A characterization of the segal entropy

We study the Segal entropy $\text{S(ψ∣τ) = -τ(}\text{dψ}\text{dτ}\text{ln}\text{dψ}\text{dτ}\text{)}$ of a normal state ψ on a W¹-algebra $\text{M}$ with respect to a faithful normal semi-finite trace τ on $\text{M}$ and we give a unique characterization of this general entropy concept by means of some natural properties.     

Symmetric space scalar field theory

Some quantum field theories, such as the chiral SU(2) ? SU(2) theory, can have a dynamics invariant under a group $\text{G}$ that is realized on a vacuum which is invariant only under a subgroup $\text{H}$ of $\text{G}$. These theories may be defined by scalar fields which are coordinates for the coset manifold $\text{G}$/$\text{H}$. They are thus non-polynomial theories on a symmetric space, with the group motions in this space described by a set of Killing vectors. We show how the Lagrange function may be constructed entirely from the Killing vectors. In particular, all physical quantities may be expressed in terms of the currents formed out of the Killing vectors. The current correlation functions do not exhibit the spurious wave function renormalizations which are encountered if ordinary Green's functions are computed. We illustrate the general method by calculating one-loop counter terms in a completely invariant fashion. An Appendix describes in simple terms the general theory of symmetric spaces, which should prove useful in other contexts.     

Comment on the absence of the pionic mode in τ decay

A possible suppression of the pionic mode in the τ decay is discussed under the assumption of τ being a spin $\text{3}\text{2}$ object. The computed branching ratios are compared with existing data.     

A natural theory of the K-M mixing angles, weak and strong CP

We present a natural model in which the quark mass matrices are of the symmetric Fritzsch form with the two physically relevant phases $\text{σ = τ = ±}\text{π}\text{2}$. The model is natural in the sense of 't Hooft and explains all of the known aspects of the weak interaction phenomenology of the K-M matrix (including the weak CP) in terms of the observed quark mass eigenvalues only. The model solves the strong CP problem by the Peccei-Quinn mechanism while the phases $\text{σ = τ = ±}\text{π}\text{2}$ are generated by spontaneous symmetry breaking. The invisibility of the axion is more natural than in the existing models and is related to the absence of FCNC and the observed long b-quark lifetime. The key predictions of the model are m_t < 80 GeV and $\text{5.0 × 10}{}^{\mathrm{?3}}\text{? R}{}_{\mathrm{b}}\text{≡}\text{Γ(b→ue}\text{v}\text{)}\text{Γ(b→ce}\text{v}\text{)}\text{? 1.46 × 10}{}^{\mathrm{?2}}$, while the present experimental upper bound on R_b is 3 × 10^?2. The prediction on R_b is to be tested by experiments at CLEO and CUSB in the near future.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

Observation of a narrow resonance near the pp threshold

Annihilation and elastic cross-sections of $\text{p}$p have been measured between 400 and 850 MeV/c. In both cross-sections a resonance is observed at a mass of 1939 ± 3 MeV. For its natural width τ ? 4 MeV is obtained.     

New form of dynamics and current algebra

We study a new form of dynamical system, in which the commutation relations for the dynamical variables of a quantized field are defined on a “lightlike surface $\text{τ≡}\text{(t+z)}\text{2}\text{=0}$ rather than at one instant of time t = 0. We clarify the physical implications of the use of the new variables x¹ = x, x² = y, $\text{x}{}^{\mathrm{+}}\text{=}\text{(t+z)}\text{2}\text{, x}{}^{\mathrm{?}}\text{=}\text{(t?z)}\text{2}$ and explore its significance as a new form of relativistic dynamics, which holds in any Lorentz frame but not in the so-called “infinite momentum frame.” Using the quark model, we build up a new algebra of currents, in which the current commutators are defined at equal τ. The sum rules and other results of the usual current algebra can be obtained without taking the unjustifiable limit of infinite momentum. In particular, we obtain the Gell-Mann-Okubo mass formulas in quadratic form for both mesons and baryons without the trouble due to momentum dependence. We derive the reduction formula and find the physical high energy limit (not the Bjorken limit) of an amplitude is determined by the equal τ commutator.     

