[Show abstract][Hide abstract] ABSTRACT: We compute the interference between the resonant process $pp\to H(\rightarrow
\gamma\gamma)+2 \text{ jets}$ and the corresponding continuum background at
leading order in QCD. For the Higgs signal, we include gluon fusion (GF) and
vector boson fusion (VBF) production channels, while for the background we
consider all tree-level contributions, including pure EW effects (${\cal
O}(\alpha_{QED}^4)$) and QCD contributions (${\cal O}(\alpha_{QED}^2
\alpha_{s}^2)$), plus the loop-induced gluon-initiated process. After
convolution with the experimental mass resolution, the main effect of the
interference is to shift the position of the mass peak, as in the inclusive GF
case studied previously. The apparent mass shift is small in magnitude but
strongly dependent on the Higgs width, potentially allowing for a measurement
of, or bound on, the width itself. In the $H(\rightarrow \gamma\gamma)+2 \text{
jets}$ channel, the VBF and GF contributions generate shifts of opposite signs
which largely cancel, depending on the sets of cuts used, to as little as 5 MeV
(toward a lower Higgs mass). The small magnitude of the shift makes this
channel a good reference mass for measuring the inclusive mass shift of around
60 MeV in the Standard Model.
[Show abstract][Hide abstract] ABSTRACT: Electroweak vector-boson production, accompanied by multiple jets, is an
important background to searches for physics beyond the Standard Model. A
precise and quantitative understanding of this process is helpful in
constraining deviations from known physics. We study four key ratios in $W +
n$-jet production at the LHC. We compute the ratio of cross sections for $W +
n$- to $W + (n-1)$-jet production as a function of the minimum jet transverse
momentum. We also study the ratio differentially, as a function of the
$W$-boson transverse momentum; as a function of the scalar sum of the jet
transverse energy, $H_T^{\rm jets}$; and as a function of certain jet
transverse momenta. We show how to use such ratios to extrapolate differential
cross sections to $W+6$-jet production at next-to-leading order, and we
cross-check the method against a direct calculation at leading order. We
predict the differential distribution in $H_T^{\rm jets}$ for $W+6$ jets at
next-to-leading order using such an extrapolation. We use the BlackHat software
library together with SHERPA to perform the computations.
Physical Review D 12/2014; 92(1). DOI:10.1103/PhysRevD.92.014008 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We extend the hexagon function bootstrap to the next-to-maximally-helicity-violating (NMHV) configuration for six-point scattering in planar \( \mathcal{N} \) = 4 super-Yang-Mills theory at three loops. Constraints from the \( \overline{Q} \) differential equation, from the operator product expansion (OPE) for Wilson loops with operator insertions, and from multi-Regge factorization, lead to a unique answer for the three-loop ratio function. The three-loop result also predicts additional terms in the OPE expansion, as well as the behavior of NMHV amplitudes in the multi-Regge limit at one higher logarithmic accuracy (NNLL) than was used as input. Both predictions are in agreement with recent results from the flux-tube approach. We also study the multi-particle factorization of multi-loop amplitudes for the first time. We find that the function controlling this factorization is purely logarithmic through three loops. We show that a function U , which is closely related to the parity-even part of the ratio function V , is remarkably simple; only five of the nine possible final entries in its symbol are non-vanishing. We study the analytic and numerical behavior of both the parity-even and parity-odd parts of the ratio function on simple lines traversing the space of cross ratios (u, v, w), as well as on a few two-dimensional planes. Finally, we present an empirical formula for V in terms of elements of the coproduct of the six-gluon MHV remainder function R
6 at one higher loop, which works through three loops for V (four loops for R
6).
Journal of High Energy Physics 08/2014; 2014(10). DOI:10.1007/JHEP10(2014)065 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study $W$-boson production accompanied by multiple jets at 7 TeV at the
LHC. We study the jet-production ratio, of total cross sections for $W$+$n$- to
$W$+($n-1$)-jet production, and the ratio of distributions in the total
transverse hadronic jet energy $H_{\rm T}^{\rm jets}$. We use the ratios to
extrapolate the total cross section, and the differential distribution in
$H_{\rm T}^{\rm jets}$, to $W$+6-jet production. We use the BlackHat software
library in conjunction with SHERPA to perform the computations.
