Quark and gluon helicity evolution at small x: revised and updated

• Published in: The journal of high energy physics Vol. 2022; no. 7; pp. 95 - 83
• Main Authors: Cougoulic, Florian, Kovchegov, Yuri V., Tarasov, Andrey, Tawabutr, Yossathorn
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 15.07.2022; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: Approximation; Classical and Quantum Gravitation; Deep Inelastic Scattering or Small-X Physics; Elementary Particles; Evolution; Flavor (particle physics); Gluons; Helicity; High energy physics; Logarithms; Mathematical analysis; NUCLEAR PHYSICS AND RADIATION PHYSICS; Operators; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; Resummation; String Theory; Deep Inelastic Scattering or Small-X Physics; Resummation
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2022)095

A bstract We revisit the problem of small Bjorken- x evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave ( s -channel) formalism. Earlier works on the subject in the same framework [ 1 – 3 ] resulted in an evolution equation for the gluon field-strength F 12 and quark “axial current” ψ ¯ γ + γ 5 ψ operators (sandwiched between the appropriate light-cone Wilson lines) in the double-logarithmic approximation (summing powers of α s ln 2 (1 /x ) with α s the strong coupling constant). In this work, we observe that an important mixing of the above operators with another gluon operator, D ← i D i , also sandwiched between the light-cone Wilson lines (with the repeated transverse index i = 1 , 2 summed over), was missing in the previous works [ 1 – 3 ]. This operator has the physical meaning of the sub-eikonal (covariant) phase: its contribution to helicity evolution is shown to be proportional to another sub-eikonal operator, D i − D ← i , which is related to the Jaffe-Manohar polarized gluon distribution [ 4 ]. In this work we include this new operator into small- x helicity evolution, and construct novel evolution equations mixing all three operators ( D i − D ← i , F 12 , and ψ ¯ γ + γ 5 ψ ), generalizing the results of [ 1 – 3 ]. We also construct closed double-logarithmic evolution equations in the large- N c and large- N c & N f limits, with N c and N f the numbers of quark colors and flavors, respectively. Solving the large- N c equations numerically we obtain the following small- x asymptotics of the quark and gluon helicity distributions ∆Σ and ∆ G , along with the g 1 structure function, ∆ Σ x Q 2 ∼ ∆ G x Q 2 ∼ g 1 x Q 2 ∼ 1 x 3.66 α s N c 2 π in complete agreement with the earlier work by Bartels, Ermolaev and Ryskin [ 5 ].