Solving φ1,24 field theory with Monte Carlo

We study lattice g₀φ⁴ field theory for all g₀ and fixed renormalized mass M in one and two dimensions using Monte Carlo techniques. We calculate the dimensionless renormalized coupling constant $\text{g}{}_{\mathrm{<mtext>R</mtext>}}\text{=}\text{g}{}_{\mathrm{<mtext>R</mtext>}}\text{M}{}^{\mathrm{4?d}}\text{,}\text{where}\text{d}$ is the dimension of space—time, at fixed small values of the lattice spacing a for various g₀ and lattice sizes. Our results are in quantitative agreement with the analyses of high temperature and strong coupling series which rely on extrapolation from large to small lattice spacing.     

Higgs particle production by Z→Hγ

The rate for the decay of a Z-boson into a Higgs boson and monochromatic photon is computed to leading order in the standard SU(2) × U(1) gauge theory. The coupling has contributions from fermion and W-boson loops. The W-boson loop dominates unless the number of heavy fermion generations exceeds six. The branching ratio computed from the W-boson loop contribution, B(Z→Hγ), is approximately 2 × 10^?6$\text{(1?(}\text{M}{}_{\mathrm{<mtext>H</mtext>}}{}^2\text{M}{}_{\mathrm{<mtext>Z</mtext>}}{}^2\text{))}{}^3$.     

Demythification of electroproduction local duality and precocious scaling

In an effort to develop a quantitative check of asymptotically free color-gauge theories, we analyze the logarithmic corrections to ξ-scaling coming from anomalous dimensions and coefficient functions of twist-two operators and compare with electroproduction data for 1 ? Q² ? 16 GeV². Excellent agreement is obtained using $\text{g}{}^2\text{(2}\text{GeV}\text{)}\text{4π}{}^2\text{= 0.17}$ for the effective quark-gluon coupling in the color-gauge theory. Effects of higher-twist operators are suppressed by powers of $\text{M}{}_0{}^2\text{Q}{}^2$. We use data from the resonance region to show $\text{M}{}_0\text{? 400}\text{MeV}$, in agreement with theoretical expectations. Our fit to νW₂ in the scaling region also describes the resonance region in the sense of Bloom-gilman local duality. We show that local duality is a consequence of the moment predictions obtained from the operator-product expansion in quantum chromodynamics. We resolve a paradox associated with local duality and spin-zero targets. Present measurements of $\text{R =}\text{σ}{}_{\mathrm{L}}\text{σ}{}_{\mathrm{T}}$ at large x and Q² are systematically higher than our predictions.     

The ′T Hooft-Polyakov monopole near the Prasad-Sommerfield limit

A perturbative classical monopole solution for the SO(3) gauge theory is constructed in the limit of small but non-vanishing Higgs potential. This corresponds to the limit $\text{μ}{}^2\text{2M}{}_{\mathrm{W}}{}^2\text{=}\text{λ}\text{? 1}$, where μ equals the mass of the scalar particle and M_W equals the mass of the intermediate vector particles. The monopole solution and mass are found to involve non-analytic functions of λ: $\text{γ}$ and λ ln λ. The monopole mass M_m is calculated to order $\text{μ}{}^2\text{M}{}_{\mathrm{W}}$ as

$\text{M}{}_{\mathrm{m}}\text{=}\text{4π}\text{e}{}^2\text{M}{}_{\mathrm{w}}\text{1+}\text{1}\text{2}\text{μ}\text{M}{}_{\mathrm{w}}\text{+}\text{1}\text{2}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}\text{ln}\text{μ}\text{M}{}_{\mathrm{w}}\text{+0.7071}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}$

.     

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.     

Accurate energy levels for the anharmonic oscillator and a summable series for the double-well potential in perturbation theory

We introduce a generalization of Wick-ordering which maps the anharmonic oscillator (AO) Hamiltonian for mass m and coupling λ exactly into a “Wick-ordered” Hamiltonian with an effective mass M which is a simple analytic function of λ and m. The effective coupling $\text{Λ =}\text{λ}\text{M}{}^3$ is bounded. We transform the AO perturbation series in λ into one in Λ. This series may then be summed using Borel summation methods. We also introduce a new summation method for the AO series (which is a practical necessity to obtain accurate energy levels of the excited states). We obtain a numerical accuracy for $\text{(E}{}_{\mathrm{PT}}\text{? E}{}_{\mathrm{exact}}\text{)}\text{E}{}_{\mathrm{exact}}$ of at least 10^?7 (using 20 orders of perturbation theory) and 10^?3 (using only 2 orders of perturbation theory) for all couplings and all energy levels of the anharmonic oscillator. The methods are applicable also to the double-well potential (DWP, the AO with a negative mass-squared). The only change is that now the effective coupling is unbounded as λ → 0. The series in Λ is, however, still summable. The relative accuracy in the energy levels for 20 orders of perturbation theory varies from 10^?7 for large coupling to 1% at λ = 0.1 and to 10% at λ = .05. We also present results for the sextic oscillator.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

