Regge couplings and intercepts from the planar dual bootstrap

Planar unitarization of dual models is examined in terms of renormalized diagrams. The shift of the Reggeon intercept 1 ? α(0) and the renormalized coupling $\text{g}{}^2\text{N}\text{16π}$ are both expected of order unity in a model with SU(N) Chan-Paton factors. In four space-time dimensions Regge behaviour makes the shift of the dual photon mass reminiscent of Schwinger's mechanism.     

Asymptotic energy scale factors for pseudoscalar meson scattering and charmed meson couplings

Energy scale factors ν₀ for PP → PP scattering amplitudes are related via the absence of exotic resonances to ratios of tensor to vector coupling strengths. These same ratios are extracted from FESR's for non-exotic reactions. The scale factors obtained are all of the order of 1.0 GeV²or less, independent of quantum numbers. This contradicts the expectations of dual amplitudes in which ν₀ = 1/α′, and trajectory slopes are smaller for charmed mesons. Decay widths for tensor mesons are predicted. An observed SU(3) violation for the ratio $\text{A}{}_2\text{→}\text{K}\text{K}\text{/}\text{K}{}^7\text{→}\text{K}\text{π}$ is shown to be consistent with the FESR results. Charmed meson decays are predicted to be factors of 2–3 larger than those predicted by SU(4).     

The relation between reggeon and photon couplings

We propose (a) the “vector coupling hypothesis” (VCH) that the leading normal-parity Regge trajectories (P, f, ω, ? and A₂) couple to hadrons like vector particles, and (b) the “γ-analogy hypothesis” (GAH), that the couplings of P, f, and ω to any vertex are proportional to the isoscalar photon coupling (the transition form factor), while ? and A₂ couple like the isovector photon. These hypotheses are motivated by duality and vector dominance. They allow us to interconnect such well-known results as (a) the relation between s-channel helicity conservation for P, f and ω at the $\text{N}\text{N}$ vertex and the equality of the nucleon's electric and magnetic isoscalar form factors, (c) the Stodolsky-Sakurai flip ? and A₂ couplings to $\text{N}\text{N}$ and the isovector form factors, (c) the Stodolsky-Sakurai magnetic dipole ?-N$\text{Δ}$ coupling. They also permit us to predict, with just a single free parameter, the differential cross section for $\text{pp}\text{→}\text{pN}{}^1$, at all energies, in terms of that for pp → pp. A detailed method for relating the transition form factors to the reggeon couplings for any spin is presented.     

γ-W0 mixing as an alternative to unified weak-electromagnetic gauge theories

A very simple model based on γ-W⁰ mixing (but not on spontaneously broken gauge symmetry) is shown to reproduce all the quantitative predictions of the standard (Weinberg-Salam) model as far as low-energy phenomenology is concerned. The model predicts intermediate-boson mass relations weaker than Weinberg's. Weinberg's mass formulae, however, can be accommodated in our model provided the γ-W⁰ mixing parameter and the coupling constants (e and g) satisfy a special relation. This relation also guarantees asymptotic SU(2) × U(1), decent high-energy behavior in processes like $\text{v +}\text{v}\text{→}\text{W}{}^{\mathrm{+}}\text{+}\text{W}{}^{\mathrm{?}}$ and the SU(2) × U(1) value for the W^± boson gyromagnetic ratio. Speculative attempts are made to understand the sign and magnitude of “sin² θ_W”.     

Z(N) topological excitations in Yang-Mills theories: duality and confinement

We investigate the properties of Z(N) topological excitations in Wilson's lattice formulation of SU(N) Yang-Mills theories. We exhibit the Z(N) topological excitations as exact classical solutions on the lattice. After giving detailed qualitative discussions about the Z(N) excitations and their relevance to confinement, we investigate the Z(N) lattice gauge theories with the Wilson action and show that Z(2), Z(3) and Z(4) models are self-dual systems. (The self-duality of the Z(2) case has been known previously.) This property enables us to locate the critical points exactly in those systems under the assumption that the phase transition occurs at only one point in the coupling constant space. We then derive the effective action for the Z(N) topological excitations in the lattice SU(N) Yang-Mills theories in the steepest descent approximation. The critical coupling constants in the SU(N) models corresponding to the phase transition caused by the Z(N) excitations are estimated by using the information on the Z(N) models with the Wilson action. It is quite probable that the estimated value $\text{g}{}_{\mathrm{<mtext>r</mtext>}}{}^2\text{/4π}{}^2\text{～}\text{1}\text{31}$ (for SU(3)) is an upper bound. This indicates that the Wilson model of the SU(3) gauge field can be effective action of the QCD gluons which exhibit permanent quark confinement and, at the same time, freedom up to the distance characterized by the energy, at least, ～1 TeV.     

SU(5) Higgs problem with adjoint + vector representations

Recently Kim has given a general method, using group-invariant orbit parameters, for determining the energy and residual symmetry of the Higgs potential minimum. In this paper we illustrate the method by working out the case of a quartic SU(5) Higgs potential with $\text{5}$ and $\text{24}$ higgsons. In this method the Gell-Mann-Slansky conjecture concerning possible little groups of the potential minimum takes a geometric form, which is verified for our case. The results are used to discuss the hierarchical symmetry breaking of SU(5) grand unification theory. We generalize our results to the SU(N) adjoint + vector models, which are all closely related.     

