arXiv subjects

Florian Goertz

Publications and source records attributed to Florian Goertz.

At least 19 recordsLinked to original sources

arXiv2026

Large-Field Vacuum Decay in General Multi-Scalar Theories

Many theories beyond the standard model exhibit multiple scalar particles. Such multi-scalar theories can in principle host lower-energy vacua, and thus predict that our universe has a finite lifetime due to false vacuum decay. This scenario cannot be ruled out a priori as even the standard model's electroweak vacuum has been shown to be metastable; however, for theoretical consistency, we still require that the model does not predict a lifetime much smaller than the age of the universe. The calculation of these tunneling rates at leading order for multi-scalar theories typically includes numerical approaches, or approximations which are frequently not analytically controlled. In this article we show that, in the large-field regime, a one-dimensional radial bounce always produces the exact dominant contribution to the leading order tunneling rate, with corrections being exponentially suppressed. This allows us to write simple analytical expressions to calculate the tunneling rate in multi-scalar theories, in terms of an effective quartic coupling $\lambda_\text{eff}$. For theories with biquadratic scalar potentials, we also derive straightforward analytical expressions for $\lambda_\text{eff}$ in terms of the original theory's couplings. Finally, we provide example applications of our results to study the vacuum stability of the 2HDM+a model and the 3-3-1 model.

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arXiv2026

Emergent axion and Higgs boson from strong dynamics

We propose a unified model that simultaneously addresses the hierarchy problem and the strong CP problem by considering the most simple fundamental composite Higgs setup and showing that it can feature a viable emergent axion that could be accessible at collider experiments. To maintain a low decay constant, and therefore address the hierarchy problem, while simultaneously avoiding experimental bounds on the axion couplings, we increase the axion mass via additional small instanton contributions coming from a new hidden gauge sector with a confinement scale larger than $\Lambda_{\text{QCD}}$. Specifically, the axion will be identified with the CP-odd scalar singlet contained in the $SU(4)/Sp(4)$ coset of the minimal fundamental composite Higgs model. Both the SM color group and the additional hidden sector group are then embedded into a larger non-Abelian \textit{grandcolor} group, such that the topological angles of the two sectors are guaranteed to agree at tree-level. Beyond that, we show that radiative corrections and other CP-violating sources can be controlled. After examining the field content and the gauge structure of the model, we analyze the pNGB spectrum, potential, and couplings, as well as the resulting phenomenology. We focus in particular on the axion potential, to understand under which conditions the CP-odd scalar singlet can solve the strong CP problem while maintaining a naturally low compositeness scale, identifying interesting viable parameter space for an axion in the GeV range.

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arXiv2025

Gauge Coupling Unification in Gauge-Higgs GUT: Theory and Phenomenology

We present a concise survey of the running of gauge couplings in realistic models of gauge-Higgs grand unification in a slice of AdS$_5$ space and investigate their potential unification. Besides unifying the gauge groups of the Standard Model, these models can address various unresolved puzzles, such as the lightness of the Higgs boson and the strong hierarchies within fermion masses and mixings, as well as provide a common origin of the gauge symmetries and the sector that spontaneously breaks them. At the same time, they furnish interesting LHC signatures in the form of TeV-scale resonances of the $X,Y$-like bosons, providing a trace of the grand-unified group, accessible at low energies. Using the method of Planck-brane correlators allows us to evolve the couplings consistently from the electroweak scale up to the Planck scale, avoiding shortcomings of other frequently-used approaches and including the effects of bulk scalars, fermions, and gauge-bosons within a common framework. We thereby revisit, contrast, and supplement results in the literature, the latter for example by including brane masses and the gauge-Higgs vacuum expectation value. Moreover, in a phenomenology section, we apply our results to the concrete case of Georgi-Glashow-like unification with a SU(6) $\supset$ SU(5) symmetry in the 5D bulk, presenting a quantitative survey of the quality of unification. We find that grand unification is possible in such models in the presence of moderately large brane kinetic terms.

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arXiv2025

Characterizing LHC-Resonances in extended HEFT: information on the nature of extended scalar sectors

In theories with extended scalar sectors the lightest new scalar degree of freedom might be accessible at colliders. Going beyond simplified models, such a theory can be described in a gauge-invariant and agnostic way via an EFT with a non-linearly realized electroweak symmetry. In this extended HEFT, depending on the $SU(2)$ nature of the new scalar in the UV, operators will be suppressed by different powers of a heavy mass scale. We use dimensional analysis to systematically evaluate expected hierarchies between Wilson coefficients, leading to structural relations between potential LHC observables, such as di-boson resonances, tau pair production or the di-photon channel. Once future collider data reveals a hint of a new scalar field, it can be fitted to this extended HEFT and such a structural analysis will help interpret it with respect to possible UV models, circumventing the need to individually test each possible model on the data or to fix the $SU(2)$ representation of the new scalar beforehand. For illustration, the framework is applied to the tentative 95 GeV resonance. In addition to its usefulness for collider physics, the extended HEFT can also be beneficial for low-energy observables, allowing to describe new scalars in an agnostic way.

