The $$q_T$$ subtraction method: electroweak corrections and power suppressed contributions

Abstract

Abstract Building upon the formulation of transverse-momentum resummation for heavy-quark hadroproduction, we present the first application of the $$q_T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>q</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math> subtraction formalism to the computation of electroweak corrections to massive lepton pairs through the Drell–Yan mechanism. We then study the power suppressed contributions to the $$q_T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>q</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math> subtraction formula in the parameter $$r_{\mathrm{cut}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>r</mml:mi><mml:mi>cut</mml:mi></mml:msub></mml:math> , defined as the minimum transverse momentum of the lepton pair normalised to its invariant mass. We analytically compute the leading power correction from initial and final-state radiation to the inclusive cross section. In the case of initial-state radiation the power correction is quadratic in $$r_{\mathrm{cut}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>r</mml:mi><mml:mi>cut</mml:mi></mml:msub></mml:math> and our analytic result is consistent with results previously obtained in the literature. Final-state radiation produces linear contributions in $$r_{\mathrm{cut}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>r</mml:mi><mml:mi>cut</mml:mi></mml:msub></mml:math> that may challenge the efficiency of the $$q_T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>q</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math> subtraction procedure. We explicitly compute the linear power correction in the case of the inclusive cross section and we discuss the extension of our calculation to differential distributions.

Topics & Concepts