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.     

Finite crossing sum rules for helicity amplitudes of multiparticle reactions with general spins and masses

Using one-tetrad amplitudes, it is shown how to derive finite crossing sum rules for a reaction of the form n particles→n′ particles, where the particles have general spins and masses. The case of 2→3 particles is worked out in detail, and general formulas are given for the sum rules. An application is made to a reaction with spin structure $\text{1}\text{2}\text{+}\text{1}\text{2}\text{→}\text{1}\text{2}\text{+}\text{1}\text{2}\text{+0}$.     

A computation of Adler's β sum rule

We try to check Adler's β sum rule for q² = μ². The integral of β can be divided into two parts: a first part which, if q² = μ², involves only an integral of the experimental πN cross section, and a second one which is a priori of order μ² compared to the first. This second term can be approximated by an explicit calculation of the $\text{N}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext><mtext>3</mtext><mtext>2</mtext>}}{}^1$ contribution in the framework of Adler's model for the $\text{ν}\text{N}\text{→ μ}\text{N}{}^1$ reactions. The sum rule is not too well balanced and different hypotheses are presented to explain the defect.     

Planar limit of the singlet spectrum for SU(N)-invariant quantum hamiltonians by the quantum collective field method

We calculate the quantum fluctuations around the classical vacuum of the quantum collective field in the case of SU(N)-invariant quantum mechanical systems. We obtain in this way the singlet spectrum up to corrections of order $\text{1}\text{N}$. Difficulties in the calculation of higher order terms in $\text{1}\text{N}$ are pointed out.     

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.     

Duality in the current propagator

The idea of local duality between generalized vector dominance and light cone algebra or parton model is applied to the propagator of vector currents. A set of sum rules reminiscent of the generalized first Weinberg sum rules but involving certain unknown parameters are derived. These parameters are fixed from the leptonic decay modes of ?, ω, ?. The sum rules are used to calculate the ω-? mixing angle and thereby predict $\text{Γ(?→}\text{K}\text{K}\text{) = 3.24±0.34}\text{MeV}$, in agreement with experiment. Simple mass mixing or current mixing model for the vector mesons seem to be inconsistent with data. The total cross section for e⁺e^?→hadrons is calculated in the scaling region. If scaling is achieved at $\text{s ? 9–16}\text{GeV}{}^2$ then it is argued that about 22% of the events in this energy region will include strange particles.     

The bare parameters of Gribov's lagrangian in a simple t-dependent dual bootstrap model

In the context of the “$\text{1}\text{N}$ Dual Unitarization” scheme, we present an explicit dynamical study of the triple bare pomeron mechanism which governs the interaction term in Gribov's lagrangian. Together with the previously established bare pomeron slope and intercept, controlling respectively, the kinetic and mass terms in Gribov's lagrangian, this work demonstrates the viability of the “$\text{1}\text{N}$ Dual Unitarization” approach for a field theory of interaction bare pomerons.     

Non-diffractive Pomeron renormalization,multiplicities, and the topological expansion

The renormalization of the Pomeron due to nondiffractive K$\text{K}$, B$\text{B}$ production thresholds is considered within a simple generalization of the Chew-Rosenzweig multiperipheral realization of Veneziano's topological expansion. The results are consistent with the existence of both the “low-energy” bare Pomeron with intercept $\text{α=0.85}$ and Gribov bare Pomeron with intercept above one. The vacuum exchange part of 2σ_KN?σ_πN basically rises with energy. Qualitatively correct features of shrinkage and breaks of $\text{d}\text{σ}\text{d}\text{t}$ emerge. The multiplicity of product clusters (n) increases with energy faster than 1ns and agrees with experiment for an average number of particles per cluster of 3–4. Independently of our model the Harari-Freund multiperipheral realization of the topological expansion is shown to be in serious difficulty with multiplicities, requiring around 20 particles per cluster.     

Current algebra theorems for the U(1) “Goldstone boson”

The U(1) problem is reconsidered from the point of view of the $\text{1}\text{N}$ expansion. It is argued that various heuristic ideas about the η′ are valid from this point of view. Current algebra theorems, similar to soft π theorems, are derived for the η′. They are valid to lowest order in $\text{1}\text{N}$.     

Perturbation theory with instantons

We develop “perturbation theory” rules for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the “dilute gas” approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form where b is the coefficient in the expansion of the β function: β = bg³ + 3. .     

Multipole moments and spin-dependent sum rules and their applications to f72 and s-d shell nuclei

Matrix elements of multipole operators, defined separately for neutrons and protons, are related to spin-dependent sums of spectroscopic factors. A clarification of their relation to the matrix elements of single-particle operators enables the overlap representation to be formally extended to a stripping form for J ≠ 0 operators. Multipole moments obtained from $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ transfer data are found to be dominated by the quadrupole moments when the final nucleus is odd-odd.A previously found (2J + 1) rule for spectroscopic sums, which arises when the odd-J multipole moments vanish, is shown to lead to approximate sum rules which apply separately to stripping and pickup data. The sum rules are generally well satisfied for transfers leading to odd-odd nuclei in the s-d shell.     

