Photoproduction Amplitudes Research Articles

Gauge invariant unitary theory for pion photoproduction.

The Ward-Takahashi identities are central to the gauge invariance of the photoproduction amplitude. Here we demonstrate that unitarity and in particular the inclusion of both the $\pi N$ and $\gamma\pi N$ thresholds on equal footing yields a photoproduction amplitude that satisfies both two-body unitarity and the generalized Ward-Takahashi identities. The final amplitude is a solution of a set of coupled channel integral equations for the reactions $\pi N\rightarrow\pi N$ and $\gamma N\rightarrow\pi N$. % Figures available from the authors upon request, % e-mail: phchv@pippin.cc.flinders.edu.au % Submitted to Physical Review C

The Electric Dipole Amplitudes of the Neutral Pion Photoproduction on the Proton near Threshold

The electric dipole amplitude E 0+ for p (γ, π 0 ) p near threshold has been extracted from the experimental data by fitting the total cross section in high energy region, E γ >160 MeV. The result is (-1.56±0.10)×10 -3 m π+ -1 . This amplitude is calculated by taking the vector mesons into account in the pole model of t-channel. Our analysis manifests a favor of negative sign for the ρπγ coupling constant.

Color transparency and final-state interactions in photonuclear charmonium production.

The final-state interactions of quasielastically photoproduced charmonium have been computed in a quantum-mechanical QCD-inspired model for a range of photon energies and nuclear targets. In this model, charmonium in its rest frame interacts with an array of nucleon flux tubes via its color dipole moment as color electric fields ``flash'' on and off around it. The photoproduction amplitude is modeled as the narrowest superposition of open charmonium channels available at a given photon energy. A complete calculation of the final-state interactions has been performed; this involves retaining all the charmonium states present in the initial amplitude and produced upon interactions with the medium, and allowing them to scatter into each other upon further medium interactions. This work permits the computation of ${\mathit{A}}^{\mathit{e}\mathit{f}\mathit{f}}$/A with and without ``transparency''; the results support the utility of a study of the energy dependence of ${\mathit{A}}^{\mathit{e}\mathit{f}\mathit{f}}$/A in elucidating transparency in the exclusive process considered. Moreover, a comparison of the underlying J/\ensuremath{\psi}-nucleon cross section with that deduced from a Glauber analysis of the computed A dependence shows the Glauber analysis to be misleading.

Photodisintegration of the deuteron in the Δ-resonance region

Photodisintegration of the deuteron in the Δ-resonance region is calculated treating the final state interaction within a N N− NΔ coupled channel approach including explicit pion degrees of freedom. For the electromagnetic interaction the nucleonic one-body current, meson exchange currents and the direct Δ-excitation are taken into account. The γN Δ-coupling is fixed in accordance with the M 1+ ( 3 2 ) multipole amplitude for pion photoproduction on the nucleon. The resulting total cross section underestimates the experimental data for photon energies below 340 MeV, whereas a good agreement is achieved by uaing a modified γN Δ-coupling effectively including the nonresonant Born terms. Furthermore, results for differential cross section, photon asymmetry and nucleon polarization are compared with experiment.

FEYNMAN AND THE QUARK MODEL

As a student and later research fellow working with Richard Feynman at Caltech in the period 1969–74, I was in the happy situation of getting him interested in the quark model. This resulted in the construction of the relativistic harmonic oscillator quark model with the proviso of involving as few parameters and ad hoc assumptions as possible. The detailed predictions of the model and in particular for the nucleon photoproduction amplitudes were so good that in Feynman’s mind the quarks were to be considered real particles and identified by the partons seen in deep inelastic scattering. This article is a short account of my part in those developments and my collaboration with Feynman.

Gauge-invariant projection method for the pion photoproduction and electroproduction amplitudes.

We propose here a practical projection method to make non-gauge-invariant amplitudes for N(γ,π)N and N(e,e’π)N gauge invariant.Received 23 November 1992DOI:https://doi.org/10.1103/PhysRevC.48.455©1993 American Physical Society

Pion-photoproduction pole terms in the Skyrme model

We derive the isolated-pole terms for pion photoproduction on a nucleon in the Skyrme model. We employ a quantization method in which the Born terms of pion-nucleon elastic scattering are described by a pion-baryon linear interaction of O(N C − 1 2 ) and a pion-baryon quadratic interaction of O( N C 0). The baryon and pion pole terms in the photoproduction amplitude are generated by the pion-baryon linear interaction and the interactions with the external electromagnetic field. The identical result is also obtained by the use of a unitary-transformation method which reproduces the Yukawa coupling missing in the quantized hamiltonian. We also present a method which enables us to extract relations between the meson-baryon interactions and the Yukawa coupling diagrammatically.

