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Normalizing flows have arisen as a tool to accelerate Monte Carlo sampling for lattice field theories. This work reviews recent progress in applying normalizing flows to 4-dimensional nonabelian gauge theories, focusing on two advancements: an architectural improvement referred to as learned active loops, and the application of correlated ensemble methods to QCD with $N_f=2$ dynamical fermions., Comment: 10 pages, 2 figures, Contribution to the 41st International Symposium on Lattice Field Theory, July 28th - August 3rd 2024, Liverpool, UK

We present results on the large $N_\text{c}$ scaling of meson-meson scattering amplitudes. We work in a theory with $N_\text{f}=4$ degenerate quark flavors and run lattice simulations with $N_\text{c}=3-6$ and pion mass $M_\pi\approx 590$ MeV. We focus on three different scattering channels, two of which have the same quantum numbers as some tetraquark candidates recently found at LHCb. Finite-volume energies are extracted using a large set of operators, containing two-particle operators corresponding to two pions or two vector mesons, and local tetraquark operators. Using L\"uscher's quantization condition, we constrain the infinite-volume scattering amplitudes and investigate subleading $N_\text{c}$ corrections to the large $N_\text{c}$ limit. For one of the channels, we find indications of a virtual bound state at $N_\text{c}=3$, which may be related to one of the aforementioned exotic states., Comment: 11 pages, 5 figures. Talk presented at the 41st International Symposium on Lattice Field Theory (Lattice2024), 28 July - 3 August 2024, Liverpool, UK

This paper describes an approach to assessing semantic annotation activities based on formal concept analysis (FCA). In this approach, annotators use taxonomical ontologies created by domain experts to annotate digital resources. Then, using FCA, domain experts are provided with concept lattices that graphically display how their ontologies were used during the semantic annotation process. In consequence, they can advise annotators on how to better use the ontologies, as well as how to refine them to better suit the needs of the semantic annotators. To illustrate the approach, we describe its implementation in @note, a Rich Internet Application (RIA) for the collaborative annotation of digitized literary texts, we exemplify its use with a case study, and we provide some evaluation results using the method., Comment: pre-print

Current evaluations of defenses against prompt attacks in large language model (LLM) applications often overlook two critical factors: the dynamic nature of adversarial behavior and the usability penalties imposed on legitimate users by restrictive defenses. We propose D-SEC (Dynamic Security Utility Threat Model), which explicitly separates attackers from legitimate users, models multi-step interactions, and expresses the security-utility in an optimizable form. We further address the shortcomings in existing evaluations by introducing Gandalf, a crowd-sourced, gamified red-teaming platform designed to generate realistic, adaptive attack. Using Gandalf, we collect and release a dataset of 279k prompt attacks. Complemented by benign user data, our analysis reveals the interplay between security and utility, showing that defenses integrated in the LLM (e.g., system prompts) can degrade usability even without blocking requests. We demonstrate that restricted application domains, defense-in-depth, and adaptive defenses are effective strategies for building secure and useful LLM applications., Comment: Niklas Pfister, V\'aclav Volhejn and Manuel Knott contributed equally

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., Comment: Proceedings contribution to "The 41st International Symposium on Lattice Field Theory (LATTICE2024)"

This work presents preliminary results of the first determination of the energy-momentum tensor form factors of the scalar glueball, referred to as gravitational form factors (GFFs). The calculation has been carried out in lattice Yang-Mills theory at a single lattice spacing. Using variationally optimized operators, the matrix elements are extracted from ratios of three-point functions to two-point functions. The glueball GFFs and their kinematic dependence are compared to those of other hadrons from previous calculations., Comment: 9 pages, 3 figures, Contribution to the 41st International Symposium on Lattice Field Theory, July 28th - August 3rd 2024, Liverpool, UK, v2 Acknowledgments update

We develop a comprehensive framework for extracting the pole position and properties of the doubly-charmed tetraquark $T_{\rm cc}^+(3875)$ from lattice QCD data using the relativistic three-particle formalism. This approach incorporates the effect of the one-pion exchange diagram in $DD\pi$ and $DD^*$ scattering, making it applicable at energies coinciding with the left-hand cut in the partial-wave projected $DD^*$ amplitude. We present an example application of this framework to existing lattice QCD data at $m_\pi = 280$ MeV. We solve the integral equations describing the $DD\pi$ reaction, use LSZ reduction to determine the corresponding $DD^*$ amplitude, and find the values of the infinite-volume two- and three-body $K$ matrices that lead to agreement with lattice $DD^*$ phase shifts within their uncertainties. Using these $K$ matrices in the three-particle quantization condition, we describe the finite-volume $DD^*$ spectrum and find good agreement with the lattice QCD energies. Our results suggest that, at this pion mass, the tetraquark appears as a pair of subthreshold complex poles whose precise location strongly depends on the value of the $DD\pi$ three-particle $K$ matrix., Comment: 60 pages, 11 figures

