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

Abstract

Abstract We construct a QCD coupling A $$ \mathcal{A} $$ (Q 2) in the Effective Charge (ECH) scheme of the canonical part d(Q 2) of the (inelastic) polarised Bjorken Sum Rule (BSR) Γ ¯ 1 p − n $$ {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} $$ (Q 2). In the perturbative domain, the coupling A $$ \mathcal{A} $$ (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, A $$ \mathcal{A} $$ (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 A $$ \mathcal{A} $$ (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: Γ ¯ 1 p − n $$ {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} $$ (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 Γ ¯ 1 p − n $$ {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} $$ (Q 2) in the entire N f = 3 regime 0 < Q 2 ≲ 5 GeV2.

Keywords

• The Strong Coupling
• Deep Inelastic Scattering or Small-x Physics
• Resummation