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.     

1N-expanded ϕ2X model. I. Phase transition

We consider the ?²X model in a $\text{1}\text{N}$ expansion in six-dimensional Euclidean spacetime. Using the path-integral formalism and the method of stationary phase we show the existence of two phases in the model: with broken O(N) symmetry and with O(N) maintained. In both phases the massless ? fields acquire masses. -Expressions for the masses including $\text{1}\text{N}$ order are given.     

Rising total cross sections and the flavoring of the pomeron

The relationship of the non-diffractive renormalization of the bare pomeron via$\text{K}\text{K}$ and $\text{B}\text{B}$ production - or its “flavoring” by λ quark loops and di-quark loops - and the shape of the NN total cross section is studied in some detail. The “unflavored” bare pomeron P? generated by non-strange quark loops with intercept $\text{α}\text{=0.85}$ is non-diffractively renormalized into the “flavored” (Gribov) bare pomeron P with intercept α above one (α = 1.06 here). We utilize inclusive data on $\text{K}\text{K}\text{and}\text{B}\text{B}$ production as well as inelastic diffraction to constrain parameters, and we fit the combination $\text{1}\text{2}\text{(σ}{}_{\mathrm{<mtext>pp</mtext>}}\text{+ σ}{}_{\mathrm{<mtext>p</mtext><mtext>p</mtext>}}\text{)}$ from s = 10 GeV² through ISR energies, including the new Fermilab data, to high accuracy. No pronounced long wavelength oscillations are observed. We suggest that these data favor the Chew-Rosenzweig realization of the topological expansion over that of Harari-Freund. We show that our scheme is consistent with the rising behavior of 2σ_KN ? σ_πN.     

Masterfields and the phases of quantum chromodynamics in two dimensions with fermions

The phase structure of two-dimensional quantum chromodynamics is analyzed in the large-N limit. Using a variational approximation, we show that a first-order phase transition occurs as the quark bare mass squared m₀² is made less than $\text{g}{}^2\text{N}\text{π}$. This novel phase structure goes beyond summing the perturbative large-N planar graphs.     

Effective lagrangian of mesons and baryons in the strong-coupling expansion of lattice QCD

U(N) and SU(N) lattice QCD are considered. By using a method of the strong-coupling expansion, the effective lagrangian of hadrons is calculated up to the first order in 1/(g²N). For the Susskind lattice fermions, it is shown that chiral symmetry is spontaneously broken and as a result there appears the Nambu-Goldstone boson (pion). The fermion condensation 〈$\text{ψ}\text{ψ}$t>, the masses of hadrons and the pion decay constant are calculated and compared with the results of Monte Carlo (MC) simulations. In the strong-coupling region, our result of the order parameter 〈$\text{ψ}\text{ψ}$〉 coincides very well with that calculated by MC simulations.     

Light cone and mass shells

We propose a hypothesis which generalizes the notion of duality to off-mass-shell current matrix elements. The hypothesis, referred to as strong light-cone dominance, is formulated in terms of the light-cone sum rules, which reflect causality and the light-cone structure of current commutators: We postulate that these sum rules are saturated quasilocally by individual resonance peaks, in a similar manner as duality requires resonances to saturate the FESR for the hadronic on-shell amplitudes. This reconstitutes scaling in an average sense in regions where the leading light-cone singularity does not dominate. In coordinate space this hypothesis implies that the leading light-cone singularity regulates (tames) the entire light-cone expansion in a neighbourhood of the surface of the light-cone, whose extension is of the order of an inverse mass difference between consecutive resonances. We investigate the hypothesis of strong light-cone dominance in the framework of narrow resonance models for the vertex and show that the leading light-cone singularity indeed normalizes the single particle contributions by means of a relation of the Drell-Yan-West type. A simple Veneziano-like vertex model is exhibited, which is strongly light-cone dominated. Furthermore, we show how to exploitthe hypothesis in a rather model-independent way. We present some applications to the non-forward four-point function and show in particular that strong light-cone dominancerequires scaling for exclusive electroproduction processes like $\text{γ}{}^1\text{+}\text{N}\text{→ π +}\text{N}$.     

Fixed-mass sum rules in a non-perturbative parton-model framework

The formulation of the parton model due to Landshoff and Polkinghorne is used to discuss the various fixed-mass sum rules that can be derived for the structure functions measurable in inelastic electroproduction, including those dependent on the target spin and also allowing for an extension to the non-Abelian case of isovector currents. The model is re-expressed in terms of light-cone variables which achieves some simplification and gives some new results, in particular concerning the leading terms of the longitudinal structure function in the scaling limit for $\text{spin}\text{-}\text{1}\text{2}$ theories. Careful attention is paid to verifying the consistency of the results with current conservation, which is achieved by embedding the model in simple field theories so as to introduce the necessary dynamics. Those sum rules which appear to diverge are shown to be made finite by becoming statements concerning the residue of fixed J-plane poles, for which an analysis is given.