall…
We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constants. An approach to identify the…