Electromagnetic corrections to neutrino processes in the leading logarithmic approximation,the value of sin θ and the W and Z masses

The parameters of the Weinberg-Salam model can be defined by amplitudes at a momentum scale M = O(M_W, M_Z). We derive the leading logarithmic e.m. correction to the relations giving the neutrino amplitudes at a momentum scale μ ? M in terms of sin²θ(M), α(M), M_W and M_Z. For leptonic processes, the Fermi constant is not corrected, but a running, universal, sin²θ(μ) > sin²θ(M) should be used. The Fermi constant for semileptonic processes is renormalized by a factor $\text{?(μ) > 1}$, for charged currents, and is not renormalized, for neutral current processes. The latter are described by the same sin²θ(μ) as the leptonic ones. We estimate that sin²θ(M) is about 0.013 smaller than the value of sin²θ obtained from semileptonic data with no correction, thereby improving the agreement with grand unified theories. The prediction for W (Z) masses and widths in terms of the low energy parameters are discussed. Using previous calculations at order α, we obtain predictions for the masses which are accurate up to and including terms of order (αlnM²)².     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

Slope parameter and scaling of differential cross-section of Λ-p scattering

The claim of Mohapatra and Maharana thattb(s) is a better scaling variable thant(lns)² is put to test in the case of Λ-p scattering, after parametrizingb(s) asC ₁ +C ₂(lns)α. It was observed that in this case the data also prefer anα value which is close to those obtained by Mohapatra and Maharana for other scattering processes.     

Die Stromdichte eines quadratisch integrierbaren Klein-Gordon-Feldes mit Wechselwirkung

A four vector is constructed for the statistical interpretation of a relativistic scalar wave function which is not a solution of an interaction-free Klein-Gordon equation. The zero component of the four vector is positive definite, whereas the four components satisfy the equation of continuity. It is proved that these components, which are bilinear forms inΨ(x)=∫d ⁴pa(p)e^?ipxsatisfying the normalization condition(2π) ⁴(2m)^?1∫ d⁴pθ(p⁰)θ6(p²)¦a(p)¦²=1 reduce to the four-vector ofPetzold and co-workers if the transition fromΨ(x) to the free-particle wave functionΦ(x)=∫d ³¯pa(¯p)e^?ipxsatisfying(2π) ³ (2m)^?1∫(2p₀)^?1¦a (¯p)¦²d³¯p=1 is made in the proper way. The nonrelativistic limit in the case of relativistic interactions is also discussed.     

Messung der Winkelverteilung der Neutronenpolarisation bei Streuung von 15,85 MeV-Neutronen am Kohlenstoff

AtE _n=15.85 MeV the angular distributions of neutron polarizationP(θ) for¹²C(n, n)¹²C and of scattering asymmetry A(θ) for¹² C(n,n′)¹² C ^*(Q=?4.43 MeV) have been measured. In a neutron time-of-flight method with a plastic scintillator as scatterer carbon recoil nuclei were used for detection. Polarized neutrons were produced in thed-t reaction atE _d=1.90 MeV at a reaction angle of 70° (lab.). WithP _n=?0.135 scattering polarizations P(θ) are forθ _lab=30, 40, 50, 60, 70, and 80° respectively ?27.0±2.1, ?48.4±2.7, ?68.7±3.6, ?20.7±6.2, +5.3±3.9, and +2.1±4.5%.     

The angular dependence of flux,mean energy and speed ratio for D2 molecules desorbing from a Ni(111) surface

Experimental data are presented for the angular dependence of the relative flux, the mean energy and the speed ratio of deuterium molecules desorbing from a Ni(111) crystal surface at a surface temperature of T_s = 1143 K and at sulphur coverages ranging between 30% and less than 2% of a monolayer.The angular flux distribution is sharply peaked in the forward direction (cos^dθwith 3 ? d ? 5) and the mean energy 〈E〉 of the desorbate depends strongly on the desorption angle θ. For normal desorption $\text{(θ = 0°)}\text{〈E〉}\text{2k}$ is about 700 K higher than T_s and for glancing angles (θ = 80°) it decreases to about 400 K below T_s The results obtained on sulphur free and sulphur covered Ni(111) surfaces are compared with our former data on polycrystalline nickel. The main differences in the kinetic features can be ascribed to the surface roughness. Accordingly, the angular distributions of flux, mean energy, and speed ratio, which deviate strongly from the Knudson and Maxwellian law, do not seem to depend considerably on sulphur coverage and surface structure. A qualitative explanation for these deviations is presented using the principle of detailed balancing.     

