arXiv subjects

Ciaran Williams

Publications and source records attributed to Ciaran Williams.

At least 19 recordsLinked to original sources

arXiv2025

Electroweak corrections to $gg\rightarrow \gamma\gamma$

We present the electroweak corrections for the production of a photon pair through gluon fusion, focusing on the contribution from the first two generations of quarks. The two-loop amplitude is calculated using a series of projection operators which define scalar form factors. In order to evaluate the Master Integrals which appear in this process we employ both generalized polylogarithms and Chen-iterated integrals. In order to perform a phenomenological study we develop a semi-numerical evaluation of the Master Integrals employing a fitting procedure to speed up the evaluation of burdensome higher weight contributions. We present results for the LHC, finding corrections of around a couple of percent to the leading order $gg \rightarrow \gamma\gamma$ process. Our results are implemented into the parton-level Monte Carlo code \texttt{MCFM}.

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arXiv2024

Pseudoscalar Higgs plus jet production at Next-to-Next-to-Leading Order in QCD

We present a calculation of pseudoscalar Higgs production in association with a jet at Next-to-Next-to Leading Order (NNLO) accuracy in QCD. We work in an effective field theory in which $m_t \rightarrow \infty$ resulting in effective operators which couple the pseudoscalar to gluons and (massless) quarks. We have calculated all of the relevant amplitudes for the two-loop, one-loop and tree-level contributions. As a cross-check of our calculation we have re-calculated all of the scalar Higgs plus parton amplitudes and perform a detailed comparison to the literature. In order to regulate the infra-red singularities present at this order we employ the $N-$jettiness slicing method. In addition to a detailed validation of our calculation at this order we investigate LHC phenomenology for a selection of pseudoscalar Higgs masses. Our results are implemented into the parton-level Monte Carlo code MCFM.

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arXiv2024

Ad interim recommendations for the Higgs boson production cross sections at $\sqrt{s} = 13.6$ TeV

This note documents predictions for the inclusive production cross sections of the Standard Model Higgs boson at the Large Hadron Collider at a centre of mass energy of 13.6 TeV. The predictions here are based on simple extrapolations of previously documented predictions published in the CERN Yellow Report "Deciphering the Nature of the Higgs Sector". The predictions documented in this note should serve as a reference while a more complete and update-to-date derivation of cross section predictions is in progress.

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arXiv2023

Four-jet event shapes in hadronic Higgs decays

We present next-to-leading order perturbative QCD predictions for four-jet-like event-shape observables in hadronic Higgs decays. To this end, we take into account two Higgs-decay categories: involving either the Yukawa-induced decay to a $b\bar{b}$ pair or the loop-induced decay to two gluons via an effective Higgs-gluon-gluon coupling. We present results for distributions related to the event-shape variables thrust minor, light-hemisphere mass, narrow jet broadening, $D$-parameter, and Durham four-to-three-jet transition variable. For each of these observables we study the impact of higher-order corrections and compare their size and shape in the two Higgs-decay categories. We find large NLO corrections with a visible shape difference between the two decay modes, leading to a significant shift of the peak in distributions related to the $H\to gg$ decay mode.

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arXiv2023

Master Integrals for Electroweak corrections to $gg \to\gamma\gamma$ -- Light quark contributions

We present a calculation of the master integrals (MI's) required for the calculation of the Electroweak corrections to $gg\rightarrow \gamma\gamma$ production in which the process contains a light quark loop. The integrals can be broken down into five categories based on the flow of the heavy vector bosons throughout the loop. Three of the families are planar, and two are non-planar. We determine a canonical basis for each family which allows an efficient solution of the resulting differential equations via iterated integrals. We calculate the families in relevant physical kinematics and obtain an efficient numerical evaluation based on an implementation of Chen-iterated integrals.

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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.

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arXiv2021

Bottom-induced contributions to Higgs plus jet at next-to-next-to-leading order

We present a next-to-next-to-leading order (NNLO) QCD calculation of the bottom-induced contributions to the production of a Higgs boson plus a jet, i.e. the process $p p \rightarrow H +j$ to $\mathcal{O}(y_b^2 α_s^3)$. We work in the five-flavor scheme (5FS) in which the bottom quark mass is retained only in the coupling to the Higgs boson. Our calculation uses $N$-jettiness slicing to regulate infrared divergences, allowing for fully-differential predictions for collider observables. After extensively validating the methodology, we present results for the 13 TeV LHC. Our NNLO predictions show a marked improvement in the overall renormalization and factorization scale dependence, the latter of which proves to be particularly troublesome for 5FS calculations at lower orders. In addition, using the same methodology we present a NNLO computation of $b\overline{b} \rightarrow H$. Our results are implemented into MCFM.

