Renormalon-based resummation of Bjorken polarised sum rule in holomorphic QCD

Approximate knowledge of the renormalon structure of the Bjorken polarised sum rule (BSR) Γ‾₁^p−n(Q²) leads to the corresponding BSR characteristic function that allows us to evaluate the leading-twist part of BSR. In our previous work [1], this evaluation (resummation) was performed using perturbative QCD (pQCD) coupling a(Q²)≡α_s(Q²)/π in specific renormalisation schemes. In the present paper, we continue this work, by using instead holomorphic couplings [a(Q²)↦A(Q²)] that have no Landau singularities and thus require, in contrast to the pQCD case, no regularisation of the resummation formula. The D=2 and D=4 terms are included in the Operator Product Expansion (OPE) of inelastic BSR, and fits are performed to the available experimental data in a specific interval (Q_min²,Q_max²) where Q_max²=4.74GeV². We needed relatively high Q_min²≈1.7GeV² in the pQCD case since the pQCD coupling a(Q²) has Landau singularities at Q²≲1GeV². Now, when holomorphic (AQCD) couplings A(Q²) are used, no such problems occur: for the 3δAQCD and 2δAQCD variants the preferred values are Q_min²≈0.6GeV². The preferred values of α_s in general cannot be unambiguously extracted, due to large uncertainties of the experimental BSR data. At a fixed value of α_s^MS‾(M_Z²), the values of the D=2 and D=4 residue parameters are determined in all cases, with the corresponding uncertainties.