Conservation laws for classical and relativistic collisions. II

On the basis of elementary symmetry arguments it is shown that (1) if in classical mechanics there exists a quantity λ+Σ_iμ_iυ_i+1/2νυ ² that is conserved, where λ,μ _i, andν are particle parameters, then theμ _i andν are all proportional to a single parameterμ and the quantityAμ+Σ_iB_iμυ_i+C(λ+ 1/2Dμυ ²), whereD ≡ν/μ, is conserved for all values ofA, B _i, andC; (2) if in relativistic mechanics there exists a quantity λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc[1−(υ ²/c ²)]^−1/2 that is conserved, then theμ _i andν are all proportional to a single parameterμ and the quantityAλ+Σ_iB_iμν_i[1−(υ ²/c ²)]^−1/2+Cμc [1−(υ ²/c ²)]^−1/2 is conserved for all values ofA, B _i, andC.     

Rare t-quark decays t → clj+lk? and t → c?jvk induced by doublets of scalar leptoquarks within the minimal four-color-symmetry model

The rare t-quark decays t → cl _j ⁺ l _k ⁻ and t → cṽ _j k _k induced by scalar-leptoquark doublets are considered within the minimal model involving four-color quark-lepton symmetry and the Higgs mechanism of quark and lepton mass splitting. The partial widths with respect to the decays being considered and the total widths Γ(t → cl ⁺′l ⁻) = Σ_j,k Γ(t → cl _j ⁺ l _k ⁻ ) and Γ(t → cl ⁺′l ⁻) = Σ_j,kΓ(t → cṽ _j v _k ) with respect to, respectively, the charged leptonic and neutrino modes are calculated. It is shown that, at scalar-leptoquark masses higher than the t-quark mass (m _S > m _t), the branching ratios for these modes are Br(t → cl ⁺′l ⁻) ≈ (3.5−0.4) × 10⁻⁵ and Br(t → cṽ′v) ≈ (7.1−0.8) × 10⁻⁵ at m _s = 180–250 GeV and an appropriate value of the leptoquark-mixing angle (sin β ≈ 0.2) and can increase for m _S < m _t to Br(t → cl ⁺′l ⁻) ≈ 0.03−0.002 and Br(t → cl ⁺′l ⁻) ≈ 0.46−0.05 for the charged mode at m _S = 150–170 GeV for sin β ≈ 1 and sin β ≈ 0.2, respectively. In the cases being considered, t-quark decays to pairs of charged leptons can be accessible to detection at LHC. In the last case, these decays could manifest themselves (for example, in dilepton events) at the Tevatron as well. Original Russian Text ? P.Yu. Popov, A.D. Smirnov, 2006, published in Yadernaya Fizika, 2006, Vol. 69, No. 6, pp. 1006–1016.     

Confrontation of nucleus deformation and multipole mixture parameters in (2+0 n ?2+01) transitions with rotational band structure for K π = 0 2+ and 0 3+

The difference of the energies of levels Δ _n = E _lev(2⁺0 _n ) − E _lev(0⁺0 _n ) at n = 1, 2, and 3 and the multipole-mixture parameter δ for (2⁺0₂−2⁺0₁) and (2⁺0₃−2⁺0₁) transitions are contrasted against the structure of the K ^π = 0₂⁺ and 0₃⁺ rotational bands that was calculated on the basis of the quasiparticle-phonon model. The values of (Δ₂ − Δ₁), (Δ₃ − Δ₁), and (Δ₂ − Δ₃) are found to correlate with the sign of the parameter δ and with the calculated structure of the K ^π = 0₂⁺ and 0₃⁺ bands. Original Russian Text ? A.M. Demidov, L.I. Govor, V.A. Kurkin, I.V. Mikhailov, 2009, published in Yadernaya Fizika, 2009, Vol. 72, No. 2, pp. 236–240.     

Search for the f1(1285) → π+π-π0 decay with the VES detector

The isospin-violating decay f ₁(1285) → π⁺π^-π⁰ has been studied at the VES facility. This study is based on the statistics acquired in π^- Be interactions at 27, 36.6 and 41 GeV/c in the diffractive reaction π^- N → (f ₁π^-)N . The f ₁(1285) → π⁺π^-π⁰ decay is observed. The preliminary ratio of decay probabilities BR(f ₁(1285) → π⁺π^-π⁰) to BR(f ₁(1285) → ηπ⁺π^-)^. BR(η → γγ) is ∼ 2% . Original article based on material presented at HADRON 2007.     

