Session NJ: Hadron Polarizabilities

High-Accuracy Analysis of Compton Scattering in Chiral EFT: Proton and Neutron Polarisabilities

Compton scattering from protons and neutrons provides important insight into the structure of the nucleon. A new extraction of the static electric and magnetic dipole polarisabilities $\alpha_{E1}$ and $\beta_{M1}$ of the proton and neutron from all published elastic data below 300~MeV in Chiral Effective Field Theory shows that within the statistics-dominated errors, the proton and neutron polarisabilities are identical, i.e.~no iso-spin breaking effects of the pion cloud are seen. Particular attention is paid to the precision and accuracy of each data set, and to an estimate of residual theoretical uncertainties. ChiEFT is ideal for that purpose since it provides a model-independent estimate of higher-order corrections and encodes the correct low-energy dynamics of QCD, including, for few-nucleon systems used to extract neutron polarisabilities, consistent nuclear currents, rescattering effects and wave functions. It therefore automatically respects the low-energy theorems for photon-nucleus scattering. The $\Delta(1232)$ as active degree of freedom is essential to realise the full power of the world's Compton data.Its parameters are constrained in the resonance region. A brief outlook is provided on what kind of future experiments can improve the database.   

Measurement of the Proton Scalar Polarizabilities at MAMI

The scalar polarizabilities, $\alpha_{E1}$ and $\beta_{M1}$, as fundamental properties of the nucleon, play a crucial role not only in our understanding of the nucleon, but also in other areas such as atomic physics, where they provide e.g. corrections to the Lamb Shift. To date, these observables were extracted in parallel from unpolarized cross-sections of Compton scattering on the proton. At the MAMI accelerator facility in Mainz, Germany, the proton polarizabilities were measured using a linearly polarized photon beam for the first time in a photon energy range from 110 to 150 MeV. The photon beam, produced in the Glasgow-Mainz Photon Tagger, impinged on a liquid Hydrogen target and the reaction products were detected in the Crystal Ball and TAPS $4\pi$ spectrometer setup. The beam asymmetry $\Sigma_{3}$ was measured for the first time below pion threshold. This measurement will allow the first independent extraction of the observables $\alpha_{E1}$ and $\beta_{M1}$. The current status of the $\Sigma_{3}$ measurement as function of incoming photon energy and polar angle of the outgoing photon will be presented and the $\alpha_{E1}$ and $\beta_{M1}$ extraction will be discussed.   

Measuring the Spin-Polarizabilities of the Proton in Polarized Compton scattering at MAMI-Mainz

At $O(\omega^{3})$ four new structure constants are present in the nucleon Compton scattering amplitude; these are the spin-polarizabilities $\gamma _{E1E1} $, $\gamma_{M1M1} $, $\gamma_{E1M2} $, and $\gamma_{M1E2} $. The most model independent way to determine the spin-polarizabilities is by measuring a double-polarized Compton scattering asymmetry with polarized target and circularly polarized photons, and by measuring an in-plane/transverse-plane Compton scattering asymmetry with linearly polarized photons ($\Sigma_{3} )$. This talk will present new Compton scattering asymmetry data taken in the $\Delta $ region by the A2 Collaboration using the Crystal Ball at Mainz, with transverse polarized proton target and circularly polarized photons, the $\Sigma_{2x} $ asymmetry (1). A dispersion model and an EFT calculation of Compton scattering are used to fit the four spin-polarizabilities to the new experimental data on $\Sigma_{2x} $, earlier results (2) on $\Sigma_{3} $, and previous determinations of $\gamma_{0} $ and $\gamma_{\pi } $. The results of the fits are compared with theoretical calculations. \\[4pt] [1] P. Martel, Ph.D. thesis, University of Massachusetts, unpublished (2012).\\[0pt] [2] G. Blanpied, et al., Phys. Rev. C, 64, 025203 (2001)   

Low Q$^2$ Pion Electroproduction and VCS in the Delta Resonance Region

The study of the N$\rightarrow \Delta$ transition has been historically essential in order to achieve a better understanding of the nucleon structure and of the underlying nucleon dynamics. The pion electroproduction and VCS channels of the transition allow exploration for non-spherical angular momentum amplitudes in hadrons through the measurement of the transition quadrupole amplitudes. The VCS channel also provides access to the generalized polarizabilities of the nucleon. New, precise measurements of the pion excitation channel from JLab/Hall-A and from MAMI will be presented. Furthermore, new results from the first high precision measurement of the VCS channel at the $\Delta$ resonance from MAMI will also be presented and discussed.   

