88 research outputs found
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 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
-subjettiness, energy correlation functions, and planar flow.Comment: 43 pages plus appendices, 8 figures. v2 as published in JHEP. minor
typos correcte
Factorization and Resummation for Groomed Multi-Prong Jet Shapes
Observables which distinguish boosted topologies from QCD jets are playing an
increasingly important role at the Large Hadron Collider (LHC). These
observables are often used in conjunction with jet grooming algorithms, which
reduce contamination from both theoretical and experimental sources. In this
paper we derive factorization formulae for groomed multi-prong substructure
observables, focusing in particular on the groomed observable, which is
used to identify boosted hadronic decays of electroweak bosons at the LHC. Our
factorization formulae allow systematically improvable calculations of the
perturbative distribution and the resummation of logarithmically enhanced
terms in all regions of phase space using renormalization group evolution. They
include a novel factorization for the production of a soft subjet in the
presence of a grooming algorithm, in which clustering effects enter directly
into the hard matching. We use these factorization formulae to draw robust
conclusions of experimental relevance regarding the universality of the
distribution in both and collisions. In particular, we show that
the only process dependence is carried by the relative quark vs. gluon jet
fraction in the sample, no non-global logarithms from event-wide correlations
are present in the distribution, hadronization corrections are controlled by
the perturbative mass of the jet, and all global color correlations are
completely removed by grooming, making groomed a theoretically clean QCD
observable even in the LHC environment. We compute all ingredients to one-loop
accuracy, and present numerical results at next-to-leading logarithmic accuracy
for collisions, comparing with parton shower Monte Carlo simulations.
Results for collisions, as relevant for phenomenology at the LHC, are
presented in a companion paper.Comment: 66 pages, 18 figure
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.Comment: 46 pages + appendices, 10 figures. v2: added current figures 4 and 5,
as well as corrected several typos in appendices. v3: corrected some typos,
added current figure 9, and added more discussion of fixed-order versus
dressed gluon expansions. v4: fixed an error in numerics of two-dressed
gluon; corrected figure 8, modified comparison to BMS. Conclusions unchanged.
v5: fixed minor typ
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 Pythia 8 and Herwig++. We also use the example of quark versus gluon discrimination to demonstrate the limits of the power counting technique.United States. Dept. of Energy (Contract DE-SC00012567)United States. Dept. of Energy (Contract DE-SC0011090)MIT Department of Physics Pappalardo ProgramNatural Sciences and Engineering Research Council of Canad
Analytic boosted boson discrimination
Observables which discriminate boosted topologies from massive QCD jets are of great importance for the success of the jet substructure program at the Large Hadron Collider. Such observables, while both widely and successfully used, have been studied almost exclusively with Monte Carlo simulations. In this paper we present the first all-orders factorization theorem for a two-prong discriminant based on a jet shape variable, D 2, valid for both signal and background jets. Our factorization theorem simultaneously describes the production of both collinear and soft subjets, and we introduce a novel zero-bin procedure to correctly describe the transition region between these limits. By proving an all orders factorization theorem, we enable a systematically improvable description, and allow for precision comparisons between data, Monte Carlo, and first principles QCD calculations for jet substructure observables. Using our factorization theorem, we present numerical results for the discrimination of a boosted Z boson from massive QCD background jets. We compare our results with Monte Carlo predictions which allows for a detailed understanding of the extent to which these generators accurately describe the formation of two-prong QCD jets, and informs their usage in substructure analyses. Our calculation also provides considerable insight into the discrimination power and calculability of jet substructure observables in general.United States. Department of Energy (Contract Numbers DE-SC00012567 and DE-SC0011090)MIT Department of Physics Pappalardo ProgramNatural Sciences and Engineering Research Council of Canad
Building a better boosted top tagger
Distinguishing hadronically decaying boosted top quarks from massive QCD jets is an important challenge at the Large Hadron Collider. In this paper we use the power-counting method to study jet substructure observables designed for top tagging, and gain insight into their performance. We introduce a powerful new family of discriminants formed from the energy correlation functions which outperform the widely used N-subjettiness. These observables take a highly nontrivial form, demonstrating the importance of a systematic approach to their construction.United States. Dept. of Energy (Cooperative Research Agreement DE-SC00012567)United States. Dept. of Energy (Cooperative Research Agreement DE-SC0011090)MIT Department of Physics Pappalardo Program (Fellowship)Natural Sciences and Engineering Research Council of Canad
The analytic structure of non-global logarithms: convergence of the dressed gluon expansion
Non-global logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon ex-pansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an all-orders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and large-Nc master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluon expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of αslog. We explain this finite radius of convergence using the dressed gluon expansion, showing how the dynamics of the buffer region, a region of phase space near the boundary of the jet that was identified in early studies of NGLs, leads to large contributions to the fixed order expansion. We also use the dressed gluon expansion to discuss the convergence of the next-to-leading NGL series, and the role of collinear logarithms that appear at this order. Finally, we show how an understanding of the analytic behavior obtained from the dressed gluon expansion allows us to improve the fixed order NGL series using conformal transformations to extend the domain of analyticity. This allows us to calculate the NGL distribution for all values of αslog from the coefficients of the fixed order expansion.United States. Dept. of Energy (DE-FG02-05ER-41360, DE-SC0011090, DE-AC52-06NA25396)Los Alamos National Laboratory (Laboratory Directed Research & Development
Ab initio vibrational free energies including anharmonicity for multicomponent alloys
A density-functional-theory based approach to efficiently compute numerically
exact vibrational free energies - including anharmonicity - for chemically
complex multicomponent alloys is developed. It is based on a combination of
thermodynamic integration and a machine-learning potential. We demonstrate the
performance of the approach by computing the anharmonic free energy of the
prototypical five-component VNbMoTaW refractory high entropy alloy
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