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Register a new userDetermination of the scalar polarizabilities of the proton using beam asymmetry $Sigma_{3}$ in Compton scattering
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Vahe Sokhoyan Vahe Sokhoyan
Publication date
2016
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English
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The scalar dipole polarizabilities, $alpha_{E1}$ and $beta_{M1}$, are fundamental properties related to the internal dynamics of the nucleon. The currently accepted values of the proton polarizabilities were determined by fitting to unpolarized proton Compton scattering cross section data. The measurement of the beam asymmetry $Sigma_{3}$ in a certain kinematical range provides an alternative approach to the extraction of the scalar polarizabilities. At the Mainz Microtron (MAMI) the beam asymmetry was measured for Compton scattering below pion photoproduction threshold for the first time. The results are compared with model calculations and the influence of the experimental data on the extraction of the scalar polarizabilities is determined.
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The spin polarizabilities of the nucleon describe how the spin of the nucleon responds to an incident polarized photon. The most model-independent way to measure the nucleon spin polarizabilities is through polarized Compton scattering. Double-polarized Compton scattering asymmetries on the proton were measured in the $Delta(1232)$ region using circularly polarized incident photons and a transversely polarized proton target at the Mainz Microtron. Fits to asymmetry data were performed using a dispersion model calculation and a baryon chiral perturbation theory calculation, and a separation of all four proton spin polarizabilities in the multipole basis was achieved. The analysis based on a dispersion model calculation yields $gamma_{E1E1} = -3.5 pm 1.2$, $gamma_{M1M1}= 3.16 pm 0.85$, $gamma_{E1M2} = -0.7 pm 1.2$, and $gamma_{M1E2} = 1.99 pm 0.29$, in units of $10^{-4}$ fm$^4$.
We present the first attempt to extract the scalar dipole dynamical polarizabilities from proton real Compton scattering data below pion-production threshold. The theoretical framework combines dispersion relations technique, low-energy expansion and multipole decomposition of the scattering amplitudes. The results are obtained with statistical tools that have never been applied so far to Compton scattering data and are crucial to overcome problems inherent to the analysis of the available data set.
Differential cross sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz tagging spectrometer at the Mainz MAMI accelerator together with the Mainz 48 cm $oslash$ $times$ 64 cm NaI(Tl) photon detector and the Gottingen SENECA recoil detector. The data cover photon energies ranging from 200 MeV to 400 MeV at $theta^{LAB}_gamma=136.2^circ$. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction $p(gamma,pi^+ n)$. The free proton Compton scattering cross sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross section for free scattering from quasi-free data. Differential cross sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron have been obtained to be $alpha-beta= 9.8pm 3.6(stat){}^{2.1}_1.1(syst)pm 2.2(model)$ in units $10^{-4}fm^3$. In combination with the polarizability sum $alpha +beta=15.2pm 0.5$ deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, $alpha_n=12.5pm 1.8(stat){}^{+1.1}_{-0.6}pm 1.1(model)$ and $beta_n=2.7mp 1.8(stat){}^{+0.6}_{-1.1}(syst)mp 1.1(model)$ are obtained. The backward spin polarizability of the neutron was determined to be $gamma^{(n)}_pi=(58.6pm 4.0)times 10^{-4}fm^4$.
The Compton double-polarization observable $Sigma_{2z}$ has been measured for the first time in the $Delta(1232)$ resonance region using a circularly polarized photon beam incident on a longitudinally polarized target at the Mainz Microtron. This paper reports these results, together with the model-dependent extraction of four proton spin polarizabilities from fits to additional asymmetry data using dispersion relation and chiral perturbation theory calculations, with the former resulting in: $gamma_{E1E1} = -3.18 pm 0.52$, $gamma_{M1M1} = 2.98 pm 0.43$, $gamma_{E1M2} = -0.44 pm 0.67$ and $gamma_{M1E2} = 1.58 pm 0.43$, in units of $10^{-4}~mathrm{fm}^{4}$.
Double-polarization observables in the reaction $vec{e}p rightarrow evec{p}gamma{}$ have been measured at $Q^2=0.33 (GeV/c)^2$. The experiment was performed at the spectrometer setup of the A1 Collaboration using the 855 MeV polarized electron beam provided by the Mainz Microtron (MAMI) and a recoil proton polarimeter. From the double-polarization observables the structure function $P_{LT}^perp$ is extracted for the first time, with the value $(-15.4 pm 3.3 (stat.)^{+1.5}_{-2.4} (syst.)) GeV^{-2}$, using the low-energy theorem for Virtual Compton Sattering. This structure function provides a hitherto unmeasured linear combination of the generalized polarizabilities of the proton.
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