Studies of chiral symmetry breaking in SU(2) lattice gauge theory

We study chiral symmetry breaking (_χSB) in SU(2) lattice gauge theory with quarks in the $\text{l =}\text{1}\text{2}\text{, l = 1, l =}\text{3}\text{2}$, and l = 2 representations of the color group. We perform Monte Carlo evaluations of $\text{〈}\text{ψ}\text{ψ〉}$ in the quenched approximation and extract the relevant length scales for _χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain $\text{T}{}_{\mathrm{l\; =\; 1}}\text{/T}{}_{\mathrm{l}}\text{=}\text{1}\text{2}\text{～ 8}$. Our results for the higher representations, $\text{l =}\text{3}\text{2}\text{and}\text{l = 2}$, are consistent with Casimir scaling and give C₂g_mom² ～ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between _χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices.     

Radiative decays of the Jψ and evidence for a new heavy resonance

The three photon final state produced in e⁺e^? collisions has been measured at the mass of the $\text{J}\text{ψ}$ resonance using the nonmagnetic part of the double arm spectrometer DASP. The decays $\text{J}\text{ψ}\text{→ ηγ, η'γ}$ and π^oγ were observed and their branching ratios are given. A four standard deviation signal was observed in the γγ mass spectrum at a mass of (2.83 ± 0.03) GeV. An upper limit is given for the direct decay $\text{J}\text{ψ}\text{→ 3γ}$.     

Instantons and condensates in supersymmetric CPN−1 models

The partition function in the multi-instanton background for the supersymmetric CP^N?1 model is calculated and is shown to be supersymmetry invariant. This is used to calculate Green's function involving N pairs of $\text{ψ}\text{ψ(x}{}_{\mathrm{i}}\text{)}$, and this turns out to be independent of the positions. A possible interpretation is that the composite field $\text{ψ}\text{ψ}$ acquires a vacuum expectation value. The results are in agreement with those obtained in the 1/N expansion.     

Chiral phase transition in lattice QCD with dynamical quarks

The effect of virtual light quark loops on the chiral phase transition in lattice QCD with staggered fermions is investigated by employing the pseudo-fermion Monte Carlo method on a 6³ × 2 lattice. The variation in the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ is found to become less sharp than the quenched case, indicating a second order chiral phase transitioon in the full theory.     

Chiral symmetry,the 1/N expansion and the SU(N) thirring model

In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, $\text{〈}\text{ψ}\text{ψ(x)}\text{ψ}\text{ψ(0)〉}$ vanishes in this model as |x|^?1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model.     

Jψ and ψ′ decays into two hadrons

Branching ratios have been determined for the decays of $\text{J}\text{ψ}$ and ψ ′ into π⁺π^?, K⁺K^?, $\text{p}\text{p}$, π^±?^? and $\text{K}{}^{\mathrm{\pm }}\text{K}{}^1\text{(892)}{}^{\mathrm{?}}$. Results on a search for other two body decays of $\text{J}\text{ψ}$ and ψ′ are given. Also presented are values for the π and K from factors at $\text{s}\text{= 3.1}\text{and}\text{3.7}\text{GeV}$.     

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.     

Dirac spinor solitons or bags

Explicit solutions of a non-linear Dirac equation in the four-dimensional Minkowski space have been found. They are continuous eigenfunctions of spin $\text{1}\text{2}$, energy and parity, and are confined to the interior of a sphere of definite radius a, with no tails outside the sphere. They are called solitons in the paper though the name of spinor droplets or bags may be more appropriate. Because of the Lorentz covariance of the Dirac equations, arbitrarily moving solitons can be obtained from the rest system solutions by applying proper Lorentz transformations.     

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.     

Inclusive Jψ production in e+e− annihilation in the energy range from 4.0 to 5.0 GeV

We report on inclusive production of $\text{J}\text{ψ}$ (3.1)-mesons observed in e⁺e^?-annihilation in the energy range $\text{s}\text{= 4.0–5.0}\text{GeV}$. After substraction of the radiative tail of the ψ(3.7) direct production of the $\text{J}\text{ψ}$ (3.1) is found to be in the order of 0.1% of the total hadronic cross section. No enhancements are seen at $\text{s}\text{= 4.03}\text{GeV}$ and 4.4 GeV. The level is in agreement with expectations from violation of the Zweig-rule.     