The polarization of protons from the 2H(d, p)3H reaction for deuteron energies below 1 MeV

The angular distribution of proton polarization P^γ' (θ) from the ${}^2\text{H}\text{(}\text{d,}\text{p}\text{)}{}^3\text{H}$ reaction has been measured at 975 keV deuteron energy. Moreover, the energy dependence of P^γ′(E_d) was measured at 45°(lab) for deuteron energies between 250 and 975 keV. The values of σ₀(θ)P^γ' (θ) were fitted in terms of an associated Legendre polynomial expansion. The measured energy dependence of P^γ' (E_d) has been analyzed in terms of barrier-penetration parameters.     

The analyzing power Aγ(θ) for the elastic scattering of 12 MeV neutrons from deuterons

The analyzing power A_γ(θ) was obtained at 10° intervals between 30° (lab) to 120° (lab) for ²H(n, n)²H at 12.0 MeV. The polarized neutron beam employed in the measurement was obtained by using neutrons emitted at 0° from the polarization transfer reaction ${}^2\text{H}\text{(}\text{d}\text{,}\text{n}\text{)}{}^3\text{He}$. The accuracy in the A_γ(θ) values that was achieved ranged from ± 0.006 to ± 0.013. Comparison of the data to A_γ(θ) results obtained at 12 MeV for the charge symmetric reaction ²H(p, p)²H shows that the two A_γ(θ) distributions are equal to within the above accuracy.     

Observation of interband transitions in polarized electron energy loss spectra of Gd(0001)

We have detected the 4f ⁷(5d6s)³→4f ⁸(5d6s)² interband transition in an angular-resolved, inelastic scattering experiment with spin-polarized, low-energy electrons from ferromagnetic Gd(0001). The spectrum of the inelastic scattering asymmetry clearly reveals the dominant spin-dependent energy loss mechanism involved. Furthermore its comparison with elastic scattering data allows a characterization of the combined role of diffraction and energy loss processes in inelastic electron scattering.     

Laser-rf double-resonance hyperfine structure measurements of the metastable 3d 4s 1 D 2 state of43Ca

The hyperfine structure of the (3(d 4s)¹ D ₂metastable state of⁴³Ca has been measured using theABMR-LIRF method (atomic beam magnetic resonance, detected by laser induced resonance fluorescence). The measurements yielded for the magnetic dipole and electric quadrupole constantsA=?17.650(2) MHz andB=?4.642(12) MHz, respectively. From the measuredB factor the spectroscopic electric quadrupole moment (uncorrected for shielding effects) has been calculated to beQ(⁴³Ca)=?0.062(12) barn. In addition, isotope shifts in the lines (3d 4s)¹ D ₂(3d 4p)¹ F ₃ ⁰ and (3d 4s)¹ D ₂(4s 5p)¹ p ₁ ⁰ for the stable calcium isotopes have been obtained by high resolution laser spectroscopy.     

Statistics of long-wavelength fluctuations and the expansion rate of Richtmyer-Meshkov turbulence zone

The important problem of Richtmyer-Meshkov turbulence (RMT) is solved. Much work has been devoted to the experimental, numerical (direct numerical simulation), and semiphenomenological (turbulent diffusion and bubble envelope models) analysis of RMT.All of them were of approximate character. They considered the evolution of a mixing layer, and its average thickness h(t) was found. Then, the approximate value of the most important exponent θ (h ∝ t ^θ) was judged from the slope of the h(t) curve in the lnt-lnh coordinates. In this work, the theoretical approach for the exact determination of θ is developed.     

Perturbation of the Laplacian supported by null sets,with applications to polymer measures and quantum fields

We discuss hamiltonians in L²(R^d, dx) of the form H = ?Δ + V, with V a potential supported by a zero measure set C. In particular if C is a path of a brownian motion b such that V(x) = ∫₀¹λ(x, ω)δ(x-b(s, ω)) ds, we show that H exists as a nontrivial, self-adjoint, lower bounded perturbation of ?Δ when d ?5. We must choose λ to be an infinitesimal, negative function for d = 4,5, but for d ? 3 any bounded real-valued function λ will do. The connection with Edward's model of polymers as well as with quantum fields of the ?_d⁴-type is also discussed. The proofs use methods of nonstandard analysis.     

Leading non-cancelling infrared divergences in perturbative QCD

In perturbative QCD, for the inclusive cross section for the scattering of two coloured particles, we identify graphs which contribute to the general leading order α_s(α_s lnλ)ⁿ of uncancelled IR divergences, and we sum these contributions (λ is the IR cut-off). The work is done in the Coulomb gauge; an appendix discusses the Feynman gauge.     

