QCD Analysis of the Scale-Invariance of Jets

Studying the substructure of jets has become a powerful tool for event discrimination and for studying QCD. Typically, jet substructure studies rely on Monte Carlo simulation for vetting their usefulness; however, when possible, it is also important to compute observables with analytic methods. Here, we present a global next-to-leading-log resummation of the angular correlation function which measures the contribution to the mass of a jet from constituents that are within an angle R with respect to one another. For a scale-invariant jet, the angular correlation function should scale as a power of R. Deviations from this behavior can be traced to the breaking of scale invariance in QCD. To do the resummation, we use soft-collinear effective theory relying on the recent proof of factorization of jet observables at e+ e- colliders. Non-trivial requirements of factorization of the angular correlation function are discussed. The calculation is compared to Monte Carlo parton shower and next-to-leading order results. The different calculations are important in distinct phase space regions and exhibit that jets in QCD are, to very good approximation, scale invariant over a wide dynamical range.Comment: Updated to PRD version, added discussion of relative importance of NLL vs. NLO contribution

Conformal Invariance of the Subleading Soft Theorem in Gauge Theory

In this note, I show that the recently proposed subleading soft factor in massless gauge theory uniquely follows from conformal symmetry of tree-level gauge theory amplitudes in four dimensions.Comment: v1: 6 pages, no figures, JHEP style; v2: 7 pages, added some discussion and references; v3: 5 pages, PRD accepted version, minor wording change

Unsafe but Calculable: Ratios of Angularities in Perturbative QCD

Infrared- and collinear-safe (IRC-safe) observables have finite cross sections to each fixed-order in perturbative QCD. Generically, ratios of IRC-safe observables are themselves not IRC safe and do not have a valid fixed-order expansion. Nevertheless, in this paper we present an explicit method to calculate the cross section for a ratio observable in perturbative QCD with the help of resummation. We take the IRC-safe jet angularities as an example and consider the ratio formed from two angularities with different angular exponents. While the ratio observable is not IRC safe, it is "Sudakov safe", meaning that the perturbative Sudakov factor exponentially suppresses the singular region of phase space. At leading logarithmic (LL) order, the distribution is finite but has a peculiar expansion in the square root of the strong coupling constant, a consequence of IRC unsafety. The accuracy of the LL distribution can be further improved with higher-order resummation and fixed-order matching. Non-perturbative effects can sometimes give rise to order one changes in the distribution, but at sufficiently high energies Q, Sudakov safety leads to non-perturbative corrections that scale like a (fractional) power of 1/Q, as is familiar for IRC-safe observables. We demonstrate that Monte Carlo parton showers give reliable predictions for the ratio observable, and we discuss the prospects for computing other ratio observables using our method.Comment: 41 pages, 14 figures, 1 table, small changes in v.

Aspects of Jets at 100 TeV

We present three case studies at a 100 TeV proton collider for how jet analyses can be improved using new jet (sub)structure techniques. First, we use the winner-take-all recombination scheme to define a recoil-free jet axis that is robust against pileup. Second, we show that soft drop declustering is an effective jet grooming procedure that respects the approximate scale invariance of QCD. Finally, we highlight a potential standard candle for jet calibration using the soft-dropped energy loss. This latter observable is remarkably insensitive to the scale and flavor of the jet, a feature that arises because it is infrared/collinear unsafe, but Sudakov safe.Comment: 9 pages, double column, 7 figures, based on a talk by A.L. at the "Workshop on Physics at a 100 TeV Collider" at SLAC from April 23-25, 2014; v.2: PRD versio

How Much Information is in a Jet?

Machine learning techniques are increasingly being applied toward data analyses at the Large Hadron Collider, especially with applications for discrimination of jets with different originating particles. Previous studies of the power of machine learning to jet physics has typically employed image recognition, natural language processing, or other algorithms that have been extensively developed in computer science. While these studies have demonstrated impressive discrimination power, often exceeding that of widely-used observables, they have been formulated in a non-constructive manner and it is not clear what additional information the machines are learning. In this paper, we study machine learning for jet physics constructively, expressing all of the information in a jet onto sets of observables that completely and minimally span N-body phase space. For concreteness, we study the application of machine learning for discrimination of boosted, hadronic decays of Z bosons from jets initiated by QCD processes. Our results demonstrate that the information in a jet that is useful for discrimination power of QCD jets from Z bosons is saturated by only considering observables that are sensitive to 4-body (8 dimensional) phase space.Comment: 14 pages + appendices, 10 figures; v2: JHEP version, updated neural network, included deeper network and boosted decision tree result

Automating the Construction of Jet Observables with Machine Learning

Machine-learning assisted jet substructure tagging techniques have the potential to significantly improve searches for new particles and Standard Model measurements in hadronic final states. Techniques with simple analytic forms are particularly useful for establishing robustness and gaining physical insight. We introduce a procedure to automate the construction of a large class of observables that are chosen to completely specify $M$-body phase space. The procedure is validated on the task of distinguishing $H\rightarrow b\bar{b}$ from $g\rightarrow b\bar{b}$, where $M=3$ and previous brute-force approaches to construct an optimal product observable for the $M$-body phase space have established the baseline performance. We then use the new method to design tailored observables for the boosted $Z'$ search, where $M=4$ and brute-force methods are intractable. The new classifiers outperform standard $2$-prong tagging observables, illustrating the power of the new optimization method for improving searches and measurement at the LHC and beyond.Comment: 15 pages, 8 tables, 12 figure

Constructing Amplitudes from Their Soft Limits

The existence of universal soft limits for gauge-theory and gravity amplitudes has been known for a long time. The properties of the soft limits have been exploited in numerous ways; in particular for relating an n-point amplitude to an (n-1)-point amplitude by removing a soft particle. Recently, a procedure called inverse soft was developed by which "soft" particles can be systematically added to an amplitude to construct a higher-point amplitude for generic kinematics. We review this procedure and relate it to Britto-Cachazo-Feng-Witten recursion. We show that all tree-level amplitudes in gauge theory and gravity up through seven points can be constructed in this way, as well as certain classes of NMHV gauge-theory amplitudes with any number of external legs. This provides us with a systematic procedure for constructing amplitudes solely from their soft limits.Comment: minor change