On the high-statistics investigation of the <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) resonance in the γγ → π<Superscript>0</Superscript>η reaction

High-statistics data on the γγ → π⁰η reaction will make it possible to conclude whether the K ⁺ K ⁻-loop rescattering mechanism, γγ → K ⁺ K ⁻ → a ₀(980) → π⁰η, is the main mechanism of the production of a ₀(980) isovector resonance. This mechanism provides a reasonable value of 20–30 nb at the maximum for the manifestation of a ₀(980) in the γγ → π⁰η cross section. It also gives rise to a noticeable narrowing of the a ₀(980) peak to its effective (observed) width ≈20–30 MeV in the γγ → π⁰η channel. The decay width averaged over the resonance mass distribution is 〈Γ_{α 0} → K ⁺ K ⁻ → γγ〉_πη ≈ 0.13 keV. The experimental confirmation of this scenario would be important evidence in favor of the q ² $ \bar q $ \bar q ² nature of light scalar mesons.     

Conservation laws for classical and relativistic collisions. I

On the basis of simple kinematic arguments it is shown that any quantity, depending only on the nature and velocity of a particle, that is conserved in a collision must, in classical mechanics, be of the form λ+Σ_iμ_iυ_i+1/2vυ ² or in relativistic mechanics of the form λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc [1−(υ ²/c ²)]^−1/2 where λ,μ _i, andν are particle parameters.     

The K * Kπ and ρππ couplings in QCD

The light cone QCD sum rules are derived for the K ^* Kπ coupling g _K ^* Kπ and the ρππ coupling g _ρππ. The contribution from the excited states and the continuum is subtracted cleanly through the double Borel transform with respect to the two external momenta, p ₁ ², p ₂ ²= (p−q)². Our result g _K ^* Kπ= (8.7 ± 0.5) and g _ρππ= (11.5 ± 0.8) is in good agreement with the experimental value. Received: 31 July 1998 / Revised version: 20 November 1998     

Electron-vibrational energy exchange in collisions of Ar atoms in the 3P2 metastable state with N2(X1S g+ ) molecules

Rate constants for electron-vibrational energy exchange Ar(³ P ₂) + N₂(X ¹Σ _g ⁺, ν = 0) → Ar(¹ S ₀) + N₂(C ³Π _u , ν′), where ν′ = 0, 1, 2, were calculated. Calculations were performed taking into account the presence of a resonance in electron scattering by N₂(X ¹Σ _g ⁺). As a result, the interaction of Ar(³ P ₂) with N₂(X ¹Σ _g ⁺, ν = 0) was characterized by attraction and, in the end, intersection of electron-vibrational potential surfaces correlating with Ar(³ P ₂) + N₂(X ¹Σ _g ⁺, ν = 0) and Ar(¹ S ₀) + N₂(C ³Π _u , ν′) at interparticle distances of 2.5–3.5 ?. Exchange interaction at which electron-vibrational transitions in the region of intersection of electron-vibrational transitions in the region of intersection of electron-vibrational potential surfaces accompanied by spin exchange were induced was calculated by the asymptotic method. The rate constants determined at 300–600 K were on the order of 10⁻¹¹−10⁻¹² cm³/s and weakly increased as the temperature grew. Mainly the C ³Π _u , ν′ = 0 state of the N₂ molecule was populated. The calculation results were in satisfactory agreement with the experimental data obtained at 300 K.     

Fluorescence studies of CS2 and SO2 at 121.6, 73.6–74.4 and 58.4 nm

The fluorescence spectra of CS₂ and SO₂ have been studied at three incident photon wavelengths of 121.6, 73.6–74.4 and 58.4 nm and relative production cross sections for different product states have been measured. The CS(A ¹Π→X ¹Σ⁺) system between 240 and 290nm has been obtained when CS₂ is photoexcited at 121.6nm whereas CS ₂ ⁺ (B ²Σ _u ⁺ →X ²Π _g ) and CS ₂ ⁺ (A ²Π _u →X ²Π _g ) systems have been produced between 276 and 295 and 437 and 555nm respectively when excited by both the incident photon wavelengths of 73.6–74.4 and 58.4nm. The fluorescence spectra of SO₂ obtained at 121.6 and 73.6–74.4nm include the vibrational bands of SO(A ³Π→X ³Σ⁻) and SO(B ²Π⁻→X ³Σ⁻) systems from 240 to 268 and 268 to 442nm respectively whereas the emission spectrum at 58.4nm, has contributions from the two SO systems and SO⁺(A ²Π→X ²Π) system. In all these emission spectra, the fluorescence bands of different systems have been analyzed and their relative production cross sections have been measured. The results obtained in the present investigations have been compared with a few recent reliable measurements reported in literature.     

