Measurement of spin polarizabilities of the proton

Spin polarizabilities are as-yet experimentally unknown fundamental structure constants that describe the response of the nucleon spin to the action of a changing electromagnetic field. The A2 Collaboration at the Institute for Nuclear Physics in Mainz (Institut für Kernphysik, Mainz) performed the first measurements of the energy and angular dependences of spin asymmetries of the cross section for doubly polarized (polarized-photon beam incident to a polarized proton target) Compton effect in the Δ-resonance region, these asymmetries being sensitive to values of the spin polarizabilities. The preparation of spin-asymmetry measurements at energies below the pion-production threshold with an active (scintillating) polarized target is in progress. These measurements will make it possible to determine individual spin polarizabilities of the proton in a model-independent way.     

Spin polarizabilities of the nucleon from polarized low-energy Compton scattering

As a guideline for forthcoming experiments, we present predictions from Chiral Effective Field Theory for polarized cross-sections in low-energy Compton scattering for photon energies below 170 MeV, both on the proton and on the neutron. Special interest is put on the role of the nucleon spin polarizabilities which can be examined especially well in polarized Compton scattering. We present a model-independent way to extract their energy dependence and static values from experiment, interpreting our findings also in terms of the low-energy effective degrees of freedom inside the nucleon: The polarizabilities are dominated by chiral dynamics from the pion cloud, except for resonant multipoles, where contributions of the -resonance turn out to be crucial. We therefore include it as an explicit degree of freedom. We also identify some experimental settings which are particularly sensitive to the spin polarizabilities.Received: 19 August 2003, Revised: 30 October 2003, Published online: 27 April 2004PACS: 13.40.-f Electromagnetic processes and properties - 13.60.Fz Elastic and Compton scattering - 14.20.Dh Protons and neutronsH.W. Grießhammer: Permanent address: Technische Universität MünchenT.R. Hemmert: Permanent address: Technische Universität München     

Active polarized target: Measurement of proton spin polarizabilities

The static (electric and magnetic) polarizabilities of the proton are known from measurements of low-energy Compton scattering of real photons. However, no experimental data are so far available about its spin polarizabilities, which describe the response of the proton spin to a varying electromagnetic field. These fundamental structure constants can be obtained in the most model-independent way from measurements of double-polarized Compton scattering at energies below the pion threshold using a polarized photon beam and a polarized proton target. An active polarized target based on polystyrene doped with a scintillator allows recoil protons to be detected directly in the target material, background from the coherent Compton effect on heavier nuclei (¹²C etc.) to be eliminated and precise data on spin polarizabilities to be obtained.     

Dispersion relations and the spin polarizabilities of the nucleon

A forward dispersion calculation is implemented for the spin polarizabilities γ₁,,γ₄ of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are structure-constants of the Compton scattering amplitude at . In the absence of a direct experimental measurement of these quantities, a dispersion calculation serves the purpose of constraining the model building, and of comparing with recent calculations in heavy baryon chiral perturbation theory.     

Compton scattering from the deuteron and extracted neutron polarizabilities

Differential cross sections for Compton scattering from the deuteron were measured at MAX-Lab for incident photon energies of 55 and 66 MeV at nominal laboratory angles of 45 degrees, 125 degrees, and 135 degrees. Tagged photons were scattered from liquid deuterium and detected in three NaI spectrometers. By comparing the data with theoretical calculations in the framework of a one-boson-exchange potential model, the sum and the difference of the isospin-averaged nucleon polarizabilities, alpha(N)+beta(N)=17.4+/-3.7 and alpha(N)-beta(N)=6.4+/-2.4 (in units of 10(-4) fm(3)), have been determined. By combining the latter with the global-averaged value for alpha(p)-beta(p) and using the predictions of the Baldin sum rule for the sum of the nucleon polarizabilities, we have obtained values for the neutron electric and magnetic polarizabilities of alpha(n)=8.8+/-2.4(total)+/-3.0(model) and beta(n)=6.5-/+2.4(total)-/+3.0(model), respectively.     

