The muon spectra from decays ofW- andZ-bosons produced ine + e −-collisions

The muon spectra from the decays ofW-andZ-bosons, produced ine ⁺ e ^?→W ⁺ W ^?,e ⁺ e ^?→Zγ,e ⁺ e ^?→ZZ ande ⁺ e ^?→ZH reactions have been obtained (H is the Higgs boson). It has been shown (in terms of Glashow-Weinberg-Salam theory) that the main source of muons are thee ⁺ e ^?→Zγ ande ⁺ e ^?→W ⁺ W ^? processes (over theW-boson production threshold). The contribution of thee ⁺ e ^?→ZZ ande ⁺ e ^?→ZH reactions to the inclusive muon spectra is small. It has been also shown, that it is possible to distinguish contributions of thee ⁺ e ^?→Zγ ande ⁺ e ^?→W ⁺ W ^? reactions if the decay muons move at a small angle to the initial electron momentum.     

High-resolution Fourier spectroscopy of 14N2 and 15N2 infrared emission spectrum: Analysis of the B′3Σu−-B3Πg system

The rotational analysis of some bands of the B′³Σ_u^?-B³Π_g system of nitrogen (¹⁴N₂ and ¹⁵N₂) excited in a microwave discharge and recorded under high resolution with a Fourier transform interferometer allowed the determination of molecular constants for the v = 0, 1, 2 levels in the B′³Σ_u^? state. Main equilibrium constants of the B′³Σ_u^? state for ¹⁴N₂ and ¹⁵N₂ are (in cm^?1) T_e = 5789.2178 (relative to B³Π_g (v = 0); ω_e = 1516.6239; ω_ex_e = 11.9721; B_e = 1.473 098; α_B = 0.01 664; ω_eⁱ = 1465.3549; ω_ex_eⁱ = 11.1783; B_eⁱ = 1.375 209; α_Bⁱ = 0.01 505.     

On the scaling factors α(z) and δ(z)

We introduce a new method to determine the scaling factors α(z) and δ(z) for the period-doubling route to chaos in dissipative systems, exemplified by the one-dimensional mapping x_n+1=1−λ∣x_n∣^z. With the help of the Feigenbaum universal functions g(x) and h(x) we derive the inequality α^z−α<δ(z)<α^z, implying in particular that δ(z) remains finite (≲30) in the limit z → ∞.     

Is every approximate trajectory of some process near an exact trajectory of a nearby process?

This paper deals with the problem “Can a noisy orbit be tracked by a real orbit?” In particular, we will study the one-parameter family of tent maps and the one-parameter family of quadratic maps. We writeg _μ for eitherf _μ orF _μ withf _μ (x)=μx forx≦1/2 andf _μ (x)=μ(1?x) forx≧1/2, andF _μ (x)=μx(1?x). For a given μ we will say:g _μ permits increased parameter shadowing if for each δ _x >0 there exists someδ _μ >0 and some δ _f >0 such that every δ _f -pseudog _μ -orbit starting in some invariant interval can be δ _x -shadowed by a realg _α -orbit with α=μ+δ _μ . We show thatg _μ typically permits increased parameter shadowing.     

A measurement of the electromagnetic form factor of the eta meson and of the branching ratio for the eta Dalitz decay

In an optical spark chamber experiment we have obtained a sample of 80 eta Dalitz decays (η → e⁺e^?γ) and have measured the eta electromagnetic form factor to be F(X) = 1.0?(0.22 ±0.45)X, where X=M_ee²/M_η², and the branching ratio (η→e⁺e^?γ/(η→π⁺π^?π⁰)= (0.0082 ± 0.0020).     

Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions

We analyze the renormalized strong coupling series for lattice g₀φ⁴ field theory which is a double series in x = M⁴a⁴/g₀a_4?dandy = 1/M²a², where M is the renormalized mass, a the lattice spacing, g₀ the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M^4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g₀ from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y⁵ and in x up to x³ show that for fixed lattice spacing a, G/M^4?d is a monotonic function of g₀ ranging from zero at g₀ = 0 to a maximum at g₀ = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.     

Measurement of the spin parameters A and Ann in pp elastic scattering in the 1–3 GeV/c region

We have measured the asymmetry parameter A and the spin correlation parameter A_nn in pp elastic scattering, using the Argonne ZGS polarized proton beam and a polarized proton target. Angular distributions of A and A_nn for |t| ? 0.2 (GeV/c)²wereobtainedateightmomentabetween 1.10 and 2if2.75 GeV/c. We find significant structure in both the energy and t-dependence of A_nn at these energies. At p_lab ≈ 1.34 GeV/cA_nn reaches a very large value of about 0.8–0.9 near θ_cm = 90°.     

