Measuring the number of hadronic jets

Abstract

A quantitative description of the qualitative feature of multihadron final states known as the "number of jets" is given by a sequence of infrared finite shape observables (jet discriminators) that: take continuous values between 0 and 1; are stable-unlike clustering algorithms-against small variations of the input (data errors, Sudakov effects etc.); have a form of multiparticle correlators that is natural in the context of quantum field theory and hence are better suited for a systematic study of theoretical uncertainties (logarithmic and power corrections).

Master integrals for the 2-loop QCD virtual corrections to the forward–backward asymmetry

“…2. method of [11], but also the Lorentz invariance identities [12] and the symmetry relations, that can occur in particular mass configurations. The identities can then be solved by standard techniques (Gauss substitution rule), whose implementation is, however, algebraically very demanding.…”

Three-loop electroweak correction to the rho parameter in the large Higgs mass limit

“…The I 6 integrals coming from region 1 can be classified into ten different kinds, according to the distribution of massless and massive denominators they contain. For two of these categories, we follow the integration-by-parts [20] reduction algorithm obtained by Broadhurst [21], to reduce them to master integrals. Reductions for the eight other categories have been indicated by Avdeev [22], but here, we prefer to use our own reduction routines.…”

Algebraic algorithms for multiloop calculations The first 15 years. What's next?

“…The concept of algebraic algorithms for multiloop integrals [1]- [4] has brought about an industry of analytical multiloop calculations a , so it would not be inappropriate to reminisce upon the anguish of its birth [1], given a non-negligible amount of research funds being misallocated through misinformation b .…”

“…The identity depends on how Q is passed through the propagators, so I started writing out all possible variants and trying to combine them in all sorts of ways. It would have been easier to deal with 2-loop diagrams, but I did not know the answer and chose the 3-loop ladder as my playing ground, so it took several months to stumble upon the celebrated triangle relation [1]. That took care of planar diagrams.…”

“…When actual programming of the algorithm based on pure recursions [1], [2] was attempted, it proved a failure (the huge program simply would not work as a whole). The project remained at a standstill until an explicit solution of the triangle recursion was found [3].…”