Formal solutions for response functions of superconductors and 3He(B): II. Applications to acoustic and quasihomogeneous regime

Formal solutions for the autocorrelation functions of density and the transversal current are discussed in the acoustic and quasihomogeneous regime. The poles of these functions are obtained without any restrictions imposed on Landau parameters. The formula for sound dispersion at T = 0 is generalized by the inclusion of terms of the relative order of $\text{(}\text{kv}\text{2Δ}\text{)}{}^2$, (k is the wave vector, v is the Fermi velocity, Δ is the energy gap, $\text{h}\text{?}\text{≡ 1}$). The dispersion formulae for transversal and longitudinal excitations with a gap for ³He(B) are also given, with an accuracy up to the terms of the order of $\text{(}\text{kv}\text{2Δ}\text{)}{}^2$, for 0 ? T ? T_c, and without any restrictions imposed on Landau parameters. Under these last assumptions our autocorrelation functions are calculated in the polar as well as non-polar regions. It is shown that if T > 0, the transversal function vanishes at some ω, such that $\text{0 ? ω}{}^2\text{? (}\text{12}\text{5}\text{)Δ}{}^2$. Moreover,the zero of the density autocorrelation function is distanced from its pole by an amount of the order of $\text{(}\text{kv}\text{2Δ}\text{)}{}^2$.     

νμp and νμn charged-current interactions unfolded from high energy νμ interactions in neon

We have developed a method to separate $\text{ν}$n and $\text{ν}$p interactions from antineutrino-neon interactions by using the final state electric charge. We present the distributions of the scaling variables x and y for $\text{ν}$n and $\text{ν}$p interactions separately , along with the $\text{ν}$n and $\text{ν}$p cross section ratios as a function of x and y. We obtain a total $\text{ν}$n to $\text{ν}$p cross section ratio of 0.45± 0.08. Our results are consistent with the predictions of the simple quark parton model.     

Spin-dependent structure functions for the proton and neutron

We present a phenomenological model for the spin-dependent structure functions g₁(x) of the proton and neutron. The model is an extension of the one proposed by Carlitz and Kaur. We use improved unpolarized structure functions and include effects due to the mass difference between up and down quark and due to the mass difference between spin $\text{1}\text{2}$ and $\text{3}\text{2}$ baryons. Our results for the proton agree with the data.     

A new electronic band system of PbO

The chemiluminescence spectrum of atomic Pb reacting with O₃ under single-collision conditions includes a series of 55 bands in the regions 450–850 nm. A vibrational analysis is obtained which shows emission is to the ground state of PbO from excited electronic states not previously analyzed. Forty-nine of the bands are assigned to the a(1)-X(0⁺) transition and the remaining six are tentatively identified as the forbidden b(0^?)-X(0⁺) transition. Both the a and b states are believed to be Hund's case (c) components of the ³Σ⁺ states arising from the configuration $\text{σ}{}^2\text{π}{}^3\text{π}{}^1$. The vibrational parameters of the a state are ν₄ = 16 029 ± 8, ω_e′ = 478.7 ± 1.9, and ω_ex_e′ = 2.292 ± 0.128 cm^?1, where the uncertainties represent two standard deviations of the least-squares fit. Emission is also observed from the PbO B state produced in the reaction of metastable Pb atoms with O₃. Using pulsed laser excitation, an attempt is made to determine radiative lifetimes. We find for the PbO A(0⁺) state τ = 3.74 ± 0.3 μsec, and for the PbO B(1) state τ = 2.58 ± 0.3 μsec, while for the a(1) state τ is estimated to be greater than 10 μsec. From the vibrational analysis, energy conservation arguments place a lower limits to the ground state dissociation energy of $\text{D}{}_0{}^0\text{(}\text{PbO}\text{) ≥ 3.74 ± 0.03}\text{eV}$ (86.2 ± 0.7 kcal/mole). For the Pb + O₃ reaction we find less than 1% of the products are PbO¹ molecules that emit in the visible. Correlations are made with the low-lying states of other Group IV chalconides based on the assignment of the PbO $\text{a}{}^3\text{Σ}{}^{\mathrm{+}}\text{(1)}$ state and the correspondence between the low-lying triplet states of PbO and CO.     

