Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.     

Quark mass dependence of the pion vector form factor

We examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the ρ   to pions, g_ρππ$g_{\rho \pi \pi }$, is largely independent of the quark mass while the quark mass dependence of the ρ mass is given by recent lattice data. By employing the Omnès representation we can provide a very clean estimate for a certain combination of the curvature and the square radius, whose quark mass dependence could be determined from lattice computations. This study provides an independent access to the quark mass dependence of the ρππ   coupling and in this way a non-trivial check of the systematics of chiral extrapolations. We also provide an improved value for the curvature for physical values for the quark masses, namely 〈r⁴〉=0.73±0.09 fm⁴$〈r^4〉=0.73\pm 0.09{\text{fm}}^4$ or equivalently cV=4.00±0.50 GeV−4$c_V=4.00\pm 0.50{\text{GeV}}^{-4}$.     

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%     

Pion form factor from 480 MeV to 1100 MeV

The pion form factor is measured in the reaction e⁺e^? → π⁺π^? for center of mass energies in the range 480–1100 MeV. Our results are first analysed in terms of the conventional Vector Meson Dominance formalism, and then taking into account the ωπ inelastic channel. The result of this later formalism is a pion form factor (F_π) which fits quite well all the existing data on F_π both in the timelike and spacelike regions, and pion mean square radius of 〈r_π²〉 = 0.460 ± 0.011 fm² or $\text{〈r}{}_{\mathrm{\pi }}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.678 ± 0.008}\text{fm}$.     

Baryon mass splitting by the strong hyperfine interaction and SU(3) breaking

We calculate mass splittings of strange and non-strange baryons in the [56, 0⁺] and the [70, 1^?]. As the most important spin-dependent force we only analyse the hyperfine interaction. The exact treatment of the quark mass breaking shows contributions which have not been considered in similar investigations up to now. Taking $\text{mλ}\text{m}{}_{\mathrm{<mtext>p</mtext>}}\text{? 2}$ and popular values for the slope of the linear potential a, the strong coupling constant α_s and the p-quark mass, we get excellent results for the four mass splittings 〈Σ-Λ〉, $\text{〈Σ}{}^1\text{? Σ〉}$, 〈Δ-N〉 and $\text{〈Ξ}{}^1\text{? Ξ〉}$ in the [56, 0⁺]. The structure of mass spectrum in the [70, 1^?] is well described, too; the strong SU(3) mixing of Σ and Λ states is seen to be due to the quark mass breaking. Predictions for missing Σ states in the [70, 1^?] as as for splittings between charmed baryons can be made.     

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.     

Chiral symmetry breaking in QCD; Mesons as spin waves

The strong chiral symmetry breaking in Wilson's lattice version of QCD is discussed and interpreted as a necessary manifestation of the triangle anomaly. At strong coupling the effective hamiltonian acting in the s-wave hadron sector is found to describe a generalized antiferromagnet which is analyzed with the $\text{1}\text{2}\text{S}\text{(= 1/N, N = N}{}_{\mathrm{<mtext>color</mtext>}}\text{)}$ expansion known in the theory of magnetism. Mesons emerge as spin waves: pseudoscalars as Nambu-Goldstone bosons, vectors as “dormant” Goldstone bosons. Current and dynamical quark masses are identified, such that m_P² ∫ m(cur), m_v≈2[m(cur) + m(fyn)], and a fit to the particle spectrum gives m(dyn) = 390 MeV, m_u,d(cur) = 5.4 MeV, m_s(cur) = 140 MeV, m_c(cur) = 1.07 GeV. Static baryons emerge with a mass m_B = N[m(dyn) + m(cur)] + a contribution which is argued to vanish in the continuum limit. Vector and axial vector currents are defined on the lattice and studied at strong coupling. The relations $\text{1 =}\text{3}\text{5}\text{g}{}_{\mathrm{<mtext>A</mtext>}}\text{γ}{}_{\mathrm{?}}\text{(f}{}_{\mathrm{\pi }}\text{/m}{}_{\mathrm{?}}\text{)(Z}{}_{\mathrm{\pi }}\text{/Z}{}_{\mathrm{?}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, Z_π/Z_? = 3.0 are found to agree with experiment. The resolution of the U(1) problem at strong coupling is discussed.     

