Meson decay constants and bare quark masses from duality for current two-point functions

Duality is applied in a quasi-local form to the SU(4) × SU(4) current two-point functions. Interpolating functions for some of their space-time components are assumed to be given by the free quark model. Mass intervals in the finite energy sum rules are taken to be approximately SU(3) × SU(3) invariant and a linear dependence of the hadronic mass spectrum upon the radial quantum number is assumed. The correct order of magnitude of various meson decay constants is reproduced provided the color gauge group is SU(3). The bare uncharmed quark masses are given by the formulae: $\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ M}{}_{\mathrm{\pi }}\text{F}{}_{\mathrm{\pi }}\text{/F}{}_{\mathrm{\pi }}\text{√6 ≌ 40}\text{MeV}\text{, m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ 1 = 6}$. The η-η mixing problem is discussed. Predictions are made for the masses and decay constants of the vector mesons of the first L = 2 level of SU(6) × O(3), as well as for the decay constants of the radially excited pseudoscalar mesons; estimates of corrections to PCAC in Goldberger-Treiman relations are presented. The bare charmed quark mass is found to be of the order of 1.1–1.2 GeV. Some decay constants of charmed mesons are evaluated.     

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.     

Quark mass effects as isospin and SU(3) violations in radiative decays of vector mesons

Radiative decays of vector mesons, V → Pγ, are discussed in terms of the QCD quark model, in the chiral limit. By taking into account isospin and SU(3) breaking by the quark mass matrix good agreement is found with the experimental data. In particular, the hitherto unexplained smallness of the K¹⁰ → K⁰γ and ?^? → π^?γ rates is justified provided $\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{≈ 20}$ and $\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{? 50}$.     

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%     

An experimental study of the form factor in the decay K+ → πoe+ν

The q² variation of the factor $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)}$ in the decay K⁺→π⁰e⁺ν has been studied using a sample of even detected in the CERN 1.1 m³ heavy-liquid bubble chamber. The data are consistent with a linear development $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)=?}{}_{\mathrm{+}}\text{(0) (1+λ}{}_{\mathrm{+}}\text{q/m}{}^2{}_{\mathrm{\pi }}\text{)}$ with λ₊=0.027±0.008.     

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.     

Correlations between neutral and charged pions in multiparticle production

We make a theoretical and phenomenological study of correlations between neutral and charged pions in multiparticle production in the framework of the so-called σ, π, ? and ?-? models. Following the method of Drijard and Pokorski, we express the predictions of various models in terms of the negative multiplicity distribution, which is known experimentally. In particular we compute the average number of $\text{π}{}^0\text{,}\text{n}{}_0\text{(n\_)}$, and the integral of π⁰?π⁰ correlations, f₀²(n_), as a function of the number of negative pions; we study also the total multiplicity distribution P(N) and its first two moments $\text{N}\text{and}\text{D}{}_{\mathrm{<mtext>tot</mtext>}}{}^2$. We show that with the present experimental accuracy neither $\text{n}{}_0\text{(n\_)}$ allow us to discriminate between the different models.     

The ππ and KK amplitudes,the S1 and the quark structure of 0++ resonances

The nature of mesons in the 0⁺⁺ nonet is studied. In particular we discuss the parameterization of the I = 0 S wave in terms of the S¹ and possible ? mesons. The S¹ parameters are determined by fitting to π^?π⁺ and K^?K⁺ production data. In particular we find .     

The derivative rule for helicity-flip amplitudes

Consequences of the derivative relation $\text{f}{}_{\mathrm{+-}}\text{=}\text{λ?f}{}_{\mathrm{++}}\text{?√?t}$, proposed empirically and also in various models for s-channel helicity amplitudes, are explored. A comparison with π^?p→π⁰n charge-exchange data is made, imposing the usual Regge pole form on f_+-. The assumptions are seen to conflict with the s-dependence of the cross-section dip and the polarization structure. There are also difficulties with finite energy sum rules and with-experimental data on some other reactions.     

