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Duff Neill

Publications and source records attributed to Duff Neill.

48 records · Page 3Linked to original sources
arXiv2015

Non-Global Logarithms, Factorization, and the Soft Substructure of Jets

An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and resummed down to an unresolved infrared scale by making sufficiently many measurements on a jet or other restricted phase space region. Resummation is accomplished by renormalization group evolution of the objects in the factorization theorem and anomalous dimensions can be calculated to any perturbative accuracy and with any number of colors. To connect with the NGLs of more inclusive measurements, we present a novel perturbative expansion which is controlled by the volume of the allowed phase space for unresolved emissions. Arbitrary accuracy can be obtained by making more and more measurements so to resolve lower and lower scales. We find that even a minimal number of measurements produces agreement with Monte Carlo methods for leading-logarithmic resummation of NGLs at the sub-percent level over the full dynamical range relevant for the Large Hadron Collider. We also discuss other applications of our factorization theorem to soft jet dynamics and how to extend to higher-order accuracy.

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arXiv2015

The Edge of Jets and Subleading Non-Global Logs

A persistent and fascinating problem at the high energy colliders are jets. Often trying to observe physics underlying the hard interactions at colliders requires experimental cuts in phase space, defining several jet or beam regions. QCD being a gauge theory that readily decays into infra-red modes, correlations between jet regions is almost inevitable, spoiling the predictivity of fixed order QCD calculations. One is faced with the task of calculating the evolution of a reduced density matrix, where successively less energetic (jet) regions are integrated out, to gain control of the calculation. I relate the decay rates governing the flow into the IR to an effective field theory expansion in soft jets, allowing a systematic and resummed calculation of these rates, while further relating them to physically observable features of the QCD cascade. To demonstrate the utility of the soft jet expansion, I present a factorization theorem for a soft subjet collinearly splitting in and out of a parent fat jet. Using the resummation properties of this factorization theorem, I elucidate the structure of the subleading non-global logs (encoding the jet correlations) in the hemisphere jet mass distribution, as well as give a collinear improvement of the leading order resummation equation, the BMS equation. I compare to other approaches to subleading resummation of NGLs, and find the collinear improvement of the leading order equation removes the need for kinematic-dependent corrections in the IR averaging procedure of the reduced density matrix, so that no further large logs can be generated in the IR. Finally I end with speculation about connections with collinear improvements of the NLO B-JIMWLK hierarchy for small-$x$ resummation.

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arXiv2015

Soft Theorems from Effective Field Theory

The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.

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arXiv2015

The Higgs Transverse Momentum Distribution at NNLL and its Theoretical Errors

In this letter, we present the NNLL-NNLO transverse momentum Higgs distribution arising from gluon fusion. In the regime $p_\perp\ll m_H$ we include the resummation of the large logs at next to next-to leading order and then match on to the $α_s^2$ fixed order result near $p_\perp \sim m_h$. By utilizing the rapidity renormalization group (RRG) we are able to smoothly match between the resummed, small $p_\perp$ regime and the fixed order regime. We give a detailed discussion of the scale dependence of the result including an analysis of the rapidity scale dependence. Our central value differs from previous results, in the transition region as well as the tail, by an amount which is outside the error band. This difference is due to the fact that the RRG profile allows us to smoothly turn off the resummation.

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arXiv2014

Power Counting to Better Jet Observables

Optimized jet substructure observables for identifying boosted topologies will play an essential role in maximizing the physics reach of the Large Hadron Collider. Ideally, the design of discriminating variables would be informed by analytic calculations in perturbative QCD. Unfortunately, explicit calculations are often not feasible due to the complexity of the observables used for discrimination, and so many validation studies rely heavily, and solely, on Monte Carlo. In this paper we show how methods based on the parametric power counting of the dynamics of QCD, familiar from effective theory analyses, can be used to design, understand, and make robust predictions for the behavior of jet substructure variables. As a concrete example, we apply power counting for discriminating boosted Z bosons from massive QCD jets using observables formed from the n-point energy correlation functions. We show that power counting alone gives a definite prediction for the observable that optimally separates the background-rich from the signal-rich regions of phase space. Power counting can also be used to understand effects of phase space cuts and the effect of contamination from pile-up, which we discuss. As these arguments rely only on the parametric scaling of QCD, the predictions from power counting must be reproduced by any Monte Carlo, which we verify using Pythia8 and Herwig++. We also use the example of quark versus gluon discrimination to demonstrate the limits of the power counting technique.

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arXiv2014

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 $α_s^4$ 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.

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arXiv2014

Jet Shapes with the Broadening Axis

Broadening is a classic jet observable that probes the transverse momentum structure of jets. Traditionally, broadening has been measured with respect to the thrust axis, which is aligned along the (hemisphere) jet momentum to minimize the vector sum of transverse momentum within a jet. In this paper, we advocate measuring broadening with respect to the "broadening axis", which is the direction that minimizes the scalar sum of transverse momentum within a jet. This approach eliminates many of the calculational complexities arising from recoil of the leading parton, and observables like the jet angularities become recoil-free when measured using the broadening axis. We derive a simple factorization theorem for broadening-axis observables which smoothly interpolates between the thrust-like and broadening-like regimes. We argue that the same factorization theorem holds for two-point energy correlation functions as well as for jet shapes based on a "winner-take-all axis". Using kinked broadening axes, we calculate event-wide angularities in e+e- collisions with next-to-leading logarithmic resummation. Defining jet regions using the broadening axis, we also calculate the global logarithms for angularities within a single jet. We find good agreement comparing our calculations both to showering Monte Carlo programs and to automated resummation tools. We give a brief historical perspective on the broadening axis and suggest ways that broadening-axis observables could be used in future jet substructure studies at the Large Hadron Collider.

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arXiv2013

A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory

Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the rele- vant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any scenario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form factor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are uni- versal. We present details of the factorization and resummation of the jet broadening cross section including a renormalization in pT space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to allow for a consistent resummation.

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arXiv2013

Two-Loop Matching onto Dimension Eight Operators in the Higgs-Glue Sector

This letter presents results for the two-loop matching coefficients for the dimension eight operators that contribute to Higgs production via gluon fusion. The coefficients can be used to calculate the first correction to the infinite top mass limit to Higgs production with large transverse momentum at two loops. To date such processes have been studied at two loop order only in the leading term in the top mass expansion. These corrections become enhanced in processes with large final state invariant mass, typical of multijet processes.

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arXiv2013

Classical Space-Times from the S Matrix

We show that classical space-times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space-time as a series in $G_N$. At no point of the derivation is any use made of the Einstein-Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space-time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space-times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang-Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity three point functions shows that the seeds that generate solutions in the two theories are algebraically related. From a technical standpoint our methodology can also be utilized to calculate quantities relevant for the binary inspiral problem more efficiently than the more traditional Feynman diagram approach.

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arXiv2011

The Rapidity Renormalization Group

We introduce a systematic approach for the resummation of perturbative series which involve large logarithms not only due to large invariant mass ratios but large rapidities as well. Series of this form can appear in a variety of gauge theory observables. The formalism is utilized to calculate the jet broadening event shape in a systematic fashion to next to leading logarithmic order. An operator definition of the factorized cross section as well as a closed form of the next-to leading log cross section are presented. The result agrees with the data to within errors.

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