[Show abstract][Hide abstract] ABSTRACT: We describe the hexagon function bootstrap for solving for six-gluon
scattering amplitudes in the large $N_c$ limit of ${\cal N}=4$ super-Yang-Mills
theory. In this method, an ansatz for the finite part of these amplitudes is
constrained at the level of amplitudes, not integrands, using boundary
information. In the near-collinear limit, the dual picture of the amplitudes as
Wilson loops leads to an operator product expansion which has been solved using
integrability by Basso, Sever and Vieira. Factorization of the amplitudes in
the multi-Regge limit provides additional boundary data. This bootstrap has
been applied successfully through four loops for the maximally helicity
violating (MHV) configuration of gluon helicities, and through three loops for
the non-MHV case.
[Show abstract][Hide abstract] ABSTRACT: We present next-to-leading order QCD predictions for cross sections and for a
comprehensive set of distributions in diphoton + 2-jet production at the Large
Hadron Collider. We consider the contributions from loop amplitudes for two
photons and four gluons, but we neglect top quarks. We use BlackHat together
with SHERPA to carry out the computation. We use a Frixione cone isolation for
the photons. We study standard sets of cuts on the jets and the photons, and
also sets of cuts appropriate for studying backgrounds to Higgs-boson
production via vector-boson fusion.
Physical Review D 02/2014; 90(5). DOI:10.1103/PhysRevD.90.054004 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present the four-loop remainder function for six-gluon scattering with
maximal helicity violation in planar N=4 super-Yang-Mills theory, as an
analytic function of three dual-conformal cross ratios. The function is
constructed entirely from its analytic properties, without ever inspecting any
multi-loop integrand. We employ the same approach used at three loops, writing
an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz
using the multi-Regge limit and the operator product expansion in the
near-collinear limit. We express the result in terms of multiple
polylogarithms, and in terms of the coproduct for the associated Hopf algebra.
From the remainder function, we extract the BFKL eigenvalue at
next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at
NNNLLA. We plot the remainder function along various lines and on one surface,
studying ratios of successive loop orders. As seen previously through three
loops, these ratios are surprisingly constant over large regions in the space
of cross ratios, and they are not far from the value expected at asymptotically
large orders of perturbation theory.
Journal of High Energy Physics 02/2014; 2014(6). DOI:10.1007/JHEP06(2014)116 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present results from a recent calculation of prompt photon-pair production
in association with two jets to next-to-leading order (NLO) at the LHC. The
virtual contribution is evaluated using the BlackHat library, a numerical
implementation of on-shell methods for one-loop amplitudes, in conjunction with
SHERPA. We study four sets of cuts: standard jet cuts, a set of Higgs-related
cuts suggested by ATLAS, and corresponding sets which isolate the kinematic
region where the process becomes the largest background to Higgs production via
vector-boson fusion.
[Show abstract][Hide abstract] ABSTRACT: We present an event-file format for the dissemination of
next-to-leading-order (NLO) predictions for QCD processes at hadron colliders.
The files contain all information required to compute generic jet-based
infrared-safe observables at fixed order (without showering or hadronization),
and to recompute observables with different factorization and renormalization
scales. The files also make it possible to evaluate cross sections and
distributions with different parton distribution functions. This in turn makes
it possible to estimate uncertainties in NLO predictions of a wide variety of
observables without recomputing the short-distance matrix elements. The event
files allow a user to choose among a wide range of commonly-used jet algorithms
and jet-size parameters.
We provide event files for a $W$ or $Z$ boson accompanied by up to four jets,
and for pure-jet events with up to four jets. The files are for the Large
Hadron Collider with a center of mass energy of 7 or 8 TeV.
A C++ library along with a Python interface for handling these files are also
provided and described in this article. The library allows a user to read the
event files and recompute observables transparently for different pdf sets and
factorization and renormalization scales.
[Show abstract][Hide abstract] ABSTRACT: I provide a basic introduction to modern helicity amplitude methods,
including color organization, the spinor helicity formalism, and factorization
properties. I also describe the BCFW (on-shell) recursion relation at tree
level, and explain how similar ideas - unitarity and on-shell methods - work at
the loop level. These notes are based on lectures delivered at the 2012 CERN
Summer School and at TASI 2013.
