Light cone constraints and two asymptotic domains in lepton-nucleon and meson-nucleon scattering

Effective bare masses of the “current-quarks” are estimated from some testable inequalities, linking deep inelastic lepton-nucleon structure functions and high energy meson-nucleon total cross-sections, derived on the basis of the light-cone commutators of the pseudoscalar densities of quark-field theory.     

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.     

Departures from chiral symmetry

We review the physical concepts supporting the notion of an approximate hadron symmetry with special emphasis on the Nambu-Goldstone realizations of chiral SU (2) × SU (2) and SU (3) × SU (3). We stress the role of perturbation theory in the symmetry breaking as the technical instrument to connect broken symmetries with experiment. This is an alternate to the treatments that stress PCAC and current algebra. We find that chiral SU (2) × SU (2) is a good hadron symmetry to within 7% making it the best hadron symmetry after isotopic symmetry. The nonrenormalization theorem, Σ-terms, K_l3 decay, η→3π decay, the Goldberger-Treiman relation and many other specific processes and their relation to approximate chiral symmetry are discussed.     

Current algebra of quarks confined to a cavity

Equal-time commutators of fields with charges are calculated in a cavity approximation to the MIT bag model, with N flavours of non-interacting quarks confined to a rigid spherical cavity and SU(N) symmetry arbitrarily broken by mass terms. It is proved that inside the cavity the algebra is identical with that of free field theory, whilst on the boundary quark fields commute with axial charges. Vector divergences and sigma commutators belong to a $\text{(N,}\text{N}\text{) + (}\text{N}\text{, N)}$ multiplet of chiral SU(N) × SU(N). Axial divergences contain additional surface terms which do not contribute to sigma commutators. A non-strange quark mass in the range 20–44 MeV is required to give a value 30–70 MeV for the nucleon matrix element of the sigma commutator relevant to pion-nucleon scattering.     

Pseudoscalars and vector mesons in a unitary and self-consistently broken SU(6) W scheme

We estimate hadronic self-energy effects to “bare” pseudoscalar (P) and vector (V) meson states due to theP→PV→P, P→VV→P, V→ PP→V, V→PV→V andV→VV→V loops. We simulate higher order diagrams by consistently requiring external and internal particles to have the same mass. We find good agreement with all the experimental masses (exceptm _π), widths and mixing angles. The “bare”P andV states are heavy (≈1.26 GeV) and degenerate up to a smallm _s?m_u quark mass difference term. The “bare” coupling constants for thePPV, PVV andVVV vertices obey exact OZI rule and almost exact SU(6) _W symmetry. We use a common cut-off ofk _cm?0.7 GeV/c corresponding to a harmonic oscillator radius of ?0.7 fm for all SU(6) _W related thresholds except for the pion.     

Second class currents and broken SU(3)-symmetry

In the SU(3) limit, a second class, T-normal axial vector current, which transforms like an octet, can give rise to pseudotensor terms in the matrix elements for leptonic decays of baryons. With first order symmetry breaking, this second class current may generate pseudovector and pseudoscalar form factor contributions. It is an anti-hermitian current, but, even with SU(3) breaking, it does not need to disturb the chiral SU(2) × SU(2) algebra of charges.     

Effective meson lagrangian with chiral and heavy quark symmetries from quark flavor dynamics

By bosonization of an extended NJL model we derive an effective meson theory which describes the interplay between chiral symmetry and heavy quark dynamics. This effective theory is worked out in the low-energy regime using the gradient expansion. The resulting effective lagrangian describes strong and weak interactions of heavy B and D mesons with pseudoscalar Goldstone bosons and light vector and axial-vector mesons. Heavy meson weak decay constants, coupling constants and the Isgur-Wise function are predicted in terms of the model parameters partially fixed from the light quark sector. Explicit SU(3)_F symmetry breaking effects are estimated and, if possible, confronted with experiment.     

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.     

