arXiv : Logarithmic accuracy of parton showers: a fixed-order study

Dasgupta, Mrinal; Salam, Gavin P.; Monni, Pier Francesco; Dreyer, Frédéric A.; Hamilton, Keith

doi:10.1007/JHEP09(2018)033

Article
Report number	arXiv:1805.09327 ; CERN-TH-2018-113
Title	Logarithmic accuracy of parton showers: a fixed-order study
Author(s)	Dasgupta, Mrinal (Manchester U.) ; Dreyer, Frédéric A. (MIT, Cambridge, CTP) ; Hamilton, Keith (University Coll. London ; CERN) ; Monni, Pier Francesco (CERN) ; Salam, Gavin P. (CERN ; MIT)
Publication	2018-09-07
Imprint	2018-05-23
Number of pages	33
Note	23+10 pages, 5+1 figures; v2 updates acknowledgements and references; v3 includes additional references, published in JHEP; v4 corrects the results for the thrust and vector pt, with unchanged conclusions
In:	JHEP 09 (2018) pp.033
DOI	10.1007/JHEP09(2018)033 10.1007/JHEP03(2020)083 (Erratum)
Subject category	hep-ex ; Particle Physics - Experiment ; hep-ph ; Particle Physics - Phenomenology
Abstract	We formulate some first fundamental elements of an approach for assessing the logarithmic accuracy of parton-shower algorithms based on two broad criteria: their ability to reproduce the singularity structure of multi-parton matrix elements, and their ability to reproduce logarithmic resummation results. We illustrate our approach by considering properties of two transverse momentum ordered final-state showers, examining features up to second order in the strong coupling. In particular we identify regions where they fail to reproduce the known singular limits of matrix elements. The characteristics of the shower that are responsible for this also affect the logarithmic resummation accuracies of the shower, both in terms of leading (double) logarithms at subleading $N_C$ and next-to-leading (single) logarithms at leading $N_C$.
Copyright/License	publication: (License: CC-BY-4.0) preprint: (License: CC BY-NC-SA 4.0)

$(a) The accessible contour of emissions in the $\eta{-}\ln p_\perp$ (``Lund'' \cite{Andersson:1988gp}) plane for fixed values of the ordering variable $v$, for splittings of a right-going quark, shown for both the \pythia and \dire shower kernels. The phase-space boundary is sometimes alternatively described as the hard-collinear limit. (b) The splitting weights associated with emissions as a function of rapidity from the (right-going) quark and (left-going) anti-quark, normalised so as to be $1$ in the soft-collinear region. This holds for both \pythia and \dire. The weights are independent of $v$, as long as $v/Q \ll e^{-|\eta|}$, i.e.\ as long as one is far from the phase-space boundary shown in (a). The rapidity is defined in the $q\bar q$ dipole centre-of-mass frame.$ $Difference between the third-order expansion of the dipole showers considered in this manuscript and the correct result obtained from analytic resummation at NLL, both for thrust (\ref{fig:thrust_as3}) and for the vectorial $p_t$ sum (\ref{fig:ptsum_as3}). The data points correspond to the Monte Carlo result, divided by $\abar^3 L^2$ so that a term proportional to $\abar^3 L^3$ appears as a straight line, while the solid line is the resulting fit in the $L\in[-14,-6]$ range.$ $(a) The accessible contour of emissions in the $\eta{-}\ln p_\perp$ (``Lund'' \cite{Andersson:1988gp}) plane for fixed values of the ordering variable $v$, for splittings of a right-going quark, shown for both the \pythia and \dire shower kernels. The phase-space boundary is sometimes alternatively described as the hard-collinear limit. (b) The splitting weights associated with emissions as a function of rapidity from the (right-going) quark and (left-going) anti-quark, normalised so as to be $1$ in the soft-collinear region. This holds for both \pythia and \dire. The weights are independent of $v$, as long as $v/Q \ll e^{-|\eta|}$, i.e.\ as long as one is far from the phase-space boundary shown in (a). The rapidity is defined in the $q\bar q$ dipole centre-of-mass frame.$ Show more plots

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