arXiv subjects

Jacob Finkenrath

Publications and source records attributed to Jacob Finkenrath.

At least 37 records · Page 2Linked to original sources

arXiv2025

Hessian-free force-gradient integrators and their application to lattice QCD simulations

We present initial results on Hessian-free force-gradient integrators for lattice field theories. Integrators of this framework promise to provide substantial performance enhancements, particularly for larger lattice volumes where higher-order integrators demonstrate greater efficiency. Numerical results demonstrate the superior efficiency of the proposed integrators compared to commonly employed non-gradient schemes, particularly due to enhanced stability properties. It is anticipated that the advantages of the Hessian-free framework will become even more pronounced in nested integration approaches and for smaller fermion masses, where the numerical stability properties of the integrators become increasingly important.

hep-lat↗

arXiv2025

Update on two-level sampling for glueball observables in quenched QCD

We report our progress in combining a two-level sampling algorithm with distillation techniques for calculations of disconnected diagrams in quenched QCD. The simulations are performed on a single ensemble at $β=6.0$ and volume $V=16^3\times 64$, and at a pion mass of $m_π\approx 760~\mathrm{MeV}$.

hep-lat↗

arXiv2024

Hessian-free force-gradient integrators

We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for separable Hamiltonian systems with quadratic kinetic energy may be particularly useful when applied to Hamiltonian systems where an evaluation of the Hessian is significantly more expensive than an evaluation of its gradient, e.g. in molecular dynamics simulations of classical systems. Numerical experiments of an N-body problem, as well as applications to the molecular dynamics step in the Hybrid Monte Carlo (HMC) algorithm for lattice simulations of the Schwinger model and Quantum Chromodynamics (QCD) verify these expectations.

math.NA↗

arXiv2024

$\bar b \bar b u d$ and $\bar b \bar b u s$ tetraquarks from lattice QCD using symmetric correlation matrices with both local and scattering interpolating operators

We study the $\bar b \bar b u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$ as well as the $\bar b \bar b u s$ tetraquark with quantum numbers $J^P = 1^+$ using lattice QCD. We improve on existing work by including both local and scattering interpolating operators on both sides of the correlation functions and use symmetric correlation matrices. This allows not only a reliable determination of the energies of QCD-stable tetraquark ground states, but also of low-lying excited states, which are meson-meson scattering states. The latter is particularly important for future finite-volume scattering analyses. Here, we perform chiral and continuum extrapolations of just the ground-state energies, for which finite-volume effects are expected to be small. Our resulting tetraquark binding energies, $-100 \pm 10\:^{+36}_{-51}\:\:{\rm MeV}$ for $\bar b \bar b u d$ and $-30 \pm 3\:^{+11}_{-31}\:\:{\rm MeV}$ for $\bar b \bar b u s$, are consistent with other recent lattice-QCD predictions.

hep-lat↗

arXiv2024

Quark and gluon momentum fractions in the pion and in the kaon

We present the full decomposition of the momentum fraction carried by quarks and gluons in the pion and the kaon. We employ three gauge ensembles generated with $N_f=2+1+1$ Wilson twisted-mass clover-improved fermions at the physical quark masses. For both mesons we perform a continuum extrapolation directly at the physical pion mass, which allows us to determine for the first time the momentum decomposition at the physical point. We find that the total momentum fraction carried by quarks is 0.532(56) and 0.618(32) and by gluons 0.388(49) and 0.408(61) in the pion and in the kaon, respectively, in the $\overline{\mathrm{MS}}$ scheme and at the renormalization scale of 2 GeV. Having computed both the quark and gluon contributions in the continuum limit, we find that the momentum sum is 0.926(68) for the pion and 1.046(90) for the kaon, verifying the momentum sum rule.

hep-lat↗

arXiv2024

Shallow Bound States and Hints for Broad Resonances with Quark Content $\bar{b}\bar{c}ud$ in $B$-$\bar{D}$ and $B^*$-$\bar{D}$ Scattering from Lattice QCD

We present the first determination of the energy dependence of the $B$-$\bar{D}$ and $B^*$-$\bar{D}$ isospin-0, $S$-wave scattering amplitudes both below and above the thresholds using lattice QCD, which allows us to investigate rigorously whether mixed bottom-charm $\bar{b}\bar{c}ud$ tetraquarks exist as bound states or resonances. The scattering phase shifts are obtained using Lüscher's method from the energy spectra in two different volumes. To ensure that no relevant energy level is missed, we use large, symmetric $7 \times 7$ and $8 \times 8$ correlation matrices that include, at both source and sink, $B^{(*)}$-$\bar{D}$ scattering operators with the lowest three or four possible back-to-back momenta in addition to local $\bar{b}\bar{c}ud$ operators. We fit the energy dependence of the extracted scattering phase shifts using effective-range expansions. We observe sharp peaks in the $B^{(*)}$-$\bar{D}$ scattering rates close to the thresholds, which are associated with shallow bound states, either genuine or virtual, a few MeV or less below the $B^{(*)}$-$\bar{D}$ thresholds. In addition, we find hints for resonances with masses of order $100$ MeV above the thresholds and decay widths of order $200$ MeV.

