Within a dynamical coupled-channels model which has already been fixed from analyzing the data of the pi N -> pi N and gamma N -> pi N reactions, we present the predicted double pion photoproduction cross sections up to the second resonance region, W< 1.7 GeV. The roles played by the different mechanisms within our model in determining both the single and double pion photoproduction reactions are analyzed, focusing on the effects due to the direct gamma N -> pi pi N mechanism, the interplay between the resonant and non-resonant amplitudes, and the coupled-channels effects. The model parameters which can be determined most effectively in the combined studies of both the single and double pion photoproduction data are identified for future studies.
Threshold neutral pion photoproduction on light nuclei is studied in the framework of baryon chiral perturbation theory. We obtain a general formula for the electric dipole amplitude in the special case of neutral pion photoproduction on a nucleus. To third order in small momenta, the amplitude is a sum of 2- and 3-body interactions with no undetermined parameters. With reasonable input from the single nucleon sector, our result for neutral pion photoproduction on the deuteron is in agreement with experiment.
We consider the chiral expansion of the threshold amplitude for the reaction $γp \to π^0 π^0 p$ to order ${\cal O}(M_π^2)$. We substantiate a claim that this photoproduction channel is significantly enhanced close to threshold due to pion loops. A precise measurement of the corresponding cross sections is called for which allows to test chiral perturbation theory.
We investigate pion photoproduction off the proton in a manifestly gauge-invariant chiral unitary extension of chiral perturbation theory. In a first step, we consider meson-baryon scattering taking into account all next-to-leading order contact interactions. The resulting low-energy constants are determined by a fit to s-wave pion-nucleon scattering and the low-energy data for the reaction pi- p --> eta n. To assess the theoretical uncertainty, we perform two different fit strategies. Having determined the low-energy constants, we then analyse the data on the s-wave multipole amplitudes E0+ o…
We analyze the $γN\toπN$ process in the negative parity channel with Hamiltonian effective filed theory which is successful in studying the nucleon resonances associated with the meson-nucleon scattering and lattice QCD simulations. We provide the scattering amplitude of pion photoproduction and extract the electric dipole amplitudes $E_{0+}$. The triquark component in $N^*(1535)$ is important for improving the consistence between our results and the experimental data.
We investigate near threshold neutral pion photoproduction off protons to fourth order in heavy baryon chiral perturbation theory in the light of the new data from MAMI. We show that the unitarity cusp at the secondary π^+ n threshold is in agreement with expectations from the final state theorem. We also analyze the fourth order corrections to the P-wave low-energy theorems and show that potentially large Delta-isobar contributions are cancelled by sizeable pion loop effects. This solidifies the parameter free third order predictions, which are in excellent agreement with the data.
Unambiguous isospin violation in the strong interaction sector is a key issue in low energy hadronic physics, both experimentally and theoretically. Bernstein has employed the Fermi-Watson theorem to demonstrate that pion photoproduction is a process where isospin violation in the pi N system can be revealed, an approach we review here. Here we propose a general operator approach to the phenomenon in pion photoproduction, thereby providing an analogue for the framework that was proposed for pi N scattering by Kaufmann and Gibbs. The resulting set of amplitudes could form the basis for determin…
We apply the nuclear model with explicit mesons to photoproduction of neutral pions off protons at the threshold. In this model the nucleons do not interact with each other via a potential but rather emit and absorb mesons that are treated explicitly on equal footing with the nucleons. We calculate the total cross section of the reaction for energies close to threshold and compare the calculations with available experimental data. We show that the model is able to reproduce the experimental data and determine the range of the parameters where the model is compatible with the experiment.