A study of charge symmetry breaking effects in elastic π±d scattering

We computed external and internal Coulomb distortions as well as strong charge symmetry breaking (CSB) effects in π^±d→ π^±d. Available data for T_π = 143 MeV indicate the presence of CSB on the level of observed and deduced parameters for different Δ-isobars and the pn mass difference. Data for $\text{T}{}_{\mathrm{\pi }}\text{1}\text{?}\text{80}\text{MeV}$ are predicted to better suit the extraction of a measure of charge symmetry breaking. This note also contains a critical analysis of a previous study of CSB effects on σ_πd^tot.     

Bag confinement chiral breaking effect on a goldstone pion

We present a model in which the pion is a bound-state Goldstone boson in QCD and then the quarks are confined by a MIT bag-like boundary condition. We depart from the MIT cavity approximation in that we dynamically break chiral symmetry prior to confinement and we confine only in the $\text{q}\text{q}$ relative coordinate, leaving translation invariance in the total coordinate. We find M_π= 120 MeV, and a bag diameter R_π=7 GeV^?1.     

Hadron masses and the sigma commutator in light of chiral perturbation theory

We analyze carefully the impact of non-analytic chiral corrections to the mass spectrum of the pseudoscalar meson octet J^P = 0^? and the baryon octet $\text{J}{}^{\mathrm{<mtext>P</mtext>}}\text{=}\text{1}\text{2}{}^{\mathrm{+}}$. We find that the quark mass ratios must lie in the range $\text{21 ≤}\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{m}\text{?}\text{≤ 32}$ and $\text{1.6 ≤}\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{≤ 2.2}$. We also calculate the analogous corrections to the pion-nucleon sigma commutator σ_πN. It turns out that the value σ_πN = 60 MeV is not compatible with the structure of the meson and baryon spectrum, unless the nucleon mass is smaller than 600 MeV in the chiral limit m_u = m_d = m_s = 0.     

Chiral symmetry breaking in the action formulation of lattice gauge theory

We show, in the euclidean path-integral formulation of strong-coupling lattice gauge theory, that continuous chiral symmetry is dynamically broken, and obtain the standard current algebra result that $\text{m}{}_{\mathrm{<mtext>pseudo-Goldstone</mtext>}}{}^2\text{～ m}{}_{\mathrm{<mtext>quark</mtext>}}\text{〈}\text{ψ}\text{ψ〉}$. We also remark that the center of the gauge group does not seem very relevant for this result; chiral symmetry breaking is a property of strong-coupling lattice theories both in the case where quark color is confined, and also in the case where it is screened by gauge field fluctuations.     

Is Coleman-Weinberg symmetry breaking in the standard model ruled out?

In the standard model with Coleman-Weinberg symmetry breaking a symmetric vacuum (〈φ〉 = 0) always exists at any non-zero temperature; the transition to the symmetry-breaking vacuum can only occur after much supercooling. Witten has shown that this transition occurs when the strong interactions break chiral symmetry; the transition temperature is O(200) MeV and a large (but not fatal) amount of entropy is produced. It is noted here that since the strong coupling grows as the universe cools in the metastable symmetric vacuum, the Yukawa coupling to the top quark will also grow. This causes top quark loops to dominate the effective potential at small scales, drastically altering the nature of the transition. We show that if $\text{m}{}_{\mathrm{<mtext>t</mtext>}}\text{? 65}\text{GeV}$, a metastable vacuum at 〈φ〉 ≈ 0(1) GeV forms which persists to T = 0; the resulting transition would generate far too much entropy to be compatible with the current baryon to entropy ratio, ruling out the CW mechanism. If m_t ? 65 GeV, we argue that a metastable vacuum might also exist, but a breakdown of perturbation theory precludes a definitive statement.     

Unitarized hard-meson calculation of Kl3 form factors

K_l3 form factors are studied in the analytic hard-meson framework. The Gell-Mann-Oakes-Renner model for chiral SU(3) × SU(3) symmetry breaking is employed to determine the so called σ-terms and current divergences. PCAC is used for the π^? and K-mesons, and two-particle unitarity is used for the 1^? and 0⁺ channels. The results depend on the Kappa-meson mass. Results are presented for the slope of the divergence form factor λ₀, the ratio $\text{ξ =}\text{?}{}_{\mathrm{?}}\text{(0)}\text{?}{}_{\mathrm{+}}\text{(0)}$, and the width of the Kappa meson, for m_κ = 900 and 1100 MeV. It is found that the κ has a large width, and the prediction for λ₀ and ξ are in quantitative agreement with the recent experiments.     

