Measurements of Nonsinglet Moments of the Nucleon Structure Functions and Comparison to Predictions from Lattice QCD for $Q^2=4{\mathrm{GeV}}^2$

We present extractions of the nucleon nonsinglet moments utilizing new precision data on the deuteron $F_2$ structure function at large Bjorken-$x$ determined via the Rosenbluth separation technique at Jefferson Lab Experimental Hall C. These new data are combined with a complementary set of data on the proton previously measured in Hall C at similar kinematics and world datasets on the proton and deuteron at lower $x$ measured at SLAC and CERN. The new Jefferson Lab data provide coverage of the upper third of the $x$ range, crucial for precision determination of the higher moments. In contrast to previous extractions, these moments have been corrected for nuclear effects in the deuteron using a new global fit to the deuteron and proton data. The obtained experimental moments represent an order of magnitude improvement in precision over previous extractions using high $x$ data. Moreover, recent exciting developments in lattice QCD calculations provide a first ever comparison of these new experimental results with calculations of moments carried out at the physical pion mass, as well as a new approach that first calculates the quark distributions directly before determining moments.

Figure 1

Jefferson Lab experiment E06-009 data on deuteron $F_2$ before and after subtraction of the QE contribution. The band at the bottom represents the estimated systematic uncertainty from this procedure. The dot dashed curve is the QE model, the short dashed curve is the total ($\mathrm{QE}+\text{inelastic}$) model and the solid curve is the inelastic model.

Figure 2

Top curve: Data on $F_2^d$ at $Q^2=4{\mathrm{GeV}}^2$ from SLAC, CERN, and Jefferson Lab experiment E06-009. Top curve is shifted up for comparison to bottom. Bottom curve: Same as top data after Fermi correction.

Figure 3

A collection of recent lattice QCD calculations for $N=2$ and $Q^2=4{\mathrm{GeV}}^2$ including some (clover) performed at the real pion mass. The experimental result for the $N=2$ moment is included in the plot for comparison.