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the non-perturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential, $\mu_I$, bounds the partition function for a baryon chemical potential $\mu_B=3\mu_I/2$, these calculations also provide rigorous non-perturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time., Comment: 17 pages, 14 figures, updated to journal version

Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open question how flows can improve lattice QCD at state-of-the-art scales. We discuss and demonstrate two applications of flows in replica exchange (parallel tempering) sampling, aimed at improving topological mixing, which are viable with iterative improvements upon presently available flows., Comment: 9 pages, 5 figures, proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023)

Scale separation is an important physical principle that has previously enabled algorithmic advances such as multigrid solvers. Previous work on normalizing flows has been able to utilize scale separation in the context of scalar field theories, but the principle has been largely unexploited in the context of gauge theories. This work gives an overview of a new method for generating gauge fields using hierarchical normalizing flow models. This method builds gauge fields from the outside in, allowing different parts of the model to focus on different scales of the problem. Numerical results are presented for $U(1)$ and $SU(3)$ gauge theories in 2, 3, and 4 spacetime dimensions., Comment: Submitted as a proceedings to the 40th International Symposium on Lattice Field Theory (Lattice 2023)

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors., Comment: Version accepted for publication at JHEP, includes Appendix A, 35 pages, 6 figures

The three-particle $K$-matrix, $\mathcal{K}_{\mathrm{df},3}$, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the three-pion threshold., Comment: 44 pages, 8 figures, 10 tables

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman-Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting., Comment: 12 pages, 2 tables, 5 figures. v2: accepted for publication

We generalize the relativistic field-theoretic three-particle finite-volume scattering formalism to describe generic $DD\pi$ systems in the charm $C=2$ sector. This includes the isospin-0 channel, in which the recently discovered doubly-charmed tetraquark $T_{cc}(3875)^+$ is expected to manifest as a pole in the $DD \pi \to DD \pi$ scattering amplitude. The formalism presented here can also be applied to lattice QCD settings in which the $D^*$ is bound and, in particular, remains valid below the left-hand cut in $D D^*$ scattering, thus resolving an issue in previous analyses of lattice-determined finite-volume energies., Comment: 56 pages, 2 figures. v4: updated convention for isospin states, version accepted for publication

We study the large $N_\text{c}$ scaling of meson-meson scattering amplitudes in a theory with $N_\text{f}=4$ degenerate quark flavors. We focus on two different scattering channels, one having the same quantum numbers as some recently found tetraquark states at LHCb. Using L\"uscher's formalism, we study the $N_\text{c}$ dependence of the scattering phase shift and investigate the presence of exotic resonances in the scattering amplitude. We analyze the impact of including two-vector-meson and tetraquark-like operators to extract the finite-volume energies., Comment: 8 pages of main content, 5 figures. Talk presented at the 40th International Symposium on Lattice Field Theory (Lattice2023), 31 July - 4 August 2023, Fermi National Accelerator Laboratory

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 Schr\"{o}dinger 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., Comment: Proceedings of The 40th International Symposium on Lattice Field Theory (Lattice 2023)

Studies of the $\Delta$ baryon resonance and the $K_0^\ast(700)$ and $a_0(980)$ meson resonances using $N_f=2+1$ lattice QCD for pion masses near 200 MeV are presented. The $s$-wave scattering lengths for both the $I=1/2$ $N \pi$ and $I=3/2$ $N \pi$ channels and properties of the $\Delta$ resonance are identified from the finite-volume energy levels of the lattice simulation. The importance of a three-quark $\Delta$-operator in the $N\pi$ system and tetraquark operators in the mesonic systems is investigated., Comment: 10 pages, 5 figures, 3 tables

This work presents technical details of determining the finite-volume energy spectra for the scattering amplitude of the coupled-channel $\pi\Sigma - \bar{K}N$ from lattice QCD data. The importance of reliably extracting such spectra lies in the crucial dependence of the hadronic scattering amplitudes analysis on the energy spectrum when using L\"{u}scher's formalism. Results of the methods used are presented and the final finite-volume spectra are shown. The analysis of the scattering amplitude based on these results, exhibits a two-pole structure for the $\Lambda(1405)$, a virtual bound state below the $\pi\Sigma$ threshold and a resonance pole right below the $\bar{K}N$ threshold.