Generalized spin polarizabilities of the nucleon in heavy-baryon chiral perturbation theory at order Omicron(p(4))

We present the first heavy-baryon chiral perturbation theory calculation at order Omicron(p(4)) for the spin-dependent amplitudes for virtual Compton scattering off the nucleon and extract the Omicron(p(4)) results for the generalized spin polarizabilities of the nucleon.     

Measurement of the generalized polarizabilities of the proton in virtual Compton scattering at MAMI

Virtual Compton scattering off the proton has been studied at Q ² = 0.33 (GeV/c)² at the MAMI accelerator in Mainz (Germany). The goal of the experiment is to measure the generalized polarizabilities (GPs) of the proton using the double polarized e p→e' p'γ reaction. This paper reports the measurement of the unpolarized photon electroproduction cross-section for the new data and the extraction of two linear combinations of GPs, which are essential for the analysis of the double spin asymmetry.     

Generalized polarizabilities of the nucleon studied in the linear sigma model (II)

In a previous paper virtual Compton scattering off the nucleon has been investigated in the one-loop approximation of the linear sigma model in order to determine the 3 scalar generalized polarizabilities. We have now extended this work and calculated the 7 vector polarizabilities showing up in the spin-dependent amplitude of virtual Compton scattering. The results fulfill 3 model-independent constraints recently derived. Compared to the constituent quark model there exist enormous differences for some of the vector polarizabilities. At vanishing three-momentum of the virtual photon, the analytical results of the sigma model and of chiral perturbation theory can be related. The influence of the π⁰ exchange in the t channel has been discussed in some detail. Besides, the vector polarizabilities determine 2 linear combinations of the third order spin-polarizabilities appearing in real Compton scattering.     

Generalized polarizabilities of the nucleon studied in the linear sigma model

The generalized polarizabilities of the nucleon have been calculated in the one-loop approximation of the linear sigma model in the limit of infinite sigma mass. In particular, we have investigated the spin-independent amplitude of virtual Compton scattering off the nucleon. The dependence of the polarizabilities on the momentum transfer Q has been compared with two recent model calculations. It has been shown in the linear sigma model that only two of the three scalar polarizabilities are independent quantities. Particular attention has been paid to the real photon point (Q² = 0), where the results of the relativistic chiral perturbation theory have been recovered.     

Generalized polarizabilities of the nucleon studied in the linear sigma model

The generalized polarizabilities of the nucleon have been calculated in the one-loop approximation of the linear sigma model in the limit of infinite sigma mass. In particular, we have investigated the spin-independent amplitude of virtual Compton scattering off the nucleon. The dependence of the polarizabilities on the momentum transferQ has been compared with two recent model calculations. It has been shown in the linear sigma model that only two of the three scalar polarizabilities are independent quantities. Particular attention has been paid to the real photon point (Q ²=0), where the results of the relativisitc chiral perturbation theory have been recovered.     

Nucleon polarizabilities in real and virtual Compton scattering: Recent theoretical issues

We review recent developments in the theoretical investigation of the nucleon polarizabilities. We first report on the static polarizabilities as measured in real Compton scattering, comparing and interpreting the results from various theoretical approaches. In a second step, we extend the discussion to the generalized polarizabilities which can be accessed in virtual Compton scattering, showing how the information encoded in these quantities can provide a spatial interpretation of the induced polarization densities in the nucleon.     

Single spin asymmetries in the (quasi)elastic electron-proton and electron-deuteron scattering Strangeness in the nucleon and two-photon exchange amplitude

Single spin asymmetries in (quasi)elastic electron-proton and electron-deuteron scattering give insight into the structure of the nucleon. In case of a longitudinally polarized electron beam, the parity violating asymmetries can be used to determine the contribution of strange quarks to the vector form factors of the nucleon, whereas the asymmetries using a transversely polarized electron beam allow a determination of the imaginary part of the two-photon exchange amplitude which is related to the nucleon structure due to excited intermediate proton states. Both cases are presented here.     

Towards a Microscopic Understanding of Nucleon Polarizabilities

We outline a microscopic framework to calculate nucleon Compton scattering from the level of quarks and gluons within the covariant Faddeev approach. We explain the connection with hadronic expansions of the Compton scattering amplitude and discuss the obstacles in maintaining electromagnetic gauge invariance. Finally we give preliminary results for the nucleon polarizabilities.     

