Factorization for groomed jet substructure beyond the next-to-leading logarithm

Abstract

Jet grooming algorithms are widely used in experimental analyses at hadron colliders to remove contaminating radiation from within jets. While the algorithms perform a great service to the experiments, their intricate algorithmic structure and multiple parameters has frustrated precision theoretic understanding. In this paper, we demonstrate that one particular groomer called soft drop actually makes precision jet substructure easier. In particular, we derive a factorization formula for a large class of soft drop jet substructure observables, including jet mass. The essential observation that allows for this factorization is that, without the soft wide-angle radiation groomed by soft drop, all singular contributions are collinear. The simplicity and universality of the collinear limit in QCD allows us to show that to all orders, the normalized differential cross section has no contributions from non-global logarithms. It is also independent of process, up to the relative fraction of quark and gluon jets. In fact, soft drop allows us to define this fraction precisely. The factorization theorem also explains why soft drop observables are less sensitive to hadronization than their ungroomed counterparts. Using the factorization theorem, we resum the soft drop jet mass to next-to-next-to-leading logarithmic accuracy. This requires calculating some clustering effects that are closely related to corresponding effects found in jet veto calculations. We match our resummed calculation to fixed order results for both e + e − → dijets and pp → Z + j events, producing the first jet substructure predictions (groomed or ungroomed) to this accuracy for the LHC. arXiv:1603.09338v2 [hep-ph] 11 Jul 2016 Contents 1. Recluster the jet with a sequential k T -type [45-47] jet algorithm. This produces an infrared and collinear (IRC) safe branching history of the jet. The k T clustering metric 1 While we will not do it in this paper, one could use the results of Ref. [36] which calculates the anomalous dimension of the soft function for event-wide (recoil-free) angularities [37-40] or energy correlation functions with arbitrary angular exponent. This would enable us to extend our results to the case with α = 2. 2 The jet mass has been calculated at NNLL using other methods [41-43] as has 2-subjettiness [44]. However, without grooming the jets, there are non-global logarithms which are not resummed (and which may or may not be quantitatively important) and uncontrollable sensitivity to pileup (which is very quantitatively important).

Improved jet substructure methods: Y-splitter and variants with grooming

“…[8,12]. Analytical calculations have also been performed for the SoftDrop method [13][14][15] and for radiation constraining jet shapes [16,17] based on the N-subjettiness class of variables [18] and energy correlation functions (ECFs) [19]. These calculations have enabled a much more detailed and robust understanding of jet substructure methods than was possible with purely numerical studies from Monte Carlo event generators.…”

“…(2.8) can be written in the form 1 σ dσ dρ 14) where the first term on the r.h.s. contains the leading logarithms in ρ while the second term is subleading in ρ (being purely single logarithmic), although it is enhanced by logarithmic terms in y.…”

“…Furthermore, (4.8) is also largely unaffected by a possible mMDT or trimming one would apply after the Y m -splitter condition since the latter guarantees that the emission that dominates the mass carries a momentum fraction larger than y cut . 14 Compared to the pure Y-splitter case, eq. (2.16), we should expect the pre-groomed result (4.8) to show a worse performance.…”

“…Between Y-splitter and Y m -splitter conditions, we have limited ourselves to the latter, since it has a slightly better performance than the former. 15 We have considered both a y cut and a z cut type of JHEP12 (2016) condition, using in practice y cut = z cut = 0.1. We have then studied 4 grooming options: the ungroomed (or pure) case which acts as a baseline, mMDT and trimming both applied after the Y m -splitter condition, and SoftDrop pre-grooming for which the Y m -splitter condition is applied after the pre-grooming.…”

Novel subjet observables for jet quenching in heavy-ion collisions

“…However, in all these measurements the treatment of the background originating from the copiously produced particles not associated to hard scatterings poses an experimental challenge for precise and unbiased measurements. Previous works that addressed the effect of filtering a e-mail: liliana@lip.pt b e-mail: guilherme.milhano@ist.utl.pt c e-mail: mploskon@lbl.gov d e-mail: xiaoming.zhang@cern.ch on subjet analysis [26] and the recent analytic calculations of the momentum distributions of subjets [27][28][29] and groomed jet mass distributions [30][31][32] that were recently measured in proton-proton collisions [33,34], provide a strong motivation for novel studies. In this writeup, following previous works [35], we propose observables that are sensitive to the internal jet structure but significantly alleviate the difficulties associated to the effects of the background.…”