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arXiv2025

The goofy-symmetric Standard Model and the Hierarchy Problem

A new class of so-called "goofy" symmetries has been shown to lead to renormalization-group stable relations between parameters in two-Higgs-Doublet Models, not known before. In this work we investigate goofy transformations in the Standard Model (SM), extending them to the fermion sector. We show that the SM action is goofy "symmetric", if the Higgs mass term vanishes, while other SM interactions are allowed. Goofy symmetry could thus add another option to the very few means to successfully forbid the Higgs mass term, providing an alternative to conformal symmetry or shift symmetry. We further consider how electroweak symmetry breaking can be realized in the goofy symmetric SM via higher dimensional operators or an extended scalar sector. A viable Higgs mass can be obtained via spontaneous breaking of goofy symmetry, which can be realized via operators that would not be allowed by shift symmetry or conformal symmetry. We find that goofy-symmetric extensions of the SM are strongly constrained, but offer for example a straightforward dark matter candidate.

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arXiv2025

The quantum criticality of the Standard Model and the hierarchy problem

The naturalness principle has long guided efforts to understand physics beyond the Standard Model, with the hierarchy problem as the central issue. We revisit the role of quantum corrections in the fine-tuning of the low-energy effective description and its phase structure. We implement, for the first time in this context, the full Standard Model within the Wilsonian functional renormalization group. Crucially, this method captures conveniently both logarithmic and quadratic scalings, which must both be considered in the tuning, and allows us to provide a new generic and quantitative study of fine-tuning and its interpretation in terms of critical phenomena. We emphasize on the connection between the hierarchy problem and the near-criticality of the Standard Model and extract scheme-independent information on the infrared Higgs phases and the associated quantum phase transition as well as discuss a related enhanced fine-tuning usually not considered in tuning estimates. Finally, we illustrate the framework's versatility by exploring new physics coupled to the Higgs sector that can soften high-scale sensitivity, recovering also the large-anomalous-dimension solution to the hierarchy problem.

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arXiv2024

Gauge-Fermion Cartography: from confinement and chiral symmetry breaking to conformality

We study, for the first time, the interplay between colour-confining and chiral symmetry-breaking dynamics in gauge-fermion systems with a general number of flavours and colours. Specifically, we work out the flavour dependence of the confinement and chiral symmetry breaking scales. We connect the QCD-like regime, in quantitative agreement with lattice data, with the perturbative conformal limit, thereby exploring uncharted region of theory space. This analysis is done within the first-principles functional renormalisation group approach to gauge-fermion systems and is facilitated by a novel approximation scheme introduced here. This novel scheme enables a relatively simple access to the confining dynamics. This allows us to investigate the whole landscape of many-flavour theories and to provide a cartography of their phase structure. In particular, we uncover a novel phase with the locking of confining and chiral dynamics at intermediate flavour numbers. We also explore the close-conformal region that displays a walking behaviour. Finally, we provide a quantitative estimate for the lower boundary of the conformal Caswell-Banks-Zaks window, with a $N^{\rm crit}_f(N_c=3)= 9.60^{+0.55}_{-0.53}$. This work offers a self-consistent framework for charting the landscape of strongly interacting gauge-fermion theories necessary to reliably study strongly coupled extensions of the Standard Model of particle physics.

hep-th↗

arXiv2024

Dark Particles at the LHC: LHC-Friendly Dark Matter Characterization via Non-Linear EFT

In this work we illustrate a general framework to describe the LHC phenomenology of extended scalar (and fermion) sectors, with focus on dark matter (DM) physics, based on an effective field theory (EFT) with non-linearly realized electroweak symmetry. Generalizing Higgs EFT (HEFT), the setup allows to include a generic set of new scalar resonances, without the need to specify their UV origin, that could for example be at the interface of the Standard Model (SM) and the DM world. In particular, we study the case of fermionic DM interacting with the SM via two mediators, each of which can possess either CP property and originate from various electroweak representations in the UV theory. Besides trilinear interactions between the mediators and DM or SM pairs (including pairs of gauge field-strength tensors), the EFT contains all further gauge-invariant operators up to mass dimension $D=5$. While remaining theoretically consistent, this setup offers enough flexibility to capture the phenomenology of many benchmark models used to interpret the results of experimental DM and BSM searches, such as two-Higgs doublet extensions of the SM or singlet extensions. Furthermore, the presence of two mediators with potentially sizable couplings allows to account for a broad variety of interesting collider signatures, as for example detectable mono-$h$ and mono-$Z$ signals. Correlations can be employed to diagnose the nature of the new particles.

