Higher-order soft and virtual corrections in $$p p \rightarrow \gamma W$$ production at the LHC

Abstract We study higher-order QCD corrections beyond NLO for the associated production of a photon with a W boson ( $$\gamma W^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> and $$\gamma W^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> production) at the Large Hadron Collider. We calculate the NNLO soft-plus-virtual QCD corrections as well as the $$\hbox {N}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>N</mml:mtext> <mml:mn>3</mml:mn> </mml:msup> </mml:math> LO soft-gluon corrections to the total production cross section and the photon transverse-momentum distribution in single-particle-inclusive kinematics. The higher-order corrections provide a significant enhancement to the cross section. This is the first calculation of the complete soft-gluon corrections at $$\hbox {N}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>N</mml:mtext> <mml:mn>3</mml:mn> </mml:msup> </mml:math> LO in single-particle-inclusive kinematics for a Standard Model process.