Baryon masses in large N c chiral perturbation theory

We analyse the baryon mass spectrum in a framework which combines the 1/N _c expansion with chiral perturbation theory. Meson loop contributions involving the full SU(3) octet of pseudoscalar Goldstone bosons are evaluated, and the influence of explicit chiral and flavor symmetry breaking by non-zero and unequal quark masses is investigated. We also discuss sigma terms and the strangeness contribution to the nucleon mass. Received: 29 June 1998 / Revised version: 25 November 1998     

Phenomenology of dynamical symmetry breaking in QCD

A consistent treatment of the QCD quark propagator and quark-antiquark bound state equations is presented which follows the Nambu and Jona-Lasinio approach to the discussion of chiral symmetry breaking. An expression is obtained for the dynamical, momentum dependent, mass. In the approximation used here the dynamical mass is determined byM ₀, its value at zero momentum, and by the strong coupling constant α _s and bare quark massm ₀. In the limiting case of no explicit chiral symmetry breaking. i.e.,m ₀=0, this expression coincides in form with the one obtained by Chang and Chang in their renormalization-group analysis. In this limit chiral symmetry remains broken and we show the explicit appearance of a Nambu-Goldstone pion. A consistent calculation of the pseudoscalar, scalar and vector meson masses gives values ofm ₀, α _s andM ₀ well in step with other estimates. This makes possible a calculation off _π, the pion decay constant, in reasonable agreement with experiment.     

Asymptotic restrictions and ππ scattering lengths in non-linear chiral SU(2) × SU(2) dynamics

The most general effective lagrangian for ππ scattering, that takes into account the exchange of scalar (0⁺), tensor (2⁺) and ? mesons, is constructed within the framework of non-linear chiral SU(2) × SU(2) dynamics. Asymptotic restrictions proposed by Weinberg are imposed on the amplitude of ππ scattering. These restrictions allow one to obtain four independent sum rules containing particle masses, coupling constants and the coefficient A₂ in an expansion of the symmetry-breaking term in a power series of π². The use of only the f⁰ meson in the obtained sum rules leads to the following values of the ππ scattering lengths, the width of ?(700) → 2π decay, and the parameter A₂: α₀⁰ = 0.92m_π^?1, α₀² = 0.27 m_π^?1, α₁¹ = 0.033 m_π^?3, Γ[ε(700) → 2π] = 390 MeV, A₂ = + 1.6. It is shown that the inclusion of heavier mesons results in some increase of the ππ scattering lengths and the parameter A₂, but a decrease of the value of Γ(? → 2π). The field-algebra requirements lead to negligible changes in the results. Analysis of the sum rules shows the incompatability of the asymptotic restrictions with a symmetry breaking which has the transformation properties of the fourth component of a chiral vector.     

Mixing of pseudoscalar mesons and M1 radiative decays

We discuss the mixing of pseudoscalar mesons, in particular SU(3) breaking effects, based on ideas abstracted from QCD. The admixtures of η and η′ in η_c are calculated and utilized to estimate the M1 radiative decays ψ → ηγ, η′γ. A reasonably consistent picture emerges for these decays as well as others involving only the light quarks.     

A Monte Carlo analysis of an SU(5) scalar model

Spontaneous symmetry breaking is studied in an SU(5) model of adjoint scalars with quartic couplings λ₁ (tr φ²)² + λ₂ trφ⁴ and with a negative mass term. The breaking for λ₂ > 0 is to SU(3)?SU(2)?U(1), and for λ₂ > 0 to SU(3)?SU(2)?U(1), in agreement with the standard tree-level analysis of the scalar potential.     

Static hyperon properties in a linearizedSU(3)-Chiral Bag model

We use a linearized Chiral Bag model to describe the strange octet and decuplet baryons. The approach is canonically extended to spontaneously broken chiral SU(3)_L × SU(3)_R, and the corresponding Goldstone Bosons are identified with the pseudoscalar meson octet. We include explicit symmetry breaking corrections both for baryons and mesons. The linearized quark-meson intraction is applied in a self-consistent calculation of the masses and, for Δ, Σ^* and Ξ^*, of the decay widths. Our special interest is in the influence of theK- andη-cloud (in addition to theπ) on hyperon static properties. We show results for radii, masses, decay widths and renormalization constants as obtained by a fit to the experimental hyperon spectra. The effects of theK- andη-mesons are found to be non-negligible, although supressed by symmetry breaking effects. The effective gluon coupling α is reduced in comparison to the SU(2)_L × SU(2)_R case. In addition, we discuss the dependence on the bag constantB. It turns out that the lightest hyperon states, Λ and Σ are well described and stable for B^1/4 < 130 MeV. The heavier strange baryons have stable solutions also for larger values ofB. The bag radii determined at the minimal energies are R₀?1.15 fm for the octet and R₀?1.25 fm for the decuplet baryons.     

