Factorization theorems underly our ability to make predictions for many processes involving the strong interaction. Although typically formulated at leading power, the study of factorization at subleading power is of interest both for improving the precision of calculations, as well as for understanding the all orders structure of QCD. We use the SCET helicity operator formalism to construct a complete power suppressed basis of hard scattering operators for e + e − → dijets, e − p → e − jet, and constrained Drell-Yan, including the first two subleading orders in the amplitude level power expansion. We analyze the field content of the jet and soft function contributions to the power suppressed cross section for e + e − → dijet event shapes, and give results for the lowest order matching to the contributing operators. These results will be useful for studies of power corrections both in fixed order and resummed perturbation theory.

We provide a precise statement of hard-soft-collinear factorization of scattering amplitudes and prove it to all orders in perturbation theory. Factorization is formulated as the equality at leading power of scattering amplitudes in QCD with other amplitudes in QCD computed from a product of operator matrix elements. The equivalence is regulator independent and gauge independent. As the formulation relates amplitudes to the same amplitudes with additional soft or collinear particles, it includes as special cases the factorization of soft currents and collinear splitting functions from generic matrix elements, both of which are shown to be process independent to all orders. We show that the overlapping soft-collinear region is naturally accounted for by vacuum matrix elements of kinked Wilson lines. Although the proof is self-contained, it combines techniques developed for the study of pinch surfaces, scattering amplitudes, and effective field theory.

In applications of machine learning to particle physics, a persistent challenge is how to go beyond discrimination to learn about the underlying physics. To this end, a powerful tool would be a framework for unsupervised learning, where the machine learns the intricate high-dimensional contours of the data upon which it is trained, without reference to pre-established labels. In order to approach such a complex task, an unsupervised network must be structured intelligently, based on a qualitative understanding of the data. In this paper, we scaffold the neural network's architecture around a leading-order model of the physics underlying the data. In addition to making unsupervised learning tractable, this design actually alleviates existing tensions between performance and interpretability. We call the framework Junipr: "Jets from UNsupervised Interpretable PRobabilistic models". In this approach, the set of particle momenta composing a jet are clustered into a binary tree that the neural network examines sequentially. Training is unsupervised and unrestricted: the network could decide that the data bears little correspondence to the chosen tree structure. However, when there is a correspondence, the network's output along the tree has a direct physical interpretation. Junipr models can perform discrimination tasks, through the statistically optimal likelihood-ratio test, and they permit visualizations of discrimination power at each branching in a jet's tree. Additionally, Junipr models provide a probability distribution from which events can be drawn, providing a data-driven Monte Carlo generator. As a third application, Junipr models can reweight events from one (e.g. simulated) data set to agree with distributions from another (e.g. experimental) data set.

Jet substructure has emerged as a critical tool for LHC searches, but studies so far have relied heavily on shower Monte Carlo simulations, which formally approximate QCD at leading-log level. We demonstrate that systematic higher-order QCD computations of jet substructure can be carried out by boosting global event shapes by a large momentum Q, and accounting for effects due to finite jet size, initial-state radiation (ISR), and the underlying event (UE) as 1/Q corrections. In particular, we compute the 2-subjettiness substructure distribution for boosted Z → qq events at the LHC at next-to-next-to-next-to-leading-log order. The calculation is greatly simplified by recycling the known results for the thrust distribution in e + e − collisions. The 2-subjettiness distribution quickly saturates, becoming Q independent for Q > ∼ 400 GeV. Crucially, the effects of jet contamination from ISR/UE can be subtracted out analytically at large Q, without knowing their detailed form. Amusingly, the Q = ∞ and Q = 0 distributions are related by a scaling by e, up to next-to-leading-log order.The Large Hadron Collider (LHC) is exploring a new regime where the collision energy far exceeds the masses of known standard model particles. At such energies, heavy particles such as W/Z bosons and top quarks are often produced with large Lorentz boost factors, which leaves their hadronic decay products collimated into a single energetic "fat jet". Jet substructure techniques extract information from these fat jets to distinguish boosted heavy objects from the QCD background of jets initiated by light quarks and gluons. Examples of variables defined for this purpose include planar flow [1,2] In this paper, we develop a framework for performing jet substructure computations analytically, in the limit where the boosted object of interest has a large momentum Q. We find a mapping between global e + e − event shapes-which have been calculated to high precisionand jet substructure variables in the large Q limit, treating finite jet size, initial state radiation (ISR), and underlying event (UE) as 1/Q corrections. Concretely, we consider the jet substructure observable N -subjettiness T N [4], which is the subjet version of the global event shape N -jettiness [16]. The ratio T N /T N −1 is a robust probe for N -prong decays [17], and compares favorably to other methods for boosted object identification.Here, we focus on 1-and 2-subjettiness (T 1 and T 2 ), which are relevant for LHC searches involving W/Z and Higgs bosons. We compute the distribution for the ratio T 2 /T 1 from Z → qq decays to next-to-next-tonext-to-leading-log (N 3 LL) order, using ingredients from higher-order calculations of the classic e + e − thrust event shape [18][19][20][21][22][23][24]. From a calculational point of view, the use of this ratio is crucial, since it has a finite limit when Q → ∞. We will show that our full subjet distribution is equal to the global distribution generated by the Z decay products, up to 1/Q power-suppressed corrections. The dominant had...

Factorization is possible due to the universal behavior of Yang-Mills theories in soft and collinear limits. Here, we take a small step towards a more transparent understanding of these limits by proving a form of perturbative factorization at treelevel using on-shell spinor helicity methods. We present a concrete and self-contained expression of factorization in which matrix elements in QCD are related to products of other matrix elements in QCD up to leading order in a power-counting parameter determined by the momenta of certain physical on-shell states. Our approach uses only the scaling of momenta in soft and collinear limits, avoiding any assignment of scaling behavior to unphysical (and gauge-dependent) fields. The proof of factorization exploits many advantages of helicity spinors, such as the freedom to choose different reference vectors for polarizations in different collinear sectors. An advantage of this approach is that once factorization is shown to hold in QCD, the transition to SoftCollinear Effective Theory is effortless.