Abstract
We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.
Highlights
For qT ∼ Q m, Z is a good approximation of the full cross section, but as qT decreases the accuracy of the collinear approximation diminishes, which breaks down as qT approaches m
In this paper we introduce a new scheme, the inverse-error weighting (InEW for short), where the power corrections to the factorization theorems are used to quantify the trustworthiness associated to the respective contributions, and employed to build a weighted average
This work contributes to such an effort by introducing a new matching scheme: the inverse-error weighting (InEW )
Summary
In processes with a hard scale Q and a measured transverse momentum qT , for instance the mass and the transverse momentum of an electroweak boson produced in proton–proton collisions, the qT -differential cross section can be expressed through two different factorization theorems. This work contributes to this effort by introducing a new approach, whose main features are its simplicity and its easy and fast implementation in phenomenological analyses (fits and/or Monte Carlo event generators) This scheme provides an automatic estimate of the theoretical uncertainty associated to the matching procedure. [15]), which refines the original CSS subtraction approach [16,17,18,19] The latter, in simple terms, is based on adding the TMD-based resummed (W ) and collinear-based fixed-order (Z) results, and subtracting the double-counted contributions (A ). We avoid the double counting (and therewith the subtraction of A ) by weighting both contributions to the matched cross section, with the condition that the weights add up to unity.
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