Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

We revisit F _π(Q ²) and F _Pγ(Q ²), P = π, η, η′, making use of the local-duality (LD) version of QCD sum rules. We give arguments that the LD sum rule provides reliable predictions for these form factors at Q ² ≥ 5–6 GeV², the accuracy of the method increasing with Q ² in this region. For the pion elastic form factor, the well-measured data at small Q ² give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q ² ≈ 4–8 GeV²; we therefore conclude that large deviations from LD in the region Q ² = 20–50 GeV² seem very unlikely. The data on the (η, η′) → γγ* form factors meet the expectations from the LD model. However, the BaBar results for the π ⁰ → γγ* form factor imply a violation of LD growing with Q ² even at Q ² ≈ 40 GeV², at odds with the η, η′ case and with the general properties expected for the LD sum rule.     

Target independence of the EMC-SMC effect

An approach to deep inelastic scattering is described in which the matrix elements arising from the operator product expansion are factorised into composite operator propagators and proper vertex functions. In the case of polarised μp scattering, the composite operator propagator is identified with the square root of the QCD topological susceptibility √x′(0) , while the corresponding proper vertex is a renormalisation group invariant. We estimate x′(0) using QCD spectral sum rules and find that it is significantly suppressed relative to the OZI expectation. Assuming OZI is a good approximation for the proper vertex, our predictions, f₀¹ d x g₁^p (x; Q²= 10 GeV²) = 0.143 ± 0.005 and G_A⁰ = ΔΣ = 0.353 ± 0.052, are in excellent agreement with the new SMC data. This result, together with one confirming the validity of the OZI rule in the η′ radiative decay, supports our earlier conjecture that the suppression in the flavour singlet component of the first moment of gp observed by the EMC-SMC Collaboration is a target-independent feature of QCD related to the U(1) anomaly and is not a property of the proton structure. As a corollary, we extract the magnitude of higher twist effects from the neutron and Bjorken sum rules.     

Instantons: Dynamical mass generation,chiral Ward identities and the topological charge correlation function

When dynamical mass generation resulting from the breakdown of chiral symmetry is taken into account, instanton dynamics treated within the dilute gas approximation may satisfy the constraints on the quark condensates and the topological charge correlation function derived by Crewther from an analysis of the chiral Ward identities assuming the absence of a physical axial U(1) Goldstone boson. From a consideration of the contribution of the η′ to the topological charge correlation function, a relationship is derived in which m_η′²f_η′² is proportional to the vacuum energy density.     

Two schemes ofη−η′-mixing

Proceeding from the expansion of composite operators in interpolating hadronic fields, the width of the decays η(η′)→γγ andJ/ψ→η(η′)γ have been calculated. Two mechanisms of pseudoscalar field mixing (“mass-mixing” and “current-mixing”) are considered. In the given schemes, the values of η?η′-mixing angle θ _p are, respectively, (?15.0±1.8)^o and (?19.7±2.2)^o.     

Radiative decays and transition form factors of strange mesons in the relativistic constituent quark model

Motivated by the recent lattice QCD results indicating that the topological charge contribution to the flavor singlet axial vector current can be traded off by the constituent quark masses, we investigate the radiative decays of pseudoscalar (π,K, η, η′), vector (ρ,K*, ω, ?) and axial vector (A ₁) mesons using a simple relativistic constituent quark model. For both simplicity and relativity, we take advantage of the distinguished features in the light-cone quantization method: (1) the Fock-state expansion of meson wavefunctions are not contaminated by the vacuum fluctuation, (2) the assignment of meson quantum numbers are given by the Melosh transformation. Except the well-known constituent quark masses of (u,d,s) quarks and the spin-averaged meson masses, the only parameter in the model is the gaussian parameter β which determines the broadness (or sharpness) of radial wavefunction. The computed decay widths and the transition form factors of ρ, ω → π(η)γ*,K* →Kγ* andA ₁ → πγ* at 0≤Q ²≤5 GeV² and π⁰(η) → γ*γ at 0≤Q ²≤3 GeV² are in a remarkably good agreement with the experimental data and the result forA ₁ ⁺ → π₊ γ* transition is quite consistent with the experiments of pion scattering on a nucleus using Primakoff effect. This model is potentially useful in the cocktail analyses of the dilepton productions in proton-proton, proton-nucleus and nucleus-nucleus collisions at SPS energies and a little above.     

η and η' mesons from lattice QCD

The large mass of the ninth pseudoscalar meson, the η', is believed to arise from the combined effects of the axial anomaly and the gauge field topology present in QCD. We report a realistic, 2+1-flavor, lattice QCD calculation of the η and η' masses and mixing which confirms this picture. The physical eigenstates show small octet-singlet mixing with a mixing angle of θ=-14.1(2.8)°. Extrapolation to the physical light quark mass gives, with statistical errors only, mη=573(6) MeV and mη'=947(142) MeV, consistent with the experimental values of 548 and 958 MeV.     