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arXiv2020

Top-induced contributions to $H\rightarrow b\bar{b}$ and $H\rightarrow c\bar{c}$ at $\mathcal{O}(α_s^3)$

In this paper we present a fully-differential calculation for the contributions to the partial widths $H\rightarrow b\bar{b}$ and $H\rightarrow c\bar{c}$ that are sensitive to the top quark Yukawa coupling $y_t$ to order $α_s^3$. These contributions first enter at order $α_s^2$ through terms proportional to $y_t y_q$ ($q=b,c$). At order $α_s^3$ corrections to the mixed terms are present as well as a new contribution proportional to $y_t^2$. Our results retain the mass of the final-state quarks throughout, while the top quark is integrated out resulting in an effective field theory (EFT). Our results are implemented into a Monte Carlo code allowing for the application of arbitrary final-state selection cuts. As an example we present differential distributions for observables in the Higgs boson rest frame using the Durham jet clustering algorithm. We find that the total impact of the top-induced (i.e. EFT) pieces is sensitive to the nature of the final-state cuts, particularly b-tagging and c-tagging requirements. For bottom quarks, the EFT pieces contribute to the total width (and differential distributions) at around the percent level. The impact is much bigger for the $H\rightarrow c\bar{c}$ channel, with effects as large as 15%. We show however that their impact can be significantly reduced by the application of jet-tagging selection cuts.

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arXiv2019

$H \rightarrow b\overline{b}j$ at Next-to-Next-to-Leading Order Accuracy

We present the calculation of the decay $H \rightarrow b\overline{b}j$ at next-to-next-to-leading order (NNLO) accuracy. We consider contributions in which the Higgs boson couples directly to bottom quarks, i.e. our predictions are accurate to order $\mathcal{O}(α_s^3 y_b^2)$ . We calculate the various components needed to construct the NNLO contribution, including an independent calculation of the two-loop amplitudes. We compare our results for the two-loop amplitudes to an existing calculation finding agreement. We present multiple checks on our two-loop expression using the known infrared factorization properties as the emitted gluon becomes soft or collinear. We use our results to construct a Monte Carlo implementation of $H \rightarrow b\overline{b}j$ and present jet rates and differential distributions in the Higgs rest frame using the Durham jet algorithm.

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arXiv2019

The interplay between SM precision, BSM physics and measurements of $α_{\rm{had}}$ in $μ$-$e$ scattering

Muon electron scattering experiments such as the proposed MUonE experiment, offer an opportunity for an improved measurement of the Leading Order hadronic running of $α$, denoted $Δα_{\rm{had}}$. Such a measurement could be utilized to reduce the theoretical uncertainty on the prediction of the anomalous magnetic moment of the muon, $g-2$. Currently there is a discrepancy between theory and data for this observable which could potentially be explained by Beyond the Standard Model (BSM) physics. Here we investigate the possible impact of missing Standard Model (SM) higher order corrections and BSM physics on the proposed measurement of $Δα_{\rm{had}}$. In principle either could be indirectly fitted into $Δα_{\rm{had}}$, causing inconsistencies if used in a $g-2$ application. The literature suggests a target of 10 ppm on the cross section for the theoretical accuracy. We assess the validity of this target in detail using a variety of methods, finding that a 1 ppm target is a more conservative estimate to ensure missing higher orders do not dominate the theoretical uncertainty. For the potential BSM contributions we study various models which contribute first at tree- and loop-level. Of particular interest is the impact from dark photon models, which can potentially affect the measurement of $Δα_{\rm{had}}$ at the desired accuracy. At loop-level there exists in general a kinematic suppression adequate to reduce the BSM contributions to a level which can be neglected for the extraction of $Δα_{\rm{had}}$.

