A pion-nucleus optical potential containing effects of genuine pion absorption and emission

We derive in two ways a lowest-order optical potential $\text{V}$_πA using the projectile and a pair of target nucleons as the basic interacting unit. The first derivation—a heuristic one—uses a multiple-scattering theory, while the second employs a field theory where pions can be absorbed and emitted as well as scattered. The lowest-order terms of $\text{V}$_πA contain the two-particle ground state density and the πNN → πNN scattering matrix. In the same field-theoretical model one analyzes the latter in standard multiple-scattering contributions and genuine absorption corrections. The form of these corrections and their relation to often ad hoc assumed forms is discussed.     

Primordial two-component maximally symmetric inflation

We propose a two-component inflation model, based on maximally symmetric supergravity, where the scales of reheating and the inflation potential at the origin are decoupled. This is possible because of the second-order phase transition from SU(5) to SU(3)×SU(2)×U(1) that takes place when φ?φ_c<φ₀, when φ₀?O(M) is the value of the inflation at the global minimum, and leads to a reheating temperature T_R?(10¹⁵–10¹⁶) GeV. This makes it possible to generate baryon asymmetry in the conventional way without any conflict with experimental data on proton lifetime. The mass of the gravitinos is $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{?10}{}^{12}\text{GeV}$, thus avoiding the gravitino problem. Monopoles are diluted by residual inflation in the broken phase below the cosmological bounds if φ_c?0.3M.     

Crossing relations for deep-inelastic and annihilation processes

We calculate in a model field theory [φ³]_σ the structure functions $\text{F}\text{?}\text{(ω), F(ω)}$ for the processes e⁺+e^?→h+X and e^?+h→e^?+X in the next to leading logarithm approximation. We find that $\text{F}\text{(ω) and F(ω)}$ satisfy the analytic continuation relation but not the Gribov-Lipatov reciprocity relation.     

O(18) revived: Splitting the spinor

We propose an O(18) theory which is perturbatively unifiable and which accounts for the absence of right-handed families in the low-energy world. The theory predicts a fourth left-handed family as well as four right-handed families at energies near the weak scale. It also implies the existence of eight light neutrinos, all of which contribute to the width of the Z⁰. Cosmological arguments suggest that four of these neutrinos should have masses between 2 and 35 GeV, and that the other four should be much lighter. They also suggest the existence of a doubly charged scalar φ⁺⁺ and a singly charged scalar φ⁺. Dramatic signatures include the production of four right-handed charged leptons and eight right-handed quarks, $\text{Z}{}^0\text{→ v′}{}_{\mathrm{<mtext>R</mtext>}}\text{+}\text{v}\text{′}{}_{\mathrm{<mtext>R</mtext>}}\text{→ v}{}_{\mathrm{<mtext>R</mtext>}}\text{γ +\_}\text{v}{}_{\mathrm{<mtext>R</mtext>}}\text{γ}$, and e⁺e^? → φ⁺⁺ + φ^??. The lightest right-handed charged quark should be surprinsingly long-lived $\text{(τ?10}{}^{\mathrm{?2}}\text{sec}\text{)}$ for a particle of mass ? 100 GeV.     

A convergent expansion about mean field theory: I. The expansion

We give a convergent expansion for nearly Gaussian quantum field theory in the multiphase region. The expansion combines (1) an expansion in phase boundaries, (2) a cluster expansion, and (3) a perturbation expansion to isolate dominant behavior. We study in detail the ground state of the $\text{P}$(φ)₂ = (λφ⁴ ? φ² ? μφ)₂ model, with ∥ μ ∥ ? λ² ? 1. The ground state is close to the classical free field, obtained by replacing $\text{P}$(φ) by the quadratic mean field polynomial $\text{P}$_c(φ), tangent to $\text{P}$ at a global minimum. Selecting one minimum gives a pure phase (ergodic ground state) satisfying the Wightman-Osterwalder-Schrader axioms with a positive mass. We also establish analyticity in λ for μ = 0 in the sector ∥ Im λ ∥ < ? Re λ ? 1, for ? ? 1.     