The phase φ+− of CP violation in the K0 → π+π− decay

The phase φ_+? is evaluated on the basis of measurements of the K_S-K_L interference in the π⁺π^? decay mode and the mass difference Δm, both reported previously by this group. The result is: φ_{+? = 45.9° ± 1.6°}. This, together with previous results on $\text{|η}{}_{\mathrm{+?}}\text{|, |}\text{η}{}_{00}\text{η}{}_{\mathrm{+?}}\text{|}$ and the charge asymmetry δ in leptonic decay, is compared with the prediction of the superweak model, with good agreement.Finally the result is used to find, on the basis of unitarity, a new upper limit on CP violation in the decay K⁰ → 3π⁰. This limit is |η₀₀₀|^2? 0.21.     

Spectrum and structure of the He2 molecule: Characterization of the singlet and triplet states associated with the UAO's 4s, 4dσ, 4dπ, and 4dδ

The emission spectrum of the He₂ molecule has been rephotographed in the ～4000–～5700 Å region and the $\text{4d(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$, $\text{4d(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^1\text{Π}{}_{\mathrm{u}}\text{,}{}^1\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$, $\text{4s}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$ and $\text{4s}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$ transitions analyzed. The 4dδj³Δ_u, 4dπj³Π_u, $\text{4dσj}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{4sh}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states have been characterized through v = 2 and the 4dδJ¹Δ_u, 4dπJ¹Π_u, $\text{4dσJ}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{4sH}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states for v = 0. The term levels for these perturbed and l-uncoupled states have been confirmed (a) by analyses of bands with common levels from Δv = 0, ±1 sequences and (b) by analyses of the transitions between the above states from 4d and 4s and the $\text{c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ and $\text{C}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ states associated with 3pσ. Molecular constants are reported which have been partially corrected for the effects of l-uncoupling and the homogeneous perturbations between the state pairs J, H and j, h.     

A comment on the phenomenology of the SU(3) Skymre model

We find that the realistic baryon mass spectrum in the SU(3) Skyrme model with massive 0^? mesons can be obtained only for F_π < 70 MeV. We fit m_Λ and and obtain baryon masses within the limits of ± 16% of the experimental val ues, but at the expense of very low ifF_π=46.32 MeV.     

Evidence for double dissociation in K-p interactions at 14.3 GeV/c

We have studied the reaction K^-p → K^-π⁺π^-π⁺π^-p at 14.3 GeV/c to search for evidence of the double dissociation process $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{QN}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1$. In the channel $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{K}{}^{10}\text{(890)}$π₁^-π₂^-Δ⁺⁺ (1236) there is evidence for simultaneous production of low-mass enhancements in the $\text{K}{}^{10}\text{π}{}_1{}^{\mathrm{-}}$ and Δ⁺⁺(1236)π₂^- subsystems which correspond to the $\text{Q}\text{→}\text{K}{}^1\text{(890)π}$ and $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1\text{→ Δπ}$ decay modes. In this particular final state the double fragmentation system is produced with a cross section of the order of a few microbarns. Our data are consistent with the factorizable pomeron exchange model of double diffractive dissociation.     

Deep inelastic sum rules at fixed hadron energy

Experimentally, it is much easier to measure structure functions at fixed hadron energy E_h, rather than at fixed Q². We prove the sum rules

,

$\text{h}{}_{\mathrm{NS}}\text{=}\text{4}\text{3}\text{(}\text{1}\text{6}\text{π}{}^2\text{?}\text{5}\text{8}\text{),}$

$\text{h}{}_{\mathrm{S}}\text{=}\text{4}\text{16+3n}{}_{\mathrm{<mtext>f</mtext>}}\text{(2π}{}^2\text{+}\text{1}\text{6}\text{π}{}^2\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{?}\text{65}\text{12}\text{?}\text{5}\text{72}\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{).}$

Here s = 2m_pE_h and F_2,3 are the standard functions for scattering of neutrinos on an isoscalar target. K is an unknown constant, and the corrections to the sum rules are O(α_s²), O(α_s^1.75), respectively.     

