arXiv subjects

Stefan Weinzierl

Publications and source records attributed to Stefan Weinzierl.

At least 127 records · Page 7Linked to original sources

arXiv2011

The SISCone jet algorithm optimised for low particle multiplicities

The SISCone jet algorithm is a seedless infrared-safe cone jet algorithm. There exists an implementation which is highly optimised for a large number of final state particles. However, in fixed-order perturbative calculations with a small number of final state particles, it turns out that the computer time needed for the jet clustering of this implementation is comparable to the computer time of the matrix elements. This article reports on an implementation of the SISCone algorithm optimised for low particle multiplicities.

hep-ph↗

arXiv2011

NLO results for five, six and seven jets in electron-positron annihilation

We present next-to-leading order corrections in the leading colour approximation for jet rates in electron-positron annihilation up to seven jets. The results for the two-, three-, and four-jet rates agree with known results. The NLO jet rates have been known previously only up to five jets. The results for the six- and seven-jet rate are new. The results are obtained by a new and efficient method based on subtraction and numerical integration.

hep-ph↗

arXiv2011

Does one need the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes in an NNLO calculation ?

This article discusses the occurences of one-loop amplitudes within a next-to-next-to-leading order calculation. In an NNLO calculation the one-loop amplitude enters squared and one would therefore naively expect that the O(epsilon)- and O(epsilon^2)-terms of the one-loop amplitudes are required. I show that the calculation of these terms can be avoided if a method is known, which computes the O(epsilon^0)-terms of the finite remainder function of the two-loop amplitude.

hep-ph↗

arXiv2011

Jet algorithms in electron-positron annihilation: Perturbative higher order predictions

This article gives results on several jet algorithms in electron-positron annihilation: Considered are the exclusive sequential recombination algorithms Durham, Geneva, Jade-E0 and Cambridge, which are typically used in electron-positron annihilation. In addition also inclusive jet algorithms are studied. Results are provided for the inclusive sequential recombination algorithms Durham, Aachen and anti-kt, as well as the infrared-safe cone algorithm SISCone. The results are obtained in perturbative QCD and are NNNLO for the two-jet rates, NNLO for the three-jet rates, NLO for the four-jet rates and LO for the five-jet rates.

hep-ph↗

arXiv2010

Numerical NLO QCD calculations

We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the integration contour for the loop integration into the complex space. The algorithm is formulated at the amplitude level and does not rely on Feynman graphs. Therefore all required ingredients can be calculated efficiently using recurrence relations. The algorithm applies to massless partons as well as to massive partons.

hep-ph↗

arXiv2010

The MHV Lagrangian for a spontaneously broken gauge theory

Starting from the standard Lagrangian for a SU(2) x U(1) gauge theory plus a Higgs field we derive the corresponding "maximal helicity violating" (MHV) Lagrangian. From this MHV Lagrangian one deduces simple diagrammatic rules for the calculation of multi-particle scattering amplitudes. We arrive at the MHV Lagrangian by a canonical change of the field variables in the light-cone gauge. We comment on the modifications which occur in a spontaneously broken gauge theory as compared to a pure (unbroken) Yang-Mills theory.

hep-ph↗

arXiv2010

Introduction to Feynman Integrals

In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced topics: Mathematical aspects of loop integrals related to periods, shuffle algebras and multiple polylogarithms are covered as well as practical algorithms for evaluating Feynman integrals.

hep-ph↗

arXiv2010

Feynman graph polynomials

The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.

hep-ph↗

arXiv2010

A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes

We show that a well-known simple formula for the explicit infrared poles of one-loop QCD amplitudes has a corresponding simple counterpart in unintegrated form. The unintegrated formula approximates the integrand of one-loop QCD amplitudes in all soft and collinear singular regions. It thus defines a local counter-term for the infrared singularities and can be used as an ingredient for the numerical calculation of one-loop amplitudes.

hep-ph↗

arXiv2010

NNLO predictions for event shapes and jet rates in electron-positron annihilation

The strong coupling constant is a fundamental parameter of nature. It can be extracted from experiments measuring three-jet events in electron-positron annihilation. For this extraction precise theoretical calculations for jet rates and event shapes are needed. In this talk I will discuss the NNLO calculation for these observables.

hep-ph↗

arXiv2009

Feynman graphs in perturbative quantum field theory

In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own right -- allow to derive algorithms for the computation of these graphs. Topics covered are the relations of Feynman integrals to periods, shuffle algebras and multiple polylogarithms.

math-ph↗

arXiv2009

Moments of event shapes in electron-positron annihilation at NNLO

This article gives the perturbative NNLO results for the moments of the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: Thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter and the Durham three-to-two jet transition variable.

hep-ph↗

arXiv2009

The infrared structure of e+ e- --> 3 jets at NNLO reloaded

This paper gives detailed information on the structure of the infrared singularities for the process e+ e- --> 3 jets at next-to-next-to-leading order in perturbation theory. Particular emphasis is put on singularities associated to soft gluons. The knowledge of the singularity structure allows the construction of appropriate subtraction terms, which in turn can be implemented into a numerical Monte Carlo program.

hep-ph↗

arXiv2009

Event shapes and jet rates in electron-positron annihilation at NNLO

This article gives the perturbative NNLO results for the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: Thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter and the Durham three-to-two jet transition variable. In addition the NNLO results for the jet rates corresponding to the Durham, Geneva, Jade-E0 and Cambridge jet algorithms are presented.

hep-ph↗

arXiv2009

Some remarks on dipole showers and the DGLAP equation

It has been argued recently that parton showers based on colour dipoles conflict with collinear factorization and do not lead to the correct DGLAP equation. We show that this conclusion is based on an inappropriate assumption, namely the choice of the gluon energy as evolution variable. We further show numerically that Monte Carlo programs based on dipole showers with "infrared sensible" evolution variables reproduce the DGLAP equation both in asymptotic form as well as in comparison to the leading behaviour of second-order QCD matrix elements.

hep-ph↗

arXiv2009

Periods and Feynman integrals

We consider multi-loop integrals in dimensional regularisation and the corresponding Laurent series. We study the integral in the Euclidean region and where all ratios of invariants and masses have rational values. We prove that in this case all coefficients of the Laurent series are periods.

hep-th↗

arXiv2008

NNLO corrections to 3-jet observables in electron-positron annihilation

I report on a numerical program, which can be used to calculate any infrared safe three-jet observable in electron-positron annihilation to next-to-next-to-leading order in the strong coupling constant alpha_s. The results are compared to a recent calculation by another group. Numerical differences in three colour factors are discussed and explained.

hep-ph↗

arXiv2008

Blowing up Feynman integrals

In this talk we discuss sector decomposition. This is a method to disentangle overlapping singularities through a sequence of blow-ups. We report on an open-source implementation of this algorithm to compute numerically the Laurent expansion of divergent multi-loop integrals. We also show how this method can be used to prove a theorem which relates the coefficients of the Laurent series of dimensionally regulated multi-loop integrals to periods.

hep-ph↗