Two-loop QCD corrections to the coefficient functions of the deep inelastic structure functionsF 2 andF L

We present the analytic two-loop perturbative QCD corrections in the leading twist approximation to the coefficient functions of the operator product expansion for the second to tenth moments of the nonsinglet and singlet deep inelastic structure functionsF ₂ andF _L .     

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 for breakup of invariant tori

We present renormalization group operators for the breakup of invariant tori with winding numbers that are quadratic irrationals. We find the simple fixed points of these operators and interpret the map pairs with critical invariant tori as critical fixed points. Coordinate transformations on the space of maps relate these fixed points, and also induce conjugacies between the corresponding operators.     

Origin of the Q 2-dependence of the DIS structure functions

We consider in detail Q ²-dependence of the DIS structure functions. Very often this dependence is claimed to be originated by the Q ²-dependence of the QCD coupling. This leads to the small-x asymptotics of the structure functions with Q ²-dependent intercepts. We demonstrate that the DGLAP parametrization α _s = α _s (Q ²) is an approximation valid in the region of large x (where 2pq can be approximated by Q ²) only, providing the factorization scale is also large. Outside this region, the DGLAP parametrization fails, so α _s should be replaced by an effective coupling which is independent of Q ² at small x. As a consequence, intercepts of the structure functions are independent of Q ² . Nevertheless, the small-x asymptotics of the structure functions explicitly depend on Q ² , even when the coupling does not depend on it. We also consider the structure functions at small Q ² and give a comment on power-Q ² corrections to the structure functions at large and small Q ² .     

Renormalization group invariant average momentum of non-singlet parton densities

We compute, within the Schrödinger functional scheme, a renormalization group invariant renormalization constant for the first moment of the non-singlet parton distribution function. The matching of the results of our non-perturbative calculation with the ones from hadronic matrix elements allows us to obtain eventually a renormalization group invariant average momentum of non-singlet parton densities, which can be translated into a preferred scheme at a specific scale.     

The invariant charges of the Nambu-Goto theory in WKB-approximation: Renormalization

We discuss the one loop renormalization of the reparametrization invariant non-local conserved charges of the Nambu-Goto string theory. In addition we show the stability of a special well-known state under the corresponding infinitesimal symmetry transformations — at least in the WKB-approximation.Work supported by Deutsche Forschungsgemeinschaft     

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 group functions for the radiative symmetry breaking scheme

We obtain the renormalization group (RG) functions for the massless scalar field theory where symmetry breaking occurs radiatively. After obtaining the effective potential for the radiative symmetry breaking scheme by finite transformations for the classical field and coupling constant, we obtain the corresponding RG functions from that of the minimal subtraction (MS) scheme.     

Regularization scheme dependence of virtual corrections to DY and DIS

One loop virtual corrections to the quark photon vertex are calculated under various assumptions and their sensitivity to the manner in which infra-red and mass singularities are regularized is studied. A method based on the use of Mellin-transforms in the Feynman parametric space is developed and shown to be convenient in calculating virtual diagrams beyond the leading logarithm in perturbative QCD.     

Measurement of the structure functionsF 2 andxF 3 and comparison with QCD predictions including kinematical and dynamical higher twist effects

The isoscalar nucleon structure functionsF ₂(x, Q ²) andxF ₃(x, Q ²) are measured in the range 0<Q ²<64 GeV², 1.7<W ²<250 GeV²,x<0.7 using ν and \(\bar v\) interactions on neon in BEBC. The data are used to evaluate possible higher twist contributions and to determine their impact on the evaluation of the QCD parameter Λ. In contrast to previous analyses reaching to such lowW ² values, it is found that a low \(\Lambda _{\overline {MS} } \) value in the neighbourhood of 100 MeV describes the data adequately and that the contribution of dynamical higher twist effects is small and negative.     

Renormalization of the fine structure constant at high energies

Continuing the discussion in [1], the renormalization of the fine-structure constant in the high-energy range, where a logarithmic increase in the constant is observed, is considered. It is shown that within the framework of the quantum electrodynamics of bilocal fields, when the energy increases the logarithmic "form" ln² of the constant changes into a power drop 1/². Hence, problems with the "Moscow zero" do not arise in this theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–12, January, 1996.     

QCD factorization for the DIS structure functions at small x

We suggest a new form of QCD factorization for inclusive processes at high energies and then reduce it to K _T -factorization. In turn, K _T -factorization can be reduced to collinear factorization when the unintegrated parton distributions have at least one maximum in k _⊥. This property of the parton distributions can be checked with studying data of experiment. The sharper the maximum is, the more accurate the transition to collinear factorization can be done. We apply our results to deduce theoretical restrictions requirements on fits for parton distributions in both K _T - and collinear factorizations contrary to the present situation where the fits are introduced from purely phenomenological consideration so that any formula for them is acceptable if it matches experimental data.     

Regge behavior of DIS structure functions in scalar theories

The Bethe-Salpeter formalism is used to incorporate the valence Regge behavior into the total DIS amplitude. For a special case of scalar quarks with massless scalar exchange, the model is solved both analytically and numerically and exact scaling is found for the valence quark contribution F ₂(x) ∼ (1/x) ^l(0)−1 which mimicks the ρ-trajectory term. The solution solves a long-standing problem by showing that the coefficient in the Regge pole expansion is indeed fine-tuned to give the expected scaling. The method allows for generalization to the region of nonzero momentum transfer and calculation of the DVCS amplitude. The text was submitted by the authors in English.     

Magnetic transition from the paramagnetic to long-period structure in RMn2O5 multiferroics: Renormalization group analysis of critical behavior

A transition from the paramagnetic state to a long-period magnetic structure with an incommensurate wave vector along one crystallographic axis in RMn₂O₅ multiferroics is considered. An effective Hamiltonian for these oxides is constructed with allowance for spin fluctuations. Critical points are found, and their stability is analyzed using the renormalization group approach. It is shown that critical fluctuations in these compounds admit a second-order phase transition with respect to a multicomponent order parameter.     

QCD analysis of DIS and SIDIS data

The combined analysis of polarized DIS and SIDIS data is performed in NLO QCD using two alternative procedures: standard fitting procedure and the recently developed direct new method. The results from two methods are compared. The especial attention is paid to the light sea and strange PDFs.