Renormalization of the next-to-leading-power soft function for the Drell-Yan off-diagonal channel

A bstract We renormalize the soft function entering the factorization and resummation of the qg parton-scattering channel of the Drell-Yan process near the kinematic threshold $$ \hat{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> </mml:math> → Q 2 at next-to-leading power in the expansion around z ≡ Q 2 / $$ \hat{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> </mml:math> = 1, and solve its renormalization-group equation.