arXiv subjects

Fabian Zierler

Publications and source records attributed to Fabian Zierler.

At least 19 recordsLinked to original sources

arXiv2026

Resonant scattering in two-flavored Sp(4) lattice gauge theories

We apply Lüscher's method to the vector channel of the scattering amplitude of Pseudo-Nambu-Goldstone-Bosons (PNGBs), in the $Sp(4)$ lattice gauge theory coupled to $N_f=2$ flavors of Wilson-Dirac fundamental fermions. We generalize existing algorithms and numerical implementations of the method, to adapt them to this prominent candidate for the completion of proposed extensions of the Standard Model (SM). We present the first ab initio measurements of key properties of the vector resonances in the theory, including the coupling to the PNGBs, that are relevant to direct and indirect new physics searches, both for composite Higgs models (CHMs), as well as for strongly interacting massive particle (SIMP) realizations of dark matter. We also present a global update of the spectroscopy of the mesons in the theory, improving both the statistics and analysis systematics in respect to previous lattice measurements reported in the literature.

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arXiv2026

Chiral symmetry restoration effects onto the meson spectrum from a Dyson-Schwinger and Bethe-Salpeter approach

Light meson spectra are studied in a Dyson-Schwinger/Bethe-Salpeter approach to QCD. By varying the interaction strength of three sets of models for the quark-antiquark interaction, the transition from the chiral symmetric to the chirally broken regime in the vacuum is studied. The simplest type of these models leads to degenerate meson spectra for a large domain of the strength parameter. The more sophisticated and thus more realistic models show significantly smaller parameter domains for which degenerate meson spectra are obtained. The underlying mechanism for obtaining and then lifting degeneracies is traced back to the location of the quark propagators' poles, in particular, whether they are beyond or within the domain of integration in the Bethe-Salpeter equation. In view of this mechanism the potential relation of the obtained degeneracies to the dynamical emergence of symmetries is discussed, adding thereby another point of view on the conjectured chiral spin symmetry of QCD in the temperature domain right above the crossover.

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arXiv2026

Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit

A first-order, confinement/deconfinement phase transition appears in the finite temperature behavior of many non-Abelian gauge theories. These theories play an important role in proposals for completion of the Standard Model of particle physics, hence the phase transition might have occurred in the early stages of evolution of our universe, leaving behind a detectable relic stochastic background of gravitational waves. Lattice field theory studies implementing the density of states method have the potential to provide detailed information about the phase transition, and measure the parameters determining the gravitational-wave power spectrum, by overcoming some the challenges faced with importance-sampling methods. We assess this potential for a representative choice of Yang-Mills theory with $Sp(4)$ gauge group. We characterize its finite-temperature, first-order phase transition, in the thermodynamic (infinite volume) limit, for two different choices of number of sites in the compact time direction, hence taking the first steps towards the continuum limit extrapolation. We demonstrate the persistence of non-perturbative phenomena associated to the first-order phase transition: coexistence of states, metastability, latent heat, surface tension. We find consistency between several different strategies for the extraction of the volume-dependent critical coupling, hence assessing the size of systematic effects. We also determine the minimum choice of ratio between spatial and time extent of the lattice that allows to identify the contribution of the surface tension to the free energy. We observe that this ratio scales non-trivially with the time extent of the lattice, and comment on the implications for future high-precision numerical studies.

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arXiv2026

Lattice studies of chimera baryons in Sp(4) gauge theory

We study chimera baryons, fermion bound states composed of two (hyper)quarks transforming in the fundamental and one in the antisymmetric representation of a non-Abelian gauge group. While in QCD they coincide with ordinary baryons, in composite Higgs models (CHMs) with top partial compositeness, spin-1/2 chimera baryons serve as partners of the top quark and are responsible for its large mass. We perform non-perturbative lattice calculations of the low-lying spectrum of the chimera baryons, in a specific realization of CHMs based on a Sp(4) gauge theory. In the quenched approximation, we present the numerical results in the continuum and massless limits. Then, for dynamical fermions, we measure the spectrum and matrix elements by employing a newly developed spectral density analysis for several choices of the lattice parameters.

