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Joshua Davies

Publications and source records attributed to Joshua Davies.

At least 37 records · Page 2Linked to original sources
arXiv2021

Top quark mass corrections to single and double Higgs boson production in gluon fusion

In this talk we discuss recent computations of the top quark mass dependence of QCD amplitudes describing Higgs boson production in gluon fusion. We compute terms in the expansion for a large top quark mass, which reduces the Feynman diagrams to products of massless integrals and massive tadpole integrals which contain the top mass dependence. In particular we discuss the real and virtual corrections to double Higgs production at NNLO, and the virtual corrections to single Higgs production at N3LO.

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arXiv2021

General Gauge-Yukawa-Quartic $β$-Functions at 4-3-2--Loop Order

We determine the full set of coefficients for the completely general 4-loop gauge and 3-loop Yukawa $ β$-functions for the most general renormalizable four-dimensional theories. Using a complete parametrization of the $ β$-functions, we compare the general form to the specific $ β$-functions of known theories to constrain the unknown coefficients. The Weyl consistency conditions provide additional constraints, completing the determination.

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arXiv2021

Real corrections to Higgs boson pair production at NNLO in the large top quark mass limit

In this paper we consider the next-to-next-to-leading order total cross section of Higgs boson pair production in the large top quark mass limit and compute four expansion terms in $1/m_t^2$. Good convergence is observed below the top quark threshold, which makes our results a valuable input for approximation methods which aim for next-to-next-to-leading order corrections over the whole kinematic range. We present details on various steps of our calculation; in particular, we provide results for three- and four-particle phase-space master integrals and describe in detail the evaluation of the collinear counterterms.

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arXiv2021

Higgs boson decay into photons at four loops

Future precision measurements of Higgs boson decays will determine the branching fraction for the decay into two photons with a precision at the one percent level. To fully exploit such measurements, equally precise theoretical predictions need to be available. To this end we compute four-loop QCD corrections in the large top quark mass expansion to the Higgs boson--photon form factor, which enter the two-photon decay width at next-to-next-to-next-to-leading order. Furthermore we obtain corrections to the two-photon decay width stemming from the emission of additional gluons, which contribute for the first time at next-to-next-to-leading order. Finally, we combine our results with other available perturbative corrections and estimate the residual uncertainty due to missing higher-order contributions.

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arXiv2020

Virtual corrections to $gg\to ZH$ in the high-energy and large-$m_t$ limits

We compute the next-to-leading order virtual corrections to the partonic cross-section of the process $gg\to ZH$, in the high-energy and large-$m_t$ limits. We use Padé approximants to increase the radius of convergence of the high-energy expansion in $m_t^2/s$, $m_t^2/t$ and $m_t^2/u$ and show that precise results can be obtained down to energies which are fairly close to the top quark pair threshold. We present results both for the form factors and the next-to-leading order virtual cross-section.

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arXiv2020

Top quark mass dependence of the Higgs-gluon form factor at three loops

We compute three-loop corrections to the Higgs-gluon form factor, incorporating the top quark mass dependence. Our method is based on the combination of expansions around the top threshold and for large top quark mass, using conformal mapping and Padé approximation to describe the form factor over the full kinematic range.

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arXiv2020

Padé approach to top-quark mass effects in gluon fusion amplitudes

Gluon fusion processes like single and double Higgs production exhibit slow convergence and pose severe computational challenges. We show how the top-quark mass dependence of the virtual amplitudes can be reconstructed with a conformal mapping and Padé approximants based on the expansion in the inverse top-quark mass and the non-analytic terms in the expansion around the top threshold. The method is then applied at two- and three-loop order.

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arXiv2020

$gg\to ZZ$: analytic two-loop results for the low- and high-energy regions

We compute next-to-leading order virtual two-loop corrections to the process $gg\to ZZ$ in the low- and high-energy limits, considering the contributions with virtual top quarks. Analytic results for all 20 form factors are presented including expansion terms up to $1/m_t^{12}$ and $m_t^{32}$. We use a Padé approximation procedure to extend the radius of convergence of the high-energy expansion and apply this approach to the fini\ te virtual next-to-leading order corrections.

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arXiv2019

Gauge coupling beta functions to four-loop order in the Standard Model

We compute the beta functions of the three Standard Model gauge couplings to four-loop order in the modified minimal subtraction scheme. At this order a proper definition of $γ_5$ in $D=4-2ε$ space-time dimensions is required; however, in our calculation we determine the $γ_5$-dependent terms by exploiting relations with beta function coefficients at lower loop orders.