Neutral decays ofη′(958)

The partial widths of the η′(958) decays into 2γ, ωγ, 3π⁰ andηπ⁰π⁰ have been measured with the GAMS-2000 spectrometer at the 70 GeV IHEP accelerator. Upper limits for the η′ decays into 3γ, π⁰γγ, 2π⁰ and 4π⁰ have also been obtained. The slope of a linear matrix element for theG-parity violating decayη′→3π⁰ has been determined.     

Are the ψ′→η c γ,ψ″→η c γ decays due to the gluon admixture?

We propose a new method for estimating the radiative transitions between the excited 1^? charmonium levels and η_c. The method is based on QCD (plus the hypothesis of local duality) and makes no reference to the standard potential picture. It is argued that the decay ψ′(3.698)→η _c γ is essentially due to the gluon admixture in the Ψ′ wave function. The most naive analysis yields approximately 0.15 keV for the ψ′→η _c γ decay width, five times smaller than preliminary data. The experimental number for Γ(ψ′→η _c γ)—0.7 keV—can be reproduced only at a price of introducing a rather large ψ″(3.772)→η _c γ amplitude, Γ(ψ″→η _c γ)～1 keV. As a byproduct, we get a reliable prediction for the ρ→πγ decay rate, Γ(ρ→πγ)≈70 keV, in good agreement with a recent measurement.     

Spectral function sum rules for gluonic currents

We determine the masses and the decay amplitudes of the 2⁺⁺, 0^?+ and 0⁺⁺ gluonia in anSU(3) _c Yang-Mills theory. We estimate the so-called topological susceptibility of theU(1) sector. We discuss theSU(3) _F breaking effects to the η′(896) massrelation from current algebra and predict the η′ parameter values.     

The role of instantons in generation of mesonic mass spectrum

It is suggested that instantons play the leading role in the mixing of $\text{s}\text{s and}\text{u}\text{u}\text{+}\text{d}\text{d}$ quark states in mesonic nonets and in the explanation of the Okubo-Zweig-Iizuka (OZI) rule. The non-diagonal polarization operator Π^su = 〈0|T{j^s(x)j^u(y)}0〉 is considered where $\text{j}{}^{\mathrm{<mtext>s</mtext>}}\text{=}\text{s}\text{O}\text{s}$ and $\text{j}{}^{\mathrm{<mtext>u</mtext>}}\text{=}\text{u}\text{O}\text{u}$ are the currents of the s and u quarks. It is proved that in the dilute instanton gas approximation for quarks in the external instanton field Π^su = 0 for the vector and tensor currents and Π^su≠0 for the axial current. Hence, after saturating Π^su by the low-lying mesonic states, we obtain the qualitative explanation of the OZI rule. The Q² dependence of the non-diagonal polarization operator of the axial currents, Π^su(Q²), is calculated and compared with the η′ meson pole term. Taking account of terms ～m_q² allows one, using the experimentally known ηη′ mixing angle, to find the η′ meson coupling constant with the axial current F_η′ ≈ 150 MeV and to estimate the η′π mixing angle.     

铝-铜-镓三元系合金相图

铝-铜-镓三元系合金相图的室温截面已经用X射线方法测定出来了。室温固相截面包含11个单相(即α, γ₂, γ′, δ, ζ₁, ζ₂, η₂, θ, θ′,α_铝和镓)相区,14个双相(即α + ζ₁, α+ γ₂, α + γ′, γ₂ + γ′, γ′+ ζ₁, γ₂+δ, γ′+δ,δ +ζ₂, ζ₂+η₂, η₂+θ,η₂+ θ′, γ′ + θ′, θ′+ 镓和θ+α_铝)相区和9个三相(即α + γ′+ζ₁, α+ γ₂+ γ′, γ₂+ γ′ + δ,γ′ + δ + θ′, δ+ζ₂+θ′, ζ₂ + η₂ + θ′, η₂+ θ′ + 镓, η₂ +θ + 镓和θ +镓+ α_铝)相区。所有单相和三个二元系内室温存在的单相相同,没有新相出现。 关键词：     

Instanton-induced flavour mixing in mesons

The U_L(N_f)×U_R(N_f) chiral symmetric version of the Nambu-Jona-Lasinio model is extended by the 't Hooft determinant and bosonized for an arbitrary number of flavours N_f. The resulting effective meson lagrangian is explicitly calculated to leading order in the derivatives for three flavours. The 't Hooft determinant induces flavour mixing of the mesons with diagonal flavour content (π⁰, η, η′, and their scalar chiral partners δ⁰, S, ϵ) and pushes up the physical η′-mass. The η-η′ mixing angle is found to be −31°.     