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.     

Experimental comparison of Jψ production by π±, K±, p and p̄ beams at 39.5 GeV/c

Measurements have been made of relative production cross sections of the $\text{J}\text{ψ}$ by π^±, K^±, p and p? at 39.5 GeV/c incident on copper. $\text{J}\text{ψ}$ production rates from π^?, K^? and p? are similar. The $\text{J}\text{ψ}$ relative particle/anti-particle production cross sections for x>0 are $\text{σ(π}{}^{\mathrm{+}}\text{)}\text{σ(π}{}^{\mathrm{?}}\text{)=(0.87±0.14)}$, σ(K⁺)/σ(K^?)=(0.85±0.5) and $\text{σ(}\text{p}\text{)}\text{σ(}\text{p}\text{?}\text{)=(0.15 ±0.08)}$. The small p/p? cross section ratio disagrees with models of J/ψ production by gluon amalgamation.     

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 $\text{κ?}\text{1}\text{8}$.     

Self-consistent solutions for fermions in constant SU(2) gauge potentials

We derive self-consistent solutions for $\text{isospin}\text{-}\text{1}\text{2}$ Dirac particles coupled to constant SU(2) vector potentials. Such solutions can be identified as classical approximations to non-topological fermionic solitons. We discuss the stability of these states under quantum fluctuations.     

Monte Carlo simulation of the massive Schwinger model

In this article we apply a previously proposed defermionization method to the study of two-dimensional QED (massive Schwinger model). We find good evidence for the spontaneous breaking of axial symmetry, i.e., $\text{〈}\text{ψ}\text{ψ〉≠0}$ in the massless limit.     

Radiative transitions and the P wave levels in charmonium

A value of $\text{1}\text{2}$ or less for the ratio $\text{[E(2}{}^{\mathrm{++}}\text{) ? E(1}{}^{\mathrm{++}}\text{)]}\text{[E(1}{}^{\mathrm{++}}\text{) ? E(0}{}^{\mathrm{++}}\text{)]}$ of the P level splittings in approximate agreement with the assignment of the states at 3.41, 3.50 and 3.55 to the 0⁺⁺,and 2⁺⁺ P-wave levels, is obtained with a short-range Coulomb (Lorentz vector) potential together with a long-range linear (Lorentz scalar) confining potential. The radiative transition widths Γ(ψ′ → 3.41 + γ), Γ(ψ′ → 3.50 + γ), Γ(χ′ → 3.55 + γ) are significantly smaller than those obtained in previous (one-channel) charmonium calculations. The best results were obtained by allowing the Coulomb coupling constant α_s to have a momentum dependence suggested by asymptotic freedom formulae.     

Some properties of the (ψψ)2 model in two dimensions

We show that the two-dimensional $\text{(}\text{ψ}\text{ψ)}{}^2$ model is, for N = 3, equivalent to the supersymmetric sine-Gordon equation, and for N = 4, equivalent to two decoupled sine-Gordon systems. In addition, we argue that the kinks of this model are isospinors, and we construct some of the higher conservation laws that are responsible for the exact solubility of this system.     

Author index to volume 68B

The decay of J/ψ (3.1) into final states containing no charged particles has been studied experimentally. The partial decay width for the observed neutral decays is (470 ± 160) eV. The decay modes J/ψ → γη → 3γ and J/ψγη′ → 3γ are identified and the branching ratios

$\text{J}\text{ψ}\text{→ γη}\text{J}\text{ψ}\text{→}\text{all}\text{= (1.3 ±0.4) × 10}{}^{\mathrm{?3}}\text{,}\text{and}\text{J}\text{ψ}\text{→ γη′}\text{J}\text{ψ}\text{→ γη}\text{= 1.8 ±0.8}$

, are derived. Upper limits for the decay modes J/ψ → γπ⁰ and J/ψ → γγ are given.     

An alternative mechanism of Jψ suppression in heavy ion collisions

We argue that $\text{J}\text{ψ}$ suppression observed recently in high energy oxygen-uranium collisions by the NA38 Collaboration at CERN need not imply that the quark-gluon plasma was produced. A considerable part of the effect may be caused by the disintegration of $\text{J}\text{ψ}$'s in collisions with dense hadronic matter (below the phase transition into quark-gluon plasma) produced simultaneously with $\text{J}\text{ψ}$ in heavy ion interactions.