Evolution of twist-3 multi-parton correlation functions relevant to single transverse-spin asymmetry

TL;DR

The paper develops a comprehensive framework to understand the scale dependence of twist-3 multi-parton correlation functions that generate single transverse-spin asymmetries in QCD collinear factorization. By constructing two sets of twist-3 correlators, including diagonal and off-diagonal (x and x+x2) components and fermionic-pole related functions, the authors derive a closed but gauge-consistent set of evolution equations and compute the corresponding order αs evolution kernels using a Feynman-diagram approach with cut vertices. They demonstrate that all kernels are infrared-safe and show that diagonal kernels closely follow DGLAP-like behavior, while off-diagonal contributions become significant at small x, necessitating a global analysis for SSA phenomenology. The work lays groundwork for incorporating NLO corrections into SSA predictions and for extracting twist-3 correlators from data via a full QCD analysis. Future studies will extend to the complete off-diagonal sector and perform global fits to SSA measurements.

Abstract

We constructed two sets of twist-3 correlation functions that are responsible for generating the novel single transverse-spin asymmetry in the QCD collinear factorization approach. We derive evolution equations for these universal three-parton correlation functions. We calculate evolution kernels relevant to the gluonic pole contributions to the asymmetry at the order of $α_s$. We find that all evolution kernels are infrared safe as they should be and have a lot in common to the DGLAP evolution kernels of unpolarized parton distributions. By solving the evolution equations, we explicitly demonstrate the factorization scale dependence of these twist-3 correlation functions.

Figures (17)

• Figure 1: Feynman diagrams that contribute to the twist-3 quark-gluon (a) and tri-gluon (b) correlation functions. $\alpha,\beta,\mu$ and $a,b,c$ are Lorentz and color indices of gluon field operators, respectively.
• Figure 2: Feynman diagrams that contribute to the flavor non-singlet change of the twist-3 quark-gluon correlation function where $\mu,\rho$ and $c$ are Lorentz and color indices of gluon field operators, respectively. The lower part of quark and gluon lines are contracted to the cut vertex that define the quark-gluon correlation function.
• Figure 3: Partonic Feynman diagrams that contribute to the evolution kernels of the twist-3 correlation functions.
• Figure 4: Feynman diagrams that contribute to the change of the twist-3 tri-gluon correlation functions where $\alpha,\beta,\mu,\rho$ and $a,b,c$ are Lorentz and color indices of gluon field operators, respectively. The lower part of gluon lines are contracted to the cut vertices that define the tri-gluon correlation functions.
• Figure 5: Feynman diagrams that contribute to the change of the twist-3 quark-gluon correlation function where $\alpha,\beta,\mu,\rho$ and $a,b,c$ are Lorentz and color indices of gluon field operators, respectively. The lower part of quark and gluon lines are contracted to the cut vertex that defines the quark-gluon correlation function.