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arXiv2026

Vector-channel scattering of dark particles in a Sp(4) gauge theory

We report new results obtained in our lattice studies of the $Sp(4)$ gauge theory coupled to two fundamental Dirac fermions. This theory provides a candidate for the dynamical origin of dark matter models within the strongly interacting massive particle paradigm. We employ Lüscher's formalism to analyse finite-volume energy levels and study the scattering amplitude of two pseudoscalar states in the spin-1 channel. We present our preliminary findings for a set of ensembles generated within a broad range of (Wilson) fermion masses.

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arXiv2026

Finite-temperature Sp(4) Yang-Mills theory: towards the continuum

We present numerical results obtained in a finite-temperature study of the Sp(4) Yang-Mills theory on the lattice. We study its first-order confinement/deconfinement phase transition, by reconstructing the density of states via the Logarithmic Linear Relaxation (LLR) algorithm. We perform our measurements on lattices with different extents of space and time (and aspect ratios). We estimate the size of discretisation and finite-volume artefacts. We find clear signatures of a first-order transition. We determine the critical coupling, the specific heat, and the surface tension, for finite extents of the thermal circle, and use the results to set bounds for the continuum theory.

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arXiv2025

Chimera baryons and mesons on the lattice: a spectral density analysis

We develop and test a spectral-density analysis method, based on the introduction of smeared energy kernels, to extract physical information from two-point correlation functions computed numerically in lattice field theory. We apply it to a $Sp(4)$ gauge theory and fermion matter fields transforming in distinct representations, with $N_{\rm f}=2$ Dirac fermions in the fundamental and $N_{\rm as}=3$ in the 2-index antisymmetric representation. The corresponding continuum theory provides the minimal candidate model for a composite Higgs boson with partial top compositeness. We consider a broad class of composite operators, that source flavored mesons and (chimera) baryons, for several finite choices of lattice bare parameters. For the chimera baryons, which include candidate top-quark partners, we provide the first measurements, obtained with dynamical fermions, of the ground state and the lowest excited state masses, in all channels of spin, isospin, and parity. We also measure matrix elements and overlap factors, that are important to realize viable models of partial top compositeness, by implementing an innovative way of extracting this information from the spectral densities. For the mesons, among which the pseudoscalars can be reinterpreted to provide an extension of the Higgs sector of the Standard Model of particle physics, our measurements of the renormalized matrix elements and decay constants are new results. We complement them with an update of existing measurements of the meson masses, obtained with higher statistics and improved analysis. The analysis software is made publicly available, and can be used in other lattice studies, including application to quantum chromodynamics (QCD).

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arXiv2025

Progress on lattice study of the chimera baryon spectrum in Sp(4) gauge theory

Investigation of composite Higgs models (CHMs) is of importance in contemporary particle physics. In this article, we present lattice computations of the chimera baryon masses in $Sp(4)$ gauge theory with two and three Dirac flavours of hyperquarks (beyond the Standard Model fermions coupled to the $Sp(4)$ gauge fields) in the fundamental and antisymmetric representations, respectively. The chimera baryons are crucial for generating the Standard Model fermion masses through the partial compositeness mechanism in this gauge theory that can serve as the ultraviolet completion of the CHM with pseudo-Nambu-Goldstone bosons in the coset $SU(4)/Sp(4)$. Results shown here are primarily from a completed quenched computation, while those from our ongoing work with dynamical simulations are also discussed.

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arXiv2025

Scattering of SIMPlectic Dark Pions

We study the scattering of two identical pNGBs (pseudo-Nambu-Goldstone Bosons) in Sp(4) gauge theory with two mass-degenerate Dirac fermions in the pseudo-real fundamental representation. This theory serves as a realization of a SIMP (Strongly Interacting Massive Particles) Dark Matter model. SIMPs are an exciting dark matter candidate as they make use of a new relic density mechanism and provide potential solutions to the so-called small-scale structure problems. These theories are realized by a confining dark sector which includes non-perturbative signatures. While most of the research focuses on ChPT (Chiral Perturbation Theory), first-principle verification of these models is indispensable. In these proceedings we give an update on scattering properties in the most common channel and give an outlook on the projects that lie ahead.

