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-wave contributions are negligible in the near-threshold region.
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 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.
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.
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.
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…
With the availability of the new neutral pion photoproduction from the proton data from the A2 and CB-TAPS Collaborations at Mainz it is mandatory to revisit Heavy Baryon Chiral Perturbation Theory (HBChPT) and address the extraction of the partial waves as well as other issues such as the value of the low-energy constants, the energy range where the calculation provides a good agreement with the data and the impact of unitarity. We find that, within the current experimental status, HBChPT with the fitted LECs gives a good agreement with the existing neutral pion photoproduction data up to $\s…
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.
We compute the photon asymmetry $B_γ$ for near threshold parity violating (PV) pion photoproduction through sub-leading order. We show that sub-leading contributions involve a new combination of PV couplings not included in previous analyses of hadronic PV. We argue that existing constraints on the leading order contribution to $B_γ$ -- obtained from the PV $γ$-decay of $^{18}$F -- suggest that the impact of the subleading contributions may be more significant than expected from naturalness argumen
We present a theoretical study of the radiative pion photoproduction on the nucleon ($γN \to πN γ'$) in the $\De$-resonance region, with the aim to determine the magnetic dipole moment (MDM) of the $Δ^+(1232)$. The study is done within the framework of chiral effective-field theory where the expansion is performed (to next-to-leading order) in the $δ$ power-counting scheme which is an extension of chiral perturbation theory to the $Δ$-resonance energy region. We present the results for the absorptive part of the $Δ$ MDM, as well as perform a sensitivity study of the dependence of $γN \to πN γ'…
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…
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 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.
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.
In a recent preprint, hep-ph/0012253, Zhu et al. calculated a part of the next-to-leading order corrections to parity-violating pion photoproduction (pol)gamma p-> pi^+ n in heavy-baryon chiral perturbation theory. They claim they have found the contribution as large as the leading-order. If correct, the process will not be a clean way to extract the longest range PV pion-nucleon coupling constant h_{πNN}^(1), as was asserted in our previous publications (hep-ph/0011230, nucl-th/0011100). In this comment we show that there is no solid evidence to support Zhu et al.'s claim. Moreover, we show t…
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.
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…
The reactions $γp\toπ^0 p$ and $γp\toπ^+ n$ are analyzed in a semi-phenomenological approach up to $E\sim2.3$ GeV. Fits to differential cross section and single and double polarization observables are performed. A good overall reproduction of the available photoproduction data is achieved. The Jülich2012 dynamical coupled-channel model -which describes elastic $πN$ scattering and the world data base of the reactions $πN\toηN$, $KΛ$, and $KΣ$ at the same time - is employed as the hadronic interaction in the final state. The framework guarantees analyticity and, thus, allows for a reliable extra…
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.
{ {\bf Background:} Knowing the difference between the neutron and proton densities of nuclei is a significant topic because of its importance for understanding neutron star structures and cooling mechanisms. The coherent-nuclear photoproduction of pions, $({\g,π^0})$, combined with elastic electron scattering, has been suggested to be a very accurate probe of density differences. {\bf Purpose:} Study the ${(\g,π^0})$ reaction mechanism so as to better access the uncertainties involved in extracting the neutron density. {\bf Methods:} Include the effects of final-state pion-nucleus charge-exch…
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.
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 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.
Partial-wave analysis of meson and photon-induced reactions is needed to enable the comparison of many theoretical approaches to data. In both energy-dependent and independent parametrizations of partial waves, the selection of the model amplitude is crucial. Principles of the $S$-matrix are implemented to different degree in different approaches, but a many times overlooked aspect concerns the selection of undetermined coefficients and functional forms for fitting, leading to a minimal yet sufficient parametrization. We present an analysis of low-energy neutral pion photoproduction using the …
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 assess the energy limit up to which Heavy Baryon Chiral Perturbation Theory (HBChPT) can be applied to the process of neutral pion photoproduction from the proton by analyzing the latest data collected by the MAMI/A2 collaboration at Mainz. The high-quality differential cross section and the photon asymmetry measured data allow to test the theory at a level not previously achieved. We find that, within the current experimental status, the agreement between theory and experiment is excellent up to $\sim$170 MeV. Above this energy HBChPT fails to provide high-quality fits while an empirical p…
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 $- 3.5 \%$.
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…
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 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.
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.
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.
A description of low-energy scattering of pions and nuclei within a BUU transport model is presented. Implementing different scenarios of medium modifications, the mean free path of pions in nuclear matter at low momenta and pion absorption reactions on nuclei have been studied and compared to data and to results obtained via quantum mechanical scattering theory. We show that even in a regime of a long pionic wave length the semi-classical transport model is still a reliable framework for pion kinetic energies greater than ~20-30 MeV. Results are presented on pion-absorption cross sections in …
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 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 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.
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…
Contributions of $D$ waves to physical observables for neutral pion photoproduction from the proton in the near-threshold region are studied and means to isolate them are proposed. Various approaches to describe the multipoles are employed --a phenomenological one, a unitary one, and heavy baryon chiral perturbation theory. The results of these approaches are compared and found to yield essentially the same answers. $D$ waves are seen to enter together with $S$ waves in a way that any means which attempt to obtain the $E_{0+}$ multipole accurately must rely on knowledge of $D$ waves and that c…
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 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…