Calculation of the γγ → ϱ0ϱ0 cross section at high energies

The processes with the cross sections not decreasing with energy become important at high energies. The simplest processes of this kind are γγ → V_i⁰V_j⁰ where V⁰ = ?⁰, ω, ?, ….. We calculate their cross sections in the high-energy small angle region s ? |t| ? μ². The cross section γγ → ?⁰?⁰ at high energies (s ? 10 GeV²) exceeds those of γγ → ππ, ?⁺?^? considerably. At $\text{s ? 10}{}^4\text{GeV}{}^2$ (this is the characteristic energy for the VLEPP and SLC colliders) and $\text{|t| ? 2}\text{GeV}{}^2$, the ratio $\text{(}\text{d}\text{σ/}\text{d}\text{t)(γγ → ?}{}^0\text{?}{}^0\text{)/(}\text{d}\text{σ/}\text{d}\text{t)(γγ → μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{) ? 70}$.     

Vector meson pole dominance in Jψ decays into mesons

The validity of the assumption that $\text{J}\text{ψ}$ decays into mesons proceed via ω, φ and ?⁰ poles followed by cascade decays is examined. $\text{Λ(}\text{J}\text{ψ}\text{→}\text{B}\text{π)}$ is well reproduced by using $\text{Λ(}\text{J}\text{ψ}\text{→ ?π), Λ(ω → ?π), Λ(}\text{B}\text{→ ωπ)}$ and the B → ωπ helicity structure. The structure of OZI-violating $\text{J}\text{ψ}\text{?}\text{V}{}^0$ transitions including the electromagnetic contribution is examined, and compared with the data on inclusive $\text{J}\text{ψ}$ decay.     

Matter fields and metric deformations in multidimensional unified theories

This paper describes a first study of the effects due to including matter fields in generalized Kaluza-Klein (KK) theories with nonabelian compact gauge group G and nontrivial fibres $\text{V}$^K. The approach is based on the first-order Einstein-Cartan (EC) general relativity in (4 + K) dimensions. In the EC theory there are two basic mechanisms which can lead to a spontaneously compactified KK background geometry R⁴ × $\text{V}$^K: (A) a particular kind of energy-momentum density matter condensate in the quantized ground state, or (B) a particular kind of spin-density matter condensate. If (A) or (B) are operating, the inconsistencies usually found between the KK ansatz and the matter-free EC theory are avoided. Mechanism (B) works only when $\text{V}$^K is parallelizable. It is shown that the expansion of matter fields in normal modes on $\text{V}$^K implies that one must include deformations of the Yang-Mills (YM) potentials contained in the usual KK metrics. We discuss and characterize one class of such deformations. As a case study, we consider fibres $\text{V}$^K ～ G′, where G′ is a semisimple compact Lie group. We allow for the “maximal” YM gauge group G_L′ × G_R′. We carry out the harmonic analysis for spinor fields and study the mass spectrum and YM quantum numbers of the normal modes. We rely on mechanism (B) to provide a curvature-free connection (“parallelization”) on $\text{V}$^KG′ by means of a suitable vertical constant torsion. Minimal YM couplings are of size $\text{l}\text{L}\text{≡ g}$, where l is the Planck length and L is the length of the fibre; nonminimal YM couplings are of size L. Nonzero masses are of size L^?1. The massless modes are found and discussed. There would be no massless modes if the parallelizing vertical torsion were absent. This torsion also implies the vanishing of the cosmological constant. When the theory is restricted to massless modes, the YM deformations disappear and the dimensional reduction to four dimensions yields an effective YM theory, which is renormalizable at energies far below L^?1: the effective theory is obtained by letting L → 0 with g ? 1 fixed and by neglecting all masses of order L^?1; g corresponds to the bare YM coupling constant. The surviving effective YM gauge group is G_L′ and the matter fields are in a particular representation of G_L′ × G_R′, corresponding to the zero mass eigenvalue. Explicit examples are discussed for G′ = SU(2) and G′ = SU(3).     

