Abstract
The search for new interactions and particles in high-energy collider physics relies on precise background predictions. This has led to many advances in combining precise fixed-order cross-section calculations with detailed event generator simulations. In recent years, fixed-order qcd calculations of inclusive cross sections at n3lo precision have emerged, followed by an impressive progress at producing differential results. Once differential results become publicly available, it would be prudent to embed these into event generators to allow the community to leverage these advances. This note offers some concrete thoughts on me+ps matching at third order in qcd. As a method for testing these thoughts, a toy calculation of e+e− → u overline{u} at mathcal{O} ( {alpha}_s^3 ) is constructed, and combined with an event generator through unitary matching. The toy implementation may serve also as blueprint for high-precision qcd predictions at future lepton colliders. As a byproduct of the n3lo matching formula, a new nnlo+ps formula for processes with “additional” jets is obtained.
Highlights
Introduction to matching up toNNLO precisionIntegrating fixed-order calculations into event generators almost always requires removing the overlap between the parton shower approximation embedded in the event generator and the fixed-order result
The final formula eq (4.12) appears a bit daunting at first glance, but should be easy to understand with the visual help of pairwise cancelling boxes
The Tomte matching formula had been implemented in the Pythia + Dire generator, assuming that the fixed-order results can be supplied by external calculations
Summary
Integrating fixed-order calculations into event generators almost always requires removing the overlap between the parton shower approximation embedded in the event generator and the fixed-order result. Some examples of this notation that will appear repeatedly are given in table 2 Using this notation, the action F of the parton-shower on an ensemble of particles Φn with distribution dσn(0)(Φn) either leads to no change in any observable O (i.e. O will be still evaluated at the phase-space point Φn, i.e. O = O(Φn) ≡ On), or to the decay of one or. Equation (2.3) shows that by construction, no interval [t+, t−] will add to the overall cross section — because the integrated radiation pattern between any two scales is subtracted from the semi-exclusive lowest-multiplicity contribution, such that integrating over the last line will lead to the original distribution dσn(0)(Φn) Viewed slightly differently, this “parton-shower unitarity” can be interpreted as calculating a radiation pattern in the collinear approximation, regularizing the radiation pattern through all-order Sudakov factors (i.e. the second line of eq (2.2)), and subtracting the regularized radiation pattern from the next-lower multiplicity (i.e. the first line of eq (2.2)). This reasoning can be exploited to obtain a more precise calculation, by following the steps
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