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 ( Q 2 ) 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 ( Q 2 ) ≡ α s ( Q 2 ) / π in specific renormalisation schemes. In the present paper, we continue this work, by using instead holomorphic couplings [ a ( Q 2 ) ↦ A ( Q 2 ) ] 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 min 2 , Q max 2 ) where Q max 2 = 4.74 GeV 2 . We needed relatively high Q min 2 ≈ 1.7 GeV 2 in the pQCD case since the pQCD coupling a ( Q 2 ) has Landau singularities at Q 2 ≲ 1 GeV 2 . Now, when holomorphic (AQCD) couplings A ( Q 2 ) are used, no such problems occur: for the 3 δ AQCD and 2 δ AQCD variants the preferred values are Q min 2 ≈ 0.6 GeV 2 . 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 Z 2 ) , the values of the D = 2 and D = 4 residue parameters are determined in all cases, with the corresponding uncertainties.