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arXiv2019

NNLO real corrections to $gg\to HH$ in the large-$m_t$ limit

In this contribution we consider NNLO real radiation corrections to the total cross section for Higgs boson pair production in gluon fusion. Special emphasis is put on the cross check of the asymptotic expansion in the inverse top quark mass.

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arXiv2019

Three-loop form factors for Higgs boson pair production in the large top mass limit

We consider the virtual corrections to Higgs boson pair production at next-to-next-to-leading order, in the large top quark mass limit. We compute five expansion terms for the box-type form factors and eight expansion terms for the triangle form factor, which serve as useful input for the construction of approximations. We present analytic results for the form factors in the soft-virtual approximation. From a technical point of view the calculation is quite challenging since huge intermediate expressions are produced. We describe our methods and optimizations to overcome these difficulties, which might be useful for other calculations.

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arXiv2019

Double Higgs boson production at NLO: combining the exact numerical result and high-energy expansion

We consider the next-to-leading order QCD corrections to Higgs boson pair production, using our recent calculation of the form factors in the high-energy limit. We compute the virtual corrections to the partonic cross section, applying Padé approximations to extend the range of validity of the high-energy expansion. This enables us to compare to the exact numerical calculation in a significant part of the phase space and allows us to extend the virtual matrix element grid, based on the exact numerical calculation, to larger values of the (partonic) transverse momentum of the Higgs boson, which is important for boosted Higgs studies. Improved predictions for hadron colliders with centre-of-mass energies of $14\ \mathrm{TeV}$ and $100\ \mathrm{TeV}$ are presented. The updated grid is made publicly available.

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arXiv2019

Real-virtual corrections to Higgs boson pair production at NNLO: three closed top quark loops

We compute the real-radiation corrections to Higgs boson pair production at next-to-next-to-leading order in QCD, in an expansion for large top quark mass. We concentrate on the radiative corrections to the interference contribution from the next-to-leading order one-particle reducible and the leading order amplitudes. This is a well defined and gauge invariant subset of the full real-virtual corrections to the inclusive cross section. We obtain analytic results for all phase-space master integrals both as an expansion around the threshold and in an exact manner in terms of Goncharov polylogarithms.

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arXiv2019

Double Higgs boson production at NLO in the high-energy limit: complete analytic results

We compute the NLO virtual corrections to the partonic cross section of $gg\to HH$, in the high energy limit. Finite Higgs boson mass effects are taken into account via an expansion which is shown to converge quickly. We obtain analytic results for the next-to-leading order form factors which can be used to compute the cross section. The method used for the calculation of the (non-planar) master integrals is described in detail and explicit results are presented.

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arXiv2018

Double-Higgs boson production in the high-energy limit: planar master integrals

We consider the virtual corrections to the process $gg\to HH$ at NLO in the high energy limit and compute the corresponding planar master integrals in an expansion for small top quark mass. We provide details on the evaluation of the boundary conditions and present analytic results expressed in terms of harmonic polylogarithms.

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arXiv2017

The Large-$n_f$ Limit of the Four-Loop Splitting Functions in QCD

These proceedings describe a computation of the large-$n_f$ terms contributing to the QCD splitting functions at the fourth order in the strong coupling constant $α_s$. Using the FORCER package for the reduction of four-loop two-point Feynman integrals, Mellin moments of the four-loop splitting functions have been computed. These moments are used to derive analytic Mellin-space expressions, by forming and finding solutions to systems of Diophantine equations. Expressions for the terms proportional to $n_f^3$ of the flavour singlet, and to $n_f^2$ of the flavour non-singlet splitting functions have been determined.

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arXiv2017

Hadronic Higgs boson decay at order $α_s^4$ and $α_s^5$

We compute corrections to the decay of the Standard Model Higgs boson to hadrons, to the fourth order in the strong coupling constant $α_s$. We use an effective theory in which the Higgs boson couples directly to bottom quarks and to gluons, via top quark--mediated effective couplings. Numerically, our results are of a comparable size to the previously-known "massless" contributions and complete the order $α_s^4$ corrections to the hadronic decay of the Higgs boson. In these proceedings we also provide an independent cross check of the gluonic Higgs boson decay at order $α_s^5$.

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