Measurement of the $Q^2$ Dependence of the Deuteron Spin Structure Function $g_1$ and its Moments at Low $Q^2$ with CLAS

We measured the $g_1$ spin structure function of the deuteron at low $Q^2$, where QCD can be approximated with chiral perturbation theory ($\chi \mathrm{PT}$). The data cover the resonance region, up to an invariant mass of $W\approx 1.9\mathrm{GeV}$. The generalized Gerasimov-Drell-Hearn sum, the moment ${\mathrm{\Gamma }}_1^d$ and the spin polarizability ${\gamma }_0^d$ are precisely determined down to a minimum $Q^2$ of $0.02{\mathrm{GeV}}^2$ for the first time, about 2.5 times lower than that of previous data. We compare them to several $\chi \mathrm{PT}$ calculations and models. These results are the first in a program of benchmark measurements of polarization observables in the $\chi \mathrm{PT}$ domain.

Figure 1

Example of extracted $g_1^d(W)$ vs invariant mass $W$ (circles), together with the nominal value of the parameterization used for its extraction (line). The large negative peak corresponds to the $\mathrm{\Delta }(1232)3/2^{+}$ resonance. The error bars give the statistical uncertainty and the band is the total systematic uncertainty. The data are for $⟨Q^2⟩=0.1{\mathrm{GeV}}^2$.

Figure 2

The first moment ${\mathrm{\Gamma }}_1^d(Q^2)$. The solid circles are the EG4 data integrated over the covered kinematics. The fully integrated ${\mathrm{\Gamma }}_1^d$, using a model to supplement data, is shown by the solid squares. The error bars are statistical. The systematic uncertainty is given by the horizontal band. The open symbols show data from the CLAS EG1b [14] and SLAC E143 [32] experiments. The other bands and lines show various models and $\chi \mathrm{PT}$ calculations as described in the text. The short-dash line (Model) does not include the EG4 data, to reveal the new knowledge gained.

Figure 3

The generalized spin polarizability ${\gamma }_0(Q^2)$. See Fig. 2 for legends and theoretical calculations.