Renormalization scheme invariant predictions for deep-inelastic scattering and determination ofΛ QCD

I discuss theoretical aspects of the renormalisation scheme (RS) ambiguity problem and the approaches to its solution from the point of view of QCD phenomenology and the scale Λ determination. I advocate the method of RS-invariant perturbation theory (RSIPT) as a sound basis for describing experiment in QCD. To this end the method is developed for the non-singlet structure functions (SF) of deep-inelastic scattering and recent high precision data on SF's are analysed in a RS-invariant way. It is shown that RSIPT leads to a more accurate and reliable determination of the QCD scale Λ, which is consistent with theoretical assumption about better convergence of RS-invariant perturbative series.     

Renormalization group dependence of the QCD coupling

The general relation between the standard expansion coefficients and the beta function for the QCD coupling is exactly derived in a mathematically strict way. It is accordingly found that an infinite number of logarithmic terms are lost in the standard expansion with a finite order, and these lost terms can be given in a closed form. Numerical calculations, by a new matching-invariant coupling with the corresponding beta function to four-loop level, show that the new expansion converges much faster.     

Renormalization scheme dependence of electroweak radiative corrections

We compare two renormalization schemes of the electroweak standard model: the on-shell scheme withe, M _W ,M _Z ,M _H , and the fermion masses {m _f } as free parameters, and an intermediate scheme where theW boson self energy is renormalized atq ²=0 instead ofq ²=M _W ². TheM _W ?M _Z interdependence, and the differentiale ⁺ e ^?→μ ⁺ μ ^? cross section including polarized beams are calculated in both schemes to one-loop order. We find striking differences between the forward-backward asymmetries and the polarization asymmetries near theZ resonance after inclusion of weak and QED corrections.     

Renormalization in Coulomb gauge QCD

In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ–Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ–Lee term. We find that they cannot.     

Vector boson parameters: Scheme dependence and theoretical uncertainties

The renormalization scheme dependence of electroweak parameters shifts is used to estimate uncertainties due to higher order effects. Parameter shifts are calculated from weakly scheme dependent quantities, taking care of a systematic leading log summation. A “non-standard” definition of sin² θ _W is also considered which is to be used if the ρ-parameter is kept as free parameter. Results for the leptonic decay widths of the vector bosons are also given.     

Renormalization of loop functions in QCD

We give a short overview of the renormalization properties of rectangular Wilson loops, the Polyakov loop correlator and the cyclic Wilson loop. We then discuss how to renormalize loops with more than one intersection, using the simplest non-trivial case as an illustrative example. Our findings expand on previous treatments. The generalized exponentiation theorem is applied to the Polyakov loop correlator and used to renormalize linear divergences in the cyclic Wilson loop.     

Implicit Regularization and Renormalization of QCD

We apply the Implicit Regularization (IR) technique in a non-abelian gauge theory. We show that IR preserves gauge symmetry as encoded in relations between the renormalization constants required by the Slavnov–Taylor identities at the one-loop level of QCD. Moreover, we show that the technique handles divergencies in massive and massless QFT on equal footing.     

Next-to-leading order QCD predictions for associated production of top squarks and charginos at the CERN LHC

We present the calculations of the complete next-to-leading order (NLO) inclusive total cross sections for the associated production processes in the minimal supersymmetric standard model at the CERN Large Hadron Collider. Our calculations show that the total cross sections for the production for the lighter top squark masses in the region 100 GeV 160 GeV can reach 1 pb in the favorable parameter space allowed by the current precise experiments, and in other cases the total cross sections generally vary from 10 fb to several hundred fb except for both 500 GeV and the production channel. Moreover, we find that the NLO QCD corrections in general enhance the leading order total cross sections significantly, and vastly reduce the dependence of the total cross sections on the renormalization/factorization scale, which leads to increased confidence in predictions based on these results.Received: 2 March 2003, Revised: 28 May 2003, Published online: 11 July 2003     

Renormalization group approach towards the QCD phase diagram

The idea of the functional renormalization group and one-loop improved renormalization group flows are reviewed. The associated flow equations and nonperturbative approximations schemes for its solutions are discussed. These techniques are then applied to the strong interaction in the framework of an effective quark meson model, which is introduced in great detail. The renormalization group analysis of the two flavor quark meson model is extended to finite temperature and quark chemical potential which allows for an analysis of the chiral phase diagram beyond the mean field approximation. The text was submitted by the authors in English.     

Renormalization group analysis of the τ-lepton decay within QCD

A technique to sum up the regular corrections appearing under the analytical continuation from the space like momentum region to the time like one is proposed. A perturbative part of the inclusive semileptonic decay width of the τ-lepton in analyzed in detail.