Determination of the spatial profiles of all components of the quadratic susceptibility tensor \hat \chi ^{(2)} (z, 2ω; ω, ω) of a one-dimensionally inhomogeneous absorbing medium

For a one-dimensionally inhomogeneous plate whose linear dielectric properties are also inhomogeneous and are characterized by a diagonal permittivity tensor, it is proved that the spatial profiles of all components of the complex quadratic susceptibility tensor $\hat \chi ^{(2)} $ (z, 2??; ??, ?? responsible for the second harmonic generation can be uniquely determined, and an appropriate method is proposed. To implement this method, one should measure the complex coefficient of transformation of a fundamental plane wave incident on the plate into a reflected second-harmonic wave in a certain range of angles of incidence. By varying the plane of incidence of the wave and (or) its polarization and measuring the coefficients of transformation into s- and p-polarized waves of double frequency, one can uniquely determine the spatial profiles of all components of the quadratic susceptibility tensor. The method involves the measurement of the intensities of the second-harmonic waves generated under special conditions with the use of two auxiliary reference plates and thus allows one to avoid complicated phase measurements.     

Manifestation of a singlet heavy up-type quark in the branching ratios of rare decays K → πν \bar \nu , B → πν \bar \nu , and B → Kν \bar \nu

The implications of the model with a SU(2)-singlet up-type quark, heavy enough not to be produced at the LHC, namely, the contribution of the new quark to the branching ratios of the K → πν $ \bar \nu $ , B → πν $ \bar \nu $ , and B → Kν $ \bar \nu $ decays are investigated. It is shown that the deviation from the Standard Model can be up to 10% in the case of a 5-TeV quark. Precise measurements of these branching ratios in future experiments will allow for the observation of the contributions of the new quark or to impose stronger constraints on its mass.     

Reconstruction of the coordinate dependences of quadratic susceptibility tensor \hat \chi ^{(2)} (z, ω1 ± ω2; ω1, ±ω2) components for the one-dimensionally inhomogeneous absorbing medium

A method for the unambiguous reconstruction of the spatial profiles of all components (except for ?? _zzz ) of the quadratic susceptibility complex tensor {ie165-2} (z, ??₁ + ??₂; ??₁, ??₂), which is responsible for the sumfrequency generation in a one-dimensionally inhomogeneous plate is proposed and proven for the first time. Such reconstruction is possible if the symmetry of the medium provides the diagonal character of the linear permittivity tensor {ie165-3} (z, ??). The procedure involves the measurement of the complex amplitude of the new wave with the frequency ??₁ + ??₂ that is reflected from the plate for a certain interval of the angles of incidence of the wave with the frequency ??₂. The reflected wave results from the nonlinear interaction of the wave with frequency ??₂ and the wave with frequency ??₁ that exhibits the normal incidence. A similar approach can be used to determine the profiles of the components of the quadratic susceptibility tensor {ie165-4}(z, ??₁ ? ??₂; ??₁, ? ??₂), which is responsible for the difference-frequency generation.     

Experimental determination of the branching ratiosp\bar p \to 2\pi ^0 ,\pi ^0 \gamma,and 2γ at rest

The branching ratios of \(p\bar p\) annihilations into the neutral final states 2π⁰, π⁰γ, and 2γ are measured by stopping antiprotons in liquid hydrogen. They are \(B_{2\pi ^0 } = \left( {2.06 \pm 0.14} \right) \times 10^{ - 4} \) , \(B_{\pi ^0 \gamma } = \left( {1.74 \pm 0.22} \right) \times 10^{ - 5} \) , andB _γγ<1.7×10^?6 (95% c.l.).     

Nonlinear coupling between the mean polarizability \bar \gamma of molecules and the local-field anisotropy in a liquid crystal and change of the “ \bar \gamma = const” paradigm

The nonlinear relation between the mean effective polarizability $ \bar \gamma $ of molecules and the local-field anisotropy in uniaxial liquid crystals is demonstrated. Stringent constraints on $ \bar \gamma $ from below, indicative of the dependence of $ \bar \gamma $ on the liquid-crystal state and the change of the “ $ \bar \gamma $ = const” paradigm, are established. The theoretical results are confirmed by experiments with nematic liquid crystals having high and low birefringences.     