Recent results studying the masses and widths of low-lying baryon resonances in lattice QCD are presented. The $S$-wave $N\pi$ scattering lengths for both total isospins $I = 1/2$ and $I = 3/2$ are inferred from the finite-volume spectrum below the inelastic threshold together with the $I = 3/2$ $P$-wave containing the $\Delta(1232)$ resonance. A lattice QCD computation employing a combined basis of three-quark and meson-baryon interpolating operators with definite momentum to determine the coupled channel $\Sigma\pi$-$N\overline{K}$ scattering amplitude in the $\Lambda(1405)$ region is also presented. Our results support the picture of a two-pole structure suggested by theoretical approaches based on $SU(3)$ chiral symmetry and unitarity., Comment: 5 pages, 3 figures, talk presented at the 20th International Conference on Hadron Spectroscopy and Structure (HADRON 2023) in Genova, Italy, June 5th to 9th 2023

In recent years, detailed studies of three-pion systems have become possible in lattice QCD. This has in turn led to interest in 3-to-3 scattering of pions in the chiral perturbation theory framework. In addition to being an interesting study of multi-meson dynamics in its own right, it provides a valuable handle on finite-volume effects and the pion mass dependence, thus complementing the lattice results. I present our derivation of the next-to-leading order amplitude for this process, as well as its conversion into the three-particle K-matrix, which enables direct comparison to the lattice. Our results significantly improve the agreement between theory and lattice, which was poor when only leading-order effects were taken into account., Comment: Contribution to the 26th high-energy physics international conference in quantum chromodynamics (QCD23)

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of $n$-pion correlation functions for $n \in \{ 1, \dots, N\}$ using a single $N \times N$ matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 $\pi^+$s using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass $m_\pi = 170$ MeV and spacetime volumes of $(4.4^3\times 8.8)\ {\rm fm}^4$ and $(5.8^3\times 11.6)\ {\rm fm}^4$. We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential $\mu_I\sim 1.5 m_\pi$, signalling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound in the medium is seen to exceed the ideal-gas (conformal) limit ($c_s^2\leq 1/3$) over a wide range of chemical potential before falling towards the asymptotic expectation at $\mu_I\sim 15 m_\pi$. These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD., Comment: 16 pages, 18 figures, 1 table

A lattice QCD computation of the coupled channel $\pi\Sigma-\bar{K}N$ scattering amplitudes in the $\Lambda(1405)$ region is detailed. Results are obtained using a single ensemble of gauge field configurations with $N_{\rm f} = 2+1$ dynamical quark flavors and $m_{\pi} \approx 200$ MeV and $m_K\approx487$ MeV. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering $K$-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the $\pi\Sigma$ threshold and a resonance pole just below the $\bar{K}N$ threshold., Comment: 18 pages, 11 figures, 14 tables. Final version accepted for publication in PRD with post-publication corrections

This letter presents the first lattice QCD computation of the coupled channel $\pi\Sigma-\bar{K}N$ scattering amplitudes at energies near $1405\,{\rm MeV}$. These amplitudes contain the resonance $\Lambda(1405)$ with strangeness $S=-1$ and isospin, spin, and parity quantum numbers $I(J^P)=0(1/2^-)$. However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to $m_\pi\approx200$ MeV and $m_K\approx487$ MeV, this study finds the amplitudes exhibit a virtual bound state below the $\pi\Sigma$ threshold in addition to the established resonance pole just below the $\bar{K}N$ threshold. Several parametrizations of the two-channel $K$-matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by $SU(3)$ chiral symmetry and unitarity., Comment: 7 pages, 4 figures, and 1 table. Includes various corrections made during the last stages before publication

We systematically study the optical field localization in an active three-dimensional (3D) disordered percolating system with light nanoemitters incorporated in percolating clusters. An essential feature of such a hybrid medium is that the clusters are combined into a fractal radiation pattern, in which light is simultaneously emitted and scattered by the disordered structures. Theoretical considerations, based on systematic 3D simulations, reveal nontrivial dynamics in the form of propagation of localized field bunches in the percolating material. We obtain the length of the field localization and dynamical properties of such states as functions of the occupation probability of the disordered clusters. A transition between the dynamical states and narrow point-like fields pinned to the emitters is found. The theoretical analysis of the fractal field properties is followed by an experimental study of the light generation by nanoemitters incorporated in the percolating clusters. The experimental results corroborate theoretical predictions., Comment: 10 pages, 14 figures, to be published Chaos, Solitons & Fractals