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arXiv2024

Progress on the spectroscopy of an Sp(4) gauge theory coupled to matter in multiple representations

We report progress on our lattice calculations for the mass spectra of low-lying composite states in the Sp(4) gauge theory coupled to two and three flavors of Dirac fermions transforming in the fundamental and the two-index antisymmetric representations, respectively. This theory provides an ultraviolet completion to the composite Higgs model with Goldstone modes in the SU(4)/Sp(4) coset and with partial compositeness for generating the top-quark mass. We measure the meson and chimera baryon masses. These masses are crucial for constructing the composite Higgs model. In particular, the chimera baryon masses are important inputs for implementing top partial compositeness. We employ Wilson fermions and the Wilson plaquette action in our simulations. Techniques such as APE and Wuppertal smearing, as well as the procedure of generalised eigenvalue problem, are implemented in our analysis.

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arXiv2024

Updates on the density of states method in finite temperature symplectic gauge theories

First-order phase transitions in the early universe have rich phenomenological implications, such as the production of a potentially detectable signal of stochastic relic background gravitational waves. The hypothesis that new, strongly coupled dynamics, hiding in a new dark sector, could be detected in this way, via the telltale signs of its confinement/deconfinement phase transition, provides a fascinating opportunity for interdisciplinary synergy between lattice field theory and astro-particle physics. But its viability relies on completing the challenging task of providing accurate theoretical predictions for the parameters characterising the strongly coupled theory. Density of states methods, and in particular the linear logarithmic relaxation (LLR) method, can be used to address the intrinsic numerical difficulties that arise due the meta-stable dynamics in the vicinity of the critical point. For example, it allows one to obtain accurate determinations of thermodynamic observables that are otherwise inaccessible, such as the free energy. In this contribution, we present an update on results of the analysis of the finite temperature deconfinement phase transition in a pure gauge theory with a symplectic gauge group, $Sp(4)$, by using the LLR method. We present a first analysis of the properties of the transition in the thermodynamic limit, and provide a road map for future work, including a brief preliminary discussion that will inform future publications.

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arXiv2024

Progress on the spectroscopy of lattice gauge theories using spectral densities

Spectral densities encode non-perturbative information crucial in computing physical observables in strongly coupled field theories. Using lattice gauge theory data, we perform a systematic study to demonstrate the potential of recent technological advances in the reconstruction of spectral densities. We develop, maintain and make publicly available dedicated analysis code that can be used for broad classes of lattice theories. As a test case, we analyse the Sp(4) gauge theory coupled to an admixture of fermions transforming in the fundamental and two-index antisymmetric representations. We measure the masses of mesons in energy-smeared spectral densities, after optimising the smearing parameters for available lattice ensembles. We present a summary of the mesons mass spectrum in all the twelve (flavored) channels available, including also several excited states.

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arXiv2024

Progress on pseudoscalar flavour-singlets in Sp(4) with mixed fermion representations

We measure the masses of the pseudoscalar flavour-singlet meson states in the $Sp(4)$ gauge theory coupled to two Dirac fermions transforming in the fundamental representation and three Dirac fermions in the antisymmetric representation. This theory provides a compelling ultraviolet completion for the minimal composite Higgs model implementing also partial compositeness for the top quark. The spectrum contains two, comparatively light, pseudoscalar flavour-singlet states, which mix with one another. One of them is a Nambu-Goldstone boson (in the massless limit), whereas the other receives a mass from the $U(1)_A$ axial anomaly. We demonstrate how to measure the mixing between these two states. For moderately heavy fermion masses, we find that the two wave functions are dominated by one of the fermion representations, mixing effects being small.

