Snowmass Theory Frontier Report
This report summarizes the recent progress and promising future directions in theoretical high-energy physics (HEP) identified within the Theory Frontier of the 2021 Snowmass Process.
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arXiv subjects
Z. Bern
Publications and source records attributed to Z. Bern.
Extrapolating W-Associated Jet-Production Ratios at the LHC
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.
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Universality in W+Multijet Production
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.
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Next-to-Leading Order Gamma Gamma + 2-Jet Production at the LHC
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.
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Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
We present the two-loop QCD helicity amplitudes for quark-gluon scattering, and for quark-antiquark annihilation into two gluons. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization. The transition rules for converting the amplitudes between the different variants are much more intricate than for the previously discussed case of gluon-gluon scattering. Summing our two-loop expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Anastasiou, Glover, Oleari and Tejeda-Yeomans. We describe the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-Mills theory, obtained from the QCD amplitudes by modifying the color representation and multiplicities, and verify supersymmetry Ward identities in the FDH scheme.
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Next-to-leading order diphoton+2-jet production at the LHC
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.
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Ntuples for NLO Events at Hadron Colliders
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.
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The BlackHat Library for One-Loop Amplitudes
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.
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High multiplicity W+jets predictions at NLO
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.
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Next-to-Leading Order W + 5-Jet Production at the LHC
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.
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The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
Using the method of maximal cuts, we construct the complete D-dimensional integrand of the five-loop four-point amplitude of N = 4 super-Yang-Mills theory, including nonplanar contributions. In the critical dimension where this amplitude becomes ultraviolet divergent, we present a compact explicit expression for the nonvanishing ultraviolet divergence in terms of three vacuum integrals. This construction provides a crucial step towards obtaining the corresponding amplitude of N = 8 supergravity useful for resolving the general ultraviolet behavior of supergravity theories.
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Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N=4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N=8 supergravity integrand, whose graph numerators are double copies (squares) of the N=4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N=4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D=11/2, the same dimension as for N=4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N=8 supergravity as the subleading-in-1/N_c^2 single-trace divergence in N=4 super-Yang-Mills theory.
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Four-Jet Production at the Large Hadron Collider at Next-to-Leading Order in QCD
We present the cross sections for production of up to four jets at the Large Hadron Collider, at next-to-leading order in the QCD coupling. We use the BlackHat library in conjunction with SHERPA and a recently developed algorithm for assembling primitive amplitudes into color-dressed amplitudes. We adopt the cuts used by ATLAS in their study of multi-jet events in pp collisions at \sqrt{s} = 7 TeV. We include estimates of nonperturbative corrections and compare to ATLAS data. We store intermediate results in a framework that allows the inexpensive computation of additional results for different choices of scale or parton distributions.
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Missing Energy and Jets for Supersymmetry Searches
We extend our investigation of backgrounds to new physics signals, following CMS's data-driven search for supersymmetry at the LHC. The aim is to use different sets of cuts in gamma + 3-jet production to predict the irreducible Z + 3-jet background (with the Z boson decaying to neutrinos) to searches with missing transverse energy + 3-jet signal topologies. We compute ratios of Z + 3-jet to gamma + 3-jet production cross sections and kinematic distributions at next-to-leading order (NLO) in alpha_s. We compare these ratios with those obtained using a parton shower matched to leading-order matrix elements (ME+PS). This study extends our previous work [arXiv:1106.1423 [hep-ph]] on the Z + 2-jet to gamma + 2-jet ratio. We find excellent agreement with the ratio determined from the earlier NLO results involving two instead of three jets, and agreement to within 10% between the NLO and ME+PS results for the ratios. We also examine the possibility of large QCD logarithms in these processes. Ratios of Z + n-jet to gamma + n-jet cross sections are plausibly less sensitive to such corrections than the cross sections themselves. Their effect on estimates of Z + 3-jet to gamma + 3-jet ratios can be assessed experimentally by measuring the gamma + 3-jet to gamma + 2-jet production ratio in search regions. We partially address the question of potentially large electroweak logarithms by computing the real-emission part of the electroweak corrections to the ratio using ME+PS, and find that it is 1% or less. Our estimate of the remaining theoretical uncertainties in the Z to gamma ratio is in agreement with our earlier study.
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NLO vector boson production with light jets
In this contribution we present recent progress in the computation of next-to-leading order (NLO) QCD corrections for the production of an electroweak vector boson in association with jets at hadron colliders. We focus on results obtained using the virtual matrix element library BLACKHAT in conjunction with SHERPA, focusing on results relevant to understanding the background to top production.
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The Ultraviolet Behavior of N=8 Supergravity at Four Loops
We describe the construction of the complete four-loop four-particle amplitude of N=8 supergravity. The amplitude is ultraviolet finite, not only in four dimensions, but in five dimensions as well. The observed extra cancellations provide additional non-trivial evidence that N=8 supergravity in four dimensions may be ultraviolet finite to all orders of perturbation theory.
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Precise Predictions for Z + 4 Jets at Hadron Colliders
We present the cross section for production of a Z boson in association with four jets at the Large Hadron Collider, at next-to-leading order in the QCD coupling. When the Z decays to neutrinos, this process is a key irreducible background to many searches for new physics. Its computation has been made feasible through the development of the on-shell approach to perturbative quantum field theory. We present the total cross section for pp collisions at sqrt{s} = 7 TeV, after folding in the decay of the Z boson, or virtual photon, to a charged-lepton pair. We also provide distributions of the transverse momenta of the four jets, and we compare cross sections and distributions to the corresponding ones for the production of a W boson with accompanying jets.
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N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
We expose simple and practical relations between the integrated four- and five-point one-loop amplitudes of N >= 4 supergravity and the corresponding (super-)Yang-Mills amplitudes. The link between the amplitudes is simply understood using the recently uncovered duality between color and kinematics that leads to a double-copy structure for gravity. These examples provide additional direct confirmations of the duality and double-copy properties at loop level for a sample of different theories.
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