We present HiRep v2, an open-source software suite for high-performance lattice field theory simulations with dynamical Wilson fermions in higher representations of SU(Ng) gauge groups. This new version fully supports graphics processing unit (GPU) acceleration, optimizing both gauge configuration generation and measurements for NVIDIA and AMD GPUs. HiRep v2 integrates improved gauge and fermionic lattice actions, advanced inverters, and Monte Carlo algorithms, including the (Rational) Hybrid Monte Carlo ((R)HMC) with Hasenbusch acceleration. It exhibits excellent scalability across multiple GPUs and nodes with minimal efficiency loss, making it a robust tool for large-scale simulations in physics beyond the Standard Model. PROGRAM SUMMARY Program Title: HiRep CPC Library link to program files: https://doi.org/10.17632/95bj3mssvj.1 Developer's repository link: https://github.com/claudiopica/hirep Licensing provisions: GPLv2 Programming language: C, CUDA C, C++ Nature of problem: Lattice Field Theory has proven indispensable for the quantitative understanding of strongly coupled quantum field theories, specifically in providing non-perturbative input to phenomenological models describing the dynamics of Quantum Chromodynamics (QCD) for precision tests of the Standard Model. Simulation software libraries for lattice calculations in QCD are readily available and optimized to run on heterogeneous CPU-GPU architectures with good scaling properties on modern supercomputers. In direct searches for physics beyond the Standard Model, software is needed that can simulate gauge groups other than SU(3) and allow for fermions in higher representations, catering, among other things, to classes of composite Higgs and technicolor theories [1], and predictions in the large-Ng limit [2]. There exists no other open-source library that implements the option for higher representations of Wilson fermions with general numbers of colors, that has as many capabilities in terms of actions and measurement code as HiRep. Solution method: A central element of HiRep is the implementation of a Dirac operator and optimized linear algebra routines that generalize to higher representations and general gauge groups. Since the application of the Dirac operator is one of the main bottlenecks of the numerical simulation, optimizations of the Dirac operator are a central part of any high-performance software implementations. In this work, we present a series of significant developments and enhancements to the HiRep suite. These include but are not limited to, the porting of the code to GPUs, see also [3,4] for previous progress reports, improvements in computational efficiency, and the introduction of new features to further support advanced lattice simulations. In particular, we show that independent of the theory chosen, our implementation of the Dirac operator reaches excellent performance on GPUs and that the software scales well on state-of-the-art supercomputers to a large number of compute nodes, and HiRep is suitable for simulations of light fermionic masses on large lattices. Another recent performance improvement was achieved in [5], optimizing OpenMP support.

Composite Higgs models are a class of Beyond the Standard Model (BSM) models proposed to address the hierarchy and naturalness problems associated with the Standard Model (SM) Higgs. A new QCD-like strongly interacting sector based on SU(2) with two fundamental flavours can be used to build a composite Higgs model which is not yet ruled out by experiment. The role of the singlet scalar resonance will affect Higgs phenomenology at the LHC. In this project our goal is to understand the properties of the singlet scalar state in the new strongly interacting sector in isolation as a first step to understanding the role of this state in composite Higgs models. We present here the first lattice results for the mass of the σ in SU(2) with two fundamental flavours using exponential clover Wilson fermions.

Composite Higgs models are a class of models proposed to address the hierarchy and naturalness problems associated with the Standard Model fundamental scalar Higgs. $SU(2)$ with two fundamental flavours is a minimal model for the composite Higgs sector which is not yet ruled out by experimental data. We present lattice results for $SU(2)$ with two fundamental mass degenerate flavours. For the fermion action we use the new exponential clover Wilson fermion action, which offers $O(a)$ improvement. We discuss tuning the $c_{\mathrm{SW}}$ parameter through Schrödinger functional simulations, the scale setting of the ensembles using the Wilson gauge flow, and the low energy spectroscopy of the theory including the masses of the pseudoscalar isotriplet Goldstone bosons and the vector isotriplet.

The SU(2) gauge group with two fundamental flavors is a candidate for a composite Higgs extension of the Standard Model. Central to Higgs phenomenology is a non-perturbative determination of observables of the theory, such as the decay constant of the pseudo-Nambu-Goldstone Bosons. We present preliminary results for the continuum limit of the pseudoscalar decay constant using a mixed-action setup, with non-perturbatively improved stabilized Wilson Fermions on the sea, and maximally twisted valence quarks. Pivotal to this study is the recent porting of our simulation suite HiRep to GPU architecture.