Finite-volume pionless effective field theory (FVEFT$_{ \pi\!/ }$) at next-to-leading order (NLO) is used to analyze the two-nucleon lattice QCD spectrum of Ref.~\cite{Amarasinghe:2021lqa}, performed at quark masses corresponding to a pion mass of approximately $800 $ MeV. Specifically, the effective theory is formulated in finite volume, and variational sets of wave functions are optimized using differential programming. Using these wave functions projected to the appropriate finite-volume symmetry group, variational bounds from FVEFT$_{\pi\!/ }$ are obtained for the ground state, as well as excited states. By comparison with the lattice QCD GEVP spectrum, different low energy constants (LECs) are constrained. Relativistic corrections are incorporated, allowing for the extractions of NLO LECs, as well as the leading $s$-$d$-wave mixing term in the deuteron channel., Comment: 17 pages, 8 figs, 2 tables

Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow architectures facilitating the generalization to higher-dimensional lattice geometries. Specifically, we discuss masked autoregressive transformations with tractable and unbiased Jacobian determinants, a key ingredient for scalable and asymptotically exact flow-based sampling algorithms. For concreteness, results from a proof-of-principle application to SU(3) lattice gauge theory in four space-time dimensions are reported.

The three-particle $K$-matrix, $\mathcal{K}_{\mathrm{df},3}$, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions at maximal isospin through next-to-leading order (NLO) in Chiral Perturbation Theory (ChPT). We compare the values to existing lattice QCD results and find that the agreement between lattice QCD data and ChPT in the first two coefficients of the threshold expansion of $\mathcal{K}_{\mathrm{df},3}$ is significantly improved with respect to leading order once NLO effects are incorporated., Comment: 57 pages, 12 figures, 2 tables; v2: added sec. 2.3, minor changes, typos corrected, conclusions unchanged, version published in JHEP

We generalize the relativistic field-theoretic (RFT) three-particle finite-volume formalism to systems of three identical, massive, spin-$1/2$ fermions, such as three neutrons. This allows, in principle, for the determination of the three-neutron interaction from the finite-volume spectrum of three-neutron states, which can be obtained from lattice QCD calculations., Comment: 47 pages including references, 1 figure

This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015 LRP (LRP15) and identified key questions and plausible paths to obtaining answers to those questions, defining priorities for our research over the coming decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (~ 5 years) and longer term (5-10 years and beyond) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential and maintain United States leadership in QCD physics worldwide. This White Paper is organized as follows: In the Executive Summary, we detail the Recommendations and Initiatives that were presented and discussed at the Town Meeting, and their supporting rationales. Section 2 highlights major progress and accomplishments of the past seven years. It is followed, in Section 3, by an overview of the physics opportunities for the immediate future, and in relation with the next QCD frontier: the EIC. Section 4 provides an overview of the physics motivations and goals associated with the EIC. Section 5 is devoted to the workforce development and support of diversity, equity and inclusion. This is followed by a dedicated section on computing in Section 6. Section 7 describes the national need for nuclear data science and the relevance to QCD research., Comment: QCD Town Meeting White Paper, as submitted to 2023 NSAC LRP committee on Feb. 28, 2023

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically $\pi^+K^+$, $\pi^+\pi^+K^+$ and $K^+K^+\pi^+$. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS $N_f=2+1$ ensembles with pion masses of $200$ MeV and $340$ MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to $p$ waves. This requires also results for the $\pi^+\pi^+$ and $K^+ K^+$ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in $\pi^+\pi^+K^+$ and $K^+ K^+ \pi^+$ systems, finding statistically significant nonzero results in most cases. We include $s$ and $p$ waves in the K matrix for $\pi^+ K^+$ scattering, finding evidence for an attractive $p$-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory., Comment: 64 pages, 26 tables, 13 figures. Energy levels provided in ancillary files. v3: new appendix C, updated fig 6 and other minor changes

First-principles calculations of multi-hadron dynamics are a crucial goal in lattice QCD. Significant progress has been achieved in developing, implementing, and applying theoretical tools that connect finite-volume quantities to their infinite-volume counterparts. Here, I review some recent theoretical developments and numerical results regarding multi-particle quantities in a finite volume. These results include $N\pi$ scattering, systems of two and three mesons at maximal isospin, three-body resonances in a toy model, and the formulation of effective theories in finite volume for multi-nucleon systems., Comment: 24 pages, 10 figures. Plenary talk at the Lattice 2022 conference. v2: minor improvements & references

Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the scale of toy models, and it remains to be determined whether they can be applied to state-of-the-art lattice quantum chromodynamics calculations. Assessing the viability of sampling algorithms for lattice field theory at scale has traditionally been accomplished using simple cost scaling laws, but as we discuss in this work, their utility is limited for flow-based approaches. We conclude that flow-based approaches to sampling are better thought of as a broad family of algorithms with different scaling properties, and that scalability must be assessed experimentally., Comment: 22 pages, 8 figures

We study the properties of three-body resonances using a lattice complex scalar $\varphi^4$ theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy-plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory., Comment: 26 pages, 6 figures, 4 tables