New exact solutions of the Tzitzéica type equations arising in nonlinear optics using a modified version of the improved $$\tan \left( {\varPhi \left( \xi \right)/2} \right)$$-expansion method

The paper deals with the Tzitzéica type nonlinear evolution equations arising in nonlinear optics and their new exact solutions. First, through the use of the Painlevé transformation and Lie symmetry method, the Tzitzéica, Dodd–Bullough–Mikhailov, and Tzitzéica–Dodd–Bullough equations are converted to nonlinear ordinary differential equations (NODEs), and then, a modified version of the improved \(\tan \left( {\varPhi \left( \xi \right)/2} \right)\)-expansion method, proposed by the authors, is adopted to generate new exact solutions of the reduced equations. The method truly recommends a reliable and capable technique to produce new exact solutions of a variety of nonlinear partial differential equations (NPDEs).     

Analysis of the Vibrational-Rotational Structure of 2ν1, ν1 + ν3, and 2ν3 Bands of the D2Se Molecule

The absorption spectrum of the D₂Se molecule in the region of 2₁, ₁ + ₃, and 2₃ absorption bands is registered with a high-resolution Fourier spectrometer and is studied theoretically for a Hamiltonian model with allowance for resonant interactions among (200), (101), and (002) vibrational states.     

Scattering length expansion of the coupled channels\bar pp \to \bar \Lambda \Lambda and\bar \Lambda \Lambda \to \bar \Lambda \Lambda near theΛ production threshold

We fit the scattering lengths in the triplets-,p- andd- waves for the two channels \(\bar pp \to \bar \Lambda \Lambda\) and \(\bar \Lambda \Lambda \to \bar \Lambda \Lambda\) near theΛ production threshold to the differential cross section \(\frac{{d\sigma }}{{d\Omega }}(\bar pp \to \bar \Lambda \Lambda )\) and to the polarization P.     

Plasmon-phonon mechanism of nonradiative transition 2S 1/2 → 2P 1/2 in grazing scattering of a hydrogen atom at the surface of a solid

The probability of nonradiative transition 2S _1/2 ?? 2P _1/2 in the case of grazing scattering of a hydrogen atom with an energy on the order of 1 keV at an Au and LiF surface is calculated in the semiclassical theory of nonadiabatic transitions. The transitions are induced by the interaction of the atom with the fields of surface plasmons and optical phonons, respectively. A formalism is developed which makes it possible to exceed the approximation based on the method of electrical images of charges. The value of the probability of scattering at LiF is high enough for experimental observation of the effect. The probability of this transition is determined for the motion of the atom parallel to the metal surface.     

P2—a new measurement of the weak charge of the proton

After ten years of experience with parity-violating electron-proton-scattering, the preparatory work on a new high precision parity-violation experiment in Mainz has begun. Project P2 is bound to measure the weak charge of the proton to a relative uncertainty of 1.9 %, which corresponds to a relative uncertainty of 0.15 % for $\sin^2{\theta_{W}}$ . This can be achieved by measuring the parity-violating asymmetry in elastic electron-proton-scattering to a relative precision of 1.7 % at E _beam~200 MeV and Q ²~0.005 GeV². In this proceeding, we will discuss the achievable precision within project P2 as well as the experimental concept and present first results of studies involving Monte Carlo methods.     

Contribution of a heavy singlet quark to the mass differences \Delta m_{K^o } , \Delta m_{B_d } , and \Delta m_{B_s } and to the CP-violation parameter ɛ K

It is shown that, within the Standard Model extended by including a singlet quark heavy enough to prevent its direct detection at LHC, the mass differences $ \Delta m_{B_d } $ and $ \Delta m_{B_s } $ and the parameter of CP violation in K-meson oscillations, ? _K , acquire universal corrections of about 5 to 10%. Implicit experimental constraints on the mass of this new quark are discussed.     

Strong decay of $$\Lambda _c(2940)$$ as a 2 P state in the $$\Lambda _c$$Λc family

Considering the mass, parity and \(D^0 p\) decay mode, we tentatively assign the \(\Lambda _c(2940)\) as the \(P-\)wave states with one radial excitation. Then, via studying the strong decay behavior of the \(\Lambda _c(2940)\) within the \(^3P_0\) model, we obtain that the total decay widths of the \(\Lambda _{c1}(\frac{1}{2}^-,2P)\) and \(\Lambda _{c1}(\frac{3}{2}^-,2P)\) states are 16.27 and 25.39 MeV, respectively. Compared with the experimental total width \(27.7^{+8.2}_{-6.0}\pm 0.9^{+5.2}_{-10.4}~\mathrm {MeV}\) measured by LHCb Collaboration, both assignments are allowed, and the \(J^P=\frac{3}{2}^-\) assignment is more favorable. Other \(\lambda \)-mode \(\Sigma _c(2P)\) states are also investigated, which are most likely to be narrow states and have good potential to be observed in future experiments.     