Light-Front Zero-Mode Issue for the Transition Form Factors Between Pseudoscalar and Vector Mesons

We study the light-front zero-mode contribution to the transition form factors (g, f, a _±, T _i ) (i = 1, 2, 3) for the exclusive semileptonic P → V ?ν _? and rare P → V ? ⁺?^? decays using a covariant fermion field theory model in (3+1) dimensions. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γ ^μ  = γ ^μ ? (2k ? P _V ) ^μ /D, the six form factors (g, f, a ₊, T ₁, T ₂, T ₃) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor (1/x) ⁿ of the struck quark with the power n > 0. Although the form factor a _? is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex Γ ^μ  = γ ^μ term or from the other term just with a constant D (i.e. n = 0). We identify the zero-mode operator that is convoluted with the initial- and final-state valence wave functions to generate the zero-mode contribution to a _?.     

A multi-channel scattering theory for some time dependent Hamiltonians,charge transfer problem

Scattering theory for time dependent HamiltonianH(t)=?(1/2) Δ+ΣV _j (x?q _j (t)) is discussed. The existence, asymptotic orthogonality and the asymptotic completeness of the multi-channel wave operators are obtained under the conditions that the potentials are short range: |V _j (x)|≦C _j (1+|x|)^?2?ε, roughly spoken; and the trajectoriesq _j (t) are straight lines at remote past and far future, and |q _j (t)?q _k (t)| → ∞ ast → ± ∞ (j≠k).     

1/N topological expansion for lattice QCD

A U(N_c) gauge theory with a global U(N_f) flavor symmetry is investigated in the limit both N_c and N_f large with the ratio ξ ≡ N_f/N_c fixed.     

Magnetic properties of transition metal substituted MnP

The magnetic properties of polycrystalline samples of Mn_1?tT_tP (T = V, Cr, Fe and Co for 0.00 ≦ t ≦ 0.50) are studied by magnetic susceptibility, magnetization and neutron diffraction measurements. The magnetic phase diagrams of the Mn_1?tT_tP phases exhibit paramagnetic, ferromagnetic, helimagnetic and spin glass regions depending on temperature and substitution (T, t). The concentrated spin glass regions observed in Mn_1?tV_tP and Mn_1?tCo_tP (0.30 ≦ t ≦ 0.50) are believed to result from the disorder in the metal sublattice. The variation of the magnetic moment of the ordered Mn_1?tT_tP phases with the substitution (T, t) is discussed.     

Effect of conduction band nonprabolicity on the Rashba spin splitting of AlGaN/GaN QWs

By using the perturbation expansion method and self-consistent iterative method, we evaluate the effect of the conduction band nonprabolicity on the wave vector (k_t) dependent Rashba coefficient (α) and nonlinear Rashba spin splitting (ΔE) in the Al_0.5Ga_0.5N/GaN quantum well (QW). The effective mass (energy) under the first order approximation m_t1 (E_k1) is in proximity to the iterative result m_tp (E_kp) and m_t1>m_tp, E_k1<E_kp, showing the higher order contributions to m_t (E_k) are small. The sign of the nonparabolic correction to E_k is just opposite to that of the correction to m_t. The increase of α and ΔE due to the conduction band nonparabolicity reaches about 3% at k_t=1 nm⁻¹. Around the left heterointerface, the probability density is high and E_k0>E_kp>E_k1, so α₀<α_p<α₁, ΔE₀<ΔE_p<ΔE₁. With increasing k_t, α decreases, and ΔE increases slowly. For small k_t, α₀ (ΔE₀), α₁ (ΔE₁) and α_p (ΔE_p) are nearly the same. While for large k_t, the difference between α₀ and α₁ (α_p) increases rapidly, but the difference between ΔE₀ and ΔE₁ (ΔE_p) increases slowly.     

Nonfactorizable contributions to hadronic decays of charm mesons in the Cabibbo-suppressed modes

We investigate nonfactorizable contributions to charm meson decays into D → ππ/K K?/K K?*/K? K*/D → K*K?* modes. Obtaining the contributions from spectatorquark diagrams for N _c = 3, we determine the nonfactorizable isospin amplitudes required to explain the data for these modes. For these decays, we observe that ππ, πρ, decay modes favor a nonfactorizable-isospin-amplitudes ratio A ₀ ^nf /A ₂ ^nf equal to (1.123±0.158) and for K K?, K K?*, K? K* and K*K?* modes, the ratio of nonfactorizable amplitudes A ₀ ^nf and A ₁ ^nf turns out to be unity.     

Nonfactorization and the decaysD s +→φπ +,φρ + andφl + ν l

Using the experimentally measured values ofx=A ₂(0)/A ₁(0) andy=V(0)/A ₁(0) and the measured ratiosR _st=Γ(D _s ⁺ →φl ⁺ ν _l)/Γ(D _ins ⁺ →φπ ⁺) andR _h=Γ(D _s ⁺ →φρ ⁺)/Γ(D _s ⁺ →φπ ⁺), we present evidence for significant nonfactorization contribution in the decay amplitude forD _s ⁺ →φπ ⁺. We analyze the role of nonfactorization inD _s ⁺ →φρ ⁺ and conclude that present data onR _h are consistent with factorization inD _s ⁺ →φρ ⁺. A measurement of polarization inD _s ⁺ →φρ ⁺ would greatly assist our analysis.     

