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Petioles from in vitro grown plants of interspecific grapevine hybrids cvs `Bianca', `Podarok Magaracha' and `Intervitis Magaracha' were cultured on solid NN medium supplemented with 2,4-D and BA at various concentrations. The callus developed was cultured in liquid NN medium supplemented with 0.5 mg l−1 BA to induce formation of somatic embryos. Somatic embryos of globular and heart-stage developed in suspensions of `Podarok Magaracha' and `Intervitis Magaracha'. In contrast, `Bianca' did not undergo embryogenesis beyond globular stage. This made it necessary to perform subculture of the suspensions to HTE liquid medium supplemented with 0.2 mg l−1 BA for the development of globular embryos into heart stage. Heart-stage embryos developed into torpedo-stage after subculturing suspensions of all three cultivars to liquid HTE medium supplemented with 0.1 mg l−1 IAA and 30 mg l−1 sodium hummate. Torpedo-stage embryo suspensions were subcultured in liquid HTE medium supplemented with 0.5 mg l−1 BA, 0.5 mg l−1 GA3 and 0.5 mg l−1 GA3 + 0.2 mg l−1 BA. After 12 days of incubation, plantlets were cultured on solid M2MS medium: without growth regulators and with 0.5 mg l−1 BA. Plantlets that developed in liquid HTE media with 0.5 mg l−1 GA3 or 0.5 mg l−1 GA3 + 0.2 mg l−1 BA produced 82–90% shoots on solid M2MS medium with 0.5 mg l−1 BA after 50 days of culture.

We study the heavy quark production processes with the transverse momentum dependent (unintegrated) gluon distribution function in a proton which is obtained recently using the Kimber-Martin-Ryskin prescription from the Bessel-inspired behavior of parton densities at small Bjorken x values. Our results agree with the latest HERA experimental data for reduced cross sections σccred(x,Q²) and σbbred(x,Q²), and also for deep inelastic structure functions Fc2(x,Q²) and Fb2(x,Q²) in a wide range of x and Q² values. Comparisons with the predictions based on the Ciafaloni-Catani-Fiorani-Marchesini evolution equation and with the results of conventional pQCD calculations performed at the first three orders of perturbative expansion are presented. [ABSTRACT FROM AUTHOR]

A renormalization scheme invariant analysis of the deep inelastic scattering structure functionF2 andFL is performed. Expressions for the moments are given in this approach. We find a significant improvement of the agreement withR=sL/sT-SLAC data with respect to the conventional perturvative analysis. Higher twist corrections are also required confirming previous evidence.

We study the new relation [B. A. Kniehl and A. V. Kotikov, arXiv:1702.03193.] between the anomalous dimensions, resummed through next-to-next-to-leading logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations for the first Mellin moments Dq,g(μ²) of the fragmentation functions, which correspond to the average multiplicities of hadrons in jets initiated by quarks and gluons, respectively. This relation is shown to lead to probabilistic properties of the properly rescaled parton jet multiplicities obtained from standard ones by extracting the quark and gluon "color charges" CF and CA, respectively. [ABSTRACT FROM AUTHOR]

We study the gauge covariance of the massless fermion propagator in three-dimensional quenched quantum electrodynamics in the framework of dimensional regularization in d=3-2ϵ. Assuming the finiteness of the quenched perturbative expansion, that is the existence of the limit ϵ→0, we state that, exactly in d=3, all odd perturbative coefficients, starting with the third order one, should be zero in any gauge. [ABSTRACT FROM AUTHOR]

We study the gauge-covariance of the massless fermion propagator in reduced quantum electrodynamics (QED). Starting from its value in some gauge, we evaluate an all order expression for it in another gauge by means of the Landau-Khalatnikov-Fradkin transformation. We find that the weak-coupling expansions thus derived are in perfect agreement with the exact calculations. We also prove that the fermion anomalous dimension of reduced QED is gauge invariant to all orders of perturbation theory except for the first one. [ABSTRACT FROM AUTHOR]

