The Spin Budget of the Proton at NNLO and Beyond

Abstract

We revisit the scale evolution of the quark and gluon spin contributions to the proton spin, $\frac{1}{2}\Delta \Sigma$ and $\Delta G$, using the three-loop results for the spin-dependent evolution kernels available in the literature. We argue that the evolution of the quark spin contribution may actually be extended to four-loop order, and that to all orders a single anomalous dimension governs the evolution of both $\Delta \Sigma$ and $\Delta G$. We present analytical solutions of the evolution equations for $\Delta \Sigma$ and $\Delta G$ and investigate their scale dependence both to large and down to lower "hadronic" scales. We find that the solutions remain perturbatively stable even to low scales, where they come closer to simple quark model expectations. We discuss a curious scenario for the proton spin, in which even the gluon spin contribution is essentially scale independent and has a finite asymptotic value as the scale becomes large. We finally also show that perturbative three-loop evolution leads to a larger spin contribution of strange anti-quarks than of strange quarks.

19 pages, 6 figures

References in corpus (11)

• Extraction of Spin-Dependent Parton Densities and Their Uncertainties
• Evidence for polarization of gluons in the proton
• Global Analysis of Helicity Parton Densities and Their Uncertainties
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• Interplay of Spin and Orbital Angular Momentum in the Proton
• Towards the NNLO evolution of polarised parton distributions
• Strange quark asymmetry in the proton in chiral effective theory
• On gamma_5 in higher-order QCD calculations and the NNLO evolution of the polarized valence distribution
• Flavor structure of the unpolarized and longitudinally-polarized sea-quark distributions in the nucleon
• Polarized Gluon Distribution Delta g(x) in the Proton
• Exploring the polarization of gluons in the nucleon

Cited by in corpus (3)

• Jet production in Polarized DIS at NNLO
• Proton spin after 30 years: what we know and what we don't?
• Electroweak boson production at large transverse momentum in double polarized $pp$ scattering at next-to-leading order accuracy