Proton structure from a light-front Hamiltonian

We obtain the electromagnetic form factors, the axial form factor, and the parton distribution functions of the proton from the eigenstates of a light-front effective Hamiltonian in the leading Fock representation suitable for low-momentum scale applications. The electromagnetic and the axial form factors are found to be in agreement with the available experimental data. The unpolarized, the helicity, and the transversity valence quark distributions, after QCD evolution, are consistent with the global QCD analyses. The tensor charge also agrees the experimental data, while the axial charge is somewhat outside the experimental error bar.

Figure 1

Proton Sach’s FFs $G_E^p(Q^2)$ (upper panel), and $G_M^p(Q^2)$ (lower panel) as functions of $Q^2$. The gray and cyan bands are BLFQ results, when $\{m_{\mathrm{KE}},m_{\mathrm{OGE}}\}=\{0.3,0.2\}\mathrm{GeV}$ and $\{m_{\mathrm{KE}},m_{\mathrm{OGE}}\}=\{0.3,0.3\}\mathrm{GeV}$ respectively, reflecting our ${\alpha }_s$ uncertainty of 10%. The experimental data are taken from Refs. [91, 92, 93, 94, 95, 96] and [93, 97].

Figure 2

Axial-vector form factor $G_A=G_A^u-G_A^d$ as function of $Q^2$. The gray band is the BLFQ result. The extracted data are taken from the Refs. [106, 107] and the lattice data from [108]. The dashed line represents the dipole fit of the experimental data [106].

Figure 3

Top panel: comparison for $x{f}_1(x)$ in the proton from BLFQ (gray bands) and global fits: MMHT14 [39] (cyan bands), NNPDF3.0 [38] (red bands), and CTEQ15 [40] (blue line). Second panel: comparison for $x{g}_1(x)$ in the proton from BLFQ (black bands) and measured data from COMPASS [52]. Lower two panel: Comparison for $x{h}_1(x)$ in the proton from BLFQ (gray bands) and global analyses by Radici et al. [81] (cyan bands) and Anselmino et al. [74] (pink bands), and [116] (red bands).