hep-lat↗

arXiv2024

Fine grinding localized updates via gauge equivariant flows in the 2D Schwinger model

State-of-the-art simulations of discrete gauge theories are based on Markov chains with local changes in the field space, which however at very fine lattice spacings are notoriously difficult due to separated topological sectors of the gauge field. Hybrid Monte Carlo (HMC) algorithms, which are very efficient at coarser lattice spacings, suffer from increasing autocorrelation times. This makes simulation of lattice QCD close to the continuum infeasible even with exa-scale computing. An approach, which can overcome long autocorrelation times, is based on trivializing maps, where a new gauge proposal is given by mapping a configuration from a trivial space to the target one, distributed via the associated Boltzmann factor. Using gauge equivariant coupling layers, the map can be approximated via machine learning techniques. However the deviations scale with the volume in case of local theories and extensive distributions, rendering a global update unfeasible for realistic box sizes. In this proceeding, we will discuss the potential of localized updates in case of the 2D Schwinger Model. Using gauge-equivariant flow maps, a local update can be fine grained towards finer lattice spacing. Based on this we will present results on simulating the 2D Schwinger Model with dynamical Nf=2 Wilson fermions at fine lattice spacings using scalable global correction steps and compare the performance to the HMC.

hep-lat↗

arXiv2024

Review on Algorithms for dynamical fermions

This review gives an overview on the research of algorithms for dynamical fermions used in large scale lattice QCD simulations. First a short overview on the state-of-the-art of ensemble generation at the physical point is given. Followed by an overview on necessary steps towards simulation of large lattices with the Hybrid Monte Carlo algorithm. Here, the status of iterative solvers and tuning procedures for numerical integrators within the molecular dynamics are discussed. This is followed by a review on the on-going developments for algorithms, with a focus on methods which are potentially useful to simulate gauge theories at very fine lattice spacings, i.e. well suited to overcome freezing of the topological charge. This includes modification of the HMC algorithm as well as a discussion of algorithms which includes the fermion weight via global correction steps. Parts of the discussions are on the application of generative models via gauge equivariant flows as well as multi-level algorithms.

hep-lat↗

arXiv2024

Charmonium spectroscopy with optimal distillation profiles

We use the method of optimal distillation profiles to compute the low-lying charmonium spectrum in an $N_f = 3+1$ ensemble at the $SU(3)$ light flavor symmetric point ($m_π \approx 420$ MeV), physical charm quark mass and lattice spacing $a\approx 0.0429$ fm. The spectrum and mass splittings display good agreement with their values in nature and the statistical errors are comparable, if not smaller, than those of state-of-the-art lattice calculations. We also present first results on the mixing of charmonium with glueballs and light hadrons obtained in a similar $N_f = 3+1$ ensemble but at larger pion mass.

hep-lat↗

arXiv2024

Low-lying baryon masses using twisted mass fermions ensembles at the physical pion mass

We investigate the low-lying baryon spectrum using three $N_f$=2+1+1 ensembles simulated with physical values of the quark masses and lattice spacings of 0.080, 0.069, and 0.057 fm. The ensembles are generated using twisted mass clover-improved fermions and the Iwasaki gauge action. The spatial length is kept approximately the same at about 5.1 fm to 5.5 fm fulfilling the condition $m_πL$> 3.6. We investigate isospin splitting within isospin multiples and verify that for most cases the isospin splitting for these lattice spacing is consistent with zero. In the couple of cases, for which there is a non-zero value, in the continuum limit, the mass splitting goes to zero. The baryon masses are extrapolated to the continuum limit using the three $N_f$=2+1+1 ensembles and are compared to other recent lattice QCD results. For the strange and charm quark masses, we find, respectively, $m_s$(2 GeV)=99.2(2.7) MeV and $m_c$(3 GeV)=1.015(39) GeV. The values predicted for the masses of the doubly charmed $Ξ_{cc}^\star$, $Ω_{cc}$ and $Ω_{cc}^\star$ baryons are 3.676(55) GeV, 3.703(51) GeV and 3.803(50) GeV, respectively, and for the triply charmed $Ω_{ccc}$ baryon is 4.785(71) GeV.