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arXiv2024

Mixing between flavor singlets in lattice gauge theories coupled to matter fields in multiple representations

We provide the first extensive, numerical study of the non-trivial problem of mixing between flavor-singlet composite states emerging in strongly coupled lattice field theories with matter field content consisting of fermions transforming in different representations of the gauge group. The theory of interest is the minimal candidate for a composite Higgs model that also accommodates a mechanism for top partial compositeness: the $Sp(4)$ gauge theory coupled to two (Dirac) fermions transforming as the fundamental and three as the two-index antisymmetric representation of the gauge group, respectively. We apply an admixture of APE and Wuppertal smearings, as well as the generalized eigenvalue problem approach, to two-point functions involving flavor-singlet mesons, for ensembles having time extent longer than the space extent. We demonstrate that, in the region of lattice parameter space accessible to this study, both masses and mixing angles can be measured effectively, despite the presence of (numerically noisy) contributions from disconnected diagrams.

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arXiv2024

Meson spectroscopy from spectral densities in lattice gauge theories

Spectral densities encode non-perturbative information that enters the calculation of a plethora of physical observables in strongly coupled field theories. Phenomenological applications encompass aspects of standard-model hadronic physics, observable at current colliders, as well as correlation functions characterizing new physics proposals, testable in future experiments. By making use of numerical data produced in a Sp(4) lattice gauge theory with matter transforming in an admixture of fundamental and 2-index antisymmetric representations of the gauge group, we perform a systematic study to demonstrate the effectiveness of recent technological progress in the reconstruction of spectral densities. To this purpose, we write and test new software packages that use energy-smeared spectral densities to analyze the mass spectrum of mesons. We assess the effectiveness of different smearing kernels and optimize the smearing parameters to the characteristics of available lattice ensembles. We generate new ensembles for the theory in consideration, with lattices that have a longer extent in the time direction with respect to the spatial ones. We run our tests on these ensembles, obtaining new results about the spectrum of light mesons and their excitations. We make available our algorithm and software for the extraction of spectral densities, that can be applied to theories with other gauge groups, including the theory of strong interactions (QCD) governing hadronic physics in the standard model.

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arXiv2024

Scattering of dark pions in Sp(4) gauge theory

Analyzes of astrophysical data provide first hints on the self-interactions of dark matter at low energies. Lattice calculations of dark matter theories can be used to investigate them, especially in the case of strongly-interacting dark matter. We consider Sp(4) gauge theory with two fundamental fermions as a candidate theory. We compute the scattering phase shift for the scattering of two identical dark pions and determine the parameters of the effective range expansion. Our exploratory results in the supposedly most common interaction channel provide a lower limit for the dark matter mass when compared to astrophysical data. We also provide first benchmarks of velocity-weighted cross-sections in the relevant non-relativistic domain.

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arXiv2024

On the dependence of the Landau gauge ghost-gluon-vertex on the number of flavors

The gauge-boson, ghost and fermion propagators as well as the gauge-boson--ghost vertex function are studied for SU(N), Sp(2N) and SO(N) gauge groups. We solve a set of coupled Dyson-Schwinger equations in Landau gauge for a variable, fractional number $N_f$ of massless fermions in the fundamental representation. For large $N_f$ we find a phase transition from a chirally broken into a chirally symmetric phase that is consistent with the behavior expected inside the conformal window. Even in the presence of fermions the gauge-boson--ghost-vertex dressing remains small. In the conformal window this vertex shows the expected power law behavior. It does not assume its tree-level value in the far infrared, but the respective dressing function is a constant greater than one.

hep-ph↗

arXiv2023

Scattering of dark pions in an Sp(4) gauge theory

In this work we consider strongly interacting dark matter candidates as composite states of $N_f=2$ fermions charged under a dark $Sp(4)$ gauge group in the fundamental representation. We give expressions that allow the calculation of correlation functions of two pseudo-Nambu-Goldstone-bosons with lattice field theory and present first results on the scattering phase shift in the isospin-2 channel in the theory from first principles. We give a lower limit on the dark matter particle mass by comparing our results with astrophysical constraints on the cross-section.

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