arXiv subjects

Stefan Dittmaier

Publications and source records attributed to Stefan Dittmaier.

At least 19 recordsLinked to original sources

arXiv2026

Integrating out a heavy Higgs singlet: on the edge between SMEFT and HEFT

We use a functional approach based on the background-field formalism and the expansion by regions to integrate out the heavy Higgs field (associated with the mass eigenstate H) at the one-loop level in a singlet extension of the SM, which features an additional real scalar singlet and a spontaneously broken $Z_2$ symmetry. We obtain an effective Lagrangian to $O(1/M_H^2)$ in the limit of large Higgs mass ($M_H\gg M_h=125$GeV) providing a consistent treatment of effects from Higgs mixing and the renormalization of the underlying model. The scaling behaviour of the model parameters in the large-$M_H$ limit determines whether the effective Lagrangian can be accommodated in the SM Effective Field Theory (SMEFT) or involves non-SMEFT operators within the more general Higgs Effective Field Theory (HEFT) framework. We choose a limit that ensures decoupling of beyond-SM (BSM) effects at $O(M_H^0)$ by demanding that the Higgs mixing angle $α$ is of $O(M_h/M_H)$ and putting minimal constraints on the other input parameters. The considered model is restricted to massless fermions. Bottom-up (diagrammatic) matching with only bosonic SMEFT operators at $O(1/M_H^2)$ necessarily fails, although the BSM sector does not directly couple to massless fermions. However, it is possible to match SMEFT with bosonic and fermionic operators to the SESM in the considered large-$M_H$ limit. For the emerging Effective Field Theory (EFT) we give two alternative Lagrangians: one that includes only bosonic BSM EFT operators, but necessarily involves operators of non-SMEFT type, and another one that is of SMEFT form, but involves also fermionic EFT operators. We validate our results for the effective Lagrangians at NLO in the coupling expansion by verifying that the difference between EFT and full-theory predictions vanishes faster than $1/M_H^2$ for several electroweak observables in the large-$M_H$ limit.

hep-ph↗

arXiv2026

Effective Lagrangians from functional matching

We briefly review a variant of functional matching to derive an Effective Field Theory (EFT) for heavy particles at the one-loop level in the top-down approach. The method integrates out heavy fields that correspond to mass eigenstates, i.e. after removing mixing effects by diagonalizing mass matrices. Tree- and loop-level effects are separated by employing the background-field method, hard and soft modes are separated with the use of the expansion by regions. The method is exemplified for the Higgs Singlet Extension of the Standard Model where the mass $M_\mathrm{H}$ of the additional Higgs boson is considered large, and the Higgs mixing angle $α$ is assumed to scale like $1/M_\mathrm{H}$, in order to guarantee decoupling in the large-$M_\mathrm{H}$ limit. Our calculation is agnostic w.r.t. the type (SMEFT vs. HEFT) of the emerging EFT. Eventually the emerging EFT Lagrangian can be transformed into SMEFT form, but only at the cost of introducing fermionic EFT operators, although no such operators are directly generated upon solving the functional integral over the heavy Higgs field.

hep-ph↗

arXiv2026

The status of theory in the electroweak sector: Radiative corrections, salient features, approximations

Electroweak radiative corrections form a crucial ingredient in modern precision calculations for particle processes at high-energy colliders such as the Large Hadron Collider. The salient features of electroweak corrections as well as currently used techniques and concepts for their calculation are reviewed. Recent progress in this enterprise is illustrated in a discussion of electroweak multi-gauge-boson production processes: massive di-boson production, vector-boson scattering, and massive tri-boson production.

