Person:

Feige, Ilya

Some of the most arduous and error-prone aspects of precision resummed calculations are related to the partonic hard process, having nothing to do with the resummation. In particular, interfacing to parton-distribution functions, combining various channels, and performing the phase space integration can be limiting factors in completing calculations. Conveniently, however, most of these tasks are already automated in many Monte Carlo programs, such as MadGraph, Alpgen or Sherpa. In this paper, we show how such programs can be used to produce distributions of partonic kinematics with associated color structures representing the hard factor in a resummed distribution. These distributions can then be used to weight convolutions of jet, soft and beam functions producing a complete resummed calculation. In fact, only around 1000 unweighted events are necessary to produce precise distributions. A number of examples and checks are provided, including e +e− two- and four-jet event shapes, n-jettiness and jet-mass related observables at hadron colliders. Attached code can be used to modify MadGraph to export the relevant leading-order hard functions and color structures for arbitrary processes.

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.

Factorization in gauge theories holds at the amplitude or amplitude-squared level for states of given soft or collinear momenta. When performing phase-space integrals over such states, one would generally like to avoid putting in explicit cuts to separate soft from collinear momenta. Removing these cuts induces an overcounting of the softcollinear region and adds new infrared-ultraviolet divergences in the collinear region. In this paper, we first present a regulator-independent subtraction algorithm for removing soft-collinear overlap at the amplitude level which may be useful in pertubative QCD. We then discuss how both the soft-collinear and infrared-ultraviolet overlap can be undone for certain observables in a way which respects factorization. Our discussion clarifies some of the subtleties in phase-space subtractions and includes a proof of the infrared finiteness of a suitably subtracted jet function. These results complete the connection between factorized QCD and Soft-Collinear Effective Theory .

We state and prove to all orders in perturbation theory a factorization theorem in Quantum Chromodynamics that concisely describes the separation of the physics associated with jet formation from that associated with the hard-scattering in high-energy particle collisions. We show how the factorization theorem, which provides an equality between amplitudes in gauge theories, can be readily applied to precision calculations of cross-sections. In the resulting factorized cross sections, the components relevant to jet production are universal and perturbatively calculable. Their renormalization group evolution can be used to sum large logarithms of scale ratios to all orders in perturbation theory, thus enabling quantitive predictions in the regime of disparate scales relevant to many important collider-physics observables. As an application, we calculate the observable 2-subjettiness at next-to-next-to-next-to-leading-logarithmic order for the decay of boosted heavy color-singlet particles such as Electroweak bosons. Our calculation is the first analytic calculation of a jet substructure observable.

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 → q q¯ 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.

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.