The qT and ∆ϕ spectra in W and Z production at the LHC at N3LL′+N2LO
Wan-Li Ju, Marek Schönherr
Abstract
A bstract The production of weak gauge bosons, W ± and Z , are at the core of the LHC precision measurement program. Their transverse momentum spectra as well as their pairwise ratios are key theoretical inputs to many high-precision analyses, ranging from the W mass measurement to the determination of parton distribution functions. Owing to the different properties of the W and Z boson and the different accessible fiducial regions for their measurement, a simple one-dimensional correlation is insufficient to capture the differing vector and axial-vector dynamics of the produced lepton pair. We propose to correlate them in two observables, the transverse momentum q T of the lepton pair and its azimuthal separation ∆ ϕ . Both quantities are purely transverse and therefore accessible in all three processes, either directly or by utilising the missing transverse momentum of the event. We calculate all the single-differential q T and ∆ ϕ as well as the double-differential ( q T , ∆ ϕ ) spectra for all three processes at N 3 LL ′ +N 2 LO accuracy, resumming small transverse momentum logarithms in the soft-collinear effective theory approach and including all singlet and non-singlet contributions. Using the double-differential cross sections we build the pairwise ratios $$ {\mathrm{\mathcal{R}}}_{W^{+}/Z} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℛ</mml:mi> <mml:mrow> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>Z</mml:mi> </mml:mrow> </mml:msub> </mml:math> , $$ {\mathrm{\mathcal{R}}}_{W^{-}/Z} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℛ</mml:mi> <mml:mrow> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>Z</mml:mi> </mml:mrow> </mml:msub> </mml:math> , and $$ {\mathrm{\mathcal{R}}}_{W^{+}/{W}^{-}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℛ</mml:mi> <mml:mrow> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:mrow> </mml:msub> </mml:math> and determine their uncertainties assuming fully correlated, partially correlated, and uncorrelated uncertainties in the respective numerators and denominators. In the preferred partially correlated case we find uncertainties of less than 1% in most phase space regions and up to 3% in the lowest q T region.