We study the reaction of pion photoproduction on the nucleon in the framework of chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom. In the covariant approach, we give results up to order $ε^3$ in the small scale expansion scheme. Furthermore, we provide $Δ$-less and $Δ$-full results obtained in the heavy-baryon scheme to analyze the differences to the covariant approach. Low energy constants are fitted to multipole amplitudes using theoretical truncation errors estimated by a Bayesian approach. We also compare our findings to data of neutral pion production cross sections a…
We investigate threshold pion photoproduction in the framework of heavy baryon chiral perturbation theory. We give the expansion of the electric dipole amplitude $E_{0+}$ to three orders in $μ$, the ratio of the pion to nucleon mass, and show that it is slowly converging. We argue that this observable is not a good testing ground for the chiral dynamics of QCD. In contrast, we exhibit new and fastly converging low--energy theorems in the P--waves which should be used to constrain the data analysis. We also discuss the importance of polarization observables to accurately pin down certain multip…
We present a calculation of radiative pion photoproduction in the framework of covariant chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom. The analysis is performed employing the small scale expansion scheme adjusted for the $Δ$ region. Depending on the channel, we include contributions up to next-to-next-to-leading order. We fit the available experimental data for the reaction $ γp\toγpπ^0 $ and extract the value of the $Δ^+$ magnetic moment. Errors from the truncation of the small scale expansion are estimated using the Bayesian approach. We compare our results both with…
We have applied a new approach to determine the pole positions and residues from pion photoproduction multipoles. The method is based on a Laurent expansion of the partial wave T-matrices, with a Pietarinen series representing the regular part of energy-dependent and single-energy photoproduction solutions. The method has been applied to multipole fits generated by the MAID and GWU/SAID groups. We show that the number and properties of poles extracted from photoproduction data correspond very well to results from $π$N elastic data and values cited by Particle Data Group (PDG). The photoproduct…
We have analyzed the $M_{1+}^{(3/2)}$ and $E_{1+}^{(3/2)}$ multipole amplitudes of pion photoproduction in the framework of fixed-$t$ dispersion relations. Applying the speed plot technique to our results for these multipoles, we have determined the position and the residues of the $Δ$ (1232) resonance pole. The pole is found at total $c.m.$ energy $W = (1211 - 50i)$ MeV on the second Riemann sheet, and the ratio of the electric and magnetic residues is $R_Δ = - 0.035 - 0.046 i$, resulting in an E2/M1 ratio for the "dressed" delta resonance of $- 3.5 \%$.
We compare results for the D13(1520) photon-decay amplitudes determined in analyses of eta- and pion-photoproduction data. The ratio of helicity amplitudes (A_3/2 / A_1/2), determined from eta-photoproduction data, is quite different from that determined in previous analyses of pion-photoproduction data. We consider how strongly the existing pion-photoproduction data constrain both this ratio and the individual photon-decay amplitudes.
Threshold neutral pion photoproduction on the deuteron is studied in the framework of baryon chiral perturbation theory beyond next-to--leading order in the chiral expansion. To fourth order in small momenta, the amplitude is finite and a sum of two- and three-body interactions with no undetermined parameters. With accurate theoretical and experimental input from the single nucleon sector for the proton amplitude, we investigate the sensitivity of the threshold cross section to the elementary $γn \to π^0 n$ amplitude. A precise measurement of the threshold cross section for $γd \to π^0 d$ is c…
The total cross section for Coulomb photoproduction of neutral pion pairs in the reaction gamma A --> pi0 pi0 A is estimated within the effective chiral lagrangian approach. The amplitude of gamma gamma* --> pi0 pi0 with one off-shell photon is calculated at O(p^6) in the momentum expansion; in addition, nuclear absorption is taken into account. Besides its experimental feasibility, the results of the calculation demonstrate that the reaction gamma A --> pi0 pi0 A is a powerful source of information on the process gamma gamma --> pi0 pi0 close to threshold.
We have obtained the transition matrix elements for pion photoproduction by considering the number of gamma matrices involved. The approach based on the most general conditions of gauge invariance, current conservation and transversality. The approach is fairly consistent with literatures.
We calculate electromagnetic neutral pion production off three-nucleon bound states (3H, 3He) at threshold to leading one-loop order in the framework of chiral nuclear effective field theory. In addition, we analyze the dependence of the nuclear S-wave amplitude E_{0+} on the elementary neutron amplitude E_{0+}^{pi0 n} which in the case of 3He provides a stringent test of the prediction based on chiral perturbation theory. Uncertainties from higher order corrections are estimated.
In this paper, we show that the low energy theorem (LET) of the threshold pion-photoproduction can be fully recovered in the quark model. An essential result of this investigation is that the quark-pion operators are obtained from the effective chiral Lagrangian, and the low energy theorem does not require the constraints on the internal structures of the nucleon. The pseudoscalar quark-pion coupling generates an additional term at order $μ=m_π/M$ only in the isospin amplitude $A^{(-)}$. The role of the transitions between the nucleon and the resonance $P_{33}(1232)$ and P-wave baryons are als…
The role of the nucleon resonances in the double polarization observables of pion photoproduction is investigated by using the resonance parameters predicted by Capstick and Roberts. As an example, we show that the not-well-determined two-star resonance N$^{-}_{3/2}$(1960) can be examined by performing experiments on beam-recoil polarization at large angles.