Tensor polarized γ-deuteron Compton scattering in effective field theory

The differential cross section for γ-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams. At 90° photon scattering angle, only the pion term contributes at this order to the tensor polarized differential cross section. This provides a clean way to study the photon pion dynamics in the two nucleon sector. The effect is measurable for photon energies between 40 and 80 MeV provided the uncertainty in the measured cross sections are ≲ 7%.     

Dispersion relation formalism for virtual Compton scattering off the proton

We present in detail a dispersion relation formalism for virtual Compton scattering (VCS) off the proton from threshold into the Δ(1232)-resonance region. Such a formalism can be used as a tool to extract the generalized polarizabilities of the proton from both unpolarized and polarized VCS observables over a larger energy range. We present calculations for existing and forthcoming VCS experiments and demonstrate that the VCS observables in the energy region between pion production threshold and the Δ(1232)-resonance show an enhanced sensitivity to the generalized polarizabilities. Received: 14 March 2001 / Accepted: 18 June 2001     

Quasi-elastic and elastic charge-exchange differential cross sections (critical review)

More than 50 years ago the charge-exchange of one nucleon in the quasi-elastic nucleon deuteron scattering was proposed to determine the spin independent, or the spin dependent parts of the elastic backward neutron proton differential cross section. For this purpose two measurements are to be performed using unpolarized particles only. Such a suggestion was very attractive for experimentalists, since at that time polarized beams were rare and polarized targets were nonexistent. One experiment consists in the inclusive measurement of the charge-exchange quasi-elastic nucleon deuteron differential cross section. The energy of the fast outgoing nucleon is to be approximately the same as that of the incident nucleon. The intrinsic momenta of the remaining two identical nucleons should be small. The impulse approximation has been assumed, i.e. in the final state of the two nucleons their interaction can be neglected. The quasi-elastic result is to be compared with the elastic np differential cross section in the backward direction at the same energy. The theory related the ratio R _QE (π) of the quasi-elastic to the elastic np charge-exchange differential cross sections to the spin dependent part of the np backward elastic scattering amplitude. Several experiments in the nucleon kinetic energy interval below 1 GeV were carried out, where the R _QE (π) values were determined. Recently the energy interval was extended up to 2 GeV by successful experiments at the JINR VBLHE Nuclotron. The quasi-elastic results can be compared with the values of the analogous quantity R _np (π) for the np elastic scattering, calculated from the phase shift analyses below 1.3 GeV. The present paper is a critical review checking expressions for R _np (π) in different amplitude representations, listing numerical values of elastic np quantities and results of existing quasi-elastic experiments. Conclusions and statements of some authors and the validity of the relevant theory is discussed.     

Investigating neutron polarizabilities through Compton scattering on 3He

We examine manifestations of neutron electromagnetic polarizabilities in coherent Compton scattering from the helium-3 nucleus. We calculate gamma3He elastic scattering observables using chiral perturbation theory to next-to-leading order [O(e2Q)]. We find that the unpolarized differential cross section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities.     

Quasifree compton scattering from the deuteron and nucleon polarizabilities

Cross sections for quasifree Compton scattering from the deuteron were measured for incident energies of E(gamma) = 236-260 MeV at the laboratory angle straight theta(gamma(')) = -135 degrees. The recoil nucleons were detected in a liquid-scintillator array situated at straight theta(N) = 20 degrees. The measured differential cross sections were used, with the calculations of Levchuk et al., to determine the polarizabilities of the bound nucleons. For the bound proton, the extracted values were consistent with the accepted value for the free proton. Combining our results for the bound neutron with those from Rose et al., we obtain 1-sigma constraints of alpha;(n) = 7.6-14.0 and beta;(n) = 1.2-7.6.     

Aspects of nucleon Compton scattering

We consider the spin-averaged nucleon forward Compton scattering amplitude in heavy baryon chiral perturbation theory including all terms to order . The chiral prediction for the spin-averaged forward Compton scattering amplitude is in good agreement with the data for photon energies110 MeV. We also evaluate the nucleon electric and magnetic Compton polarizabilities to this order and discuss the uncertainties of the various counter terms entering the chiral expansion of these quantities.