Renormalisation scale uncertainty in the DIS 2+1 jet cross-section

Zeitschrift für Physik C Particles and Fields - The deep inelastic scattering 2+1 jet cross-section is a useful observable for precision tests of QCD, e.g. measuring the strong coupling...     

Factorization and resummation for jet broadening

Jet broadening is an event-shape variable probing the transverse momenta of particles inside jets. It has been measured precisely in e⁺e⁻ annihilations and is used to extract the strong coupling constant. The factorization of the associated cross section at small values of the broadening is afflicted by a collinear anomaly. Based on an analysis of this anomaly, we present an all-order factorization theorem for jet-broadening distributions, which is free of large perturbative logarithms in the two-jet limit. Our formula reproduces known results at next-to-leading logarithmic order but also extends to higher orders.     

Resummation in hot field theories

There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns out that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory, the Φ-derivable approach, dimensionally reduced (DR) SPT, and the DR Φ-derivable approach.     

Zeta Function Resummation of Spectral Functions

This article continues an extensive analysis of spectral functions such as for both general and explicitly known spectra {λ_m}. In physical applications (which in quantum field theory are numerous) the spectral functions are mode sums. Our main analytic tool is the ζ-function resummation method which expresses f(s|x) in powers of x and perhaps other simple functions of x. Here the general spectrum will be replaced by its asymptotic form λ_m = (const) m^α with α > 0 (Weyl's theorem). This preserves certain global features of the general spectrum problem but enables one to work entirely in terms of known functions. This simplified problem will be fully analysed and certain aspects of it (in particular the continuum limit) studied for the first time. Several mode-sum calculations illustrate physical application of the method.     

Resummation in QCD fractional analytic perturbation theory

An analytic approach in the QCD perturbation theory that has its origin in studies by Jones, Solovtsov, and Shirkov is briefly summarized. Basic propositions of the fractional analytic perturbation theory (FAPT) are also briefly taken into account with a fixed number of quark flavors and allowing for heavy-quark thresholds in a global FAPT version. Summation of perturbative series in (F)APT is examined. Application of the developed global FAPT version to calculations of the width of Higgs boson decay H → b $ \bar b $ \bar b is described.     

Small x QCD effects in DIS with a forward jet or a forward \pi^{0}

We compare predictions based on small x (QCD) dynamics with recent data for deep inelastic events containing forward jets or forward mesons. We quantify the effect of imposing the (higher order) consistency condition on the BFKL equation and study uncertainties inherent in the QCD predictions. We also estimate the cross-section for the forward production of two jets. Received: 1 March 1999 / Published online: 30 June 1999     

Resummation with Wilson lines off the light cone

I review the resummation formalism for organizing large logarithms in perturbative expansion of collinear subprocesses through the variation of Wilson lines off the light cone. A master equation is derived, which involves the evolution kernel resulting from this variation. It is then demonstrated that all the known single- and double-logarithm summations for a parton distribution function or a transverse-momentum-dependent parton distribution can be reproduced from the master equation by applying appropriate soft-gluon approximations to the evolution kernel. Moreover, jet substructures, information which is crucial for particle identification at the Large Hadron Collider and usually acquired from event generators, can also be calculated in this formalism.     

Resummation of Mass Terms in Perturbative Massless Quantum Field Theory

The neutral massless scalar quantum field Φ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.      

Resummation methods of the Chapman-Enskog expansion for a strongly inhomogeneous plasma

We present a two-fold approach for strongly inhomogeneous plasmas for which the Chapman-Enskog asymptotic expansion breaks down: First, a heuristic one: we solve the kinetic equation by an iterative algorithm, and obtain a non-local response to the local gradients of the local maxwellian distribution function. The other approach consists in resummation methods of the Chapman-Enskog expansion for the distribution function or for its velocity moments: we use Padé or Borel-Padé approximants, and obtain with the simplest ones delocalization formulas similar to those obtained by using the iterative algorithm. These formulas are of great potential use in any situation where strong temperature gradients occur (laser plasma interaction, stellar winds, cloud evaporation).     

Resummation of angular dependent corrections in spontaneously broken gauge theories

Recent investigations of electroweak radiative corrections have revealed the importance of higher order contributions in high energy processes, where the size of typical corrections can exceed those associated with QCD considerably. Beyond one loop, only universal (angular independent) corrections are known to all orders except for massless processes, where also angle dependent corrections exist in the literature. In this paper we present general arguments for the consistent resummation of angle dependent subleading (SL) logarithmic corrections to all orders in the regime where all invariants are still large compared to the gauge boson masses. We discuss soft isospin correlations, fermion mass and gauge boson mass gap effects, the longitudinal and Higgs boson sector as well as mixing contributions including CKM effects for massive quarks. Two loop results for the right handed Standard Model are generalized in the context of the high energy effective theory based on the standard model Lagrangian in the symmetric basis with the appropriate matching conditions to include the soft QED regime. The result is expressed in exponentiated operator form in a CKM extended isospin space in the symmetric basis. Thus, a full electroweak SL treatment based on the infrared evolution equation method is formulated for arbitrary high energy processes at future colliders. Comparisons with known results are presented. Received: 12 February 2002 / Revised version: 7 March 2002 / Published online: 8 May 2002     

Azimuthal and spin asymmetries in DIS

In these lectures I want to discuss how the structure functions in deep inelastic scattering relate to quark and gluon correlation functions. In particular we will consider the issue of intrinsic transverse momenta of quarks, which becomes important in processes like 1-particle inclusive leptoproduction. Some examples of cross sections and asymmetries, in particular in polarized scattering processes are discussed. We also discuss the operator structure for azimuthal asymmetries and their evolution.     

Weak interactions in polarized semi-inclusive DIS

We calculate, within the pQCD parton model at leading orders, the expression of the polarization P of spin 1/2 hadrons (typically baryons), produced in polarized semi-inclusive DIS in all possible cases in which weak interactions are involved. We discuss how to gather new information on fragmentation and distribution functions and give numerical estimates in the cases for which data are or will soon be available. Received: 7 June 2001 / Published online: 10 August 2001