We calculate electromagnetic neutral pion production off tri-nucleon bound states (3H, 3He) at threshold in chiral nuclear effective field theory to fourth order in the standard heavy baryon counting. We show that the fourth order two-nucleon corrections to the S-wave multipoles at threshold are very small. This implies that a precise measurement of the S-wave cross section for neutral pion production off 3He allows for a stringent test of the chiral perturbation theory prediction for the S-wave electric multipole E_{0+}^{pi0 n}.
A unified description of single-pion photoproduction data, together with pion- and eta-hadroproduction data, has been achieved in a Chew-Mandelstam parametrization which is consistent with unitarity at the two-body level. Energy-dependent and single-energy partial wave analyses of pion photoproduction data have been performed and compared to previous SAID fits and multipoles from the Mainz and Bonn-Gatchina groups.
We argue that the reaction mechanism for the coherent pion production is not known with sufficient accuracy to determine the neutron radius of 208Pb to the claimed precision of 0.03 fm.
The relativistic amplitudes of pion photoproduction are evaluated by dispersion relations at t=const. The imaginary parts of the amplitudes are taken from the MAID model covering the absorption spectrum up to center-of-mass energies W = 2.2 GeV. For sub-threshold kinematics the amplitudes are expanded in powers of the two independent variables νand t related to energy and momentum transfer. Subtracting the loop corrections from this power series allows one to determine the counter terms of covariant baryon chiral perturbation theory. The proposed continuation of the amplitudes into the unphysi…
We consider multipole amplitudes for low-energy pion photoproduction, constructed with minimal model dependence, at single energies. Comparisons with fits to the full resonance region are made. Explanations are suggested for the discrepancies and further experiments are motivated.
The charged and neutral pion photoproduction reactions are investigated in a dynamical coupled-channels approach based on the formulation of Haberzettl, Huang, and Nakayama [Phys. Rev. C 83, 065502 (2011)]. The hadronic final-state interaction is provided by the Juelich pi-N model, which includes the channels pi-N and eta-N comprising stable hadrons as well as the effective pi-pi-N channels pi-Delta, sigma-N, and rho-N. This hadronic model has been quite successful in describing pi-N to pi-N scattering for center-of-mass energies up to 1.9 GeV. By construction, the full pion photoproduction cu…
We summarize results obtained in our studies of the pion-nucleon coupling constant. Several different techniques have been applied to pi-N and NN elastic scattering data, and the existing database for single-pion photoproduction. The most reliable determination comes from pi-N elastic scattering. The sensitivity in this reaction was found to be greater, by at least a factor of 3, when compared with analyses of NN elastic scattering or single-pion photoproduction.
We present a relativistic dynamical model of pion photoproduction on the nucleon in the resonance region. It offers several advances over the existing approaches. The model is obtained by extending our $πN$-scattering description to the electromagnetic channels. The resulting photopion amplitude is thus unitary in the $πN$, $\ga N$ channel space, Watson's theorem is exactly satisfied. At this stage we have included the pion, nucleon, $\De(1232)$-resonance degrees of freedom. The $ρ$ and $ω$ meson exchanges are also included, but play a minor role in the considered energy domain (up to $\sqrt{s…
The long-standing discrepancy between the Gerasimov-Drell-Hearn sum rule and the analysis of pion photoproduction multipoles is greatly diminished by use of s-wave multipoles that are in accord with the predictions of chiral perturbation theory and describe the experimental data in the threshold region. The remaining difference may be due to contributions of channels with more pions and/or heavier mesons whose contributions to the sum rule remain to be investigated by a direct measurement of the photoabsorption cross sections.
We calculate the cross sections for inclusive one-pion, two-pion and eta photoproduction in nuclei in the photon energy range from 300 MeV to 900 MeV within the framework of a semi-classical BUU transport model. Our results are compared with existing experimental data and discussed with respect to a calculation of the total photoabsorption cross section.
We investigate the influence of new Jefferson Lab polarization-transfer data, Cx and Cz, and recoil polarization, Py, measurements in multipole fits to the single-pion photoproduction database. Results are compared to those found with the addition of a double-polarization quantity associated with the Gerasimov- Drell-Hearn sum rule.
