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.     

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.     

Determination of the radiative widths of the η′ and A2 from two-photon exchange production

From the two-photon exchange processes e⁺e^? → e⁺e^?η' (958) → e⁺e^??⁰γ and e⁺e^? → e⁺e^?A₂ (1310) → e⁺e^?π⁺π^?π⁰ observed using the CELLO detector at PETRA the radiative widths of the η' and A₂ have been determined with the results: Γ_γγ(η') = 5.4 ± 1.0[stat.] ± 0.7[syst.] keV; Γ_γγ(A₂) = 0.59 ± 0.14[stat.] _?0.08^+0.31[syst.] keV.     

SU(2) ⊗ U(1) gauge theories of the generalized σ model for π0, η, η' → γγ decays

By embedding the chiral current-mixing gauge theories in the SU(2)_L ? SU(2)_R generalized σ model, it is shown that the correct sign and magnitude for π⁰ → γγ decay, as well as the SU(3) relation of π⁰, η, η' → γγ decays can be obtained within the framework of SU(2) ? U(1) gauge theories of weak and electromagnetic interactions.     

Measurement of the relative probability of the decay φ → η′γ in the channel η′ → ηπ0π0, η → γγ

The process e ⁺ e ^? → η′γ, η′ → η π⁰π⁰, η → γγ is investigated by an SND detector in experiment on a VEPP-2M equipment with colliding electron-positron beams. The analysis of experimental data yields a value of B(? → η′γ)=(6.7 _?4.2 ^+5.0 ±1.5)×10^?5 for the decay probability. Taking into account a previous measurement of this quantity by an SND detector in the decay channel η′ → π⁺π^?η, one finally obtains B(?→η ′γ)=(6.7 _?2.4 ^+2.8 ±0.8)×10^?5.     

Measurement of η' → π+π−γ in γγ collisions

The production of the pseudoscalar meson η'(958) is observed in the reaction e⁺e−→ e⁺e⁻η′→e⁺e⁻π⁺π⁻γ with the ARGUS detector at DESY. We measure the product Γ_γγ(η')Br(η′ →ϱγ) to be 1.13±0.04±0.13 keV. Using the known branching ratio s, we calculate Γ_γγ(η′) to be 3.76±0.13±0.47 keV and Γ_η' to be 203±32 keV.     

Investigation of the low-lying nucleon resonances in reactions of π<Superscript>+</Superscript>π<Superscript>−</Superscript> pair electroproduction on protons

The cross sections of the reaction ep → e′p′π⁺π^? for small photon virtualities were measured on a CEBAF large acceptance spectrometer (CLAS detector) at the Thomas Jefferson National Accelerator Facility for the first time. A complete set of one-dimensional cross sections of the reaction was obtained for photon virtualities in the range 0.2 GeV² < Q ² < 0.6 GeV² and invariant masses of the final hadronic system in the range 1.3 GeV < W < 1.6 GeV. A preliminary analysis of the obtained data in the framework of the phenomenological model demonstrated that the Q ² dependence of the electromagnetic form factors for the P ₁₁ (1440) and D ₁₃ (1520) resonances can be determined in the kinematic region (which is the most sensitive to the contribution from the meson cloud) and that the axial transition form factor p → Δ can be derived.     

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.     

Correlation function for topological charge densities within the instanton model in QCD

The QCD sum rule for the correlation of topological charge densities χ(Q ²) and for the longitudinal part of the correlation function for singlet axial currents (the latter is related to the former) is considered within the instanton model. The constant f _η′ of η′-meson coupling to the singlet axial current is determined. Its value appears to be in good agreement with that determined recently from the relation between the proton-spin fraction Σ carried by u, d, and s quarks and the derivative of the QCD topological susceptibility χ′(0). On the basis of the same sum rule, the η-η′ mixing angle θ₈ is found within the model employing two mixing angles. The value of θ₈ coincides with that in effective chiral theory. The correlation function for topological charge densities χ(Q ²) at large Q ² is calculated. It is shown that the Q ² dependence at high Q ² matches well with that at low Q ², the latter being determined by the known values χ′(0) and by the contributions of the π and η mesons.     

New low-energy theorems for γ →3 π and γγ→3π

New low energy theorems are obtained by relaxing the requirement that the γγ →3 π amplitudes vanish in the neutral soft pion limit. In the framework of a particular model it is shown that the relation eF_3π = F_πf^?2 may have to be generalized to involve also the γγ → 2π amplitudes.     

Evaluation of the Integrated Cross Sections of Reactions of Exclusive Pion and Kaon Electroproduction off Protons in the Resonance Region at Photon Virtualities from 5 to 12 GeV<Superscript>2</Superscript>

The integrated cross sections of the ep → eπ⁺n, ep → eπ⁰p, ep → eK⁺Λ, and ep → eK⁺Σ⁰ reactions are evaluated in the energy range of nucleon resonance excitation at photon virtualities Q² from 5 to 12 GeV². These exclusive channels will be explored at photon virtualities Q² > 5 GeV² for the first time in future experiments with the CLAS12 detector. The cross-section evaluation is based on the extrapolation of exclusive contributions to the inclusive structure functions F₁ and F₂ from a region of Q² < 5 GeV², in which the experimental data are available, to the region of higher Q². This evaluation of cross sections is of particular importance in the development of the program of experiments with the CLAS12 detector for studying the structure of the ground and excited nucleon states, which may reveal the dynamics of strong interactions in the nonperturbative regime.     

