Iterative Monte Carlo analysis of spin-dependent parton distributions

TL;DR

This work introduces a novel iterative Monte Carlo fitting approach to global QCD analyses of spin-dependent parton distributions, enabling robust extraction of leading- and higher-twist PDFs with statistically rigorous uncertainties. By performing calculations in Mellin space and incorporating target mass corrections, nuclear smearing, and twist-3/4 contributions, the study leverages extensive world DIS data plus new Jefferson Lab measurements to constrain valence and sea quark polarizations and the gluon polarization. The JAM15 analysis yields a precise determination of Δu^+, Δd^+, Δs^+, and ΔG with reduced uncertainties, and for the first time provides flavor-separated twist-3 D_q distributions and d2 moments, consistent with lattice QCD for protons and offering insights into neutron structure. The results demonstrate significant improvements in uncertainties, particularly at intermediate x, and set the stage for future inclusion of semi-inclusive data and polarized pp collision observables to further refine the spin decomposition of the proton.

Abstract

We present a comprehensive new global QCD analysis of polarized inclusive deep-inelastic scattering, including the latest high-precision data on longitudinal and transverse polarization asymmetries from Jefferson Lab and elsewhere. The analysis is performed using a new iterative Monte Carlo fitting technique which generates stable fits to polarized parton distribution functions (PDFs) with statistically rigorous uncertainties. Inclusion of the Jefferson Lab data leads to a reduction in the PDF errors for the valence and sea quarks, as well as in the gluon polarization uncertainty at $x \gtrsim 0.1$. The study also provides the first determination of the flavor-separated twist-3 PDFs and the $d_2$ moment of the nucleon within a global PDF analysis.

Figures (18)

• Figure 1: Schematic illustration of the workflow for the iterative Monte Carlo fitting method. In the first stage, $K$ pseudodata sets are generated, each of which is partitioned into training (T) and validation (V) subsets. For each pseudodata set, the training set is fitted and the parameters $\{ \vec{p}^{(j)} \}$ across all the minimization stages $j$ are stored. The cross-validation procedure selects a single set of best fit parameters $\vec{a}^{(l)}$ from $\{ \vec{p}^{(j)} \}$ for each pseudodata set $l$, and the collection of $\{ \vec{a}^{(l)}; l=1,\ldots,K \}$ is then used as the priors for the next iteration.
• Figure 2: Mean and two-sided standard deviations of the $\chi^2_{\rm dof}$ distribution as a function of the iteration number for the training (blue points) and validation (red points) data sets, compared with the mean (dashed horizontal line at $\chi^2_{\rm dof}=2$) and standard deviation (yellow band) for the ideal noncentral $\chi^2_{\rm dof}$ distribution.
• Figure 3: Kinematic coverage in $x$ and $Q^2$ of the polarized inclusive DIS data sets used in the JAM15 analysis. The boundaries corresponding to fixed $W^2 = M^2 + Q^2 (1-x)/x$ equal to 4 GeV$^2$ (solid curve) and 10 GeV$^2$ (dashed curve) are indicated.
• Figure 4: Dependence on $W^2_{\rm cut}$ of several moments of twist-2 PDFs ($\Delta\Sigma$ and $\Delta G$), the twist-3 $d_2$ moments, and the third moments $h_p$ and $h_n$ of the twist-4 distributions of the proton and neutron. All fits use $Q^2_{\rm cut} = 1$ GeV$^2$, and the moments are truncated moments evaluated in the measured region between $x=0.001$ and 0.8.
• Figure 5: As in Fig. \ref{['f.mom_vs_W2']}, but for varying values of $Q^2_{\rm cut}$ between 1 and 4 GeV$^2$, for a fixed $W^2_{\rm cut} = 4$ GeV$^2$.