Photo- and electroproduction of nonstrange baryon resonances in the relativized quark model.

Photoproduction amplitudes for the nonstrange baryons are calculated in a quark model with an electromagnetic transition operator containing relativistic corrections, and relativized-quark-model wave functions. A one-parameter fit to the photocouplings shows significant improvements over models using the nonrelativistic transition operator or nonrelativistic wave functions. Helicity asymmetries and other ratios in the electroproduction of some low-lying resonances are also predicted.

Photoproduction amplitudes of P11 and P33 baryon resonances in the quark model.

Predictions are made for the photoproduction amplitudes of low-lying N^(1/2)+ (P(sub)(11)) and delta^(3/2)+ (P(sub)(33)) resonances, using a quark model with relativistic corrections to the transition operator, and mixed nonrelativistic wavefunctions which are correctly orthogonal to the ground states.These amplitudes are also calculated using relativized model wavefunctions. The results for the Roper resonance N(1440) are in marked disagreement with the data.

Strong and electromagnetic meson-hyperon couplings in the bound-state soliton model

The KNΛ and KNΣ as well as the corresponding DNΛ c and DNΣ c coupling constants are calculated in the model in which the strange and charmed hyperons are described as bound states of an SU(2) soliton and heavy flavour mesons. The coupling lagrangians as well as the corresponding threshold photoproduction amplitudes are found to have approximately the same form as expected in the conventional pseudovector coupling model in spite of the chiral symmetry breaking implied by the large meson mass terms. The calculated coupling constants fall within the range of values obtained with alternative approaches and of phenomenological analyses.

Neutral pion photoproduction at threshold

We evaluate the neutral pion photoproduction amplitude at threshold to one loop in chiral perturbation theory. Virtual pions generated infrared singularities in the scattering amplitude and modify the familiar low-energy expansion of the electric dipole amplitude E o+ at next-to-leading order.

Threshold pion photoproduction and chiral models of the nucleon

We present calculations of the chiral and isospin symmetry-breaking corrections to the threshold pion photoproduction amplitude E 0+. The calculations are based on two chiral models of the nucleon: the chiral bag model and the non-topological soliton model. We find that ΔE 0+ from explicit chiral-symmetry breaking is substantial, but not sufficient to explain the discrepancy between the measured γp → π 0p threshold amplitude and its predicted value based on the chiral low-energy theorem.

Virtual and real rhos

The interpretation of the enhancement of the electric dipole sum rule due to the rho exchange potential in terms of virtual rho photoproduction is discussed. In deriving the rho photoproduction amplitude, it is shown that invariance under local gauge transformations of the SU(2)*U(1) (isospin*hypercharge) group necessary for a unitary theory, requires a Higgs mechanism to generate the rho masses. In such a scheme which intrinsically connects on the electromagnetic and strong interactions, linking part of the NN potential to the electromagnetic properties of hadrons, the vector meson dominance prescriptions automatically result, universality is explained and the desired rho photoproduction amplitude (which differs from that obtained via the minimal electromagnetic substitution in the Proca Lagrangian) is obtained. In addition 'genuine' three-body rho rho rho forces (as well as four-body ones) originating from the nonAbelian structure of the group are predicted. The free parameter of the theory is the mass of the Higgs boson which might show up in the reactions gamma N to N rho H and e+e- to rho 0H.

A dynamical model of pion photoproduction on the nucleon

Pion photoproduction on the nucleon is investigated using a model hamiltonian defined in the channel-space H = πN⊕γN⊕B with B = δ and N. The basic electromagnetic matrix elements are deduced from the low-order Feynman amplitudes calculated from a lagrangian describing interactions among γ-, π-, ρ-, ω-, N- and Δ-fields. The πN interaction is described by B↔πN vertices, and a two-body separable potential. A scattering formalism is introduced to assure that the constructed pion photoproduction amplitude is unitary and gauge invariant. The πN parameters are determined by fitting the phase-shift data up to 500 MeV incident pion energy. The remaining three free parameters of the model, cutoff Λ for the form factor which regularizes the Born (nonresonant) terms, g m and G E for the γN↔Δ vertex, are determined by fitting the M 1+( 3 2 ) and E 1+( 3 2 ) multipole data. The resulting E2/M1 ratio of the γN↔Δ excitation is −3.1%. The model can to a large extent describe the existing cross-section and polarization data for γp → π +n, γp→π 0p and γn → π −p up to 400 MeV incident photon energy. The importance of unitary in extracting the basic parameters from the data is demonstrated explicitly. It is also shown, that within the present unitary model, the πN off-shell effects can account for up to 50% of the cross section. For the interpretation of experimental data, this indicates a significant difference between the present hamiltonian approach and those that use only the Watson theorem to impose unitarity. The model is consistent with the existing unitary πNN models, and hence can be directly applied to study pion photoproduction on the deuteron and heavier nuclei.