hep-ph↗

arXiv2025

Electroweak splitting functions in the Standard Model and beyond

We derive quasi-collinear factorization formulas in generic spontaneously broken gauge theories with scalars, fermions, and vector bosons. Specifically, we obtain polarized leading-order splitting functions for all possible final-state and initial-state 1->2 processes in the considered gauge theory. The main complication lies in the presence of mass-singular terms in longitudinal polarization vectors, prohibiting the direct application of the usual factorization procedure known from Quantum Electrodynamics and Quantum Chromodynamics. We overcome this issue with two different strategies, using gauge invariance and Ward identities as guiding principle. Our derivations do not use any explicit component-wise parametrizations of momenta and wave functions and bear no reference to a particular Lorentz frame. Furthermore, our results are valid for completely general definitions of the spin reference axes of the individual external particles. The various massless limits, the special case of the Electroweak Standard Model, the reproduction of existing literature results, and symmetry relations among our splitting functions are discussed in detail.

hep-ph↗

arXiv2025

Electroweak corrections to $τ^+τ^-$ production in ultraperipheral heavy-ion collisions at the LHC

While the anomalous magnetic moments of the electron and the muon have been measured with remarkable precision, the magnetic moment of the $τ$-lepton is only known to rather limited precision. A promising approach to measure it exploits $τ^+τ^-$ production in ultraperipheral collisions of lead ions at the LHC. In this article, a state-of-the-art theory prediction for $τ^+τ^-$ production including leptonic $τ$-decays is provided. The impact of spin correlations between the $τ$-leptons, of the masses of final-state leptons, of next-to-leading-order electroweak corrections, and of the parametrization of the photon flux are discussed.

hep-ph↗

arXiv2024

Confronting a Standard Model extension with a dark $U(1)$ gauge sector with the prediction for the W-boson mass

The Dark Abelian Sector Model (DASM) is an extension of the Standard Model of particle physics with an additional spontaneously broken $U_\text{d}(1)$ gauge symmetry connected to a dark sector, i.e. the SM particles do not carry the corresponding charge. In addition to the gauge boson resulting from the extra $U_\text{d}(1)$ gauge symmetry, the particle content is extended by a further Higgs boson, one Dirac fermion as well as right-handed neutrinos. Employing the $U_Y(1)$ field-strength tensor as well as the SM Higgs mass operator (the only two singlet operators of the SM with dimension less than four) and the right-handed neutrino fields, we open three portals to the dark sector. After an introduction of the model, we discuss a renormalization scheme for the complete model with a special focus on the renormalization of the mixing angles. Finally, as an example of application, we present the prediction for the W-boson mass derived from muon decay in the DASM.

hep-ph↗

arXiv2024

Full and approximated NLO predictions for like-sign W-boson scattering at the LHC

We report on a recent calculation of next-to-leading-order (NLO) QCD and electroweak corrections to like-sign W-boson scattering at the Large Hadron Collider, including all partonic channels and W-boson decays in the process $pp \to e^+ ν_e μ^+ ν_μjj + X$. The calculation is implemented in the Monte Carlo integrator Bonsay and comprises the full tower of NLO contributions of the orders $α_s^3α^4$, $α_s^2α^5$, $α_sα^6$, and $α^7$. Our numerical results confirm and extend previous results, in particular the occurrence of large purely electroweak corrections of the order of $\sim-12\%$ for integrated cross sections, which get even larger in distributions. We construct a "VBS approximation" for the NLO prediction based on partonic channels and gauge-invariant (sub)matrix elements potentially containing the vector-boson scattering (VBS) subprocess and on resonance expansions of the Wdecays. The VBS approximation reproduces the full NLO predictions within $\sim1.5\%$ in the most important regions of phase space. Moreover, we discuss results from different versions of "effective vector-boson approximations" at leading order, based on the collinear emission of W bosons of incoming (anti)quarks. However, owing to the only mild collinear enhancement and the design of VBS analysis cuts, the quality of this approximation turns out to be only qualitative at the LHC.

hep-ph↗

arXiv2024

Mixed NNLO QCD $\times$ electroweak corrections to single-Z production in pole approximation: differential distributions and forward-backward asymmetry