Renormalizable asymptotically free quantum theory of gravity

We prove that higher derivative quantum gravity is asymptotically free in all essential coupling constants by the calculation of one-loop counterterms (correcting the previous result of Julve and Tonin) and the solution of the corresponding renormalization group (RG) equations. Strong arguments are presented in favour of the possibility that renormalizable asymptotically free gravity establishes asymptotic freedom for the effective mass parameters and non-gauge couplings in grand unified gauge theories. We also analyse the RG equations in the Einstein theory with Λ term and in the higher derivative conformal invariant theories. Among other topics discussed are the algorithm for the divergences of the determinant of the fourth-order differential operator, the consistent renormalization of the boundary terms in the action, the one-loop β-function in the fourth derivative vector gauge theory and the RG equations in the $\text{“gφ}{}^4\text{+ ηRφ}{}^2\text{”}$ theory.     

On some effective mechanism for charmed particle production in neutrino and antineutrino beams

The paper describes an effective mechanism for charmed particle production in neutrino and antineutrino reactions, which consists in production of charmed virtual vector F1-meson in a weak vertex νF1μ (without suppression by the Cabibbo angle) with further strong rescattering of F1-meson on nucleon. This “quasidiffractive” mechanism should make the basic contribution to the production of charmed particles in neutrino experiments basic energies up to some hundreds of GeV. The charmed particles are mainly produced at limited momentum transfers $\text{|q}{}^2\text{| ≈ M}{}^2{}_{\mathrm{<mtext>F</mtext>}}\text{1}$ and with equal cross sections in the neutrino and antineutrino beams.     

Parity violation in atoms in SO(3) gauge models

We have evaluated the parity-violation contribution in atoms in the framework of SO(3) gauge theory. Various hadronic models have been used: first, for simplicity, the unrealistic five-quark one, next, others involving three ordinary SU(3) triplets for which all unwanted strangeness-changing processes are suppressed, up to order $\text{Gα}\text{or}\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$. In the free quark approximation, we obtain quite similar parity-violation effects which are proportional to $\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$ (ΔM² is the difference of squared masses of leptons (M_X0² ? M_ν² = M_X0²), or of quarks (ΔM_q²)). Namely, in large atoms (Z ? 1) the electronic contribution which is proportional to

gives the largest effect ($\text{σ}{}_{\mathrm{?}}\text{,}\text{p}{}_{\mathrm{?}}\text{and}\text{m}{}_{\mathrm{?}}$are the spin, momentum operators and mass of the lepton). Parity-violating effects in SO(3) gauge models are ?10^?4 smaller than those evaluated in the Weinberg theory with a neutral parity-violating current and will remain undetectable in the near future.     

Velocity dependence of the nucleon-nucleon interaction,exchange currents and enhancement of the dipole sum rule in nuclei

A model is employed to describe the velocity dependence of the effective nucleon-nucleon interaction in nuclear matter. The interactions in this model consist of π^? and ρ-meson exchange, together with short-range correlations induced by the strongly repulsive potential resulting from ω-meson exchange. With known coupling strengths, these interactions produce an effective mass $\text{m}{}^1\text{/m = 0.75}$ in nuclear matter.Through the formalism of Fermi liquid theory, the exchange-current correction to the orbital g-factor, δg_l, can be described in terms of the velocity dependence in the neutron-proton interaction, and, within the model, this can be related to the effective mass $\text{m}{}^1$. With $\text{m}{}^1\text{/m = 0.75}$, the δg_l for the proton turns out to be 0.22, 45% of it coming from π-meson exchange.Additional contributions to $\text{m}{}^1\text{/m}$ in nuclei come from the coupling of vibrations to quasiparticles; these are especially important in the nuclear surface, and tend to increase the effective mass, when averaged over both nuclear volume and surface, so that $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{? 1}$. In so far as these contributions arise from isovector vibrations, we can use the same model as for π- and ρ-meson exchange, and show that the same relation between $\text{m}{}^1\text{/m}$ and δg_l holds, so that for $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{= 1}$, δg_l = 0. The contributions from coupling to vibrations will depend upon the single-particle state, however; states of high-angular momentum will tend to have $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{< 1}$ and δg_l > 0.Finally, the enchancement δg_l in gl can be connected with the enhancement k in the dipole sum rule originating from the giant-resonance region. This connection is not very precise, but gives a small positive κ ～ 0.2.     

Heavy flavour contributions to massive lepton pair production

Massive lepton pair production in hadronic collisions, A + B → μ⁺μ^? X, is usually assumed to proceed via ann intermediate virtual photon, $\text{ψ}{}^1\text{→ μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}$, the Drell-Yan process. We examine other contributions arising from heavy flavour production, $\text{A}\text{+}\text{B}\text{→}\text{Q}\text{Q}\text{X}\text{;}\text{Q}\text{→ μν}\text{X}$. We find that this background is comporable to the Drell-Yan signal at small values of $\text{M}{}_{\mathrm{<mtext>\mu </mtext><mtext>\mu </mtext>}}{}^2\text{/s}$ but negligible at large values. Characteristic siggnatures are described that distinguish the background from the signal.     