Low-energy η photoproduction from nucleons and nuclei

The photoproduction of η mesons off nucleons is studied near threshold based on an isobar model. Using the reactions πN→ πN, πN→ ππN and π −p→ηn to fix the hadronic vertices as well as the resonance propagators, and the process γN→ πN to constrain the electromagnetic vertices, good predictions for the γp→ ηp cross sections are obtained. This η photoproduction amplitude is then used to estimate cross sections for coherent η production on closed-shell nuclei in a standard DWIA framework. We find that the cross section is dominated by the D 13(1520) isobar while the effects of the S 11(1535) and P 11(1440) resonances are small.

Shadowing in photoabsorption on nuclei

The treatment of shadowing, as due to the interference between one and two-step processes in the nuclear photoproduction amplitude, is reconsidered. Shadowing is related to theA dependence of coherent photoproduction. It is shown not to occur in the Δ region because of the features of coherent π0 photoproduction. Its onset is predicted above the ρ production threshold. It is pointed out that the longitudinal (e, e′) response function may exhibit a different shadowing behaviour.

Unitary theory of the deuteron photodisintegration.

The deuteron photodisintegration in the \ensuremath{\Delta}-resonance region is calculated within a unitary theory of the NN-N\ensuremath{\Delta}-\ensuremath{\pi}NN system coupled to the photon. The photoexcitation amplitude of the \ensuremath{\Delta} is deduced from the ${M}_{1+}$((3/2) pion photoproduction amplitude consistently with its background term and the \ensuremath{\pi}N interaction. The NN-N\ensuremath{\Delta} transition amplitude is obtained from the coupled equations for the NN-N\ensuremath{\Delta}-\ensuremath{\pi}NN system. The one-pion-exchange currents as well as the normal single-nucleon current are included. The polarization parameters are reproduced quantitatively, but the cross section is slightly underestimated. Comparison of our results with those of the NN-N\ensuremath{\Delta} coupled-channel model is made. Effects of relativistic corrections and gauge-invariance constraints are discussed.

K+Λ photoproduction amplitudes incorporating absorptive effects and hypernuclear formation

Incorporating final-state absorptive effects, we have reexamined the γp→K+Λ elementary process to obtain amplitudes which are used for describing photoproduction of hypernuclei. Our model not only resolves the persisting trouble of the small KNΛ coupling constant, but also yields agreement with cross-section data at higher energies. Using our amplitudes, we calculate angular distributions for the reaction16O(γ, K+)Λ16N. While the forward cross-section increases with increasing energy, the total cross-section is found to remain almost constant fromEγ=1.2 GeV through 2 GeV, which suggests that rather low photon energies hold promise for exploration of hypernuclear excitations.

Virtual and real rhos

The interpretation of the enhancement of the electric dipole sum rule due to the ρ exchange potential is discussed in terms of virtual ρ photoproduction. It is explicitly shown that only a Hig0gs mechanism for the SU(2) × U(1) (isospin × charge) group under consideration, allows the construction of the elementary gauge invariant ρ photoproduction amplitude, fulfilling the rho transversality condition. In such a renormalizable theory the isovector tensor ρN N and γN N coupling constants are predicted to be in the same ratio to the corresponding vector ones. The free parameter of the theory is the mass of the Higgs boson which might show up in the reactions γN → NρH and e + e − → ρ° H.

Constraints from the Drell-Hearn-Gerasimov sum rule in chiral models of composite fermions.

We analyze a dispersion relation for a spin-flip Compton amplitude in a chiral model of composite quarks and leptons. We discuss the asymptotic behavior of the amplitude and show under what conditions the Drell-Hearn-Gerasimov sum rule holds. Using a small-mass expansion we derive a consistency condition that relates the photoproduction cross sections for different helicities. We show that this condition suggests the existence of higher-spin excited fermions, as well as relations among a priori independent photoproduction amplitudes.