Numerical evidence for a mass gap in three-dimensional SU(2)

Numerical evidence for a nonvanishing 0⁺⁺ glueball mass in three-dimensional SU(2) is presented. By using a long-distance correlation Monte Carlo method we obtain m₀⁺⁺ = (4.7±1.2)√σ in the β-range 4.0–6.5. The measurements are consistent with 1/β-scaling. The relevance of this result for SU(2) in four dimensions at finite temperature is briefly discussed.     

SU(3) lattice Monte Carlo calculation of the glueball mass spectrum

We have calculated the glueball masses of various spins and parities in SU(3) gauge theory. Our first results give m_M(0⁺⁺)=(3.6±0.2)Λ_mom, m_E(0⁺⁺)=(4.3±0.3)Λ_mom, m(0^?+)=(7.2_?0.9^+1.6)Λ_mom, m_M(2⁺⁺)=(8.1±1.1)Λ_mom and m_E(2⁺⁺)=(8.3_?1.0^+1.6)Λ_mom as well as information on the glueball wave functions.     

Strong-coupling expansions for the off-axis glueball masses

Strong-coupling expansions, up to order g^?4, for the off-axis glueball masses are developed in four-dimensional spacetime for lattice gauge theories with gauge groups SU(2), SU(3), Z₂, Z₃. Glueball mass spectra for the states 0⁺⁺, 2⁺⁺, 1^+? are obtained. Restoration of Lorentz invariance is discussed.     

Decreasing of the finite-size effects through the twisted boundary conditions II

In the large-N limit it is shown that a model with twisted boundary conditions becomes equivalent to the U(N) invariant theory which has a volume N² times larger than the theory with periodic boundary conditions. Even for finite N, it is confirmed that the finite-size effects in the models with twisted boundary conditions rather decrease, compared with the ones with periodic boundary conditions, by performing a Monte Carlo simulation for the two-dimensional SU(3) chiral models.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

The mass spectrum of 0−+, 0++, 1−-, 2++ mesons in the SU(4) and SU(8) scheme and prediction of new narrow resonances

A unified treatment of 0^?+, 0⁺⁺, 1^?-, 2⁺⁺ meson multiplets is provided, in the SU(4) and SU(8) scheme. The overall consistence is excellent and the existence of a new 1^?- resonance φ_c(2.835) is predicted.     

f mass spectrum in 7-GeV/cπp interactions

Structure in the f^o [an SU(3) companion of the A₂] is sought in more than 5000 π⁺p → f^oΔ⁺⁺ events at 7 GeV/c in a hydrogen chamber. The mass spectrum and the moments of the decay angular distribution are studied with a resolution of 7.8 MeV.     

Hot twists for the single-point model of large-N QCD

We construct two types of twists for the SU(N→∞) twisted-Eguchi-Kawai model, which mimic a periodic boundary condition in the temporal direction only and over an arbitrary extent N₀. In this way we introduce finite temperature (T=N₀^?1 in lattice units) in the single-point model. In weak coupling one gets the correct planar expansion.     

η → 3π decay and πη scattering in chiral SU(2) × SU(2) symmetry

The problem of η → 3π decay in chiral SU(2) × SU(2) symmetry is investigated. We argue that the well-known difficulties of the conventional pole model originate from underestimating the role of the η-meson pole graph. This model is shown to be suitable for describing η → 3π decay if the strong ηηππ vertex in the η-pole graph is determined by an SU(2) × SU(2)-invariant interaction. The π^o ? η transition constant g_πη is evaluated from U-spin invariance with the help of a current-mixing model: | g_πη | ≈ 0.05. It turns out that the experimental data on both the decay widths and the energy spectrum can be satisfied by fitting the value of the ηηππ coupling constant as a parameter. As a result, predictions for the s- and p-wave πη scattering lengths are obtained: |a_πη⁰| ≈ 0.2m_π^?1, |a_πη¹| ≈ 0.1m_π^?3.     

Chiral-limit theorems and corrections to PCAC in a model for the scalar Kℓ3 divergence form factor

Three sum rules on vertex functions are derived by applying a model on two-particle Kπ channels. SU(3) × SU(3) breaking is introduced by corrections to the PCAC forms of the axial currents. Taking the m_π → 0 limit the sum rules reduce to the Callan-Treiman theorem, a recent theorem by Dashen, Li, Pagels and Weinstein (DLPW) and a third relation. We encounter non-analytic correction terms in the two first sum rules. In the DLPW theorem we find, contrary to a previous suggestion, non-negligible ε and ε²ln ε terms which are due to the large K-mass. These terms are responsible for a curvature of the scalar K_?3 form factor, however negative values of the slope at the origin require also substantial SU(2) × SU(2) violations. The numerical results taking into account physical masses compare favourably with K_?3 decay and also with s-wave Kπ scattring data.     

Can the JPC = 1++ mesons form an ideal nonet?