Gluon condensate and the interquark potential

We construct a potential for qurkonium systems using as the basic ingredients the gluon condensate, i.e., 〈0∥G_μν^aG_μν^a∥0〉 ≠ 0 to incorporate nonperturbative effects and using quark screening. The potential is able to account satisfactorily for the s$\text{s}$, c$\text{c}$ and b$\text{b}$ bound states with a flavor independent, essentially constant value for the effective coupling constant $\text{(}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{≈ 0.45)}$. We also investigate heavier quark systems with the constant $\text{α}{}_{\mathrm{S}}$ and find that for quark mass ? 20 GeV the potential is essentially coulombic.     

Chiral symmetry breaking parameters from QCD sum rules

We obtain new QCD sum rules by considering vacuum expectation values of two-point functions, taking all the five quark bilinears into account. These sum rules are employed to extract values of different chiral symmetry breaking parameters in QCD theory. We find masses of light quarks, $\text{m}\text{?}\text{=}\text{1}\text{2}\text{(m}{}_{\mathrm{<mtext>u</mtext>}}\text{+m}{}_{\mathrm{<mtext>d</mtext>}}\text{) = 8.4 ± 1.2}\text{MeV}\text{, m}{}_{\mathrm{<mtext>s</mtext>}}\text{= 205 ± 65}\text{MeV}$. Further, we obtain corrections to certain soft pion (kaon) PCAC relations and the violation of SU(3) flavour symmetry by the non-strange and strange quark-antiquark vacuum condensate.     

A natural theory of the K-M mixing angles, weak and strong CP

We present a natural model in which the quark mass matrices are of the symmetric Fritzsch form with the two physically relevant phases $\text{σ = τ = ±}\text{π}\text{2}$. The model is natural in the sense of 't Hooft and explains all of the known aspects of the weak interaction phenomenology of the K-M matrix (including the weak CP) in terms of the observed quark mass eigenvalues only. The model solves the strong CP problem by the Peccei-Quinn mechanism while the phases $\text{σ = τ = ±}\text{π}\text{2}$ are generated by spontaneous symmetry breaking. The invisibility of the axion is more natural than in the existing models and is related to the absence of FCNC and the observed long b-quark lifetime. The key predictions of the model are m_t < 80 GeV and $\text{5.0 × 10}{}^{\mathrm{?3}}\text{? R}{}_{\mathrm{b}}\text{≡}\text{Γ(b→ue}\text{v}\text{)}\text{Γ(b→ce}\text{v}\text{)}\text{? 1.46 × 10}{}^{\mathrm{?2}}$, while the present experimental upper bound on R_b is 3 × 10^?2. The prediction on R_b is to be tested by experiments at CLEO and CUSB in the near future.     

Energies and orbital sizes for some Rydberg and valence states of the nitrogen molecule

Accurate SCF computations are reported on the Rydberg states of N₂ of electron configurations $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$, $\text{---1π}{}_{\mathrm{u}}{}^3\text{3σ}{}_{\mathrm{u}}$, and ---3σ_g2π_g, also on the valence states of the configuration $\text{---1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$. The Rydberg state calculations supplement those of Lefebvre-Brion and Moser. A comparison is made between the $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ states and the parallel set of states of the $\text{1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$ configuration. This comparison shows a sharp difference in the ¹Σ⁺ states of the two configurations, the ¹Σ⁺ state being very high in the latter but relatively low in the former configuration. Recknagel coefficients are given for the several states of the two configurations; as expected, these are much smaller for the $\text{1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ configuration. Also, the ¹Δ state is relatively lower for the latter configuration.     

Measurmennt of recoil proton polarization in the process of π− photoproduction from neutrons in the energy range between 700 and 1200 MeV

The recoil proton polarization for γn → π^?p was measured around the third resonance region. Both momentum vectors of the proton and the pion were determined by the magnetic spectrometers. The proton polarization was measured by means of proton-carbon scattering in the polarization analyzer located behind the proton spectrometer. Below 900 MeV incident photon energy, our data are consistent with the other existing experimental data ($\text{θ}{}_{\mathrm{\pi }}{}^1\text{= 90°}$) and the predictions of partial-wave analyses. Above 1000 MeV, however, a large discrepancy was observed between our data and the predictions of the partial-wave analyses. The discrepancy stands out as the pion c.m. angle increases. A new partial-wave analysis was made for γn → π^?p including our polarization data, and the accuracy of the experimentally determined electromagnetic coupling constant of the third resonances were greatly improved. In particular, a finite amount of the helicity $\text{3}\text{2}$ amplitude for the γn → F₁₅(1688) resonance was obtained against the predictions of the quark models, by Copley, Karl and Obryk and by Feynman, Kislinger and Ravendal but in agreement with the relativistic quark models of Sugimoto and Toya, and Kubota and Ohta.