Pion Polarizability at CERN COMPASS

The electric $\alpha_{\pi}$ and magnetic $\beta_{\pi}$ charged pion Compton polarizabilities provide stringent tests of Chiral Perturbation Theory. The combination ($\alpha_{\pi}$-$\beta _{\pi})$ was measured at CERN COMPASS via radiative pion Primakoff scattering (Bremsstrahlung of 190 GeV/c $\pi^{-}$s) in the nuclear Coulomb field: $\pi +$ Z $\to \pi + \gamma+$ Z. This reaction is identified experimentally by virtue of the very small momentum transfer to the target nucleus; and is equivalent to $\gamma +$ $\pi \to \gamma + \pi $ Compton scattering for laboratory $\gamma$'s of order 1 GeV/c incident on a target pion at rest. COMPASS data analysis (assuming $\alpha_{\pi}+\beta_{\pi}=$0 based on theory) gives a preliminary value of $\alpha_{\pi} =-\beta_{\pi} =$ (1.9 $\pm$ 0.7$_{\mathrm{stat.}}$ $\pm$ 0.8$_{\mathrm{syst.}})$ $\times$ 10$^{-4}$ fm$^{3}$.   

Measuring the Charged Pion Polarizability in the $\gamma\gamma\rightarrow\pi^{+{}}\pi^{-{}}$ Reaction

A new measurement of the charged pion polarizability $\alpha_{\pi}-\beta_{\pi}$ has been recently approved to run at Jefferson Lab using the GlueX detector in experimental Hall-D. This will be done via the $\gamma\gamma\rightarrow\pi^{+{}}\pi^{-{}}$ cross section accessed via the Primakoff mechanism on a $Sn^{116}$ target. The linearly polarized photon source in Hall-D will be used to separate the Primakoff cross-section from coherent $\rho^{\circ}$. An additional detector will also need to be constructed to help distinguish pion and muon events. The charged pion polarizability ranks among the most important tests of low-energy QCD presently unresolved by experiment. Analogous to precision measurements of $\pi^{\circ}\rightarrow\gamma\gamma$ that test the intrinsic odd-parity (anomalous) sector of QCD, the pion polarizability tests the intrinsic even-parity sector of QCD.   

Status of the PrimEx-II Analysis on the $\pi^{0}$ Lifetime Measurement

As the lightest particle in the hadron spectrum, $\pi^{0}$ plays an important role in understanding the fundamental symmetries of QCD. The $\pi^{0}\to \gamma \gamma $ decay is a key test of the QCD predictions based on the chiral anomaly and spontaneous chiral symmetry breaking. Theoretical activities over the last decade have resulted in a high precision (1{\%} level) in the calculations of the decay amplitude of the $\pi^{0}$ into two photons. The experimental measurement of this parameter with a comparable precision will be critical to test these important predictions. The PrimEx collaboration at Jefferson Lab has developed and performed experiments to measure the $\pi ^{0}$ radiative decay width via the Primakoff effect. The published result from the first experimental data (PrimEx-I) has a 2.8{\%} total uncertainty in the $\pi^{0}$ radiative decay width. The second experiment (PrimEx-II) was carried out in fall 2010 with the final goal of 1.4{\%} precision. The status of PrimEx-II data analysis will be presented.   

Impulse Approximation in Inelasitc Compton Scattering on The Deuteron and Neutron Polarizabilities

Inelastic Compton scattering on the deuteron, $\gamma d\rightarrow \gamma np$, is analysed in $\chi$EFT - a consistent model independent framework with controlled uncertainties. By doing so the applicability of $\chi$EFT is extended beyond elastic Compton scattering on the deuteron. In addition, neutron polarizability values are extracted by investigating the kinematic region of NQFP, neutron quasi-free peak, where the momentum of the outgoing proton is so small that it is considered static. This region provides access to $\gamma n \rightarrow \gamma n$ which leads to a more direct approach of computing neutron scalar polarizabilites $\alpha$ and $\beta$. To this end, current results from Impulse approximation calculation are reported. These calculations pertain to the case where incoming photon interacts with only one of the nucleon in the deuteron. The impulse approximation differential cross section $d^3\sigma/dE_nd\Omega_{\gamma'} d\Omega_n$ for photon energies ranging from 100-400MeV is presented.