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

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

Improving the Understanding of Jet Grooming in Perturbation Theory

Jet grooming has emerged as a necessary and powerful tool in a precision jet physics program. In this paper, we present three results on jet grooming in perturbation theory, focusing on heavy jet mass in $e^+e^-\to$ hadrons collisions, groomed with the modified mass drop tagger. First, we calculate the analytic cross section at leading-order. Second, using the leading-order result and numerical results through next-to-next-to-leading order, we show that cusps in the distribution on the interior of phase space at leading-order are softened at higher orders. Finally, using analytic and numerical results, we show that terms that violate the assumptions of the factorization theorem for groomed jet mass are numerically much smaller than expected from power counting. These results provide important information regarding the convergence of perturbation theory for groomed jet observables and reliable estimates for residual uncertainties in a precision calculation.Comment: 12 pages, 5 figures; v2: JHEP version, fixed typos and added discussion for $\beta >0$ and non-perturbative power correction

Toward Multi-Differential Cross Sections: Measuring Two Angularities on a Single Jet

The analytic study of differential cross sections in QCD has typically focused on individual observables, such as mass or thrust, to great success. Here, we present a first study of double differential jet cross sections considering two recoil-free angularities measured on a single jet. By analyzing the phase space defined by the two angularities and using methods from soft-collinear effective theory, we prove that the double differential cross section factorizes at the boundaries of the phase space. We also show that the cross section in the bulk of the phase space cannot be factorized using only soft and collinear modes, excluding the possibility of a global factorization theorem in soft-collinear effective theory. Nevertheless, we are able to define a simple interpolation procedure that smoothly connects the factorization theorem at one boundary to the other. We present an explicit example of this at next-to-leading logarithmic accuracy and show that the interpolation is unique up to $\alpha_s^4$ order in the exponent of the cross section, under reasonable assumptions. This is evidence that the interpolation is sufficiently robust to account for all logarithms in the bulk of phase space to the accuracy of the boundary factorization theorem. We compare our analytic calculation of the double differential cross section to Monte Carlo simulation and find qualitative agreement. Because our arguments rely on general structures of the phase space, we expect that much of our analysis would be relevant for the study of phenomenologically well-motivated observables, such as $N$-subjettiness, energy correlation functions, and planar flow.Comment: 43 pages plus appendices, 8 figures. v2 as published in JHEP. minor typos correcte