Analysis of the decays ψ′ → J/ψπ+π? and η′c → ηcπ+π? with the heavy-quark symmetry

In this article, we study the decays ψ′ → J/ψπ ⁺ π ⁻ and η′_c → η _c π ⁺ π ⁻ by taking into account the chiral symmetry breaking effects, the final-state interactions and the heavy-quark symmetry. We can confront the predictions of the η′_c → η _c π ⁺ π ⁻ decay width and differential decay width with the experimental data in the future, and obtain powerful constraints on the chiral breaking effects and the final-state interactions, and test the heavy-quark symmetry.     

Overlapping B3Π0u ← X1Σ g/+ and 1Π1u ← X1Σ g/+ non-radiative characteristic of Br2 vapour in the wavelength region 505–541 nm

The vibronic vapour phase photoacoustic spectrum of Br₂ in the wavelength region 505–541 nm (19796–18480 cm⁻¹) has been recorded using microphone as well as pump-probe method. Discrete vibronic bands superimposed on a monotonically increasing continuum background towards the dissociation limit results from the overlapping B ³Π _0u ^/+ ← X ¹Σ _g ^/+ and ¹Π_1u ← X ¹Σ _g ^/+ electronic transitions. Vibronic bands originating from υ″=0 have been used to estimate the relative rate of non-radiative relaxation as a function of the excited state B ³Π_0u vibrational quantum number υ′. A comparison with the optical absorption spectroscopy of Br₂ leads to the identification of three broad spectral regions between 505 and 541 nm (19796 and 18480 cm⁻¹) on the basis of different non-radiative relaxation processes.     

The multiphoton ionization rate and the energy shift of atoms interacting with weak dichromatic fields with commensurate frequencies are simple functions of the phase difference

By implementing a time-independent, nonperturbative many-electron, many-photon theory (MEMPT), cycle-averaged complex eigenvalues were obtained for the He atom, whose real part gives the field-induced energy shift, Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ), and the imaginary part is the multiphoton ionization rate, Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ), where ω is the frequency, F is the field strength and ϕ is the phase difference. Through analysis and computation we show that, provided the intensities are weak, the dependence of Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) on ϕ is simple. Specifically, for odd harmonics, Γ varies linearly with cos(ϕ) whilst for even harmonics it varies linearly with cos(2ϕ). In addition, this dependence on ϕ holds for Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) as well. These relations may turn out to be applicable to other atomic systems as well, and to provide a definition of the weak field regime in the dichromatic case. When the combination of (ω ₁, F ₁) and (ω ₂, F ₂) is such that higher powers of cos(ϕ) and cos(2ϕ) become important, these rules break down and we reach the strong field regime. The herein reported results refer to Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) and Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) for He irradiated by a dichromatic ac-field consisting of the fundamental wavelength λ = 248 nm and its 2nd, 3rd and 4th higher harmonics. The intensities are in the range 1.0×10¹²-3.5×10¹⁴ W/cm², with the intensity of the harmonics being 1-2 orders of magnitude smaller. The calculations incorporated systematically electronic structure and electron correlation effects in the discrete and in the continuous spectrum, for ¹S, ¹P, ¹D, ¹F, ¹G, and ¹H two-electron states of even and odd parity. Received 9 July 2000 and Received in final form 2 November 2000     

14N and35Cl nuclear quadrupole coupling constants in thiazyl chloride from microwave spectroscopy andab initio molecular orbital computations

Summary The¹⁴N and³⁵Cl nuclear quadrupole coupling constants of the¹⁴N³²S³⁵Cl isotopic species of thiazyl chloride have been determined from an analysis of the hyperfine structure of sixμ _a andμ _b transitions in the microwave spectrum as (in MHz) _χaa (³⁵CL) = −39.00(3), _χbb (³⁵CL) = 23.84(4), _χaa (¹⁴N) = −1.42(6), _χbb (¹⁴N) = −4.16(6).

---

Riassunto Le costanti di accoppiamento quadrupolare di¹⁴N e³⁵Cl della specie isotopica¹⁴N³²S³⁵Cl del tiazil cloruro sono state determinate attraverso l'analisi della struttura iperfine di sei transizioni di tipoμ _a eμ _b dello spettro a microonde. Si sono ottenuti i seguenti valori (in MHz): _χaa (³⁵CL) = −39.00(3), _χbb (³⁵CL) = 23.84(4), _χaa (¹⁴N) = −1.42(6), _χbb (¹⁴N) = −4.16(6).