We present the first calculation of the scattering amplitude in the singlet channel beyond QCD. The calculation is performed in SU (2) gauge theory with N_f=2 fundamental Dirac fermions and based on a finite-volume scattering formalism. The theory exhibits a SU(4) → Sp(4) chiral symmetry breaking pattern that is used to design minimal composite Higgs models currently tested at the LHC. Our results show that, for the range of underlying fermion mass considered, the lowest flavour singlet state is stable.

We calculate the coupling between a vector resonance and two Goldstone bosons in SU(2) gauge theory with N f = 2 Dirac fermions in the fundamental representation. The considered theory can be used to construct a minimal Composite Higgs models. The coupling is related to the width of the vector resonance and we determine it by simulating the scattering of two Goldstone bosons where the resonance is produced. The resulting coupling is g VPP = 7 . 8 ± 0 . 6, not far from g ρππ ≃ 6 in QCD. This is the first lattice calculation of the resonance properties for a minimal UV completion. This coupling controls the production cross section of the lightest expected resonance at the LHC and enters into other tests of the Standard Model, from Vector Boson Fusion to electroweak precision tests. Our prediction is crucial to constrain the model using lattice input and for understanding the behavior of the vector meson production cross section as a function of the underlying gauge theory. We also extract the coupling g_VPP^KSRF = 9 . 4 ± 0 . 6 assuming the vector-dominance and find that this phenomenological estimate slightly overestimates the value of the coupling.

In the post-Higgs discovery era, the primary goal of the Large Hadron collider is to discover new physics Beyond the Standard Model. One fundamental question is does new beyond the Standard Model composite dynamics provides the origin of the Higgs field and potential. After reviewing the main motivations to consider composite models based on a new strongly interacting sector, we summarise the efforts of the lattice community to investigate the viability of models featuring a composite Higgs sector. We argue that first principle calculations are necessary in view of the fast improvements in accuracy of experimental measurements in the Higgs sector. We stress the importance for lattice calculations to provide a testing benchmark for non perturbative mechanisms. It is highlighted that the rich phenomenology of non-abelian gauge theories raises a number of questions that can be explored using lattice calculations. First principle results therefore provide crucial insights in the theory landscape that could guide the next generation of Composite Higgs models.

Composite Higgs models are promising candidate models to address the long-standing naturalness problem in the Standard Model. Among them, the most minimal one is the SU(2) with 2 flavours of fermions in the fundamental representation of the gauge group. An important prediction in these models is the existence of resonance spectrum in vector boson scattering. Here we study the lowest such resonance, which is the equivalent of rho resonance in QCD. We describe the scan of the parameter space using the clover-improved Wilson fermions with Symanzik improved gauge action and then show the first results for the mass and width of the rho resonance in this model.

Within the HMC algorithm, we discuss how, by using the shadow Hamiltonian and the Poisson brackets, one can achieve a simple factorization in the dependence of the Hamiltonian violations upon either the algorithmic parameters or the parameters specifying the integrator. We consider the simplest case of a second order (nested) Omelyan integrator and one level of Hasenbusch splitting of the determinant for the simulations of a QCD-like theory (with gauge group SU(2)). Given the specific choice of the integrator, the Poisson brackets reduce to the variances of the molecular dynamics forces. We show how the factorization can be used to optimize in a very economical and simple way both the algorithmic and the integrator parameters with good accuracy.

We present a non perturbative study of SU(2) gauge theory with two fundamental Dirac flavours. This theory provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics, such as a minimal realization of composite Higgs models. We present an update on the status of the meson spectrum and decay constants based on increased statistics on our existing ensembles and the inclusion of new ensembles with lighter pion masses, resulting in a more reliable chiral extrapolation.

Conference Proceedings, 7 pages and 20 figures. Talk presented at the 32nd International Symposium on Lattice Field Theory, Columbia University, New York City, NY

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We present a lattice study of a Nambu Jona-Lasinio (NJL) model using Wilson fermions. Four fermion interactions are a natural part of several extensions of the Standard Model, appearing as a low energy description of a more fundamental theory. In models of dynamical electroweak symmetry breaking they are used to endow the Standard Model fermions with masses. In infrared conformal models these interaction, when sufficiently strong, can alter the dynamics of the fixed point, turning the theory into a (near) conformal model with desirable features for model building. As a first step toward the nonperturbative study of these models, we study the phase space of the ungauged NJL model.