Investigation of rare non-strange decay modes of the f meson in Π+p interactions at 5GeVc

Rare decay modes of the f meson are studied in the final states Δ⁺⁺π⁺π^?π⁺π^?, Δ⁺⁺π⁺π^?MM and Δ⁺⁺π⁺π^?π⁺π^?MM. The ratio $\text{Γ (f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{π}{}^0\text{)}\text{Γ(f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ is 0.23 ± 0.09 and Γ(f → 4 π) saturates the f inelasticity. A 2 s.d. upper limit of 0.09 is found for the branching ratio $\text{(f → ηη)}\text{(f → 2π)}$.     

A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.     

Line reversal in baryon exchange reactions and the energy dependence of dip locations

An empirical investigation of $\text{p}\text{p}\text{→ππ}\text{and}\text{π}\text{p}\text{→π}\text{p}$ data provides evidence for a dynamical variable connected with the boundary of the physical region. Absence of a fixed u = ?0.2 dip in recent $\text{p}\text{p}\text{→π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ high-energy data disagrees with nucleon-exchange (N) line-reversal expectations from π⁺p→pπ⁺ backward scattering. We notice however that the π⁺p→pπ⁺ dip is not located at fixed u but remains with a surprising accuracy at a fixed distance u' = u ? u_min from the physical boundary. Conjecturing that dips associated with particle exchanges occur at fixed u', we predict that the N-exchange dip in $\text{p}\text{p}\text{→π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ will be considerably displaced at non-asymptotic energies. Our conjecture places the fixed u' = ?0.2 dip near $\text{u ? ?0.4}\text{in}\text{p}\text{p}\text{→π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ for momenta around 2 GeV/c. Folded $\text{p}\text{p}\text{→ ππ}$ distributions exhibit a dip structure at this location. These observations suggest that the failure of line reversal at low energies is due to direct-channel effects, since fixed u' dips occur naturally in geometrical and direct-channel models.     

The 85Rb(p,d)84Rb reaction

The spectrum seen in single neutron pickup leading to the doubly odd nucleus ⁸⁴Rb is remarkably clean, with only five levels populated by l = 4 and six by l = 1 transitions. A simple 2J+1 weighting for the l = 4 data, combined with previous information on ⁸⁴Rb, allowed the J^π = 2^?–7^? states of the ($\text{v}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}{}^{\mathrm{?3}}\text{? π}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}{}^{\mathrm{?3}}$) multiplet to be identified. These data are used to determine the two-hole $\text{π}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{-v}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}{}^{\mathrm{?}}$ interaction matrix elements.     

Observation of interference between Iu=12 and Iu=32 baryon exchange amplitudes in 4 GeV/c backward inelastic scattering

Interference between the $\text{I}{}_{\mathrm{<mtext>u</mtext>}}\text{=}\text{1}\text{2}$ and $\text{I}{}_{\mathrm{<mtext>u</mtext>}}\text{=}\text{3}\text{2}$ baryon exchange amplitudes is observed in the reaction π^?p → pπ^?π⁰, with the proton produced forward with $\text{cos}\text{θ}{}_{\mathrm{p}}{}^1\text{>0.8}$. The Dalitz plot shows that the reaction is dominated by the quasi two body final states ρ^?p(δ exchange) and $\text{N}{}^{10}\text{(1670)π}{}^0\text{(}\text{N exchange}\text{)}$, with δ(1238), N¹(1520) and higher mass N¹'s also produced. The relative phase between the ρ and the N¹(1670) production amplitudes is measured to be 135° ± 10° and is compared with the Regge pole signature factor phase predictions.