Search for non-strange exotic mesons produced via baryon exchange

Negative results on backward production, via baryon exchange, of exotic non-strange mesons are presented. The reactions π^?p→p_forwardX^?and π^?n→ p_forwardX^?? have been studied with a 12 GeV/cπ^? beam in the Omega spectrometer at CERN. No resonant peak in $\text{X}\text{→}\text{p}\text{p}\text{π}{}^{\mathrm{?}}\text{,}\text{p}\text{p}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{?}}\text{,}\text{p}\text{p}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{,π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{?}}\text{π}{}^0$ has been seen. The upper limits obtained on cross sections for exotic meson production $\text{X}\text{→}\text{N}\text{N}\text{π,}\text{N}\text{N}\text{π, 4π}$ are lower than the ?^? backward production cross section in the π^?p→p?^? reaction; this result seems to contradict the predictions of the two-component duality model. Compared to already published experiments in the search for exotics produced via baryon exchange, the sensitivity of this experiment is increased by an order of magnitude.     

Orbital classical solutions,non-perturbative phenomena and singularity at the zero coupling constant point

We try to extend previous arguments on orbital classical solutions in non-relativistic quantum mechanics to the $\text{1}\text{4}\text{λ|φ|}{}^4$ complex relativistic field theory. The single valuedness of the Green function in the semiclassical $\text{(}\text{h}\text{?}\text{→ 0)}$ limit leads to a Bohr-Sommerfeld quantization. A path integral formalism for the Green functions analogous to that in non-relativistic quantum mechanics is employed and a semiclassical approach which uses our classical solutions indicates non-perturbative effects. They reflect and $\text{e}{}^{\mathrm{<mtext>1</mtext><mtext>\lambda </mtext>}}$ singularity at the zero coupling constant point.     

Renormalized Hartree-Fock equations in a nuclear relativistic quantum field theory

Renormalized Hartree-Fock equations are derived for an infinite system of mesons and baryons in the framework of a relativistic quantum field theory. Direct and exchange diagrams in the baryon propagator are summed self-consistently to all orders, and the effects of occupied negative-energy states in the Dirac sea are included. The required counterterm subtractions are defined by conventional renormalization conditions, but they need not be evaluated explicitly. The result is a set of finite nonlinear integral equations for the baryon self-energy that includes vacuum fluctuation effects from virtual N$\text{N}$ pairs in the many-body wavefunction at finite density.     

On some singularities in the dielectric properties of an electron gas in a uniform magnetic field

The effects of a magnetic field on the self-shielding of an electron gas against small electrostatic perturbations V are studied by use of Bloch wave functions and by the random phase approximation. V is taken to be periodic along the field lines. It is demonstrated that in the weak field limit, $\text{μ}{}_0\text{B}\text{eV}\text{→ 0}$, magnetic effects become negligible. For μ₀B ? eV such effects may be important only under limited physical conditions. Singularities discussed by Glasser and Kaplan [1] are replaced by peaks of finite amplitude and width, appearing with the frequency of neck orbit oscillations. Peak profiles and the Lindhard singularity are investigated for the case V ≠ 0.     

Elastic and inelastic φ photoproduction

The differential cross section of the reaction (γp → pφ) has been measured in the t range 0 ? t ? 0.4 GeV² and for photon energies from 3.0 to 6.7 GeV. In particular for the small t region the measurement accuracy was better than 10%. We obtained for the slope parameter B in an exponential parametrization of the differential cross section dσ/dt = Ae^?Bt values of $\text{B ? 6 ± 0.5}\text{GeV}{}^{\mathrm{?2}}$ which are significantly larger than the slopes obtained by most other experiments at higher t values. This indicates a t dependence of B particularly in the small t region.An energy dependence of the optical point (dσ/dt)_t=0, observed in our measurements, has been explained as a kinematic effect due to the VDM relation. A fit of our measurements is in excellent agreement with all other published values of (dσ/dt)_t=0(γp → φp), this implies that σ_tot(φp) must be essentially energy independent in this energy range.Spin density matrix elements of the φ have been evaluated and an analysis of the helicity amplitudes has been carried out. This analysis confirmed s-channel helicity conservation. Moments of spherical harmonics of the $\text{K}\text{K}$ angular decay distribution have been computed for 10 MeV $\text{K}\text{K}$ mass-bins from threshold to 1.3 GeV. The mass dependence of the normalized moments is generally smooth. Contributing amplitudes have essentially only even moments. The moment 〈Y₂⁰〉/〈Y₀⁰〉 changes sign above the φ mass.Differential cross sections for the inelastic φ production γp → φX have been evaluated for the first time both with respect to t?t_min and M_K. The integrated inelastic cross sections are comparable in size with the elastic ones. The slopes of the differential cross sections dσ/dt appear to become flatter with increasing M_X.     

