arXiv subjects

R. Keith Ellis

Publications and source records attributed to R. Keith Ellis.

At least 19 recordsLinked to original sources

arXiv2025

An analytic result for the $0 \to ggHHH$ amplitude

We present a fully analytic calculation of the leading-order one-loop amplitude for triple Higgs production via gluon fusion, $gg \to HHH$, retaining full dependence on the mass of the heavy quark circulating in the loop. This amplitude provides a direct probe of the triple and quartic Higgs self-couplings, the measurement of which is a central goal of current and future colliders. The amplitude can be presented in compact form thanks to the use of analytic reconstruction techniques, based on finite-field and $p$-adic evaluations, partial fraction decompositions, and primary decompositions to identify common numerator factors. Our results provide a compact and efficient representation of the matrix element for this process, enabling evaluations that are more than an order of magnitude faster than existing numerical alternatives.

hep-ph↗

arXiv2025

Analytic reconstruction with massive particles: one-loop amplitudes for $0 \to \bar{q}qt\bar{t}H$

We present an analytic reconstruction of one-loop amplitudes for the process $0 \to \bar{q}qt\bar{t}H$. Our calculation is a novel use of analytic reconstruction, retaining explicit covariance in the massive spin states through the massive spinor-helicity formalism. The analytic reconstruction relies on embedding the massive five-point kinematics in a fully massless eight-point phase space while still building a minimal ansatz directly in the five-point phase space. In order to obtain compact analytic expressions it is necessary to identify suitable partial fraction decompositions and extract common numerator factors, which we achieve through careful inspection of limits in which pairs of denominators vanish. We find that the resulting amplitudes are more numerically efficient than ones computed using automatic methods but that the gains are not as significant as in the massless case, at least at present. The method opens the door to applications at two-loop order, where numerical efficiency and improvements in the reconstruction methodology are more crucial, especially with regards to the number of free parameters in the ansatz.

hep-ph↗

arXiv2024

Analytic amplitudes for a pair of Higgs bosons in association with three partons

The pair production of Higgs bosons at the LHC can give information about the triple Higgs boson coupling. We perform an analytic one-loop calculation of the amplitudes for a pair of Higgs bosons in association with three partons, retaining the exact dependence on the quark mass circulating in the loop. These amplitudes constitute the real radiation corrections in the calculation of Higgs boson pair production at next-to-leading order in the strong coupling. The results of an analytic generalised-unitarity computation are simplified via analytic reconstruction in spinor variables. Compact ansätze for kinematic pole residues are iteratively fitted via $p$-adic evaluations near said poles and subtracted until no pole remains. A new ansatz construction is introduced to minimally parametrise coefficients of amplitudes with multiple massive external legs. The simplified expressions are faster to evaluate than automatic codes and can lead to more stable results near singular regions.

hep-ph↗

arXiv2023

Top tree amplitudes for higher order calculations

We present compact analytic results for tree-level amplitudes containing a $t \bar{t}$ pair accompanied by up to four massless partons, $t \bar{t}gg$, $t \bar{t}ggg$, $t \bar{t}gggg$, $t \bar{t}q\bar{q}$, $t \bar{t}q\bar{q}g$, $t \bar{t}q\bar{q}gg$ and $t\bar{t}q\bar{q}q^\prime \bar{q}^\prime$. The results, obtained using BCFW on-shell recursion, are based both on previous published results and on the new calculations performed in this paper. These amplitudes are sufficient to calculate the production of a $t\bar{t}$ pair and zero, one, or two light parton jets, with the option to include the tree-level decays $t \to b νe^+$ and $\bar{t} \to \bar{b} e^- \barν$ efficiently. Our results are part of the NNLO corrections to $t \bar{t}$ production including the decay correlations for on-shell top quarks.

hep-ph↗

arXiv2023

Jet-veto resummation at N$^3$LL$_\text{p}$+NNLO in boson production processes

Vetoing energetic jet activity is a crucial tool for suppressing backgrounds and enabling new physics searches at the LHC, but the introduction of a veto scale can introduce large logarithms that may need to be resummed. We present an implementation of jet-veto resummation for color-singlet processes at the level of N$^3$LL$_\text{p}$ matched to fixed-order NNLO predictions. Our public code MCFM allows for predictions of a single boson, such as $Z/γ^*$, $W^{\pm}$ or $H$, or with a pair of vector bosons, such as $W^+W^-$, $W^{\pm} Z$ or $ZZ$. The implementation relies on recent calculations of the soft and beam functions in the presence of a jet veto over all rapidities, with jets defined using a sequential recombination algorithm with jet radius $R$. However one of the ingredients that is required to reach full N$^3$LL accuracy is only known approximately, hence N$^3$LL$_\text{p}$. We describe in detail our formalism and compare with previous public codes that operate at the level of NNLL. Our higher-order predictions improve significantly upon NNLL calculations by reducing theoretical uncertainties. We demonstrate this by comparing our predictions with ATLAS and CMS results.