Phase transitions and the high temperature expansion for the reggeon calculus

We study a recently proposed lattice version of the reggeon field theory. First a simple one-dimensional system possessing many of the features of the reggeon calculus (Ising model in an imaginary magnetic field) is solved. Surprisingly, the system is found to undergo a phase transition at a non-zero critical temperature, which, although of first order obeys the universality and scaling laws previously postulated for the reggeon calculus. Returning to the full lattice theory, the machinery for performing a high temperature expansion is set up, and initial calculations carried out to order T^?3. In this order, best estimates for the critical indices η and v in the asymptotic elastic amplitude A(s,t) ～ is (ln s)^ηf(t(lns)^v) yield $\text{η = 0 (}\text{1}\text{2}\text{～ 1), v = 0(1}\text{1}\text{2}\text{～ 2)}$. Check on the method, including comparisons with known Ising model results, are also discussed.     

Einfaches Modell für monoatomare klassische Flüssigkeiten

A simple approximation for the conditional time-dependent pair distribution functionP(r′t ¦ rt) is proposed. With this approximation the van Hove-correlation-functionG _d (rt) is computed and compared with Ludwig's¹ computer results for liquid A1. Then we determine the velocity autocorrelationfunction ψ(t) under special assumptions for the particle motion. That function is compared with Rahman's² computer results for liquid Ar.     

Spin polarization of 29P produced through low energy nuclear reaction

Spin polarization of short-lived β-emitting nucleus ²⁹P (I ^π = 1/2^?+?, T _1/2 = 4.14 s) produced through the ²⁸P(d, n) ²⁹P reaction was studied as functions of the incident deuteron energy E _d and the recoil angle θ of ²⁹P. New optimum condition was found at E _d = 3.3 MeV and θ = 30° where polarization of ²⁹P is ?(4.1 ± 0.7) %.     

On the high spin expansion in the SYM theory

We study the form of the high spin expansion of the minimal anomalous dimension for long operators belonging to the sl(2) sector of SYM. Keeping fixed the ratio j between the twist and the logarithm of the spin, the minimal anomalous dimension expands as γ(g,j,s)=f(g,j)lns+f⁽⁰⁾(g,j)+O(1/lns). This particular double scaling limit is efficiently described, including the desired accuracy O((lns)⁰), in terms of a linear integral equation. By its use, we are able to evaluate both at weak and strong coupling the subleading scaling function f⁽⁰⁾(g,j) as a series in j, up to the order j⁵. Thanks to these results, the possible extension of the liaison with the O(6) non-linear sigma model may be tackled on a solid ground.     

O(α s ) corrections to the polar angle dependence of the longitudinal spin–spin correlation asymmetry in e^{+}e^{-}\to q\bar{q}

We provide analytical results for the O(α _s ) corrections to the polar angle dependence of the longitudinal spin–spin correlation asymmetry in $e^{+}e^{-}\to q\bar{q}$ . For top quark pair production the O(α _s ) corrections to the longitudinal spin–spin asymmetry are strongly polar angle dependent and can amount up to ?4% in the q ²-range from above $t\bar{t}$ threshold up to $\sqrt{q^{2}}=1000\ \mbox {GeV}$ . The O(α _s ) radiative corrections to the correlation asymmetry are below ≈1% in the forward direction where the cross section is largest. In the $e^{+}e^{-}\to b\bar{b}$ case the O(α _s ) corrections reduce the asymmetry value from its m _b =0 value of ?100% to approximately ?96% for q ²-values around the Z peak and are practically independent of the value of the polar angle θ. This reduction can be traced to finite anomalous contributions from residual mass effects which survive the m _b →0 limit. We discuss the role of the anomalous contributions and the pattern of how they contribute to spin-flip and non-flip terms.     

Angular correlation measurements in the Be9(d,p, γ)Be10 reaction

Thep-γ angular correlations in the Be⁹(d, p, γ)Be¹⁰ reaction have been measured in the reaction plane atE _d =1.3, 1.5, 1.9, 2.3 and 2.45 MeV for proton anglesθ _p =35°, 80° and 120°. The anisotropy of the angular correlations measured forθ _p =35° is independent of deuteron energy. A systematic shift of the symmetry axis from the recoil direction has been observed. The shift is 20.5° at E_d=2.45 MeV. The anisotropy decreases with increasing proton angle and vanishes atθ _p =120°.