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.

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

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

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

Tracking down hyper-boosted top quarks

The identification of hadronically decaying heavy states, such as vector bosons, the Higgs, or the top quark, produced with large transverse boosts has been and will continue to be a central focus of the jet physics program at the Large Hadron Collider (LHC). At a future hadron collider working at an order-of-magnitude larger energy than the LHC, these heavy states would be easily produced with transverse boosts of several TeV. At these energies, their decay products will be separated by angular scales comparable to individual calorimeter cells, making the current jet substructure identification techniques for hadronic decay modes not directly employable. In addition, at the high energy and luminosity projected at a future hadron collider, there will be numerous sources for contamination including initial- and final-state radiation, underlying event, or pile-up which must be mitigated. We propose a simple strategy to tag such "hyper-boosted" objects that defines jets with radii that scale inversely proportional to their transverse boost and combines the standard calorimetric information with charged track-based observables. By means of a fast detector simulation, we apply it to top quark identification and demonstrate that our method efficiently discriminates hadronically decaying top quarks from light QCD jets up to transverse boosts of 20 TeV. Our results open the way to tagging heavy objects with energies in the multi-TeV range at present and future hadron colliders.Comment: 19 pages + appendices, 17 figures; v2: added references, updated cross section tabl

Sudakov Safety in Perturbative QCD

Traditional calculations in perturbative quantum chromodynamics (pQCD) are based on an order-by-order expansion in the strong coupling $\alpha_s$. Observables that are calculable in this way are known as "safe". Recently, a class of unsafe observables was discovered that do not have a valid $\alpha_s$ expansion but are nevertheless calculable in pQCD using all-orders resummation. These observables are called "Sudakov safe" since singularities at each $\alpha_s$ order are regulated by an all-orders Sudakov form factor. In this letter, we give a concrete definition of Sudakov safety based on conditional probability distributions, and we study a one-parameter family of momentum sharing observables that interpolate between the safe and unsafe regimes. The boundary between these regimes is particularly interesting, as the resulting distribution can be understood as the ultraviolet fixed point of a generalized fragmentation function, yielding a leading behavior that is independent of $\alpha_s$.Comment: 4+5 pages, 4 figures, 1 table. Version accepted for publication in PR