The quantum mechanical toda lattice

The aim of this paper is to establish the exact quantization conditions for the three-body Toda lattice. The Hamiltonian consists of the kinetic energy for three particles in one dimension, and of the potential energy which couples each particle to its two companions through an exponential spring. After eliminating the center of mass motion, one is left with a system of two degrees of freedom and two constants of motion, the total energy E and a third integral A which commute. Nevertheless, no transformation has been found to separate the classical equations of motion or Schrödinger's equation. The wave function is written as a double Laurent series. Its coefficients have to satisfy two sets of recursion relations on a triangular grid where each set insures that we have a simultaneous eigenfunction of E and A. The condition for the convergence of this series can be expressed as the vanishing of a tridiagonal infinite determinant with 1 in the diagonal and the inverse of a third-order polynomial in the first off-diagonals. The coefficients in this polynomial are E and A, and the variable corresponds to a component of the wave vector associated with the wave function. This determinant can be treated exactly as Hill's, and yields the 3 components. The condition for the square integrability of the wave function requires the phase angle of the principal minors to be equal to 0, $\text{π}\text{3}$, or $\text{2π}\text{3}$ according as the representation of the cyclic groups, for each component of the wave vector. But the third condition follows from the two others. The analogy with the corresponding two-body problem is pointed out.     

Chaleur spécifique et transformation martensitique dans le système Nb1−xSnx

Experimental data on the superconducting temperature, and low temperature specific heat, together with X-ray and neutron investigations are reported for two sets of Nb_xSn_1?x, samples with the A15 type structure. The first one, intended for a study of the effect of stoichiometry, consists of cast alloys with lattice constants ranging from 5.273 to 5.289 Å, γ's from 4.9 to $\text{9}\text{mJ}\text{K}{}^2$ g-at and T_c's from 6 to 17.9 K. The second one consists of nearly stoichiometric sintered alloys with lattice constants ranging from 5.288 to 5.291 Å, γ's from 5.6 to 13.5 $\text{mJ}\text{K}{}^2$ g-at and T_c's close to 18 K. The martensitic transformation ratio has been determined by neutron diffraction in the latter set and the values 32, 77 and 95% were obtained. The analysis of the specific heat jumps at T_c shows that the superconducting T_c of the tetragonal phase is 17.9 K and both T_c and γ are reduced in the cubic phase.Phonon information inferred from specific heat data are indicative of a structure with a typical energy of 9 meV in the density of states. The agreement with spectra obtained by inelastic neutron scattering is good.     

Two-loop renormalization group equations in a general quantum field theory: (III). Scalar quartic couplings

The two-loop β-functions for the scalar quartic couplings are computed in a general renormalizable quantum field theory with scalar, $\text{spin}\text{-}\text{1}\text{2}$, and (vector) gauge fields associated with a general gauge group G, using dimensional regularization and modified minimal subtraction (^?MS). A more explicit form is given for the two-loop β-function of the quartic coupling of the Higgs doublet in the minimal QCD electroweak theory based on SU(3) × SU(2) × U(1).     

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.     

High orders isotropic exchange in symmetrical clusters

The group-theoretical classification of exchange multiplets is suggested. The exchange levels are characterized by full spin S and irreducible representations of SU(2s+1), R(2s+1) or Sp(2s+1) groups. In the cases s≤$\text{3}\text{2}$ the exchange Hamiltonian can be expressed through Casimir's operators of these groups. It makes possible to find the expression for energy of symmetrical systems in analitical form. It is shown that Schrödinger exchange operator H(s), which is the generalization of the Dirac exchange Hamiltonian, is the Casimir's operator of the corresponding unitary U(2s+1) group.     

Hierarchical fermion masses in SU(5)

Rediative masses are generated for the first and the second fermion families by exploiting the idea that their chirality is a symmetry of the “low-energy” SU(3) × SU(2) × U(1) approximation of SU(5), broken only by including the effects of superheavy particles. With only 5's of Higgs coupled to fermions and getting a non-zero vacuum expectation value, we unavoidably get (i) $\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{m}{}_{\mathrm{\mu }}\text{3}$ at the grand unification scale; (ii) the charm quark needing a direct mass as the third family; (iii) neutrino masses of size $\text{? (}\text{α}\text{π}\text{)}\text{M}{}_{\mathrm{W}}{}^2\text{M}$.     

The η-η′ mixing angle and the relative radiative decay rates Γ(ψ→ηγ)Γ(ψ→η′γ)

The problem of η-η′ mixing is reexamined within the nonet scheme. It is shown that the mixing angle θ_p is quite sensitive to a small SU(3) violating $\text{27}$ piece. Taking SU(3) violating q$\text{q}$ annihilation terms into account, we obtain a large ratio $\text{Γ(ψ→ηγ)}\text{Γ(ψ→η′γ)}$ which is largely independent of the mixing angle and agrees with the measured value to within 20–30%.     