The Landau-Khalatnikov-Fradkin transformation is a powerful and elegant transformation allowing us to study the gauge dependence of the propagator of charged particles interacting with gauge fields. With the help of this transformation, we derive a nonperturbative identity between massless propagators in two different gauges. From this identity, we find that the corresponding perturbative series can be exactly expressed in terms of a hatted transcendental basis that eliminates all even ζ-values. This explains the mystery of even ζ-values observed in multiloop calculations of Euclidean massless correlators for almost three decades now. Our construction further allows us to derive an exact formula relating hatted and standard ζ-values to all orders of perturbation theory. [ABSTRACT FROM AUTHOR]

We present a method to extract, in the leading- and next-to-leading-order approximations, the longitudinal deep inelastic scattering structure function FL(x,Q²) from the experimental data by relying on a Froissart-bounded parametrization of the transversal structure function F2(x,Q²) and, partially, on the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations. Particular attention is paid to the kinematics of low and ultralow values of the Bjorken variable x, x~10-5-10-2. Analytical expressions for FL(x,Q²) in terms of the effective parameters of the parametrization of F2(x,Q²) are presented explicitly. We argue that the obtained structure functions FL(x,Q²) within both, the leading- and next-to-leading-order approximations, manifestly obey the Froissart boundary conditions. Numerical calculations and comparison with available data from the ZEUS and H1 collaborations at HERA demonstrate that the suggested method provides reliable structure functions FL(x,Q²) at low x in a wide range of the momentum transfer (1 GeV²

The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphenelike materials, the surface states of some topological insulators, and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the Bogoliubov-Parasiuk-Hepp-Zimmermann prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultrarelativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity C*=(92-9π2)/(18π) and the anomalous dimension of the fermion field γψ(α,ξ)=2α(1-3ξ)/3-16(ζ2NF+4/27)α2+O(α3), where α=e2/(4π)2 and ξ is the gauge-fixing parameter. [ABSTRACT FROM AUTHOR]

The Bessel-inspired behavior of parton densities at small Bjorken x values, obtained in the case of the flat initial conditions for Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations, is used along with "frozen" and analytic modifications of the strong coupling constant to study the so-called European Muon Collaboration effect. Among other results, this approach allowed predicting small x behavior of the gluon density in nuclei. [ABSTRACT FROM AUTHOR]

Dynamical chiral symmetry breaking (DχSB) is studied within (2 + 1)-dimensional QED with N four-component fermions. The leading and next-to-leading orders of the 1/N expansion are computed exactly. The analysis is carried out in an arbitrary nonlocal gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavor number, Nc(ξ), where ξ is the gauge-fixing parameter, which is such that DχSB takes place for N < Nc(ξ). Neglecting the weak gauge-dependent terms yields Nc = 2.8469, while, in the general case, it is found that Nc(1) = 3.0084 in the Feynman gauge, Nc (0) = 3.0844 in the Landau gauge, and Nc (2/3) = 3.0377 in the ξ = 2/3 gauge where the leading order fermion wave function is finite. These results suggest that Dχ SB should take place for integer values N ≤ 3. [ABSTRACT FROM AUTHOR]

The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced QED4,3 with N four-component fermions (N = 2 for graphene), where photons are (3 + 1) dimensional and mediate a fully retarded interaction among (2 + 1)-dimensional fermions. A correspondence between reduced QED4,3 and QED3 allows us to derive an exact gap equation for QED4,3 up to next-to-leading order. Our results show that a dynamical gap is generated for α >αc, where 1.03 < αc < 1.08 in the case N = 2 or for N < Nc where Nc is such that αc → ∞ and takes the values 3.24 < Nc < 3.36. The striking feature of these results is that they are in good agreement with values found in models with instantaneous Coulomb interaction (including lattice simulations). At the fixed point, α = 1/137 ≪ αc, and the system is therefore in the semimetallic regime in accordance with experiments. [ABSTRACT FROM AUTHOR]

The dynamical generation of a fermion mass is studied within (2 + 1)-dimensional QED with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge, which is supposed to insure the gauge independence of the critical fermion flavor number, Nc. It is found that the dynamical fermion mass appears for N < Nc, where Nc = 3.29, which is only about 1% larger than its value at leading order. [ABSTRACT FROM AUTHOR]