  In the present paper, we first give a detailed study on the pQCD corrections
to the leading-twist part of BSR. Previous pQCD corrections to the
leading-twist part derived under conventional scale-setting approach up to
${\cal O}(\alpha_s^4)$-level still show strong renormalization scale
dependence. The principle of maximum conformality (PMC) provides a systematic
way to eliminate conventional renormalization scale-setting ambiguity by
determining the accurate $\alpha_s$-running behavior of the process with the
help of renormalization group equation. Our calculation confirms the PMC
prediction satisfies the standard renormalization group invariance, e.g. its
fixed-order prediction does scheme-and-scale independent. In low $Q^2$-region,
the effective momentum of the process is small and to have a reliable
prediction, we adopt four low-energy $\alpha_s$ models to do the analysis. Our
predictions show that even though the high-twist terms are generally power
suppressed in high $Q^2$-region, they shall have sizable contributions in low
and intermediate $Q^2$ domain. By using the more accurate scheme-and-scale
independent pQCD prediction, we present a novel fit of the non-perturbative
high-twist contributions by comparing with the JLab data.
