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

A bstract: We construct a QCD coupling $$ \mathcal{A} $$ A ( Q ² ) in the Effective Charge (ECH) scheme of the canonical part d ( Q ² ) of the (inelastic) polarised Bjorken Sum Rule (BSR) $$ {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} $$ Γ ¯ 1 p − n ( Q ² ). In the perturbative domain, the coupling $$ \mathcal{A} $$ A ( Q ² ) practically coincides with the perturbative coupling a ( Q ² ) [≡ α _s ( Q ² )/ π ] in the four-loop ECH renormalisation scheme. In the deep infrared (IR) regime, $$ \mathcal{A} $$ A ( Q ² ) behaves as suggested by the Holographic Light-Front QCD up to the second derivative. Furthermore, in contrast to its perturbative counterpart a ( Q ² ), the coupling $$ \mathcal{A} $$ A ( Q ² ) is holomorphic in the entire complex Q ² -plane with the exception of the negative semiaxis, reflecting the holomorphic properties of the BSR observable d ( Q ² ) [or: $$ {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} $$ Γ ¯ 1 p − n ( Q ² )] 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 ( Q ² ) in the entire N _f = 3 regime 0 < Q ² ≲ 5 GeV ² .