A self-consistent analysis of pion scattering and pion photoproduction within a coupled channels dynamical model is presented. In the case of pion photoproduction, we obtain background contributions to the imaginary part of the S-wave multipole which differ considerably from the result based on the K-matrix approximation. Within the dynamical model these background contributions become large and negative in the region of the S_{11}(1535) resonance. Due to this fact much larger resonance contributions are required in order to explain the results of the recent multipole analyses. For the first S…
The scattering amplitude of the photoproduction of $π^{+}$ is calculated using the helicity formalism. The pseudovector coupling $π$-N interaction with the non-perturbative term is applied to the perturbative expansion. The parameters for the self-energy are taken from the results of the $π$-N scattering in our previous study.
Incoherent photoproduction of pions on the deuteron in the Delta(1232) resonance region is studied, where besides the impulse approximation complete two-body rescattering in the nucleon-nucleon and pion-nucleon final state subsystems is included.
The possibilities of a model-independent partial wave analysis for pion, eta or kaon photoproduction are discussed in the context of complete experiments. It is shown that the helicity amplitudes obtained from at least 8 polarization observables including beam, target and recoil polarization can not be used to analyze nucleon resonances. However, a truncated partial wave analysis, which requires only 5 observables will be possible with minimal model assumptions.
The two-body currents for s-wave pion photoproduction on the NN system are derived to O(Q^4) in chiral perturbation theory. For the interesting case of 3S1 <-> 1S0 transitions, we show that an axial isovector two-nucleon contact term connects the short-distance physics of pion photoproduction to pion production and several important electroweak reactions. We also find that the standard chiral Lagrangian gives a gamma pi pi N N vertex that have not been explicitly mentioned in previous literature. The corresponding Feynman rule is presented here and some processes where it should be important a…
We show that a recent claim of huge kaon loop corrections to the electric dipole amplitude in neutral pion photoprodcution at threshold is incorrect. The difference between the two and three flavor chiral perturbation theory calculation is marginal and thus previous claims of a good understanding of this reaction remain valid.
A partial-wave analysis of single-pion photoproduction data has been completed. This study extends from threshold to 2 GeV in the laboratory photon energy, focusing mainly on the influence of new measurements and model-dependence in the choice of parameterization employed above the two-pion threshold. Results are used to evaluate sum rules and estimate resonance photo-decay amplitudes. These are compared to values obtained in the MAID analysis.
Two approaches for analysis of pion photo- and electroproduction on nucleons in the resonance energy region are checked at $Q^2=0$ using the results of GWU(VPI) partial-wave analysis of photoproduction data. The approaches are based on dispersion relations and unitary isobar model. Within dispersion relations good description of photoproduction multipoles is obtained up to $W=1.8 GeV$. Within unitary isobar model, modified with increasing energy by incorporation of Regge poles, and with unified Breit-Wigner parametrization of resonance contributions, good description of photoproduction multipo…
We shall review here our current knowledge and new frontiers of the pion photoproduction study, from threshold through the Delta resonance region, emphasizing the hadron physics program, of interest to a 250 MeV, high duty factor electron facility, such as the upgraded MAX-lab at the Lund University, Sweden, where it would be possible to produce tagged photons of high quality, with energy below approximately 200 MeV.
The influence of final state $NN$- and pi N-rescattering in incoherent pion photoproduction on the deuteron has been investigated. For the elementary photoproduction operator an effective Lagrangian model is used which describes well the elementary reaction. The interactions in the final two-body subsystems are taken in separable form. While NN-rescattering shows quite a significant effect, particularly strong for neutral pion production, pi N-rescattering is almost negligible. Inclusion of such effects leads to an improved and quite satisfactory agreement with experiment.
The $ηN$ final state is isospin-selective and thus provides access to the spectrum of excited nucleons without being affected by excited $Δ$ states. To this end, the world database on eta photoproduction off the proton up to a center-of-mass energy of $E\sim 2.3$ GeV is analyzed, including data on differential cross sections, and single and double polarization observables. The resonance spectrum and its properties are determined in a combined analysis of eta and pion photoproduction off the proton together with the reactions $πN\to πN$, $ηN$, $KΛ$ and $KΣ$. For the analysis, the so-called Jüli…
Based on a prior model on double pion photoproduction on the proton, successfully tested in total cross sections and invariant mass distributions, we make a theoretical study of the angular dependence of helicity asymmetries from the interaction of circularly polarized photons with unpolarized protons. We show that this observable is sensitive to details of the internal mechanisms and, thus, represents a complementary test of the theoretical model.
