Impact of recent COMPASS data on polarized parton distributions and structure functions

We perform a new extraction of polarized parton distribution functions (PPDFs) from the spin structure function experimental data in the fixed-flavor number scheme. In this analysis, we include recent proton and deuteron spin structure functions obtained by the COMPASS Collaboration. We examine the impact of the new COMPASS proton and deuteron data on the polarized parton densities and compare with results from our previous study (KATAO PPDFs), which used the Jacobi polynomial approach. We find the extracted PPDFs of the proton, neutron, and deuteron structure functions are in very good agreement with the experimental data. The results for extracted PPDFs are also compared with available theoretical models from the literature.

Figure 1

Experimental data sets used in our fit of proton, deuteron, and neutron structure functions in the $\{x,Q^2\}$ plane.

Figure 2

Polarized proton structure function $x{g}_1^p(x,Q^2)$ as a function of $Q^2$ in intervals of $x$ in comparison to the experimental data of COMPASS16 [68], COMPASS10 [63], EMC [61], SMC [62], E155 [60], E143 [57], HERMES06 [51], and HERMES98 [52, 53].

Figure 3

Polarized deuteron structure function $x{g}_1^d(x,Q^2)$ as a function of $Q^2$ in intervals of $x$ in comparison to the experimental data of COMPASS17 [69], SMC [62], E155 [58, 59], E143 [57], and HERMES06 [51].

Figure 4

Polarized neutron structure function $x{g}_1^n(x,Q^2)$ as a function of $Q^2$ in intervals of $x$ in comparison to the experimental data of E142 [54], E154 [56], HERMES06 [51], and HERMES98 [52, 53].

Figure 5

Our results for NLO polarized parton distributions at ${Q_0}^2=4{\mathrm{GeV}}^2$. The corresponding PPDFs (the solid lines) are shown with error bands compared to results obtained by KATAO [44], BB [37], AAC [31], DSSV [35], GRSV [27], and LSS [13, 14]. For clarity, we only present our fit B results, labeled here as “This Fit.”

Figure 6

Left panels: Polarized parton distributions at $Q_0^2$ as a function of $x$ for our different cases: base (dash-dot-dotted), fit A (dashed), and fit B (solid line) according to Table 1. Only the PPDF error bands for fit B (all data) are shown. Right panels: Polarized parton distribution ratios $\delta f/\delta f_{\text{Base}}$ for fit A (dashed) and fit B (solid line) to base, obtained from our QCD fits to the data. The impact of COMPASS data in the low-$x$ regions is shown in the inset plots.

Figure 7

The COMPASS16 [68] data for the proton structure function $x{g}_1^p(x,Q^2)$ compared with our NLO results calculated at $Q^2=10$, 20, $50{\mathrm{GeV}}^2$.

Figure 8

The COMPASS17 [69] data for the deuteron structure function $x{g}_1^d(x,Q^2)$ compared with our NLO results (“fit B”) calculated at $Q^2=10$, 20, $50{\mathrm{GeV}}^2$.

Figure 9

The strong coupling constant ${\alpha }_s(M_Z^2)$ values as compared with different QCD analyses at NLO [16, 26, 37, 44, 45, 48, 88, 89, 90, 91], NNLO [92, 93, 94, 95, 96, 97, 98], and NNNLO [92, 99]. The dashed line and yellow band shows the world average, ${\alpha }_s(M_Z^2)=0.1181\pm 0.0011$ [87].

Figure 10

NLO nonsinglet polarized structure function $x{g}_1^{\mathrm{NS}}(x,Q^2)$ as a function of $x$ in comparison with the results of KATAO [44] and HERMES experimental data [51].

Figure 11

NLO polarized structure function $x{g}_2^p(x,Q^2)$ and $x{g}_2^d(x,Q^2)$ as a function of $x$ for $Q^2=5$, $6{\mathrm{GeV}}^2$ compared to E143 [57], E155 [103], HERMES [104], and SMC [105] experimental data. We present also the results of different base (dash-dot-dotted), fit A (dashed), and fit B (solid line) QCD fits, which are compared with our previous KATAO (dash-dotted) results.

Figure 12

NLO polarized structure function $x{g}_2(x,Q^2)$ for the proton and deuteron as function of $x$ and for $Q^2=5$, 10, 20, $100{\mathrm{GeV}}^2$.

Figure 13

NLO polarized singlet parton density $x\delta \mathrm{\Sigma }(x)$ at $Q_0^2=4{\mathrm{GeV}}^2$ for this fit (“fit B”) as a function of $x$, compared with results from the literature including KATAO [44], BB [37], AAC [31], DSSV [35], GRSV [27], and LSS [13, 14].