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

Abstract

Approximate knowledge of the renormalon structure of the Bjorken polarised sum rule (BSR) Γ‾1p−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)≡αs(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 (Qmin2,Qmax2) where Qmax2=4.74GeV2. We needed relatively high Qmin2≈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 Qmin2≈0.6GeV2. The preferred values of αs in general cannot be unambiguously extracted, due to large uncertainties of the experimental BSR data. At a fixed value of αsMS‾(MZ2), the values of the D=2 and D=4 residue parameters are determined in all cases, with the corresponding uncertainties.