Spontaneous breakdown of the gauge chiral symmetry and the cabibbo angle

From the general treatment of the spontaneous breakdown of the chiral SU(3)xSU(3) group down to the electromagnetic U(l) gauge group it is conjectured that the bare Cabibbo angle isπ/4. Imposing the self-consistency condition of Cabibbo and Maiani on the weak and electromagnetic corrections to the chiral symmetry breaking Hamiltonianh=ε₀ u ₀+ +ε₃ u ₃+ε₈ u ₈ leads to the determination of the physical Cabibbo angle. The agreement with the experimental value is reached when the parametrization ofh of Brandt and Preparata is used.     

Meson-Nucleon Scatterings in an SU(3) × SU(3) σ Model

Meson-nucleon scatterings are investigated in an SU(3) x SU(3) a model with scalar, vector, pseudoscalar and pseudovector couplings between mesons and baryons. from the calculation of effective coupling constants, sigma terms and s-wave scattering lengths for πN and K⁺N scatterings in the tree approximation, we find that the pseudoscalar coupling dominates s- and u-channel baryon Born terms, and the cancellation between the scalar and vector interactions leads to reasonable meson-nucleon scattering properties.     

Light pseudoscalar and axial spectroscopy using AdS/QCD modified soft wall model

We describe the mass spectrum of light pseudoscalar and axial mesons in the context of the modified soft wall model with an extra UV cutoff. In order to include the pseudoscalar and axial states, we define an anomalous dimension that shifts the conformal dimension of the non-interacting bulk fields such that the parity behavior of those states is included, thus inducing chiral symmetry breaking. This idea contrasts with the usual approach that uses interacting scalar, vector and axial bulk fields to give rise the spectrum. Using the extra UV cutoff approach, we can fit six η and six a₁ organized in radial trajectories with an RMS error close to 21.1%. We also confirm that chiral symmetry is restored in this model after checking that highly excited ρ and a₁ states become degenerate.     

Space-time approach to anomalies in the W-T identities and commutators

The Ward-Takahashi identities of the axial-type n-point functions are analysed, assuming the conformal invariance and the chiral SU(3) × SU(3) symmetry to become exact at the short distance. The anomalies in the identities are obtained in a simple nonperturbative way, and the commutator anomalies are determined in connection with the pinching mechanism in taking the equal-time limit of commutators.     

Effects of additional Higgs doublets on the Coleman-Weinberg SU(2) × U(1) → U(1)em phase transition

In the standard electroweak theory with a Coleman-Weinberg Higgs doublet, it has been shown that the SU(2) × U(1) → U(1)_em phase transition is driven by chiral symmetry breaking and that a phenomenologically dangerous amount of entropy is produced. We show that the addition of a second, sufficiently heavy Coleman-Weinberg doublet will make the transition go via tunneling and will suppress excessive entropy generation.     

Fission fragment energy correlation measurements for the sub-barrier (nth, f) of 241Am and 243Am

Fission-fragment mass and kinetic-energy distributions and their correlations have been studied for the sub-barrier fission of the odd-odd ²⁴²Am and ²⁴⁴Am nuclei resulting from thermal neutron capture in ²⁴¹Am and ²⁴³Am. Unwanted events were eliminated by a coherence test based on the time of flight. The ²⁴³Am mass distribution is more asymmetric and shows structures at μ_H ≈ 139 and 144, compared with that for ²⁴¹Am which is smooth and structureless. The structure at μ_H ≈ 144 is caused by deformed neutron shells at N ≈ 88 in the heavy fragment and $\text{N ≧ 60}$ in the light fragment. While the 〈E_K〉 at symmetry for ²⁴¹Am is ≈ 19 MeV higher than that for ²³⁵U, it is shifted upwards only ≈ 6.5–10 MeV in the other mass regions. However, 〈E_K〉 at symmetry for ²⁴³Am is ≈ 6 MeV lower than for ²⁴¹Am and this decrease tapers down to ≈ 1 MeV for μ_H > 135. These data show a decrease in the total fragment deformation for ²⁴¹Am at symmetry as predicted by calculations. However, the ²⁴³Am data show a sudden change back to higher deformation.