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arXiv2024

Phasing out of Darkness: From Sterile Neutrino Dark Matter to Neutrino Masses via Time-Dependent Mixing

Sterile neutrinos are a compelling candidate for generating neutrino masses and for elucidating the nature of dark matter. Astrophysical X-ray constraints on sterile neutrino dark matter decays, however, largely exclude the active-sterile mixing required to produce simultaneously the correct left-handed neutrino spectrum and keV-scale right-handed neutrino dark matter within a type-I seesaw framework. In this study, we demonstrate how these X-ray constraints can be circumvented through a time-dependent approach, thereby reviving a broad range of active-sterile mixing scenarios. Our minimal model incorporates two right-handed neutrinos, which form a two-component dark matter candidate, and an auxiliary scalar field that experiences a very late and still ongoing phase transition, leading to the spontaneous breaking of a global $ U(1)_N $ symmetry. Prior to this phase transition, only the right-handed neutrinos are massive, while the left-handed neutrinos remain massless because of the scalar field's vanishing expectation value. As the phase transition develops, the growing expectation value of the scalar field increases the active-sterile mixing, thereby opening dark matter decay channels and inducing neutrino masses. The time dependence allows the scenario to be consistent with X-ray constraints as well as current measurements of left-handed neutrino masses. The anticipated level of active-sterile mixing today is within the detection capabilities of the forthcoming TRISTAN (KATRIN) tritium-beta decay project. Additionally, cosmological surveys such as DESI or EUCLID and supernova neutrino observations can test the prediction of massless left-handed neutrinos prior to the phase transition.

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arXiv2023

Third-generation-philic Hidden Naturalness

We present a solution to the electroweak hierarchy problem, where the relevant new particles are third-generation-philic and hidden in SM processes with third-generation fermions. Due to this feature, the mass bounds from direct searches are much weaker and the required fine-tuning can be reduced drastically. A concrete model is constructed based on a $SU(6)/Sp(6)$ fundamental composite Higgs model with collective symmetry breaking and extended hypercolor mechanism. The construction allows to raise the scale $f$ to $\sim 3\,$TeV, corresponding to resonances at $M_\rho \gtrsim 10$ TeV, without much tuning - employing ingredients that are naturally inherent in the (composite) Goldstone-Higgs framework. The experimental signatures are discussed in detail. It is found that current bounds allow for a model with negligible tuning.

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arXiv2023

Flavor Hierarchies in Fundamental Partial Compositeness

The idea of partial compositeness (PC) in Composite Higgs models offers an attractive means to explain the flavour hierarchies observed in nature. In this talk, predictions of a minimal UV realisation of PC, considering each Standard-Model (SM) fermion to mix linearly with a bound state consisting of a new scalar and a new fermion, are presented, taking into account the dynamical emergence of the composites. Employing the non-perturbative functional renormalisation group, the scaling of the relevant correlation functions is examined and the resulting SM-fermion mass spectrum is analysed.

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arXiv2023

The Hierarchy Problem and the Top Yukawa: An Alternative to Top Partner Solutions

We discuss the role of the top-quark Yukawa coupling $y_t$ concerning the hierarchy problem and construct an alternative scheme to the conventional solutions with top partners. In traditional models, like SUSY or composite Higgs, top partners cancel the top loop contribution to the Higgs quadratic term. The lack of evidence for such colored partners however drives these models into more and more fine-tuned regions. Here, an alternative means to mitigate the top loop, allowing for natural electroweak symmetry breaking, is presented. Emphasizing that we have not measured the top-Higgs interactions at high scales yet, we envisage scenarios where this interaction is only approaching its sizable strength in the infra-red, but gets strongly suppressed at high scales. We first discuss possible effects via a modification of the running of the top Yukawa coupling. Then, we turn to models where the top Yukawa is generated at one-loop level. Originated from a dimension-six operator, it drops when crossing the mass threshold of new degrees of freedom. In either case, the top partners are replaced by some new top-philic particles with strong interaction. Thus, a very different phenomenology, such as large top mass running and signals in four top final states, is introduced, which will be discussed in detail. With the assistance of this mechanism, the solution to the hierarchy problem can be pushed to a (well-defined) higher scale, and a final test of naturalness might be deferred to a 100 TeV Collider, like the FCC.

