Measurements of Double-Polarized Compton Scattering Asymmetries and Extraction of the Proton Spin Polarizabilities

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 extract the nucleon spin polarizabilities is through polarized Compton scattering. Double-polarized Compton scattering asymmetries on the proton were measured in the $\mathrm{\Delta }(1232)$ 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 $10^{-4}{\mathrm{fm}}^4$.

Figure 1

Missing-mass spectra for $E_{\gamma }=273–303\mathrm{MeV}$, and ${\theta }_c=100°–120°$. In addition to the actual Compton scattering distribution, each background, shown in a different color, is stacked on top of one another to show its contribution to the total initial distribution. From bottom to top; light blue is for tagger accidentals; blue is for carbon or cryostat background; magenta, red, and yellow were constructed from data to mimic where a ${\pi }^0$ decay photon was lost in the upstream CB hole, the region between CB and TAPS, and the downstream TAPS hole, respectively, each of which had their own accidental and carbon subtraction already applied; and green shows the final subtracted result.

Figure 2

Missing-mass spectrum after removing the background contributions shown in Fig. 1 for $E_{\gamma }=273–303\mathrm{MeV}$, and ${\theta }_c=100°–120°$. The solid line is the Compton scattering line shape determined from simulation. The dashed line indicates the upper integration limit used in the analysis.

Figure 3

${\mathrm{\Sigma }}_{2x}$ for $E_{\gamma }=273–303\mathrm{MeV}$. The curves are from a dispersion theory calculation [11] with $\alpha$, $\beta$, ${\gamma }_0$, and ${\gamma }_{\pi }$ held fixed at their experimental values, and ${\gamma }_{M1M1}$ fixed at 2.9. From bottom to top, the green, blue, brown, red, and magenta bands are for ${\gamma }_{E1E1}$ equal to $-6.3$, $-5.3$, $-4.3$, $-3.3$, and $-2.3$, respectively. The width of each band represents the propagated errors from $\alpha$, $\beta$, ${\gamma }_0$, and ${\gamma }_{\pi }$ combined in quadrature.