hep-ph↗

arXiv2022

Transverse momentum resummation at N3LL+NNLO for diboson processes

Diboson processes are one of the most accessible and stringent probes of the Standard Model's electroweak gauge structure at the LHC. They will be probed at the percent level at the high-luminosity LHC, challenging current theory predictions. We present transverse momentum resummed calculations at N3LL+NNLO for the processes $ZZ$, $WZ$, $WH$ and $ZH$, compare our predictions with most recent LHC data and present predictions at 13.6 TeV including theory uncertainty estimates. For $W^+W^-$ production we further present jet-veto resummed results at N3LLp+NNLO. Our calculations will be made publicly available in the upcoming MCFM release and allow future analyses to take advantage of improved predictions.

hep-ph↗

arXiv2022

Non-local slicing approaches for NNLO QCD in MCFM

We present the implementation of several processes at Next-to-Next-to Leading Order (NNLO) accuracy in QCD in the parton-level Monte Carlo program MCFM. The processes treated are $pp\to H$, $W^\pm$, $Z$, $W^\pm H$, $ZH$, $W^\pmγ$, $Zγ$ and $γγ$ and, for the first time in the code, $W^+W^-$, $W^\pm Z$ and $ZZ$. Decays of the unstable bosons are fully included, resulting in a flexible fully differential Monte Carlo code. The NNLO corrections have been calculated using two non-local slicing approaches, isolating the doubly unresolved region by cutting on the zero-jettiness, ${\cal T}_0$, or on $q_T$, the transverse momentum of the colour singlet final-state particles. We find that for most, but not all processes the $q_T$ slicing method leads to smaller power corrections for equal computational burden.

hep-ph↗

arXiv2022

The one-loop amplitudes for Higgs + 4 partons with full mass effects

We present compact analytic formulae for the one-loop amplitudes for Higgs + 4 parton scattering, $0 \to g g g g h$, $0 \to \bar{q} q gg h$ and $0\to \bar{q} q \bar{q}^\prime q^\prime h$, mediated by a loop of massive coloured quarks. We exploit the correspondence with a theory in which a massive coloured scalar circulates in the loop to avoid a proliferation in the number of terms in the result. In addition, we use momentum twistors and high precision numerical evaluations to simplify the expressions. The analytic results in this paper, in terms of spinor products, allow construction of an efficient numerical program to calculate the amplitude.

hep-ph↗

arXiv2022

Vector boson pair production at one loop: analytic results for the process $q \bar{q} \ell \bar\ell \ell^\prime \bar{\ell}^\prime g$

We present compact analytic results for the one-loop amplitude for the process $0 \rightarrow q \bar{q} \ell \bar\ell \ell^\prime \bar{\ell}^\prime g$, relevant for both the production of a pair of $Z$ and $W$-bosons in association with a jet. We focus on the gauge-invariant contribution mediated by a loop of quarks. We explicitly include all effects of the loop-quark mass $m$, appropriate for the production of a pair of $Z$-bosons. In the limit $m \to 0$, our results are also applicable to the production of $W$-boson pairs, mediated by a loop of massless quarks. Implemented in a numerical code, the results are fast. The calculation uses novel advancements in spinor-helicity simplification techniques, for the first time applied beyond five-point massless kinematics. We make use of primary decompositions from algebraic-geometry, which now involve non-radical ideals, and $p$-adic numbers from number theory. We show how to infer whether numerator polynomials belong to symbolic powers of non-radical ideals through numerical evaluations.

hep-ph↗

arXiv2021

Predictions for diphoton production at the LHC through NNLO in QCD

In this paper we present a next-to-next-to-leading order (NNLO) calculation of the process $pp\rightarrow γγ$ that we have implemented into the parton level Monte Carlo code MCFM. We do not find agreement with the previous calculation of this process in the literature. In addition to the $\mathcal{O}(α_s^2)$ corrections present at NNLO, we include some effects arising at $\mathcal{O}(α_s^3)$, namely those associated with gluon-initiated closed fermion loops. We investigate the role of this process in the context of studies of QCD at colliders and as a background for searches for new physics, paying particular attention to the diphoton invariant mass spectrum. We demonstrate that the NNLO QCD prediction for the shape of this spectrum agrees well with functional forms used in recent data-driven fits.

hep-ph↗

arXiv2021

The $pp\to W(\to lν)+γ$ process at next-to-next-to-leading order

We present details of the calculation of the $pp\to W(\to lν) γ$ process at next-to-next-to-leading order in QCD, calculated using the jettiness slicing method. The calculation is based entirely on analytic amplitudes. Because of the radiation zero, the NLO QCD contribution from the $gq$ channel is as important as the contribution from the Born $q\bar{q}$ process, disrupting the normal counting of leading and sub-leading contributions. We also assess the importance of electroweak (EW) corrections, including the EW corrections to both the six-parton channel $0\to \bar{u} d νe^+γg$ and the five-parton channel $0\to \bar{u} d νe^+ γ$. Previous experimental results have been shown to agree with theoretical predictions, taking into account the large experimental errors. With the advent of run II data from the LHC, the statistical errors on the data will decrease, and will be competitive with the error on theoretical predictions for the first time. We present numerical results for $\sqrt{s}=7$ and 13 TeV. Analytic results for the one-loop six-parton QCD amplitude and the tree-level seven-parton QCD amplitude are presented in appendices.