We demonstrate that the Dubna-Mainz-Taipei (DMT) meson-exchange dynamical model, which starts from an effective chiral Lagrangian, for pion photoproduction provides an excellent and economic framework to describe both the pi^0 threshold production and the Delta deformation, two features dictated by chiral dynamics.
We investigate the influence of new GRAAL Sigma-beam asymmetry measurements on the neutron in multipole fits to the single-pion photoproduction database. Results are compared to those found with the addition of a double-polarization quantity associated with the sum rule.
A covariant, unitary and gauge invariant theory for pion photoproduction on a single nucleon is presented. To achieve gauge invariance at the operator level one needs to include both the $πN$ and $γπN$ thresholds. The final amplitude can be written in terms of a distorted wave in the final $πN$ channel provided one includes additional diagrams to the standard Born term in which the photon is coupled to the final state pion and nucleon. These additional diagrams are required in order to satisfy gauge invariance.
Charged pion photoproduction is proposed as a new method to study halo nuclei. In particular, it is demonstrated that the reaction 17O(gamma,pi^-)17F(1/2+, 0.495 MeV) is well-suited to investigate the well-known proton halo in 17F which is not amenable to radioactive beam experiments. The cross sections are shown to be very sensitive to the halo structure of the loosely bound proton.
Using a model for two pion photoproduction on the proton previously tested in total cross sections and invariant mass distributions, we evaluate here polarization observables on which recent experiments are providing new information. We evaluate cross sections for spin 1/2 and 3/2, which are measured at Mainz and play an important role in tests of the GHD sum rule. We also evaluate the proton polarization asymmetry $Σ$ which is currently under investigation at GRAAL in Grenoble.
Photo production of pions on the deuteron is studied in the spectator nucleon model. The Born terms of the elementary production amplitude are determined in pseudovector $π$N coupling and supplied with a form factor. The $Δ$ resonance is considered both in the $s$ and the $u$ channel. The parameters of the $Δ$ resonance and the cutoff of the form factors are fixed on the leading photoproduction multipoles. Results for total and differential cross sections are compared with experimental data. Particular attention is paid to the role of Pauli correlations of the final state nucleons in the quasi…
We explore the photoproduction mechanisms for charged and neutral pion pairs off a heavy nucleus at threshold. We calculate the production of charged pairs in the Coulomb field of the nucleus in the Born approximation using explicit expressions for the differential cross sections and their connection with the total cross-section. The production of sigma mesons at threshold and their subsequent decay into pions is an important mechanism and is investigated quantitatively in a framework that can be used for both charged and neutral pions. Sigma mesons can be produced via electromagnetic (photon …
The contribution of D waves to physical observables for neutral pion photoproduction in the near threshold region is studied. Heavy Baryon Chiral Perturbation Theory to one loop, and up to ${\cal O}(q^4)$, is used to account for the S and P waves, while D waves are added in an almost model-independent way using standard Born terms and vector mesons. It is found that the inclusion of D waves is necessary to extract the $E_{0+}$ multipole reliably from present and forthcoming data and to assess the low-energy constants of Chiral Perturbation Theory. Arguments are presented demonstrating that F-w…
We investigate the pion photoproduction in the Δ(1232) region in the framework of an effective Lagrangian including pions, nulceon and Δ(1232). We work to third order in a small scale expansion with both $m_π$ and $M_Δ-M_N$ treated as light scales. We note that in the $Δ$ region, straightward power counting breaks as the amplitudes become very large, to deal with this problem, we suggest that the appropriate way to compare theoretical calculations with experimental data is via weighted integrals of the amplitudes through the $Δ$ region.
We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnes and Muskhelishvili. The free parameters were determined by a fit to the most recent data for π^{+} and π^{0} production on the proton as well as π^{-} production on the neutron, in the energy We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipol…
Based on an effective field theory of hadrons in which quantum chromodynamics is assumed to provide the necessary bare cutoff functions, a gauge-invariant theory of pion photoproduction with fully dressed nucleons is described. The formalism provides consistent dynamical descriptions of pi-N --> pi-N scattering and Gamma-N --> pi-N production mechanisms in terms of nonlinear integral equations for fully dressed hadrons. The dressed hadron currents and the pion photoproduction current satisfy gauge invariance in a self-consistent manner. Approximations are discussed that make the nonlinear form…
