A short note on a Bernstein-Bezier basis for the pyramid

We introduce a Bernstein-Bezier basis for the pyramid, whose restriction to the face reduces to the Bernstein-Bezier basis on the triangle or quadrilateral. The basis satisfies the standard positivity and partition of unity properties common to Bernstein polynomials, and spans the same space as non-polynomial pyramid bases in the literature.Comment: Submitte

Aspects of Track-Assisted Mass

Track-assisted mass is a proxy for jet mass that only uses direction information from charged particles, allowing it to be measured at the Large Hadron Collider with very fine angular resolution. In this paper, we introduce a generalization of track-assisted mass and analyze its performance in both parton shower generators and resummed calculations. For the original track-assisted mass, the track-only mass is rescaled by the charged energy fraction of the jet. In our generalization, the rescaling factor includes both per-jet and ensemble-averaged information, facilitating a closer correspondence to ordinary jet mass. Using the track function formalism in electron-positron collisions, we calculate the spectrum of generalized track-assisted mass to next-to-leading-logarithmic order with leading-order matching. These resummed calculations provide theoretical insight into the close correspondence between track-assisted mass and ordinary jet mass. With the growing importance of jet grooming algorithms, we also calculate track-assisted mass on soft-drop groomed jets.Comment: 35+17 pages, 22 figures; v3: improvements to calculation and presentation to appear in JHE

Energy flow polynomials: A complete linear basis for jet substructure

We introduce the energy flow polynomials: a complete set of jet substructure observables which form a discrete linear basis for all infrared- and collinear-safe observables. Energy flow polynomials are multiparticle energy correlators with specific angular structures that are a direct consequence of infrared and collinear safety. We establish a powerful graph-theoretic representation of the energy flow polynomials which allows us to design efficient algorithms for their computation. Many common jet observables are exact linear combinations of energy flow polynomials, and we demonstrate the linear spanning nature of the energy flow basis by performing regression for several common jet observables. Using linear classification with energy flow polynomials, we achieve excellent performance on three representative jet tagging problems: quark/gluon discrimination, boosted W tagging, and boosted top tagging. The energy flow basis provides a systematic framework for complete investigations of jet substructure using linear methods.Comment: 41+15 pages, 13 figures, 5 tables; v2: updated to match JHEP versio

Agricultural Arbitrage, Adjustment Costs, and the Intensive Margin

Farmland and capital are an important and rapidly expanding component of the agricultural economy, and empirical evidence suggests that these assets are quasi-fixed in that adjustment costs are incurred when holdings are altered. Increased interest in the rate of return for investing in farmland suggests that an important consideration is the effect of adjustment costs on this return. A novel theoretical model is developed that ties together contributions from the farmland pricing and adjustment cost literatures, and the first order conditions for a utility maximizing decision maker are rearranged into intertemporal arbitrage equations that are similar in spirit to traditional finance models. The common assumptions that land and capital are quasi-fixed assets, and that production is characterized by constant returns to scale are tested and the evidence supports these assumptions. An empirical application of the arbitrage equations provides evidence that risk aversion and adjustment costs are jointly significant components of agricultural production, and that adjustment costs generate significant changes in the rate of return to farmland. The results have important policy implications as sluggish supply response due to quasi-fixity can lead to dramatically inflated commodity prices, and an accurate measure of the farmland return can help determine how far the extensive margin will expand or contract in response to a variety of policy scenarios, such as the subsidization of corn for ethanol, an increase in the variety of subsidized crop insurance products, or the introduction of new revenue support programs such as ACRE.Arbitrage, Adjustment Costs, Farmland, Asset Pricing, Capital, Cost Function, Risk, Production, Agricultural Finance, Consumer/Household Economics, Crop Production/Industries, Farm Management, Financial Economics, Land Economics/Use, Production Economics, Risk and Uncertainty,

An operational definition of quark and gluon jets

While "quark" and "gluon" jets are often treated as separate, well-defined objects in both theoretical and experimental contexts, no precise, practical, and hadron-level definition of jet flavor presently exists. To remedy this issue, we develop and advocate for a data-driven, operational definition of quark and gluon jets that is readily applicable at colliders. Rather than specifying a per-jet flavor label, we aggregately define quark and gluon jets at the distribution level in terms of measured hadronic cross sections. Intuitively, quark and gluon jets emerge as the two maximally separable categories within two jet samples in data. Benefiting from recent work on data-driven classifiers and topic modeling for jets, we show that the practical tools needed to implement our definition already exist for experimental applications. As an informative example, we demonstrate the power of our operational definition using Z+jet and dijet samples, illustrating that pure quark and gluon distributions and fractions can be successfully extracted in a fully well-defined manner.Comment: 38 pages, 10 figures, 1 table; v2: updated to match JHEP versio