Calculation of baryon masses in quantum chromodynamics

The polarization operator of quark currents with baryon quantum numbers is considered in quantum chromodynamics. The non-zero mean vacuum values of the field operator products are taken into account. The sum rules are obtained assuming that in the virtuality region ～1 GeV, among the mean vacuum values violating the chiral invariance, the most important is $\text{〈0|}\text{ψ}\text{ψ|0〉}$. Saturating these sum rules by the lowest baryonic states one is able to calculate the masses of the isobar Δ and nucleon N, M_Δ = 1.4 GeV, M_N = 1 GeV, up to 15% through the known value $\text{〈0|}\text{ψ}\text{ψ|0〉}$. The mass splitting in the baryonic decuplet $\text{M}{}_{\mathrm{\Sigma 1}}\text{?M}{}_{\mathrm{\Delta }}\text{= 125}\text{MeV}$ is calculated in first order in the current strange quark mass m_s = 150 MeV. Certain results for other baryonic resonances have also been obtained.     

Is Coleman-Weinberg symmetry breaking in the standard model ruled out?

In the standard model with Coleman-Weinberg symmetry breaking a symmetric vacuum (〈φ〉 = 0) always exists at any non-zero temperature; the transition to the symmetry-breaking vacuum can only occur after much supercooling. Witten has shown that this transition occurs when the strong interactions break chiral symmetry; the transition temperature is O(200) MeV and a large (but not fatal) amount of entropy is produced. It is noted here that since the strong coupling grows as the universe cools in the metastable symmetric vacuum, the Yukawa coupling to the top quark will also grow. This causes top quark loops to dominate the effective potential at small scales, drastically altering the nature of the transition. We show that if $\text{m}{}_{\mathrm{<mtext>t</mtext>}}\text{? 65}\text{GeV}$, a metastable vacuum at 〈φ〉 ≈ 0(1) GeV forms which persists to T = 0; the resulting transition would generate far too much entropy to be compatible with the current baryon to entropy ratio, ruling out the CW mechanism. If m_t ? 65 GeV, we argue that a metastable vacuum might also exist, but a breakdown of perturbation theory precludes a definitive statement.     

Variational principle for general relativity with torsion and non-metricity

The variation of the field action with the scalar Lagrangian density $\text{?g}\text{R}$ is calculated with respect to the metric, torsion and non-metricity. When the non-metricity vanishes, the variation reduces to the U₄ theory of gravitation when a relativistic matter Lagrangian with minimal coupling is included.     

Some rare processes in a model of composite quarks and leptons

The branching ratios of some rare processes, i.e. meson →μe, meson →meson μe, baryon → baryon μe, are calculated in a composite quark and lepton model. Use is made of an effective Hamiltonian which originates from hypercolor singlet 0^? and 1^? bound state exchange mechanism, acting at a mass scaleM _P andM _V respectively. Under the reasonable assumptionM _P =M _V onlyK _L →μe puts a significant limit on the composite scale.     

Baryon poles in proton decay amplitudes

The decay rate of the p→π⁰e⁺ mode is calculated in SU(5) grand unified theory using a pole model with proton and $\text{1}\text{2}{}^{\mathrm{?}}$ baryon poles. Baryon-to-vacuum amplitudes are calculated in the framework of the MIT bag model. It is found that the partial decay rate [～(5×10³¹ yr)^?)] is close to the partial decay rates calculated by different methods.     

The pion propagator in relativistic quantum field theories of the nuclear many-body problem

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models: the scalar-vector theory of Walecka, extended to include π and ρ mesons in a non-chiral fashion, and the linear σ-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pion propagator is evaluated in the onenucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual $\text{N}\text{N}$ loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently. Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored. The techniques developed here allow for a consistent treatment of these models using renormalizable relativistic quantum field theores.     

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.