Features of dynamically broken gauge theories

We discuss several features of dynamical symmetry breaking in gauge theories of strong, weak and electromagnetic interactions. We speculate that in some such theories the fine structure constant calculable. A possible solution of the strong P and T violation problem in QCD by dynamical symmetry breaking is indicated. Self-energy divergences are absent in such models and we compute the finite electromagnetic self-energy of a quark in QCD. The mass hierarchy problem is examined. We find models in which the fermion-gauge boson mass ratio is $\text{M}{}_{\mathrm{<mtext>F</mtext>}}{}^2\text{M}{}_{\mathrm{<mtext>B</mtext>}}{}^2\text{～}\text{exp}$ ($\text{?1}\text{g}{}^2$), where g is a gauge boson coupling, which could account for the origin of weak interactions.     

Predictions of duality for the charmed meson masses

The constraints of duality via FESR's are applied to the processes P+P→P+V, using particles with a new quantum number (charm) as both external and internal (resonance saturation) states. The results are independent of any detailed dynamics or symmetry schemes, as well as independent of coupling strengths. We use the masses of the recently-discovered D and D¹ to set the scale. We predict , m_F = 1938 ± 33 MeV, . Thus slopes of Regge trajectories for charmed mesons are predicted to be substantially smaller than those for ordinary mesons.     

Supersymmetric pure spinor theory

A theory based solely on a 2×(N=2)-component Weyl spinor field χ(x) of subcanonical dimension $\text{1}\text{2}$ allows the local construction (without derivatives) of effective fermi and bose fields with spins up to N=2. It is demonstrated that the lagrangian $\text{～:}\text{det}\text{xx}{}^1\text{: (x)}$ studied earlier is invariant under a global N=2 supersymmetry transformation and can be cast into a form $\text{～(}\text{det DD}{}^1\text{):ππ}{}^1\text{:}$ involving the scalar chiral superfield $\text{π=}\text{exp}\text{[θ}{}_{\mathrm{x}}\text{(x + iθσθ}{}^1\text{)]}$ the components of which are finite part products of the basic field. The theory can be generalized to an N-supersymmetric theory in a 2N-dimensional space-time yielding the Thirring model as special case for N=1.     

Three body resonances in a coupled channel ND approach

Assuming a three body channel to be dominated by the formation of bound states and resonances, the three body problem is reduced to an effective two body coupled channel problem in which pairs of particles, either bound states or resonances, scatter from the remaining third particle. We treat this effective two body problem by the partial wave matrix $\text{N}\text{D}$ method. We study in particular a coupled two channel problem, one channel consisting of one resonance plus one particle, the other of one bound state plus one particle. Our main purpose is to investigate in a full coupled channel situation the possible generation of three particle resonances. With single particle exchange forces forming the dynamical input to the $\text{N}\text{D}$ integral equations, enhancements are generated in a spinless model which correspond to three-particle resonances. The model is then applied, with spin included, to the $\text{p + p +}{}^{12}\text{C}$ system at low energy, in which ($\text{p +}{}^{12}\text{C}$) can form either the bound state ¹³N (G.S.) or the resonance ¹³N¹ (1.944 Mev); the two channels are then $\text{p +}{}^{13}\text{N(G.S.)}$ and $\text{p +}{}^{13}\text{N}{}^1$. The p-p interaction is neglected. It is found that the main effect in this case is the force arising from the coupling of the channels, which is sufficiently strong to generate a three particle level in the composite system ¹⁴O.     

Hole-vibration states in 115In

The hole-vibration coupling in the Z = 50 region is investigated by calculating the level structure of ¹¹⁵In. Four proton-hole states are coupled with quadrupole and octupole core vibrations. The phonon energies and the amplitudes of the vibrational motions are taken from experiment, while the single-hole energies are treated as free parameters. Most of the observed features of a quintet of states with $\text{I}{}^{\mathrm{\pi }}\text{=}\text{5}\text{2}{}^{\mathrm{+}}\text{,}\text{7}\text{2}{}^{\mathrm{+}}\text{,}\text{9}\text{2}{}^{\mathrm{+}}\text{,}\text{11}\text{2}{}^{\mathrm{+}}\text{,}\text{13}\text{2}{}^{\mathrm{+}}$, which have enhanced E2 transition strengths to the ground state, are well reproduced by the theory. The hole-vibration coupling produces a strong fragmentation of the single-hole strengths. This is quite in agreement with the results of (d, ³He) experiments on ¹¹⁶Sn.     

Role of the effective nucleon mass for pion condensation in nuclear matter

The dependence of the threshold for pion condensation in symmetric nuclear matter on the effective nucleon mass $\text{M}{}^1$ is investigated, using extrapolations of $\text{M}{}^1\text{(?)}$ to high densities ?, based on boson exchange mechanisms. It is found that if $\text{M}{}^1\text{(?)}$ decreases below the standard value $\text{M}{}^1\text{=0.8M}$ as the density increases beyond the nuclear matter density ?₀, the critical density is raised considerably beyond ?₀ once short-range repulsive correlations are included.