Axial anomaly and vector meson dominance model

A connection between the axial anomaly and the vector meson dominance model is revealed for the processes of pseudoscalar meson-photon transitions. The analytic continuation of the anomaly sum rules, which are exact QCD relations following follow from the dispersive representation of the axial anomaly, to the time-like region is performed. Using these sum rules, the transition form factors of π⁰, η, and η′ mesons in this region are calculated. A good agreement with the available experimental data is found.     

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.     

The proton spin in the chiral bag model: Casimir contributions and Cheshire Cat Principle

The flavor singlet axial charge has been a source of study in the last years due to its relation to the so-called Proton Spin Problem. The relevant flavor singlet axial current is anomalous, i.e., its divergence contains a piece which is the celebrated U_A(1) anomaly. This anomaly is intimately associated with the η′ meson, which gets its mass from it. When the gauge degrees of freedom of QCD are confined within a volume as is presently understood, the U_A(1) anomaly is known to induce color anomaly leading to “leakage” of the color out of the confined volume (or bag). For consistency of the theory, this anomaly should be canceled by a boundary term. This “color boundary term” inherits part or most of the dynamics of the volume (i.e., QCD). In this paper, we exploit this mapping of the volume to the surface via the color boundary condition to perform a complete analysis of the flavor singlet axial charge in the chiral bag model using the Cheshire Cat Principle. This enables us to obtain the hitherto missing piece in the axial charge associated with the gluon Casimir energies. The result is that the flavor singlet axial charge is small independent of the confinement (bag) size ranging from the skyrmion picture to the MIT bag picture, thereby confirming the (albeit approximate) Cheshire Cat phenomenon.     

A model of deep inelastic polarized electroproduction

A realistic phenomenological model combining parton/QCD ideas with lower energy SU(6) constraints is proposed for the shape and evolution of the leading spin-dependent structure function G^ep(x, Q²) in polarized electroproduction. Close's broken-SU(6) ansatz is used to relate appropriately defined polarized quark-parton distribution densities to unpolarized ones at the matching momentum scale Q² = Q₀². The differences between spin and helicity distribution densities as well as the complications due to perturbative QCD and parton k_T (with related target-mass) effects are taken into account. Evolution to higher (>10 GeV²) values of Q² (where target-mass effects can be neglected) yields experimentally testable numerical predictions that are presented through various plots. The value of Q₀ is self-consistently determined to be about 0.5 GeV.     

Leptoproduction and Drell-Yan processes beyond the leading approximation in chromodynamics

The problem of going beyond the leading logarithmic approximation in QCD for leptoproduction and Drell-Yan processes is considered. All the coefficient functions for leptoproduction are evaluated to order α_sQ²) (apart from two-loop corrections to logarithmic exponents). Existing calculations are thus completed and in part corrected. Particular attention is given to the constraint imposed by the validity at all Q² of the Adler sum rule. The question of a convenient definition of effective parton densities appropriate at this level of accuracy is discussed. Phenomenological consequences for leptoproduction are considered with special emphasis on the problem of extraction from the data of the small sea densities which are particularly sensitive to the corrections. The modifications of the Drell-Yan formula relevant for proton-nucleus processes are also explictly calculated to order α_s(Q²).     

Spectral representation for singlet and triplet green's functions

Spectral representations of special Green functions are given explicitly. We consider the density correlation functionG ₂(x ₁ η ₁ x ₂ η ₂,x ₁ ⁺ η ₁ x ₂ ⁺ η′₂) and the functionG ₂(x ₁ η ₁ x ₁ ^? η₂,x ₂ η ₁ ^′ x ₂ ^? η ₂ ^′ Coupling the field operators Ψ^? (x, η), Ψ(x, η) to singlet and triplet operatorsA _{SMs TT3} (x), we obtain spectral representations for theseG-functions. The formulae derived may be of use when studying the system of equations for the Green functions, which describe many particle systems from a microscopic point of view.     

Spin structure of hadrons in supersymmetric quantum chromodynamics at short distances

We study the short-distance spin structure of nucleons in supersymmetric QCD. We calculate the Altarelli-Parisi spin transition coefficients ΔP _ba and corresponding anomalous Δ γ _ab ⁿ fora, b=quarks, gluons, gluinos and squarks and present the supersymmetric relations between them. Further analysis is divided into two parts: the parity conserving case and parity violating case, both following from the mass mixing in the squark sector. Solving theQ ²-evolution equations we determine the quark, gluon, gluino and squark spin distribution at variousQ ² above the threshold for production of supersymmetric partners. We also show the analytic solutions for the first moments in the nonsinglet and singlet sector. In particular the spin carried by the valence quarks turn out to vanish asymptotically except of one particular case of squark mixing.