Charm dimuons and determination of the strange sea

We re-examine the standard charm model for opposite-sign dimuon events in neutrino-nucleon scattering. Published dimuon rates are shown to be consistent with a simple SU(3) symmetric sea. We discuss the types of correlated studies of different dimuon observables needed to extract unambiguous information on the nucleon's strange sea from upcoming, high statistics data. Our calculations demonstrate the sizeable effects of finite energy resolution and missing final-state energy on predictions of observed dimuon rates, particularly for data obtained from wide-band incident neutrino spectra. We emphasize the crucial role of the non-zero charm mass, not only for the analysis of dimuon events, but also for the interpretation of large-y inclusive $\text{v}\text{N}\text{→}\text{μ}\text{X}$ data.     

Meson decay constants and bare quark masses from duality for current two-point functions

Duality is applied in a quasi-local form to the SU(4) × SU(4) current two-point functions. Interpolating functions for some of their space-time components are assumed to be given by the free quark model. Mass intervals in the finite energy sum rules are taken to be approximately SU(3) × SU(3) invariant and a linear dependence of the hadronic mass spectrum upon the radial quantum number is assumed. The correct order of magnitude of various meson decay constants is reproduced provided the color gauge group is SU(3). The bare uncharmed quark masses are given by the formulae: $\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ M}{}_{\mathrm{\pi }}\text{F}{}_{\mathrm{\pi }}\text{/F}{}_{\mathrm{\pi }}\text{√6 ≌ 40}\text{MeV}\text{, m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ 1 = 6}$. The η-η mixing problem is discussed. Predictions are made for the masses and decay constants of the vector mesons of the first L = 2 level of SU(6) × O(3), as well as for the decay constants of the radially excited pseudoscalar mesons; estimates of corrections to PCAC in Goldberger-Treiman relations are presented. The bare charmed quark mass is found to be of the order of 1.1–1.2 GeV. Some decay constants of charmed mesons are evaluated.     

Exact quantum Sine-Gordon soliton form factors

Soliton form factors are constructed using Zamolodchikov's proposed exact massive Thirring model S-matrix. The asymptotic behaviour of the electromagnetic form factor is $\text{～(?t)}{}^{\mathrm{<mtext>?</mtext><mtext>g</mtext><mtext>2</mtext>}}$. The quasiclassical limit is not the previously accepted result.     

Glueballs versus quarkonium-flavor symmetry signatures

Flavor symmetry selection rules provide unambiguous signatures for glueball decays at masses above 1500 MeV where many channels are open. For example, a 2⁺⁺ glueball should decay into ππ, K$\text{K}$, ηη, η'η', ωω, ?? and ψψ, but not into K¹$\text{K}$ nor ηη'. A quarkonium or a four-quark state cannot go into all channels allowed for a glueball; at least one is OZI-forbidden for any choice of flavors. But any quarkonium state that goes to K$\text{K}$ should also go to K¹$\text{K}$ and ηη'. These selection rules are shown to be stable against SU(3) symmetry breaking.     

Monte Carlo simulation of SU(2) gauge theory with fermions on a four-dimensional lattice

After integration over the fermions in an SU(2) lattice gauge theory, the effective fermionic action may be expressed as a sum over all possible closed gauge field loops with corresponding weight factors. We approximate this sum and perform a Monte Carlo simulation of a coupled fermion-gauge system on a 4⁴ lattice. We compare our results for 〈S_eff〉 and $\text{〈}\text{ψ}\text{ψ〉}$ for different values of the gauge field coupling β and fermion coupling κ with the free fermion theory on a lattice. 〈S_eff〉 turns out to be quite small for $\text{κ?}\text{1}\text{8}$.     

Yang-Mills instantons and the S-matrix

We present a scheme for calculating gauge-invariant S-matrix elements in the presence of instantons. We exploit the conformal invariance of the zero-mass field equations. The asymptotic in and out states are defined by their values on null infinity $\text{J}$. We use this method to calculate to lowest-order S-matrix elements for scalar particles and fermions in a dilute gas of SU(2) instantons and anti-instantons. The scalar particles acquire an effective mass and an effective interaction of the form $\text{exp}\text{(?(?}{}^2\text{/16π) ?}\text{?}\text{)}$, where ? is the scale of the instanton, plus other interactions which cannot be presented by a local effective lagrangian. The fermions acquire the effective lagrangian obtained by 't Hooft. In the case of a single flavour of fermions, this corresponds to a mass term.     

Deep inelastic lepton-hadron scattering in massive vector gauge models

A class of strong interaction models in which the interactions between fractionally charged colored quarks are mediated by massive neutral vector gluons is considered. All the vector gluons acquire masses via the usual Higgs mechanism. The effective coupling constants $\text{g}$ (gauge coupling) and $\text{h}$ (quartic self-coupling) are supposed to approach a limit cycle in the limit of large space-like momenta. The large Q² behavior of the moments of the deep inelastic lepton-hadron structure functions is analysed using this hypothesis. It is shown that Bjorken scaling is violated by power terms of Q² multiplied by an oscillating function of Q².