We investigate the spectrum of the SU(2) gauge theory with N-f = 2 flavors of fermions in the fundamental representation, in the continuum, using lattice simulations.This model provides a minimal template which has been used for different strongly coupled extensions of the Standard Model ranging from composite (Goldstone) Higgs models to intriguing types of dark matter candidates, such as the SIMPs. Here we will focus on the composite Goldstone Higgs paradigm, for which this model provides a minimal UV complete realization in terms of a new strong sector with fermionic matter.After introducing the relevant Lattice methods used in our simulations, we will discuss our numerical results. We show that this model features a SU(4)/Sp(4)similar to SO(6)/SO(5) flavor symmetry breaking pattern, and estimate the value of its chiral condensate. Finally, we present our results for the mass spectrum of the lightest spin one and zero resonances, analogue to the QCD rho, a(1), sigma, eta', a(0) resonances, which are relevant for searches of new, exotic resonances at the LHC.

We investigate the spectrum and IR properties of the SU(3) "sextet" model with two Dirac fermions in the two-index symmetric representation via lattice simulations. This model is a prime candidate for a realization of walking technicolor, which features a minimal matter content and it is expected to be inside or very close to the lower boundary of the conformal window. We use the Wilson discretization for the fermions and map the phase structure of the lattice model. We study several spectral and gradient flow observables both in the bulk and the weak coupling phases. While in the bulk phase we find clear signs of chiral symmetry breaking, in the weak coupling phase there is no clear indication for it, and instead the chiral limit of the model seems compatible with an IR-conformal behavior.

We present a first non perturbative study of the flavour singlet scalar and pseudoscalar spectrum of SU(2) gauge theory with two fundamental Dirac flavours. This theory provides a minimal template for a wide class of Standard Model extensions featuring novel strong dynamics. After having discussed our computational method, we present our new results for the σ , η ′ and a 0 states. We evaluate the relevant disconnected contributions and obtain benchmark results that are crucial input for model building. This work summarises our recent contribution[1].

We investigate the continuum spectrum of the SU(2) gauge theory with N-f = 2 flavors of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the strongly interacting massive particles (SIMPs). We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the w 0 parameter, and by measuring the relevant renormalization constants nonperturbatively in the regularizationin-variant momentum (RI'-MOM) scheme. Our result for the lightest isovector state in the vector channel, in units of the pseudoscalar decay constant, is m(V)/F-PS similar to 13.1(2.2) (combining statistical and systematic errors). For the axial channel our result is m(A)/F-PS similar to 14.5(3.6), which however does include a similarly sized additional systematic error due to residual excited-states contamination. In the context of the composite (Goldstone) Higgs models, our result for the spin-one resonances are m(V) > 3.2(5) TeV and m(A) > 3.6(9) TeV, which are above the current LHC constraints. In the context of dark matter models, for the SIMP case our results indicate the occurrence of a compressed spectrum at the required large dark pion mass, which implies the need to include the effects of spin-one resonances in phenomenological estimates.

SU(2) gauge theories with two quark flavours in the fundamental representation are among the most promising theories of composite dynamics describing the electroweak sector. Three out of five Goldstone bosons in these models become the longitudinal components of the W and Z bosons giving them mass. Like in QCD, we expect a spectrum of excitations which appear as resonances in vector boson scattering, in particular the vector resonance corresponding to the rho-meson in QCD. In this talk I will present the preliminary results of the first calculation of the rho-meson decay width in this theory, which is analogous to rho to two pions decay calculation in QCD. The results presented were calculated in a moving frame with total momentum (0,0,1) on two ensembles. Future plans include using 3 moving frames on a larger set of ensembles to extract the resonance parameters more reliably and also take the chiral and continuum limits.

We investigate the scalar and pseudoscalar spectrum of the SU(2) gauge theory with N_f=2 flavours of fermions in the fundamental representation using non perturbative lattice simulations. We provide first benchmark estimates of the mass of the lightest 0(0^+) (σ), 0(0^-) (η') and 1(0^+) (a_0) states, including estimates of the relevant disconnected contributions. We find m_a_0/F_PS= 16.7(4.9), m_σ/F_PS=19.2(10.8) and m_η'/F_PS = 12.8(4.7). These values for the masses of light scalar states provide crucial information for composite extensions of the Standard Model from the unified Fundamental Composi te Higgs-Technicolor theory to models of composite dark matter.

We present a practical strategy to optimize a set of Hybrid Monte Carlo parameters in simulations of QCD and QCD-like theories. We specialize to the case of mass-preconditioning, with multiple time-step Omelyan integrators. Starting from properties of the shadow Hamiltonian we show how the optimal setup for the integrator can be chosen once the forces and their variances are measured, assuming that those only depend on the mass-preconditioning parameter.