Optimized determination of the polarized Bjorken sum rule in pQCD

We present the method of numerical optimization for the perturbative series using the renormalization group in quantum chromodynamics. We apply our approach to the perturbation series in ${\alpha }_s$ for the coefficient function $C_{\mathrm{Bjp}}({\alpha }_s)$ of the Bjorken sum rule for the polarized deep inelastic lepton-hadron scattering. We optimize the Bjorken sum rule value, ${\mathrm{\Gamma }}_1^{\mathrm{p}\text{−}\mathrm{n}}$, at the COMPASS, SLAC, and JLab kinematics and compare the obtained results with the experimental measurements and also with the truncated Bjorken sum rule predictions.

Figure 1

2D domains for admissible parameters $\{{\overline{\mathrm{\Delta }}}_0,{\overline{\mathrm{\Delta }}}_1\}$ at different $t$, distinguished by different degrees of gray: $t=3$ (dark), $\dots$, $t=8$ (light). The black triangle on the right half plane corresponds to the conditions $c_2^{\prime }=c_3^{\prime }=0$. Blue points (on the left) and red points (on the right) are the bare (global) and the constrained (local) minima of the radiative corrections, respectively.

Figure 2

3D domains for admissible parameters $\{{\overline{\mathrm{\Delta }}}_0,{\overline{\mathrm{\Delta }}}_1,{\overline{\mathrm{\Delta }}}_2\}$ at $t=5$ (left) and $t=8$ (right). The large black ball on the right half plane corresponding to the conditions $c_2^{\prime }=c_3^{\prime }=c_4^{\prime }=0$ does not belong to the admissible region for both the cases. Blue (${\mathrm{\Delta }}_0<0$) and red (${\mathrm{\Delta }}_0>0$) points within the domains denote the bare (global) and the constrained (local) minima of the radiative corrections, respectively, similarly as in Fig. 1.

Figure 3

Comparison of the optimized (black solid curve) and nonoptimized (red solid lower curve) predictions on BSR with the experimental EG1-DVCS data. The impact of the twist-4 correction is also shown (dashed). For better visibility we show the error band only for the optimized plots.