Radiative corrections in pole approximation, which are based on the leading contribution in a systematic expansion of amplitudes about resonance poles, naturally decompose into factorizable corrections attributed to the production or decay of the resonance and non-factorizable corrections induced by soft photon (or gluon) exchange between those subprocesses. In this paper we complete an earlier calculation of mixed QCD$\times$electroweak corrections of $\mathcal{O}(α_sα)$ to the neutral-current Drell-Yan cross section in pole approximation by including the previously neglected corrections that are solely related to the Z-boson production process. We present numerical results both for differential distributions and for the forward-backward asymmetry differential in the lepton-pair invariant mass, which is the key observable in the measurement of the effective weak mixing angle at the LHC. Carefully disentangling the various types of factorizable and non-factorizable corrections, we find (as expected in our earlier work) that the by far most important contribution at $\mathcal{O}(α_sα)$ originates from the interplay of initial-state QCD corrections and electroweak final-state corrections.

hep-ph↗

arXiv2024

Focus topics for the ECFA study on Higgs / Top / EW factories

In order to stimulate new engagement and trigger some concrete studies in areas where further work would be beneficial towards fully understanding the physics potential of an $e^+e^-$ Higgs / Top / Electroweak factory, we propose to define a set of focus topics. The general reasoning and the proposed topics are described in this document.

hep-ph↗

arXiv2023

Like-Sign W-Boson Scattering at the LHC -- Approximations and Full Next-to-Leading-Order Predictions

We present a new calculation of next-to-leading-order corrections of the strong and electroweak interactions to like-sign W-boson scattering at the Large Hadron Collider, implemented in the Monte Carlo integrator Bonsay. The calculation includes leptonic decays of the $\mathrm{W}$ bosons. It comprises the whole tower of next-to-leading-order contributions to the cross section, which scale like $α_\mathrm{s}^3α^4$, $α_\mathrm{s}^2α^5$, $α_\mathrm{s}α^6$, and $α^7$ in the strong and electroweak couplings $α_\mathrm{s}$ and $α$. We present a detailed survey of numerical results confirming the occurrence of large pure electroweak corrections of the order of $\sim-12\%$ for integrated cross sections and even larger corrections in high-energy tails of distributions. The electroweak corrections account for the major part of the complete next-to-leading-order correction, which amounts to $15{-}20\%$ in size, depending on the details of the event selection chosen for analysing vector-boson-scattering. Moreover, we compare the full next-to-leading-order corrections to approximate results based on the neglect of contributions that are not enhanced by the vector-boson scattering kinematics (VBS approximation) and on resonance expansions for the $\mathrm{W}$-boson decays (double-pole approximation); the quality of this approximation is good within $\sim 1.5\%$ for integrated cross sections and the dominating parts of the differential distributions. Finally, for the leading-order predictions, we construct different versions of effective vector-boson approximations, which are based on cross-section contributions that are enhanced by collinear emission of $\mathrm{W}$ bosons off the initial-state (anti)quarks; in line with previous findings in the literature, it turns out that the approximative quality is rather limited for applications at the LHC.

hep-ph↗

arXiv2023

Renormalization of a Standard Model Extension with a Dark Abelian Sector and Predictions for the W-Boson Mass

The described Dark Abelian Sector Model (DASM) extends the Standard Model (SM) by a ``dark'' sector containing a spontaneously broken $U(1)_\text{d}$ gauge group. Keeping this dark sector quite generic we only add one additional Higgs boson, one Dirac fermion, and right-handed SM-like neutrinos to the SM. Using the only two singlet operators of the SM with dimension less than 4 (the $U(1)_\text{Y}$ field-strength tensor and the SM Higgs mass operator $|Φ|^2$) as well as the right-handed neutrino fields we open up three portals to the dark sector. Dark sectors, such as the one of the DASM, that introduce an additional Higgs boson $\text{H}$ as well as an additional $\text{Z}'$ gauge boson can have a large influence on the predictions for electroweak precision observables and even accommodate possible dark matter candidates. We consider one of the two Higgs bosons to be the known $125\,\text{GeV}$ Higgs boson and parameterize the extension of the scalar sector by the mass of the second Higgs boson, the Higgs mixing angle, and a Higgs self-coupling. We do not assume any mass hierarchy in the gauge sector and use the mass of the additional $\text{Z}'$ boson and a corresponding gauge-boson mixing angle to parameterize the extension of the gauge sector. The fermion sector is parameterized by the mass of the additional fermion and a fermion mixing angle. We describe an on-shell as well as an $\overline{\text{MS}}$ renormalization scheme for the DASM sectors and give explicit results for the renormalization constants at the 1-loop level, and, thus, prepare the ground for full NLO predictions for collider observables in the DASM. As a first example, we provide the DASM prediction for the W-boson mass derived from muon decay.

