Towards unifying perturbative and Holographic Light-Front QCD via holomorphic coupling

Abstract

We construct a QCD coupling $$ \mathcal{A} $$ A (Q2) in the Effective Charge (ECH) scheme of the canonical part d(Q2) of the (inelastic) polarised Bjorken Sum Rule (BSR) $$ {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} $$ Γ ¯ 1 p − n (Q2). In the perturbative domain, the coupling $$ \mathcal{A} $$ A (Q2) practically coincides with the perturbative coupling a(Q2) [≡ αs(Q2)/π] in the four-loop ECH renormalisation scheme. In the deep infrared (IR) regime, $$ \mathcal{A} $$ A (Q2) behaves as suggested by the Holographic Light-Front QCD up to the second derivative. Furthermore, in contrast to its perturbative counterpart a(Q2), the coupling $$ \mathcal{A} $$ A (Q2) is holomorphic in the entire complex Q2-plane with the exception of the negative semiaxis, reflecting the holomorphic properties of the BSR observable d(Q2) [or: $$ {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} $$ Γ ¯ 1 p − n (Q2)] as dictated by the general principles of the Quantum Field Theory. It turns out that the obtained coupling, used as ECH, reproduces quite well the experimental data for $$ {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} $$ Γ ¯ 1 p − n (Q2) in the entire Nf = 3 regime 0 < Q2 ≲ 5 GeV2.