Higher order perturbative and nonperturbative QCD corrections on the proton structure functions and parity violating electron asymmetry

Abstract

We study the nonperturbative and higher order perturbative corrections on the electromagnetic ($F_{1p,2p}^γ$) and electromagnetic-weak interference ($F_{1p,2p,3p}^{γZ}$) structure functions and their impact on the parity violating electron asymmetry in the deep inelastic scattering of longitudinally polarized electron off an unpolarized proton target. The numerical results for them are presented by including the perturbative corrections beyond the leading order (LO) up to the next-next-to-leading-order (NNLO) and nonperturbative QCD corrections due to the target mass corrections (TMC) and the higher twist (HT: twist-4) effects. We also present the numerical results for the electron beam spin asymmetry $A_{PV}^{(e)}(x,Q^2)$ corresponding to the JLab energies of 6 GeV, 12 GeV and 22 GeV and discuss the feasibility of determining the $d/u$ quark distribution ratio. The results obtained in this work may be useful for the analysis of future measurements at the Electron Ion Collider(EIC) in USA, and the Electron ion collider in China(EicC) aimed at studying parity violating effects in the deep inelastic scattering of polarized electrons from unpolarized proton targets.

Figures (11)

• Figure 1: Diagrammatic representation of parity-violating contribution to the DIS which results from the interaction of purely electromagnetic ($\gamma^\ast$ exchange) and purely weak ($Z$ exchange) amplitudes .
• Figure 2: Results for the unpolarized proton electroweak structure functions $2 x F_{1p} (x,Q^2)$ (top panel) vs $x$ at the different values of $Q^2$ incorporating the contributions from $\gamma$ and $\gamma Z$ exchanges. The evaluation is performed at LO, NLO and NNLO without and with the nonperturbative effects like TMC and HT (as mentioned in the legends of the figure). These results are obtained using MMHT14 PDFs parameterization Harland-Lang:2014zoa in the MSbar scheme. In the bottom panel of the figure relative corrections are presented to explicitly show the contributions from perturbative and nonperturbative effects (as mentioned in the legends of the figure).
• Figure 3: Results for the unpolarized proton electroweak structure functions $F_{2p} (x,Q^2)$ (top panel) vs $x$ at the different values of $Q^2$ incorporating the contributions from $\gamma$ and $\gamma Z$ exchanges. These results are compared with the experimental data corresponding to the interaction via pure photon exchange Whitlow:1991uwBenvenuti:1989rhArneodo:1996rvAubert:1985fx. The lines have the same meaning as in Fig. \ref{['res1a']}.
• Figure 4: Results for the unpolarized proton electroweak structure functions $x F_{3p} (x,Q^2)$ (top panel) vs $x$ at the different values of $Q^2$ incorporating the contributions from $\gamma$ and $\gamma Z$ exchanges ($x F_{3p}^{\gamma} (x,Q^2)=0$). The lines have the same meaning as in Fig. \ref{['res1a']}.
• Figure 5: Results for the ratio $r_{p}^{\gamma }(x,Q^2)=\frac{F_{2p}^{\gamma}(x,Q^2)}{2 x F_{1p}^{\gamma}(x,Q^2)}$ (top panel) and $r_{p}^{\gamma Z}(x,Q^2)=\frac{F_{2p}^{\gamma Z}(x,Q^2)}{2 x F_{1p}^{\gamma Z}(x,Q^2)}$ (bottom panel) vs $x$ at the different values of $Q^2$. The evaluation is performed at LO, NLO and NNLO without and with the nonperturbative effects like TMC and HT (as mentioned in the legends of the figure). These results are obtained using MMHT14 PDFs parameterization Harland-Lang:2014zoa in the MSbar scheme.