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arXiv2019

N$^{3}$LO predictions for the decay of the Higgs boson to bottom quarks

We present a fully-differential calculation of the $H\rightarrow b\overline{b}$ decay at next-to-next- to-next-to-leading order (N$^3$LO) accuracy. Our calculation considers diagrams in which the Higgs boson couples directly to the bottom quarks, i.e. the perturbative order we consider is $\mathcal{O}(α_s^3y_b^2)$. In order to regulate the infrared divergences present at this order we use the Projection-to-Born technique coupled with N-jettiness slicing. After validating our methodology at next-to-next-to-leading order (NNLO) we present exclusive jet rates and differential distributions for jet observables at N3LO accuracy using the Durham jet algorithm in the Higgs rest frame.

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arXiv2018

Direct photon production and PDF fits reloaded

Direct photon production in hadronic collisions provides a handle on the gluon PDF by means of the QCD Compton scattering process. In this work we revisit the impact of direct photon production on a global PDF analysis, motivated by the recent availability of the next-to-next-to-leading (NNLO) calculation for this process. We demonstrate that the inclusion of NNLO QCD and leading-logarithmic electroweak corrections leads to a good quantitative agreement with the ATLAS measurements at 8 TeV and 13 TeV, except for the most forward rapidity region in the former case. By including the ATLAS 8 TeV direct photon production data in the NNPDF3.1 NNLO global analysis, we assess its impact on the medium-x gluon. We also study the constraining power of the direct photon production measurements on PDF fits based on different datasets, in particular on the NNPDF3.1 no-LHC and collider-only fits. We also present updated NNLO theoretical predictions for direct photon production at 13 TeV that include the constraints from the 8 TeV measurements.

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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.

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arXiv2017

$Zγ$ production at NNLO including anomalous couplings

In this paper we present a next-to-next-to-leading order (NNLO) QCD calculation of the processes $pp\rightarrow l^+l^-γ$ and $pp\rightarrow ν\barνγ$ that we have implemented in MCFM. Our calculation includes QCD corrections at NNLO both for the Standard Model (SM) and additionally in the presence of $Zγγ$ and $ZZγ$ anomalous couplings. We compare our implementation, obtained using the jettiness slicing approach, with a previous SM calculation and find broad agreement. Focusing on the sensitivity of our results to the slicing parameter, we show that using our setup we are able to compute NNLO cross sections with numerical uncertainties of about $0.1\%$, which is small compared to residual scale uncertainties of a few percent. We study potential improvements using two different jettiness definitions and the inclusion of power corrections. At $\sqrt{s}=13$ TeV we present phenomenological results and consider $Zγ$ as a background to $H\to Zγ$ production. We find that, with typical cuts, the inclusion of NNLO corrections represents a small effect and loosens the extraction of limits on anomalous couplings by about $10\%$.

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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.

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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.

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arXiv2016

The Higgs boson at high $p_T$

We present a calculation of $H+j$ at NLO including the effect of a finite top-mass. Where possible we include the complete dependence on $m_t$. This includes the leading order amplitude, the infrared poles of the two-loop amplitude and the real radiation amplitude. The remaining finite piece of the virtual correction is considered in an asymptotic expansion in $m_t$, which is accurate to $m_t^{-4}$. By successively including more $m_t$-exact pieces, the dependence on the asymptotic series diminishes and we find convergent behavior for $p_T^H>m_t$ for the first time. Our results justify rescaling by the $m_t$-exact LO cross section to model top-mass effects in EFT results up to $p_T$ of 250 to 300 GeV. We show that the error made by using the LO rescaling becomes comparable to the NNLO scale uncertainty for such large energies. We implement our results into the Monte Carlo code MCFM.

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arXiv2016

Higher Order QCD predictions for Associated Higgs production with anomalous couplings to gauge bosons

We present predictions for the associated production of a Higgs boson at NLO+PS accuracy, including the effect of anomalous interactions between the Higgs and gauge bosons. We present our results in different frameworks, one in which the interaction vertex between the Higgs boson and Standard Model $W$ and $Z$ bosons is parameterized in terms of general Lorentz structures, and one in which Electroweak symmetry breaking is manifestly linear and the resulting operators arise through a six-dimensional effective field theory framework. We present analytic calculations of the Standard Model and Beyond the Standard Model contributions, and discuss the phenomenological impact of the higher order pieces. Our results are implemented in the NLO Monte Carlo program MCFM, and interfaced to shower Monte Carlos through the {\sc Powheg} box framework.

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