Process 3 -> 3 and crossing symmetry violation

Using the Sudakov technique we sum the perturbation series for the process $3\to 3$ and obtain the compact analytical expression for the amplitude of this process, which takes into account all possible Coulomb interactions between colliding particles. Compare it with the amplitude of the lepton pair production in heavy ion collision i.e. in the process $2\to 4$, we show that crossing symmetry between this processes holds only if one neglects the interaction of produced pair with ions (i.e. in the approximation $Z_{1,2}\alpha \ll 1$).Comment: LaTeX2e, 10 pages, 5 eps figure

Sum rule for a difference of proton and neutron total photoproduction cross-sections

Starting from very high energy inelastic electron-nucleon scattering with a production of a hadronic state $X$ to be moved closely to the direction of the initial nucleon, then utilizing analytic properties of parts of forward virtual Compton scattering amplitudes on proton and neutron, one obtains the relation between nucleon form factors and a difference of proton and neutron differential electroproduction cross-sections. In particular, for the case of small transferred momenta, one finally derives sum rule, relating Dirac proton mean square radius and anomalous magnetic moments of proton and neutron to the integral over a difference of the total proton and neutron photoproduction cross-sections.Comment: LaTeX2e, 7 pages, 1 eps figure (revised version

Radiative corrections to muon decay in leading and next to leading approximation for electron spectrum

We have noted that the electron spectrum of muon decay in the leading logarithmic approximation calculated in two lowest orders of the perturbation theory in the paper of Berman (1958), can be reproduced by the parton language. This fact permits one to generalize the result to all orders of the perturbation theory using the structure function method.Comment: 4 pages, 1 figur

Compactifiable classes of compacta

We introduce the notion of compactifiable classes -- these are classes of metrizable compact spaces that can be up to homeomorphic copies ``disjointly combined'' into one metrizable compact space. This is witnessed by so-called compact composition of the class. Analogously, we consider Polishable classes and Polish compositions. The question of compactifiability or Polishability of a class is related to hyperspaces. Strongly compactifiable and strongly Polishable classes may be characterized by the existence of a corresponding family in the hyperspace of all metrizable compacta. We systematically study the introduced notions -- we give several characterizations, consider preservation under various constructions, and raise several questions.Comment: 32 pages, 1 figure, revised versio

Breathing modes in few-layer MoTe2_2 activated by h-BN encapsulation

The encapsulation of few-layer transition metal dichalcogenides (TMDs) in hexagonal boron nitride (h-BN) is known to improve significantly their optical and electronic properties. However, it may be expected that the h-BN encapsulation may affect also vibration properties of TMDs due to an atomically flat surface of h-BN layers. In order to study its effect on interlayer interactions in few-layer TMDs, we investigate low-energy Raman scattering spectra of bi- and trilayer MoTe$_2$. Surprisingly, three breathing modes are observed in the Raman spectra of the structures deposited on or encapsulated in h-BN as compared to a single breathing mode for the flakes deposited on a SiO$_2$/Si substrate. The shear mode is not affected by changing the MoTe$_2$ environment. The emerged structure of breathing modes is ascribed to the apparent interaction between the MoTe$_2$ layer and the bottom h-BN flake. The structure becomes visible due to a high-quality surface of the former flake. Consequently, the observed triple structure of breathing modes originates from the combination modes due to interlayer and layer-substrate interactions. Our results confirm that the h-BN encapsulation affects substantially vibration properties of layered materials.Comment: 10 pages, 9 figure

Virulence of wheat leaf rust (Puccinia triticina Eriks.) in the years 2013–2015 and resistance of wheat cultivars in Slovakia

In 2013–2015 virulence in the wheat leaf rust population was evaluated on 17 Thatcher near-isogenic lines with leaf rust resistance genes. A total of 110 wheat leaf rust isolates were analyzed. Resistance genes Lr9 and Lr19 were effective to all tested isolates. Genes Lr24 and Lr28 conditioned resistance to 92% of the tested rust isolates. Thirty-seven winter wheat cultivars registered in Slovakia were analyzed for the presence of Lr10, Lr24, Lr26, Lr34 and Lr37 using tightly linked molecular markers. Gene Lr37 was the most common in the tested cultivars. Leaf rust resistance was also tested in 13 wheat cultivars at the seedling stage with representative pathotypes of leaf rust

The lepton pair production in heavy ion collisions in perturbation theory

We derive the first terms in the amplitude of lepton pair production in the Coulomb fields of two relativistic heavy ions. Using the Sudakov technique, which very simplify the calculations in momentum space for the processes at high energies, we get the compact analytical expressions for differential cross section of the process under consideration in the lowest order in fine structure constant (Born approximation) valid for any momentum transfer and in a wide kinematics region for produced particles. Exploiting the same technique we consider the next terms of perturbation series (up to fourth order in fine structure constant) and investigate their energy dependence and limiting cases. It has been shown that taking in account all relevant terms in corresponding order one obtains the expressions which are gauge invariant and finite. We estimate the contribution of the Coulomb corrections to the total cross section and discuss the cancellations of the different terms which holds in the total cross section.Comment: LaTeX2e, 18 pages, 4 eps figure

Giant valley-selective Stark and Bloch-Siegert shifts of exciton resonances in WSe2_2 and MoS2_2 monolayers

In this letter we demonstrate that the valley degeneracy of exciton states in monolayers of WSe$_2$ and MoS$_2$ can be lifted by the interaction with strong circularly-polarized infrared pulses with durations of only few periods of the electric field whose photon energy is much lower than the energy of the excitonic transition. The observed valley-sensitive blue shifts of excitonic absorption lines are consequences of optical Stark and Bloch-Siegert shifts acting exclusively on the opposite valleys of the monolayer. We measured the transient valley-selective changes of sample reflectivity for 1sA as well as for 1sB exciton transitions corresponding to the two most intensive resonances in the studied materials. For the studied phenomena we developed a theoretical description based on semiconductor Bloch equations, which goes beyond the simple two-level model used in previous investigations. The theoretical approach takes into account Coulomb many-body effects in the monolayer and provides a unified description of both types of shifts. The detected room-temperature excitonic energy shifts of up to 30\,meV pave the way for practical applications of these effects.Comment: 6 pages, 3 figures, the manuscript is related to the "Semiconductor Bloch equation analysis of optical Stark and Bloch-Siegert shifts in monolayers WSe$_2$ and MoS$_2$" manuscrip

Semiconductor Bloch equation analysis of optical Stark and Bloch-Siegert shifts in monolayers WSe2_2 and MoS2_2

We report on the theoretical and experimental investigation of valley-selective optical Stark and Bloch-Siegert shifts of exciton resonances in monolayers WSe$_2$ and MoS$_2$ induced by strong circularly polarized nonresonant optical fields. We predict and observe transient shifts of both 1sA and 1sB exciton transitions in the linear interaction regime. The theoretical description is based on semiconductor Bloch equations. The solutions of the equations are obtained with a modified perturbation technique, which takes into account many-body Coulomb interaction effects. These solutions allow to explain the polarization dependence of the shifts and calculate their values analytically. We found experimentally the limits of the applicability of the theoretical description by observing the transient exciton spectra change due to many-body effects at high field amplitudes of the driving wave.Comment: 20 pages, 9 figures, this manuscript is related to the "Giant valley-selective Stark and Bloch-Siegert shifts of exciton resonances in WSe$_2$ and MoS$_2$ monolayers" manuscrip