[Show abstract][Hide abstract] ABSTRACT: We present recent next-to-leading order (NLO) results in perturbative QCD
obtained using the BlackHat software library. We discuss the use of n-tuples to
separate the lengthy matrix-element computations from the analysis process. The
use of n-tuples allows many analyses to be carried out on the same phase-space
samples, and also allows experimenters to conduct their own analyses using the
original NLO computation.
Journal of Physics Conference Series 10/2013; 523(1). DOI:10.1088/1742-6596/523/1/012051
[Show abstract][Hide abstract] ABSTRACT: We introduce a generating function for the coefficients of the leading
logarithmic BFKL Green's function in transverse-momentum space, order by order
in alpha_s, in terms of single-valued harmonic polylogarithms. As an
application, we exhibit fully analytic azimuthal-angle and transverse-momentum
distributions for Mueller-Navelet jet cross sections at each order in alpha_s.
We also provide a generating function for the total cross section valid to any
number of loops.
Journal of High Energy Physics 09/2013; 2014(2). DOI:10.1007/JHEP02(2014)086 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a study on high-performance computing and large-scale distributed
computing for perturbative QCD calculations.
[Show abstract][Hide abstract] ABSTRACT: We study the change in the diphoton-invariant-mass distribution for Higgs boson decays to two photons, due to interference between the Higgs resonance in gluon fusion and the continuum background amplitude for gg→γγ. Previously, the apparent Higgs mass was found to shift by around 100 MeV in the standard model in the leading-order approximation, which may potentially be experimentally observable. We compute the next-to-leading-order QCD corrections to the apparent mass shift, which reduce it by about 40%. The apparent mass shift may provide a way to measure, or at least bound, the Higgs boson width at the Large Hadron Collider through "interferometry." We investigate how the shift depends on the Higgs width, in a model that maintains constant Higgs boson signal yields. At Higgs widths above 30 MeV, the mass shift is over 200 MeV and increases with the square root of the width. The apparent mass shift could be measured by comparing with the ZZ^{*} channel, where the shift is much smaller. It might be possible to measure the shift more accurately by exploiting its strong dependence on the Higgs transverse momentum.
[Show abstract][Hide abstract] ABSTRACT: In these proceedings we present results from a recent calculation for the
production of a W boson in conjunction with five jets at next-to-leading order
in perturbative QCD. We also use results at lower multiplicities to extrapolate
the cross section to the same process with six jets.
[Show abstract][Hide abstract] ABSTRACT: We present the three-loop remainder function, which describes the scattering
of six gluons in the maximally-helicity-violating configuration in planar N=4
super-Yang-Mills theory, as a function of the three dual conformal cross
ratios. The result can be expressed in terms of multiple Goncharov
polylogarithms. We also employ a more restricted class of "hexagon functions"
which have the correct branch cuts and certain other restrictions on their
symbols. We classify all the hexagon functions through transcendental weight
five, using the coproduct for their Hopf algebra iteratively, which amounts to
a set of first-order differential equations. The three-loop remainder function
is a particular weight-six hexagon function, whose symbol was determined
previously. The differential equations can be integrated numerically for
generic values of the cross ratios, or analytically in certain kinematics
limits, including the near-collinear and multi-Regge limits. These limits allow
us to impose constraints from the operator product expansion and multi-Regge
factorization directly at the function level, and thereby to fix uniquely a set
of Riemann-zeta-valued constants that could not be fixed at the level of the
symbol. The near-collinear limits agree precisely with recent predictions by
Basso, Sever and Vieira based on integrability. The multi-Regge limits agree
with the factorization formula of Fadin and Lipatov, and determine three
constants entering the impact factor at this order. We plot the three-loop
remainder function for various slices of the Euclidean region of positive cross
ratios, and compare it to the two-loop one. For large ranges of the cross
ratios, the ratio of the three-loop to the two-loop remainder function is
relatively constant, and close to -7.
Journal of High Energy Physics 08/2013; 2013(12). DOI:10.1007/JHEP12(2013)049 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present next-to-leading order QCD predictions for the total cross section
and for a comprehensive set of transverse-momentum distributions in W + 5-jet
production at the Large Hadron Collider. We neglect the small contributions
from subleading-color virtual terms, top quarks and some terms containing four
quark pairs. We also present ratios of total cross sections, and use them to
obtain an extrapolation formula to an even larger number of jets. We include
the decay of the $W$ boson into leptons. This is the first such computation
with six final-state vector bosons or jets. We use BlackHat together with
SHERPA to carry out the computation.