In the framework of asymptotic SU(3) and the chiral SU(3) ? SU(3) charge algebra, it is argued that the 1⁺⁺ mesons can form an (almost) ideal nonet along with the 1^-- mesons. Experimental implications are also discussed.     

The relation between D and A1 axial-vector meson decays

We analyse the available information on the production and three-body decays of the D(1285) meson in an attempt to establish its relationship to the A₁(J^PC = 1⁺⁺) which mounting evidence suggests has a mass and width of 1100 and 250 MeV, respectively. In particular, we demonstrate that the narrow width of the D(20 to 30 MeV) is by no means incompatible with a broad A₁ and SU(3) symmetry. Taking due account of the possible existence of a K_A meson at 1340 MeV, we predict the decay properties of the ninth member of the nonet (the D') and argue that the E(1420) is not a viable candidate for this state.     

Quark masses and cabibbo angles

A simple symmetric pattern of Higgs fields in an SU (2)_L × SU (2)_R × U (1) gauge model with six quarks yields: tan²θ_c = m_d/m_s and θ_c = 15° in good agreement with experiment. A eight-quark extension of the model leads to successful determination of the three Cabibbo-like angles connecting the first six quarks and to the prediction m_t ～ 9.3 m_c ～ 14 GeV.     

Higgs bosons and matter-antimatter oscillations in GUTS

The presence of Higgs bosons of diquark and dilepton types at intermediate mass scales in GUTs is analysed in connection with the possible generation of neutron-antineutron and hydrogen-antihydrogen oscillations. Their renormalization effects on the calculation of the parameters sin²θ_w and m_b/m_τ are investigated in SU(5) and in an SO(10) version with a left-right symmetric breaking chain. In correspondence with suitable combination of higgses, we find solutions in SU(5) for n_G=3 and reasonable values of sin²θ_w, m_b/m_τ and proton lifetime τ_p, which allow detectable $\text{n}\text{-}\text{n}$, but undetectable $\text{H}\text{-}\text{H}$ transitions. Solutions of this type, but with higher τ_p, are also found in a particular scheme of SO(10), where the intermediate mass is at the scale M_R at which the left-right symmetry is broken and is of order 10²×m_w. This modifies then conclusions of analyses of SO(10) models, where either no diquarks and dileptons or only a specific set of them are taken into account.An extension of our analysis to supersymmetric versions of SU(5) and SO(10) does not produce acceptable solutions.     

Left-right symmetry breaking scale and supersymmetry in unified theories

We propose a class of supersymmetric grand unified models where parity and SU(2)_R breaking scales are widely separated and compatible with a low-lying mass for the right-handed gauge boson W_R. The intermediate symmetry SU(4)_c×SU(2)_L×SU(2)_R and Higgs content are uniquely fixed if m_WR < 10⁹ GeV. The unification scale lies within an order of magnitude below the Planck mass.     

Top quark mass from gut mass relations

Using one-loop renormalization group equations of SU(3)×SU(2)×U(1) and mass relations of minimal SU(5) we obtain m₁=203±30 GeV and m_s=0.20±0.03 GeV for the top and strange quark masses. For general GUT with m_b=m_τ at E=M_x<M_P1 we get m_t > 165 GeV. These values appear to be consistent with recent experimental data.     

On the mass and mixings of the ZE

The experimental data on the neutral current couplings are used to derive lower bounds on the mass of Z_E, the extra neutral gauge boson appearing in the minimal ‘beyond the standard model’ scenario favoured in superstring compactifications. This is based on the gauge group SU(3)_c×SU(2)_L×U(1)_Y×U(1)_E. Taking sin²θ_w=0.229, m_W=80.76 GeV and m_Z=91.59 GeV it is found that the mixing angle θ between Z and Z_E must satisfy −0.136<sin θ<−0.007 corresponding to m_ZE>152 GeV or, assuming E₆ unification m_ZE>155 GeV.     

Charm changing weak decays 1/2+ → 3/2+ + 0−/γ in SU(4) and SU(8) w

Weak decay modes (1/2⁺ → 3/2⁺ + 0⁻/γ) of charmed baryons are studied. Relations among the various decay amplitudes are derived in isospin, SU(3), SU(4) and SU(8) _w symmetries. Sextet dominance in SU(3) forbidsB(3) →D(10) +P(3*) decays. 20″ dominance in SU(4) specifies all the decays in terms of Θ⁻ decays. Weak decays of Θ* ₃ ⁺⁺ and Θ⁻ are also discussed. SU(8) _w symmetry predictsα , which is consistent with the experimental value.     

Reduction of fermion-gluon systems on extended lattices

We develop a simple method for dealing with perturbation theory in the presence of twisted boundary conditions. We compare in detail periodic and twisted SU(N) gauge models. As an application we study staggered fermions in a reduced model for large N_colour and N_flavour. The ratio N_colour/N_flavour can be made variable by performing only partial colour conversion.