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arXiv2023

Restoring Naturalness via Conjugate Fermions

We propose a novel mechanism for cancelling the leading order contribution to the potential in composite Higgs scenarios. The mechanism relies on the splitting of a real representation of the global symmetry into a complex representation and its conjugate of the unbroken group. We identify two cosets one of which includes a custodial symmetry. A numerical analysis is performed in a phenomenological three-site model and the resulting fine-tuning is analysed. The cancelling of the leading order potential results in a drastic reduction of the fine-tuning. For a symmetry breaking scale of the strong sector as high as $f=1600$ GeV, fine-tuning can be as good as $10\%$ or even better. We discuss a possible interpretation in the 5D holographic dual. Unique signatures of the model include quarks with baryon number $B=2/3$ with highly distinctive decays which can be looked for at the LHC.

hep-ph↗

arXiv2023

Unveiling New Phases of the Standard Model Higgs Potential

We present evidence for new phases of the Standard Model Higgs potential. We study the Standard Model physical trajectory accounting for the Higgs curvature mass with the mass-dependent functional renormalisation group. New unstable and non-trivially stable phases are found at energies above the Planck scale and below the Abelian Landau pole. While the first aggravates the well-known metastable phase and threatens the viability of the Standard Model extrapolated to arbitrary scales, the latter can provide a well-defined ultraviolet completion. We investigate the phase diagram as a function of the top quark pole mass and study the effect of new physics through a scalar singlet portal coupling. The new non-trivial phase appears below the Planck scale in extensions of the Standard Model seeking stable trajectories. These findings have a significant impact on existing model building.

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arXiv2023

Flavour hierarchies from emergent fundamental partial compositeness

Composite Higgs extensions of the Standard Model provide an explanation for the large hierarchies between the Yukawa couplings. We study their realisation in the context of fundamental partial compositeness where the Standard Model fermions mix linearly with bound states of the new sector, consisting of a fermion and a scalar. The properties of this composite are unravelled with the functional renormalisation group approach using dynamically emergent composites. Specifically, we extract the scaling of correlation functions and provide indicative estimates for the minimal incarnation of the theory.

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arXiv2023

Minimal Inert Doublet Benchmark for Dark Matter and the Baryon Asymmetry

In this article we discuss a minimal extension of the Inert Doublet Model (IDM) with an effective $CP$-violating $D=6$ operator, involving the inert Higgs and weak gauge bosons, that can lift it to a fully realistic setup for creating the baryon asymmetry of the Universe (BAU). Avoiding the need to stick to an explicit completion, we investigate the potential of such an operator to give rise to the measured BAU during a multi-step electroweak phase transition (EWPhT) while sustaining a viable DM candidate in agreement with the measured relic abundance. We find that the explored extension of the IDM can account quantitatively for both DM and for baryogenesis and has quite unique virtues, as we will argue. It can thus serve as a benchmark for a minimal realistic extension of the SM that solves some of its shortcomings and could represent the low energy limit of a larger set of viable completions. After discussing the impact of a further class of operators that open the possibility for a larger mass splitting (enhancing the EWPhT) while generating the full relic abundance also for heavy inert-Higgs DM, we ultimately provide a quantitative evaluation of the induced lepton electric dipole moments in the minimal benchmark for the BAU. These arise here at the two-loop level and are therefore less problematic compared to the ones that emerge when inducing $CP$ violation via an operator involving the SM-like Higgs.

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arXiv2023

The Hierarchy Problem and the Top Yukawa

In this talk, an alternative to top partner solutions and its consequences on phenomenology are discussed. The hierarchy problem from the top loop contribution is solved by mitigating the top Yukawa coupling at high scales. In this scenario, the new degrees of freedom appearing at the cut-off scale of the top loop should then be some new top-philic particles instead of traditional top partners. The idea can be directly tested through measurements in top physics, including $t\bar{t}h$, $t\bar{t}$ differential cross section, and $t\bar{t}t\bar{t}$ cross section.

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arXiv2022

$Z_2$ Non-Restoration and Composite Higgs: Singlet-Assisted Baryogenesis w/o Topological Defects

Simple scalar-singlet extensions of the Standard Model with a (spontaneously broken) $Z_2$ symmetry allow for a strong first order electroweak phase transition, as sought in order to realize electroweak baryogenesis. However they generically also lead to the emergence of phenomenologically problematic domain walls. Here we present a framework with a real scalar singlet that features a different thermal history that avoids this problem by never restoring the $Z_2$ symmetry in the early universe. This is accomplished by considering $D>4$ operators that emerge on general grounds, understanding the model as the low energy tail of a more complete theory, like for example in composite Higgs scenarios. Sticking to the latter framework, we present a concrete $SO(6)/SO(5)$ composite realization of the idea. To this end, we additionally provide a complete classification of the structure of the Higgs potential (and the Yukawa couplings) in $SO(6)/SO(5)$ models with fermions in the ${\bf 1, 6, 15}$ or ${\bf 20^\prime}$ of $SO(6)$.

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