hep-ph↗

arXiv2023

Electroweak renormalization based on gauge-invariant vacuum expectation values of non-linear Higgs representations: 2. extended Higgs sectors

A recently proposed scheme for a gauge-invariant treatment of tadpole corrections in spontaneously broken gauge theories - called Gauge-Invariant Vacuum expectation value Scheme (GIVS) - is applied to a singlet Higgs extension of the Standard Model and to the Two-Higgs Doublet Model. In contrast to previously used tadpole schemes, the GIVS unifies the gauge-invariance property with perturbative stability. For the Standard Model this was demonstrated for the conversion between on-shell and MSbar renormalized masses, where the GIVS leads to very moderate, gauge-independent electroweak corrections. In models with extended scalar sectors, issues with tadpole renormalization exist if Higgs mixing angles are renormalized with MSbar conditions, which is the major subject of this article. In detail, we first formulate non-linear representations of the extended scalar sectors, which is an interesting subject in its own right. Then we formulate the GIVS which employs these non-linear representations in the calculation of the tadpole renormalization constants, while actual higher-order calculations in the GIVS proceed in linear representations as usual. Finally, for the considered models we discuss the next-to-leading-order (electroweak and QCD) corrections to the decay processes $h/H\to WW/ZZ\to4\,$fermions of the CP-even neutral Higgs bosons h and H using MSbar-renormalized Higgs mixing angles with the GIVS and previously used tadpole treatments.

hep-ph↗

arXiv2023

Precise predictions for same-sign W-boson scattering at the LHC

Vector-boson scattering processes are of great importance for the current run-II and future runs of the Large Hadron Collider. The presence of triple and quartic gauge couplings in the process gives access to the gauge sector of the Standard Model (SM) and possible new-physics contributions there. To test any new-physics hypothesis, sound knowledge of the SM contributions is necessary, with a precision which at least matches the experimental uncertainties of existing and forthcoming measurements. In this article we present a detailed study of the vector-boson scattering process with two positively-charged leptons and missing transverse momentum in the final state. In particular, we first carry out a systematic comparison of the various approximations that are usually performed for this kind of process against the complete calculation, at LO and NLO QCD accuracy. Such a study is performed both in the usual fiducial region used by experimental collaborations and in a more inclusive phase space, where the differences among the various approximations lead to more sizeable effects. Afterwards, we turn to predictions matched to parton showers, at LO and NLO: we show that on the one hand, the inclusion of NLO QCD corrections leads to more stable predictions, but on the other hand the details of the matching and of the parton-shower programs cause differences which are considerably larger than those observed at fixed order, even in the experimental fiducial region. We conclude with recommendations for experimental studies of vector-boson scattering processes.

hep-ph↗

arXiv2022

Electroweak renormalization based on gauge-invariant vacuum expectation values

We briefly review a recently proposed scheme for a gauge-invariant treatment of tadpole corrections in spontaneously broken gauge theories called Gauge-Invariant Vacuum expectation value Scheme (GIVS). The tadpole scheme matters in higher-order predictions of observables if not all free parameters are fixed by renormalization conditions based on S-matrix elements, such as in MSbar renormalization. In contrast to previously used tadpole schemes, the GIVS unifies the properties of gauge invariance and perturbative stability. The application of the GIVS to the Standard Model, for instance, leads to very moderate electroweak corrections in the conversion of on-shell-renormalized to MSbar-renormalized masses. Moreover, in models with extended Higgs sectors, the GIVS is less prone to perturbative instabilities in the MSbar renormalization of Higgs mixing angles than observed for the traditional gauge-independent tadpole treatment. We illustrate this by considering the next-to-leading-order (electroweak and QCD) corrections to the decay processes $h/H\to WW/ZZ\to4$fermions of the CP-even neutral Higgs bosons h and H in a singlet Higgs extension of the Standard Model and in the Two-Higgs-Doublet Model.