On the Deser,Gilbert, Sudarshan representation for functions Wi(ν, q2)(i = 1, 2) describing the electroproduction process

The Deser, Gilbert, Sudarshan representation (D.G.S.R.) for the functions W_i(ν, q²) (i = 1,2) is considered as equations determining spectral functions h_i(a, α) via the values W_i(ν, q²) in the physical region of the electroproduction channel. It is shown that if W_i(ν, q²) obey the microcausality and spectrality conditions, then the equations for h_i(a, α) have solutions in the class of Schwartz temperated distributions and thereby the D.G.S.R. is proved. Formulae are obtained expressing spectral functions in the D.G.S.R. through the values of functions W_i(ν, q²) in the physical region of the electroproduction channel.     

Anomaly in the lattice partition function

The lattice partition function Z(T)=σ_(Si) exp(−H/k_BT), where H, k_B and T are the Hamiltonian of the system, the Boltzmann constant and the absolute temperature, respectively, leads to a vanishing spontaneous magnetisation for all temperatures, independently of the lattice considered. This feature is related to the symmetry breaking in these systems. In comparing this relation to the well-known partition function Z(T)=σ_n exp(−E_n/k_BT) where E_n is energy, we observe an incompatibility which could be the reason that this partition function leads to a vanishing spontaneous magnetisation.     

Analysis of the φ → γπη and φ → γπ 0 π 0 decays

We study interference patterns in the φ → (γa ₀+π ⁰ ρ) → γπη and φ → (γf ₀+π ⁰ ρ) → γπ ⁰ π ⁰ reactions. Taking into account the interference, we fit the experimental data and show that the background reaction does not distort the π ⁰ η spectrum in the decay φ → γπη everywhere over the energy region and does not distort the π ⁰ π ⁰ spectrum in the decay φ → γπ ⁰ π ⁰ in the wide region of the π ⁰ π ⁰-system invariant mass, π ^ππ > 670 MeV, or when the photon energy is less than 300 MeV. We discuss the details of the scalar meson production in the radiative decays and note that there are reasonable arguments in favor of the one-loop mechanism φ → K ⁺ K ^? → γa ₀ and φ → K ⁺ K ^? → γf ₀. We also discuss distinctions between the four-quark, molecular, and two-quark models and argue that the Novosibirsk data give evidence in favor of the four-quark nature of the scalar a ₀(980) and f ₀(980) mesons.     

Equation of state and quantal crossover of the XY model in a longitudinal magnetic field

The equation of state of the XY model in a longitudinal (Γ) and transverse field (B) is investigated in the vicinity of a multicritical point (Γ_c, T =0) using the renormalization group method developed recently by the author and K. Walasek. For Γ = Γ_c a quantal crossover behaviour of the form H = M_{R³ψ (z)} is obtained, where H ～ B, M_R denotes the transverse magnetization, z ～ TM_R^?/βq, while ?,β_q are crossover and multicritical exponents, respectively.     

Interaction effects on atomic laboratory trapped Bose-Einstein condensates

We discuss the effect of inter-atoms interactions on the condensation temperature T _c of an atomic laboratory trapped Bose-Einstein condensate. We show that, in the mean-field Hartree-Fock and semiclassical approximations, interactions produce a shift Δ T _c /T _c ⁰ ≈ b ₁(a/λ _{T c} ) + b ₂(a/λ _{T c} )² + ψ[a / λ _{T c} ] with a the s-wave scattering length, λ _T the thermal wavelength and ψ[a / λ _{T c} ] a non-analytic function such that ψ[0] = ψ′[0] = ψ′′[0] = 0 and |ψ′′′[0]| = ∞. Therefore, with no more assumptions than Hartree-Fock and semiclassical approximations, interaction effecs are perturbative to second order in a / λ _{T c} and the expected non-perturbativity of physical quantities at critical temperature appears only to third order. We compare this finding with different results by other authors, which are based on more than the Hartree-Fock and semiclassical approximations. Moreover, we obtain an analytical estimation for b ₂ ? 18.8 which improves a previous numerical result. We also discuss how the discrepancy between b ₂ and the empirical value of b ₂ = 46 ± 5 may be explained with no need to resort to beyond-mean field effects.     

Generalizing some properties of short range classical solutions to Yang-Mills theory

We extend a theorem which states that for classical solutions of Yang-Mills theory, the field G_μν has to decrease at least as fast as the source S_μ at spatial infinity, provided G_μν decreases exponentially [G_μν ～ exp(?Mr)]. This generalization encompasses all decreases G_μν ～ exp(?Mr^η) with η > 0, r→∞. This is done by assuming an integral representation for A_μ, the vector potential, and imposing some regularity conditions on A_μ, valid as r→∞.