hep-ph↗

arXiv2020

Analytic results for scalar-mediated Higgs boson production in association with two jets

We present compact analytic formulae for all one-loop amplitudes representing the production of a Higgs boson in association with two jets, mediated by a colour triplet scalar particle. Many of the integral coefficients present for scalar mediators are identical to the case when a massive fermion circulates in the loop, reflecting a close relationship between the two theories. The calculation is used to study Higgs boson production in association with two jets in a simplified supersymmetry (SUSY) scenario in which the dominant additional contributions arise from loops of top squarks. The results presented here facilitate an indirect search for top squarks in this channel, by a precision measurement of the corresponding cross-section. However, we find that the potential for improved discrimination between the SM and SUSY cases suggested by the pattern of results in the 1- and 2-jet samples is unlikely to be realized due to the loss in statistical power compared to an inclusive analysis.

hep-ph↗

arXiv2019

H+1 jet production revisited

We revisit the next-to-next-to-leading order (NNLO) calculation of the Higgs boson+1~jet production process, calculated in the $m_t \to \infty$ effective field theory. We perform a detailed comparison of the result calculated using the jettiness slicing method, with published results obtained using subtraction methods. The results of the jettiness calculation agree with the two previous subtraction calculations at benchmark points. The performance of the jettiness slicing approach is greatly improved by adopting a definition of 1-jettiness that accounts for the boost of the Born system. Nevertheless, the results demonstrate that power corrections in the jettiness slicing method remain significant. At large transverse momentum the effect of power corrections is much reduced, as expected.

hep-ph↗

arXiv2018

On Higgs boson plus gluon amplitudes at one loop

We present analytic results for one-loop Higgs boson + $n$-gluon amplitudes for $n\le 5$ in the full theory including all dependence on the (top) quark mass. In this paper we consider only the case where the gluons all have the same helicity. The amplitudes are expressed in simple formula and display similar structure. Their limiting behaviour in small Higgs momentum and large top mass is studied.

hep-ph↗

arXiv2017

The NNLO QCD soft function for 1-jettiness

We calculate the soft function for the global event variable 1-jettiness at next-to-next-to-leading order (NNLO) in QCD. We focus specifically on the non-Abelian contribution, which, unlike the Abelian part, is not determined by the next-to-leading order result. The calculation uses the known general forms for the emission of one and two soft partons and is performed using a sector-decomposition method that is spelled out in detail. Results are presented in the form of numerical fits to the 1-jettiness soft function for LHC kinematics (as a function of the angle between the incoming beams and the final-state jet) and for generic kinematics (as a function of three independent angles). These fits represent one of the needed ingredients for NNLO calculations that use the N-jettiness event variable to handle infrared singularities.

hep-ph↗

arXiv2017

Driving Miss Data: Going up a gear to NNLO

In this paper we present a calculation of the $γ+j$ process at next-to-next-to-leading order (NNLO) in QCD and compare the resulting predictions to 8 TeV CMS data. We find good agreement with the shape of the photon $p_T$ spectrum, particularly after the inclusion of additional electroweak corrections, but there is a tension between the overall normalization of the theoretical prediction and the measurement. We use our results to compute the ratio of $Z(\to \ell^+\ell^-)+j$ to $γ+j$ events as a function of the vector boson transverse momentum at NNLO, a quantity that is used to normalize $Z(\rightarrowν\overlineν) +j$ backgrounds in searches for dark matter and supersymmetry. Our NNLO calculation significantly reduces the theoretical uncertainty on this ratio, thus boosting its power for future searches of new physics.

hep-ph↗

arXiv2016

Direct photon production at next-to-next-to-leading order

We present the first calculation of direct photon production at next-to-next-to leading order (NNLO) accuracy in QCD. For this process, although the final state cuts mandate only the presence of a single electroweak boson, the underlying kinematics resembles that of a generic vector boson plus jet topology. In order to regulate the infrared singularities present at this order we use the $N$-jettiness slicing procedure, applied for the first time to a final state that at Born level includes colored partons but no required jet. We compare our predictions to ATLAS 8 TeV data and find that the inclusion of the NNLO terms in the perturbative expansion, supplemented by electroweak corrections, provides an excellent description of the data with greatly reduced theoretical uncertainties.

hep-ph↗

arXiv2016

Top-quark loop corrections in Z+jet and Z+2 jet production

The sophistication of current predictions for $Z+$jet production at hadron colliders necessitates a re-evaluation of any approximations inherent in the theoretical calculations. In this paper we address one such issue, the inclusion of mass effects in top-quark loops. We ameliorate an existing calculation of $Z+1$~jet and $Z+2$~jet production by presenting exact analytic formulae for amplitudes containing top-quark loops that enter at next-to-leading order in QCD. Although approximations based on an expansion in powers of $1/m_t^2$ can lead to poor high-energy behavior, an exact treatment of top-quark loops demonstrates that their effect is small and has limited phenomenological interest.

hep-ph↗