New measurement of the η → π 0 γγ branching ratio and the slope parameter for η → 3π 0 decay with the crystal ball

We have measured the quadratic slope parameter α for η → 3π ⁰ decay. Our final result is α=?0.031(4). We have also obtained the branching ratio (BR) for the double radiative decay η → π ⁰ γγ. Our preliminary result is BR(η → π ⁰ γγ=3.2(9)×10^?4. These new measurements were performed using the recent (1998) high-statistics sample of 1.9 × 10⁷ η produced at the AGS at BNL in π ^? p → nη close to threshold. The η decay into neutrals was detected with the Crystal Ball multiphoton spectrometer. Both measurements provide important tests of chiral perturbation theory (χPTh). Our result for α is four times more precise than the present world data and disagrees with current χPTh calculations by about four standard deviations. Our branching ratio for η → π ⁰ γγ is about half the current value and is in agreement with the χPTh predictions.     

Determination of quark-antiquark component of the photon wave function for <Emphasis Type="Italic">u,d, s</Emphasis> quarks

Based on the data for the transitions π⁰, η, η′ → γγ*(Q²) and reactions of the e⁺e^? annihilations e⁺e^? → ρ⁰, ω, ? and e⁺e^? → hadrons at 1<E _e+e? <3.7 GeV, we determine the light-quark components of the photon wave function \(\gamma * (Q^2 ) \to q\bar q(q = u,d,s)\) for the region 0 ? Q² ? 1 (GeV/c)².     

Structure in the reaction π+p → Δ++ϱo AT 5 GeV/c

In a high statistics experiment a large dσ/dt′ slope of (23.7 ± 3.2) GeV^?2 is obtained in the forward direction. The natural parity exchange cross-section shows a dip at t′ ≈ 0.2 GeV² and peak at ≈ 0.6 GeV². The ?^o is separated from the S-wave background and we obtain ?₀₀^F ≈ 0.94, at t′ = 0.     

Theg B*Bϱ andg D*Dϱ coupling constants in QCD

Theg _B*B? andg _D*D? coupling constants are calculated at the intermediate momentum transfer interval 0.5 GeV²≤Q ²≤1.5 GeV², in the context of QCD sum rules. Our predictions are in good agreement with those of the Vector Dominance Model     

A measurement of the reaction e+e- →e+e-η′ and the radiative width Γη′→γγ at petra

The reaction e⁺e^- → e⁺e^-η' has been observed in the JADE experiment at PETRA, by detecting the final state π⁺π^-γ, resulting from the decay η' → γ?⁰. The cross section was measured at an average beam energy of 17.15 GeV to be σ(e⁺e^- → e⁺e^-η') = 2.2 ± 0.2 (stat.) ± 0.4(syst.) nb, yielding the radiative width Γ_η'γγ= 5.0 ± 0.5(stat.) ± 0.9 (syst.) keV.     

Contributions from higher twist effects to the quark fragmentation functions in neutrino data

Quark fragmentation functions are studied with ≈3500 charged current events induced in the bubble chamber Gargamelle by neutrinos of the SPS wide band beam, with 〈E_ν〉 ≈ 25 GeV. The Q² and W² regions covered by this experiment are Q² ≈ 0–40 GeV² and W² ≈ 1–100 GeV², the mean values being 〈Q²〉 = 6.5 GeV², 〈W²〉 = 22GeV². A correlation between the variables $\text{z =}\text{E}{}_{\mathrm{\pi }}\text{E}{}_{\mathrm{<mtext>H</mtext>}}$ and $\text{y =}\text{E}{}_{\mathrm{<mtext>H</mtext>}}\text{E}{}_{\mathrm{v}}$ is found in the data in the region Q² = 1–10 GeV², which can be explained in terms of higher twist effects. These effects reproduce the Q² evolution of the non-singlet moments of the fragmentation function without any need for logarithmic terms.     

DSE Perspective on QCD Modeling,Distribution Amplitudes,and Form Factors

We describe results for the pion distribution amplitude (PDA) at the non-perturbative scale μ = 2 GeV by projecting the Poincaré-covariant Bethe–Salpeter wave-function onto the light-front and use it to investigate the ultraviolet behavior of the electromagnetic form factor, F _π (Q ²), on the entire domain of spacelike Q ². The significant dilation of this PDA compared to the known asymptotic PDA is a signature of dynamical chiral symmetry breaking on the light front. We investigate the transition region of Q ² where non-perturbative behavior of constituent-like quarks gives way to the partonic-like behavior of quantum chromodynamics (QCD). The non-perturbative approach is based on the Dyson–Schwinger equation (DSE) framework for continuum investigations in QCD. The leading-order, leading-twist perturbative QCD result for Q ² F _π (Q ²) underestimates the new DSE computation by just 15 % on \({Q^2\gtrsim 8\,}\) GeV², in stark contrast with the result obtained using the asymptotic PDA.