Rapidity evolution of TMDs with running coupling

The scale of a coupling constant for rapidity-only evolution of transverse-momentum dependent (TMD) operators in the Sudakov kinematic region is calculated using the Brodsky-Lepage-Mackenzie optimal scale setting [S. J. Brodsky et al., Phys. Rev. D 28, 228 (1983).]. The effective argument of a coupling constant is halfway in the logarithmical scale between the transverse momentum and energy of TMD distribution. The resulting rapidity-only evolution equation is solved for quark and gluon TMDs.

Automated summary

The scale of a coupling constant for rapidity-only evolution of transverse-momentum dependent (TMD) operators in the Sudakov kinematic region has been calculated using the Brodsky-Lepage-Mackenzie optimal scale setting. The effective argument of a coupling constant is located halfway on the logarithmical scale between the transverse momentum and energy of TMD distributions. The resulting rapidity-only evolution equation has been solved for quark and gluon TMDs.