633 research outputs found
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
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
Employing Helicity Amplitudes for Resummation
Many state-of-the-art QCD calculations for multileg processes use helicity
amplitudes as their fundamental ingredients. We construct a simple and
easy-to-use helicity operator basis in soft-collinear effective theory (SCET),
for which the hard Wilson coefficients from matching QCD onto SCET are directly
given in terms of color-ordered helicity amplitudes. Using this basis allows
one to seamlessly combine fixed-order helicity amplitudes at any order they are
known with a resummation of higher-order logarithmic corrections. In
particular, the virtual loop amplitudes can be employed in factorization
theorems to make predictions for exclusive jet cross sections without the use
of numerical subtraction schemes to handle real-virtual infrared cancellations.
We also discuss matching onto SCET in renormalization schemes with helicities
in - and -dimensions. To demonstrate that our helicity operator basis is
easy to use, we provide an explicit construction of the operator basis, as well
as results for the hard matching coefficients, for jets,
jets, and jets. These operator bases are
completely crossing symmetric, so the results can easily be applied to
processes with and collisions.Comment: 41 pages + 20 pages in Appendices, 1 figure, v2: journal versio
N-Jettiness Subtractions for at Subleading Power
-jettiness subtractions provide a general approach for performing
fully-differential next-to-next-to-leading order (NNLO) calculations. Since
they are based on the physical resolution variable -jettiness,
, subleading power corrections in , with
a hard interaction scale, can also be systematically computed. We study the
structure of power corrections for -jettiness, , for the
process. Using the soft-collinear effective theory we analytically
compute the leading power corrections and (finding partial agreement with a previous result in the
literature), and perform a detailed numerical study of the power corrections in
the , , and channels. This includes a numerical extraction of
the and corrections, and a study of
the dependence on the definition. Including such power
suppressed logarithms significantly reduces the size of missing power
corrections, and hence improves the numerical efficiency of the subtraction
method. Having a more detailed understanding of the power corrections for both
and initiated processes also provides insight into their
universality, and hence their behavior in more complicated processes where they
have not yet been analytically calculated.Comment: 16 pages, 12 figure
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