Abstract
Discriminating quark jets from gluon jets is an important but challenging problem in jet substructure. In this paper, we use the concept of mutual information to illuminate the physics of quark/gluon tagging. Ideal quark/gluon separation requires only one bit of truth information, so even if two discriminant variables are largely uncorrelated, they can still share the same "truth overlap". Mutual information can be used to diagnose such situations, and thus determine which discriminant variables are redundant and which can be combined to improve performance. Using both parton showers and analytic resummation, we study a two-parameter family of generalized angularities, which includes familiar infrared and collinear (IRC) safe observables like thrust and broadening, as well as IRC unsafe variants like $p_T^D$ and hadron multiplicity. At leading-logarithmic (LL) order, the bulk of these variables exhibit Casimir scaling, such that their truth overlap is a universal function of the color factor ratio $C_A/C_F$. Only at next-to-leading-logarithmic (NLL) order can one see a difference in quark/gluon performance. For the IRC safe angularities, we show that the quark/gluon performance can be improved by combining angularities with complementary angular exponents. Interestingly, LL order, NLL order, Pythia 8, and Herwig++ all exhibit similar correlations between observables, but there are significant differences in the predicted quark/gluon discrimination power. For the IRC unsafe angularities, we show that the mutual information can be calculated analytically with the help of a nonperturbative "weighted-energy function", providing evidence for the complementarity of safe and unsafe observables for quark/gluon discrimination.
Highlights
Jets are collimated sprays of hadrons that act as proxies for short-distance quarks and gluons
For the infrared and collinear (IRC) unsafe angularities, we show that the mutual information can be calculated analytically with the help of a nonperturbative “weighted-energy function”, providing evidence for the complementarity of safe and unsafe observables for quark/gluon discrimination
Robust quark/gluon discrimination is a key goal for the jet substructure community, so to the extent possible, it is important to use first principles calculations to assess the challenges and opportunities
Summary
Jets are collimated sprays of hadrons that act as proxies for short-distance quarks and gluons. We will present analytic calculations and parton shower simulations to understand the quark/gluon discrimination power of the λκβ variables. For κβ 0.5, just the first (logarithmic) moment of this function enters at NLL As long as these moments are sufficiently small, we can predict the quark/gluon tagging performance for an individual λκβ to NLL accuracy, as well as study correlations between two IRC unsafe angularities to NLL. For the analytic predictions in this paper, we will adopt a pragmatic definition: a quark (gluon) jet is what results from the showering of a quark (gluon) parton. This was the strategy used in ref.
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