The interaction of nucleons with antinucleons. III. Photon and pion emission from bound states

We calculate widths and branching ratios for the emission of γ rays or pions from a bound state of the nucleon-antinucleon ($\text{N}\text{N}$) system, leading to another $\text{N}\text{N}$ bound state. We use a realistic potential model to describe the medium- and long-range parts of the $\text{N}\text{N}$ interaction, and parametrize the short-range behavior. The general features of γ and π transitions, based on the selection rules, are emphasized. We illustrate these features with typical results for several choices of the short-range cutoff. The observation of pions is a necessary supplement to the γ-ray experiments, in order to significantly constrain the possible quantum number assignments of final states. We investigate transitions between quasiatomic (QA) and more deeply bound quasinuclear (QN) states, and also QN to QN γ or π emission. The former may have been seen in experiments involving the $\text{p}\text{p}$ atom, while the latter are in some optimum cases accessible in $\text{p}\text{d}$ spectator experiments, although there is no evidence for these QN to QN transitions as yet. The role of isospin mixing in QA states is discussed, as well as the importance of maintaining orthogonality of the QA and QN wave functions.     

NMR spin lattice relaxation in dilute CuFe alloys with impurity interactions

Previous measurements by Wilkening and Hesse have shown, that the excess relaxation rate ΔT^-1₁ of the matrix nuclei in $\text{CuF}$e dilute alloys can be explained in terms of the LD-model with rapid spin diffusion. Measurements reported in this paper confirm the existence of an electric quadrupole diffusion barrier. It could be shown that the influence of the quadrupole barrier is coupled to large clusters within the alloy. The electron spin lattice relaxation time τ₁ behaves temperature independent in the range 30 K ? T ? 300 K. This can be understood if an effective correlation time τ is introduced, which results from a distrubution of temperature dependent times τ^cl(T) belonging to clusters of different size.     

Gyromagnetic ratios of excited states in 123, 125Te

The results of integral precession measurements are reported for $\text{3}\text{2}{}^{\mathrm{+}}$ and $\text{5}\text{2}{}^{\mathrm{+}}$ excited states in ^123,125Te. The measurements were made using the ion implantation perturbed angular correlation technique by recoiling the excited nuclei into polarized iron. The measured mean lifetimes and g-factors are: ${}^{123}\text{Te (440 keV,}\text{3}\text{2}{}^{\mathrm{+}}\text{) τ = 39±4 ps, g = 0.34 ± 0.06}$; $\text{(505 keV,}\text{5}\text{2}{}^{\mathrm{+}}\text{) τ = 26±3 ps, g = 0.04±0.025}$; and ${}^{125}\text{Te(443 keV,}\text{3}\text{2}{}^{\mathrm{+}}\text{) ρ = 27±3.3 ps, g = 0.39±0.06}$; $\text{(464 keV,}\text{5}\text{2}{}^{\mathrm{+}}\text{) g = 0.12±0.04}$. The results are compared with theoretical predictions.     

Baryon wave functions and nucleon decay

We apply to nucleon decay the knowledge about the short-distance structure of baryon wave functions gleaned from QCD form factor calculations nd the $\text{J}\text{gY →}\text{p}\text{?}\text{p}$ decay rate. We review the uncertainties arising when current algebra and PCAC are used to relate $\text{N}\text{→}\text{?}\text{+}$ meson decay rates to 〈0|qqq|N〉 matrix elements. We show that the relevant matrix elements are not directly related to those of the leading twist operators “measured” in conventional high momentum transfer physics, but argue for an indirect based on models that fit both form factor and $\text{J}\text{Ψ}$ decay data. We use these inputs to calculate the p → e⁺π⁰ decay rate in minimal SU(5) and other grand unified theories (GUTs) for a specified value of the heavy vector boson mass m_X. Our results combined with the recent experimental lower limit on this mode indicate that m_X > 2 × 10¹⁵ GeV in the minimal SU(5) GUT, and we derive analogous bounds for supersymmetric GUTs. Our calculated lifetime for a given value of m_X is considerably shorter than previous estimates made using non-relativistic SU(6) or the bag model, a difference traceable to the different normalizations of 2 and 3 quark wave functions at short distances.     

Decay rate of τ into odd number of pions

Decay rate of τ into 3π and 5π is calculated using current algebra and PCAC. Assuming universality for ordinary leptons and τ, satisfactory agreement with experimental data is obtained with $\text{Г}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{A}{}_1\text{) ≈ 300?400}\text{MeV}$. The branching ratio for π → 5π + ν is found to be 1%.