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Matthias Steinhauser

Publications and source records attributed to Matthias Steinhauser.

At least 73 records · Page 4Linked to original sources
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

Exact results for $Z_m^{\rm OS}$ and $Z_2^{\rm OS}$ with two mass scales and up to three loops

We consider the on-shell mass and wave function renormalization constants $Z_m^{\rm OS}$ and $Z_2^{\rm OS}$ up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters $\sqrt{1-τ^2}$ and $\sqrt{1-τ^2}/τ$ which extends the findings from Ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order ${\cal O}(ε^2)$ and ${\cal O}(ε)$ at two- and three-loop order which are crucial ingrediants for a future four-loop calculation. Compact results for the expansions around the zero-mass, equal-mass and large-mass cases allow for a fast high-precision numerical evaluation.

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arXiv2020

Matching the heavy-quark fields in QCD and HQET at four loops

The QCD/HQET matching coefficient for the heavy-quark field is calculated up to four loops. It must be finite; this requirement produces analytical results for some terms in the four-loop on-shell heavy-quark field renormalization constant which were previously only known numerically. The effect of a non-zero lighter-flavor mass is calculated up to three loops. A class of on-shell integrals with two masses is analyzed in detail. By specifying our result to QED, we obtain the relation between the electron field and the Bloch--Nordsieck field with four-loop accuracy.

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arXiv2020

Gauge and Yukawa coupling beta functions of two-Higgs-doublet models to three-loop order

We compute the beta functions for the three gauge couplings and the Yukawa matrices of a general two-Higgs-doublet model in the modified minimal subtraction scheme to three loops. The calculations are performed using Lorenz gauge in the unbroken phase. We discuss in detail the occurence of poles in anomalous dimensions and propose practical prescriptions to avoid them. We provide explicit results for the often used $\mathbb{Z}_2$-symmetric versions of the two-Higgs-doublet model of type I, II, X and Y. Furthermore, we provide the first independent cross-check of the three-loop Yukawa coupling beta functions of the Standard Model.

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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

Matching coefficients in NRQCD to two-loop accuracy

We consider the Lagrange density of non-relativistic Quantum Chromodynamics expanded up to order $1/m^2$, where $m$ is the heavy quark mass, and compute several matching coefficients up to two-loop order. Our results are building blocks for next-to-next-to-next-to-leading logarithmic and next-to-next-to-next-to-next-to-leading order corrections to the threshold production of top quark pairs and the decay of heavy quarkonia. We describe the techniques used for the calculation and provide analytic results for a general covariant gauge.

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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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arXiv2019

Four-loop quark form factor with quartic fundamental colour factor

We analytically compute the four-loop QCD corrections for the colour structure $(d_F^{abcd})^2$ to the massless non-singlet quark form factor. The computation involves non-trivial non-planar integral families which have master integrals in the top sector. We compute the master integrals by introducing a second mass scale and solving differential equations with respect to the ratio of the two scales. We present details of our calculational procedure. Analytical results for the cusp and collinear anomalous dimensions, and the finite part of the form factor are presented. We also provide analytic results for all master integrals expanded up to weight eight.

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arXiv2018

Wilson coefficients for Higgs boson production and decoupling relations to $\mathcal{O}\left(α_s^4\right)$

An important ingredient for the calculation of Higgs boson properties in the infinite top quark mass limit is the knowledge of the effective coupling between the Higgs bosons and gluons, i.e. the Wilson coefficients $C_H$ and $C_{HH}$ for one and two Higgs bosons, respectively. In this work we calculate for the first time $C_{HH}$ to four loops in a direct, diagrammatic way, discussing in detail all issues arising due to the renormalization of operator products. Furthermore, we also calculate the Wilson coefficient $C_H$ for the coupling of a single Higgs boson to gluons as well as all four loop decoupling relations in QCD with general SU$(N_c)$ colour factors. The latter are related to $C_H$ and $C_{HH}$ via low-energy theorems.

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arXiv2018

Massive quark form factors

In this contribution we provide further details to the recent calculation of QCD corrections to massive three-loop form factors presented in Ref. [1].

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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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