hep-ph↗

arXiv2022

Vector Boson Scattering Processes: Status and Prospects

Insight into the electroweak (EW) and Higgs sectors can be achieved through measurements of vector boson scattering (VBS) processes. The scattering of EW bosons are rare processes that are precisely predicted in the Standard Model (SM) and are closely related to the Higgs mechanism. Modifications to VBS processes are also predicted in models of physics beyond the SM (BSM), for example through changes to the Higgs boson couplings to gauge bosons and the resonant production of new particles. In this review, experimental results and theoretical developments of VBS at the Large Hadron Collider, its high luminosity upgrade, and future colliders are presented.

hep-ph↗

arXiv2022

Electroweak renormalization based on gauge-invariant vacuum expectation values of non-linear Higgs representations: 1. Standard Model

The renormalization of vacuum expectation value parameters, such as $v$ in the Standard Model (SM), is an important ingredient in electroweak renormalization, where this issue is connected to the treatment of tadpoles. Tadpole counterterms can be generated in two different ways in the Lagrangian: in the course of parameter renormalization, or alternatively via Higgs field redefinitions. The former typically leads to small corrections originating from tadpoles, but in general suffers from gauge dependences if MSbar renormalization conditions are used for mass parameters. The latter is free from gauge dependences, but is prone to very large corrections in MSbar schemes, jeopardizing perturbative stability in predictions. In this paper we propose a new scheme for tadpole renormalization, dubbed Gauge-Invariant Vacuum expectation value Scheme (GIVS), which is a hybrid scheme of the two mentioned types, with the benefits of being gauge independent and perturbatively stable. The GIVS is based on the gauge-invariance property of Higgs fields, and the corresponding parameters like $v$, in non-linear representations of Higgs multiplets. We demonstrate the perturbative stability of the GIVS in the SM by discussing the conversion between on-shell and MSbar renormalized masses.

hep-ph↗

arXiv2021

Integrating out heavy fields in the path integral using the background-field method: general formalism

Building on an older method used to derive non-decoupling effects of a heavy Higgs boson in the Standard Model, we describe a general procedure to integrate out heavy fields in the path integral. The derivation of the corresponding effective Lagrangian including the one-loop contributions of the heavy particle(s) is particularly transparent, flexible, and algorithmic. The background-field formalism allows for a clear separation of tree-level and one-loop effects involving the heavy fields. Using expansion by regions the one-loop effects are further split into contributions from large and small momentum modes. The former are contained in Wilson coefficients of effective operators, the latter are reproduced by one-loop diagrams involving effective tree-level couplings. The method is illustrated by calculating potential non-decoupling effects of a heavy Higgs boson in a singlet Higgs extension of the Standard Model. In particular, we work in a field basis corresponding to mass eigenstates and properly take into account non-vanishing mixing between the two Higgs fields of the model. We also show that a proper choice of renormalization scheme for the non-standard sector of the underlying full theory is crucial for the construction of a consistent effective field theory.

hep-ph↗

arXiv2021

All-order renormalization of electric charge in the Standard Model and beyond

Electric charge, as defined in the Thomson limit of the electron--photon interaction vertex, is renormalized to all orders both in the Standard Model and in any spontaneously broken gauge theory with gauge group GxU(1) with a group factor U(1) that mixes with electromagnetic gauge symmetry. In the framework of the background-field method the charge renormalization constant $Z_e$ is directly obtained from the photon wave-function renormalization constant, similar to the situation in QED, which proves charge universality as a byproduct. Exploiting charge universality in arbitrary $R_ξ$ gauge by formulating the charge renormalization condition for a ``fake fermion'' that couples only via an infinitesimal electric charge, $Z_e$ can be expressed in terms of renormalization constants that are obtained solely from gauge-boson self-energies.

hep-ph↗