---

Резюме Из анализа сверхтонкой структуры шестиμ _a иμ _b переходов в микроволновом спектре определяются ядерные квадрупольные константы связи¹⁴N и³⁵Cl в¹⁴N³²S³⁵Cl. Получены следующие значения (в МГц): _χaa (³⁵CL) = −39.00(3), _χbb (³⁵CL) = 23.84(4), _χaa (¹⁴N) = −1.42(6), _χbb (¹⁴N) = −4.16(6).kg]PACS. 33.20

     

Bounds on charged lepton mixing with exotic charged leptons

We examine the effects of mixing induced light heavy charged lepton neutral currents on the partial wave amplitude for the process l⁺l⁻ →ZZ (withl = e,μ or τ). By imposing the constraints that the amplitude should not exceed the perturbative unitarity limit at high energy (√s = Λ), we obtain bounds on light heavy charged lepton mixing parameter sin²(2θ _L ^a ) where θ _L ^a is the mixing angle of the ordinary charged lepton with its exotic partner. For Λ = 1 TeV, no bound is obtained on sin² (2θ _L ^a ) form _E < 0.69 TeV. However, sin² (2θ _L ^a ) ≤ 1.52×10⁻⁵ form _E = 5 TeV, sin² (2θ _L ^a ) ≤ 2.41 ×10⁻⁷ form _E = 10 TeV. Similarity for Λ = ∞ no bound is obtained on sin² (2θ _L ^a ) for m_E < 1.97 TeV and sin² (2θ _L ^a ) ≤ 0.15 form _E = 5 TeV and sin² (2θ _L ^a ) ≤ 3.88×10^-2 form _E = 10 TeV.     

Composite model of gauge bosons in electroweak interactions

We consider a simple Lagrangian which is constructed by only the preon and antipreon fields. By introducing the auxiliary fields φ_μ, φ _μ ^† , and ϕ_μ, it is shown that φ_μ, φ _μ ^† , and ϕ_μ correspond to the electroweak gauge bosonsW _μ ⁺ ,W _μ ⁻ , andW _μ ³ , respectively, which are composite particles of preons and antipreons.     

Optical spectra and spin-Hamiltonian parameters of trivalent ytterbium in lead tungstate

By using crystal-field theory, the optical spectra and spin-Hamiltonian parameters (abbr. SH parameters, i.e. the anisotropic g factors g _∥, g _⊥, and hyperfine structure constants A _∥, A _⊥) of ¹⁷¹Yb^3 + and ¹⁷³Yb^3 + isotopes in the tetragonal PbWO₄ are calculated. The theoretical results agree well with the experimental values. The crystal-field parameters and the signs of the hyperfine structure constants for both ¹⁷¹Yb^3 + and ¹⁷³Yb^3 + isotopes are determined. The validities of the theoretical results are discussed.     

Lattice Dislocations in a 1-Dimensional Model

The spectral properties of the Schr?dinger operator T(t)=−d ²/dx ²+q(x,t) in L ²(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ _ac (T(t))=σ _ac (T(0)) consists of intervals, which are separated by the gaps γ _n (T(t))=γ _n (T(0))=(α _n ⁻,α _n ⁺), n≥1. We prove: in each gap γ _n ≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ _n ^±(t) of the dislocation operator, such that λ _n ^±(0)=α _n ^± and the point λ _n ^±(t) runs clockwise around the gap γ _n changing the energy sheet whenever it hits α _n ^±, making n/2 complete revolutions in unit time. On the first sheet λ _n ^±(t) is an eigenvalue and on the second sheet λ _n ^±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ₀(t) in the basic gap γ₀(T(t))=γ₀(T(0))=(−∞ ,α₀ ⁺). The asymptotics of λ _n ^±(t) as n→∞ is determined. Received: 5 April 1999 / Accepted: 3 March 2000     

Thermo-optic coefficients of monoclinic KLu(WO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The three thermo-optic coefficients of the biaxial laser host KLu(WO₄)₂ are measured at 633 nm by a deflection method. Their values at 300 K amount to ∂ n _g /∂ T=−7.4×10⁻⁶ K⁻¹; ∂ n _m /∂ T=−1.6×10⁻⁶ K⁻¹ and ∂ n _p /∂ T=−10.8×10⁻⁶ K⁻¹. Nearly athermal propagation directions are found for polarizations along the N _m and N _p dielectric axes.     

Electromagnetic mass splittings of heavier hadrons in quantum chromodynamics

The electromagnetic mass splittings of heavier hadrons are estimated in the framework of gauge theory model where ligher quarks are taken to behave relativistically and the spatial wave functions are described by the spin-spin interaction affected relative distances between quarks. The predictions for (Ξ⁻-Ξ⁰), (Σ*⁰−Σ*⁺), (Ξ^*−-Ξ^*0), (D _c ⁺−D _c ⁰) and (D _c ^*+ −D _c ^*0 ) are in fair agreement with the experimental data available whereas those for (D _b ⁻ −D _b ⁰ ) and (D _b ^*− −D _b ^*0 ) are in qualitative agreement with other theoretical estimates.