Physical Review D 04/2013; 88(1). DOI:10.1103/PhysRevD.88.014025 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The connection of maximally supersymmetric Yang-Mills theory to the (2,0)
theory in six dimensions has raised the possibility that it might be
perturbatively ultraviolet finite in five dimensions. We test this hypothesis
by computing the coefficient of the first potential ultraviolet divergence of
planar (large N_c) maximally supersymmetric Yang-Mills theory in D = 5, which
occurs at six loops. We show that the coefficient is nonvanishing. Furthermore,
the numerical value of the divergence falls very close to an approximate
exponential formula based on the coefficients of the divergences through five
loops. This formula predicts the approximate values of the ultraviolet
divergence at loop orders L > 6 in the critical dimension D = 4 + 6/L. To
obtain the six-loop divergence we first construct the planar six-loop
four-point amplitude integrand using generalized unitarity. The ultraviolet
divergence follows from a set of vacuum integrals, which are obtained by
expanding the integrand in the external momenta. The vacuum integrals are
integrated via sector decomposition, using a modified version of the FIESTA
program.
Physical Review D 10/2012; 87(2):025018. DOI:10.1103/PhysRevD.87.025018 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate color-kinematics duality for gauge-theory amplitudes produced
by the pure nonabelian Yang-Mills action deformed by higher-dimension
operators. For the operator denoted by F^3, the product of three field
strengths, the existence of color-kinematic dual representations follows from
string-theory monodromy relations. We provide explicit dual representations,
and show how the double-copy construction of gravity amplitudes based on them
is consistent with the Kawai-Lewellen-Tye relations. It leads to the amplitudes
produced by Einstein gravity coupled to a dilaton field phi, and deformed by
operators of the form phi R^2 and R^3. For operators with higher dimensions
than F^3, such as F^4-type operators appearing at the next order in the
low-energy expansion of bosonic and superstring theory, the situation is more
complex. The color structure of some of the F^4 operators is incompatible with
a simple color-kinematics duality based on structure constants f^{abc}, but
even the color-compatible F^4 operators do not admit the duality. In contrast,
the next term in the alpha-prime expansion of the superstring effective action
--- a particular linear combination of D^2 F^4 and F^5-type operators --- does
admit the duality, at least for amplitudes with up to six external gluons.
Journal of High Energy Physics 08/2012; 2012(10). DOI:10.1007/JHEP10(1210)091 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We argue that the natural functions for describing the multi-Regge limit of
six-gluon scattering in planar N=4 super Yang-Mills theory are the
single-valued harmonic polylogarithmic functions introduced by Brown. These
functions depend on a single complex variable and its conjugate, (w,w*). Using
these functions, and formulas due to Fadin, Lipatov and Prygarin, we determine
the six-gluon MHV remainder function in the leading-logarithmic approximation
(LLA) in this limit through ten loops, and the next-to-LLA (NLLA) terms through
nine loops. In separate work, we have determined the symbol of the four-loop
remainder function for general kinematics, up to 113 constants. Taking its
multi-Regge limit and matching to our four-loop LLA and NLLA results, we fix
all but one of the constants that survive in this limit. The multi-Regge limit
factorizes in the variables (\nu,n) which are related to (w,w*) by a
Fourier-Mellin transform. We can transform the single-valued harmonic
polylogarithms to functions of (\nu,n) that incorporate harmonic sums,
systematically through transcendental weight six. Combining this information
with the four-loop results, we determine the eigenvalues of the BFKL kernel in
the adjoint representation to NNLLA accuracy, and the MHV product of impact
factors to NNNLLA accuracy, up to constants representing beyond-the-symbol
terms and the one symbol-level constant. Remarkably, only derivatives of the
polygamma function enter these results. Finally, the LLA approximation to the
six-gluon NMHV amplitude is evaluated through ten loops.
Journal of High Energy Physics 07/2012; 2012(10). DOI:10.1007/JHEP10(2012)074 · 6.11 Impact Factor