High-resolution spectroscopy of the v2 = 2 a ← v2 = 1 s band of 15NH3

Twenty-four transitions of the v₂ = 2 a ← v₂ = 1 s hot band of ¹⁵NH₃ have been observed by an infrared microwave sideband laser spectrometer. In addition, 149 transitions of the band have been obtained by a Fourier transform spectrometer at a resolution of 0.02 cm⁻¹. A weighted least-squares analysis has been carried out and the rms deviation of the fit is 0.00097 cm⁻¹. It was necessary to include the Δ(K − l) = ±3 interaction between the v₂ = 2 a and the v₄ = a states in the analysis.     

High-resolution spectroscopy of the v2 = 2 a ← v2 = 1 s band of 14NH3

Twenty-one transitions of the v₂ = 2 a ← v₂ = 1 s hot band of ¹⁴NH₃ have been observed by an infrared microwave sideband laser spectrometer with an absolute accuracy of 0.00002 cm⁻¹. One hundred and seventeen transitions of the band have been obtained by a Fourier transform infrared spectrometer at a resolution of 0.005 cm⁻¹. A weighted least-squares analysis of these data has been carried out to yield 17 molecular parameters for the v₂ = 2 a state. These parameters reproduce the experimental frequencies with a root mean square deviation of 0.000123 cm⁻¹. To calculate the frequencies to this accuracy it was necessary to take into account the Δ(K − l) = ±3 interaction between the v₂ = 2 a and v₄ = 1 a states.     

Magnetic properties of the quantum spin-$\frac{1}{2}$ XX diamond chain: the Jordan-Wigner approach

The Jordan-Wigner transformation is applied to study magnetic properties of the quantum spin- \frac12\frac{1}{2} XX model on the diamond chain. Generally, the Hamiltonian of this quantum spin system can be represented in terms of spinless fermions in the presence of a gauge field and different gauge-invariant ways of assigning the spin-fermion transformation are considered. Additionally, we analyze general properties of a free-fermion chain, where all gauge terms are neglected and discuss their relevance for the quantum spin system. A consideration of interaction terms in the fermionic Hamiltonian rests upon the Hartree-Fock procedure after fixing the appropriate gauge. Finally, we discuss the magnetic properties of this quantum spin model at zero as well as non-zero temperatures and analyze the validity of the approximation used through a comparison with the results of the exact diagonalization method for finite (up to 36 spins) chains. Besides the m = 1/3 plateau the most prominent feature of the magnetization curve is a jump at intermediate field present for certain values of the frustrating vertical bond.     

Investigation of the anomaly in $\eta$-photoproduction off the neutron

Quasi-free photoproduction of wmesons off the neutron and off the proton has been studied using a deuterium target and bremsstrahlung photons produced by MAMI-C with incident energies up to 1.5 GeV. The wmesons were detected in coincidence with the recoil nucleons thus a fully exclusive measurement was performed. Preliminary results show a bump-like structure in the excitation function for the neutron close to W ≈ 1675 MeV which is not seen for the proton. Considering the experimental resolution and using a Breit-Wigner fit the width of this structure was approximated below 50 MeV.     

New spectral representation and evaluation of f π and the quark condensate \left\langle {\bar qq} \right\rangle in the terms of string tension

New spectral representations for f _π and chiral condensate are derived in QCD and used for calculations in the large-N _c limit. Both quantities are expressed in this limit through string tension σ and gluon correlation length T _g without fitting parameters. As a result, one obtains $\left\langle {\bar qq} \right\rangle = - N_c \sigma ^2 T_g a_1 $ , $f_\pi = \sqrt {N_c } \sigma T_g a_2 $ , with a ₁=0.0823, a ₂=0.30. Taking σ=0.18 GeV² and T _g=1 GeV^?1, as known from analytic and lattice calculations, this yields $\left\langle {\bar qq} \right\rangle $ (μ=2 GeV)=?(0.225 GeV)³, f _π=0.094 GeV, which is close to the standard values.