hep-lat↗

arXiv2024

Nucleon axial and pseudoscalar form factors using twisted-mass fermion ensembles at the physical point

We compute the nucleon axial and pseudoscalar form factors using three $N_f=$2+1+1 twisted mass fermion ensembles with all quark masses tuned to approximately their physical values. The values of the lattice spacings of these three physical point ensembles are 0.080 fm, 0.068 fm, and 0.057 fm, and spatial sizes 5.1 fm, 5.44 fm, and 5.47 fm, respectively, yielding $m_πL$>3.6. Convergence to the ground state matrix elements is assessed using multi-state fits. We study the momentum dependence of the three form factors and check the partially conserved axial-vector current (PCAC) hypothesis and the pion pole dominance (PPD). We show that in the continuum limit, the PCAC and PPD relations are satisfied. We also show that the Goldberger-Treimann relation is approximately fulfilled and determine the Goldberger-Treiman discrepancy. We find for the nucleon axial charge $g_A$=1.245(28)(14), for the axial radius $\langle r^2_A \rangle$=0.339(48)(06) fm$^2$, for the pion-nucleon coupling constant $g_{πNN} \equiv \lim_{Q^2 \rightarrow -m_π^2} G_{πNN}(Q^2)$=13.25(67)(69) and for $G_P(0.88m_μ^2)\equiv g_P^*$=8.99(39)(49).

hep-lat↗

arXiv2023

The $η\rightarrow γ^* γ^*$ transition form factor and the hadronic light-by-light $η$-pole contribution to the muon $g-2$ from lattice QCD

We calculate the double-virtual $η\rightarrow γ^* γ^*$ transition form factor $\mathcal{F}_{η\to γ^* γ^*}(q_1^2,q_2^2)$ from first principles using a lattice QCD simulation with $N_f=2+1+1$ quark flavors at the physical pion mass and at one lattice spacing and volume. The kinematic range covered by our calculation is complementary to the one accessible from experiment and is relevant for the $η$-pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment $a_μ= (g-2)/2$ of the muon. From the form factor calculation we extract the partial decay width $Γ(η\rightarrow γγ) = 323(85)_\text{stat}(22)_\text{syst}$ eV and the slope parameter $b_η=1.19(36)_\text{stat}(16)_\text{syst}$ GeV${}^{-2}$. For the $η$-pole contribution to $a_μ$ we obtain $a_μ^{η-\text{pole}} = 13.2(5.2)_\text{stat}(1.3)_\text{syst} \cdot 10^{-11}$.

hep-lat↗

arXiv2023

Glueball Spectrum with four light dynamical fermions

We perform a calculation of the glueball spectrum for $N_f=4$ degenerate dynamical fermions with masses corresponding to light pions. We do so by making use of ensembles produced within the framework of maximally twisted fermions by the Extended Twisted Mass Collaboration (ETMC). We obtain masses of states that fall into the irreducible representations of the octahedral group of rotations in combination with the quantum numbers of charge conjugation $C$ and parity $P$; the above quantum numbers result in 20 distinct irreducible representations. We implement the Generalized Eigenvalue Problem (GEVP) using a basis that consists only of gluonic operators. The purpose of this work is to investigate the effect of light dynamical quarks on the glueball spectrum and how this compares to the statistically more accurate spectrum of $SU(3)$ pure gauge theory. Given that glueball states may have broad widths and thus need to be disentangled from all the relevant mixings, we use large ensembles of the order of ${\sim {~\cal O}}(20 {\rm K})$ configurations. Despite the large ensembles, the statistical uncertainties allow us to extract the masses for only a few irreducible representations; namely $A_1^{++}$, $A_1^{-+}$, $E^{++}$ as well as $T_2^{++}$. The results for the scalar $A_1^{++}$ representation show that an additional state appears as the lightest state in the scalar $A_1^{++}$ channel of the glueball spectrum, while the next two excited states are consistent with the lightest two states of the pure gauge theory. To further elucidate the nature of this additional state we perform a calculation using $N_f=2+1+1$ configurations and this demonstrates that it possesses a large quark content. Finally, the ground states of the $E^{++}$ and $T_2^{++}$ tensor channels and of the $A_1^{-+}$ pseudoscalar channel show, at most, minor effects due to the inclusion of dynamical quarks.

hep-lat↗

arXiv2023

An approach to performance portability through generic programming

The expanding hardware diversity in high performance computing adds enormous complexity to scientific software development. Developers who aim to write maintainable software have two options: 1) To use a so-called data locality abstraction that handles portability internally, thereby, performance-productivity becomes a trade off. Such abstractions usually come in the form of libraries, domain-specific languages, and run-time systems. 2) To use generic programming where performance, productivity and portability are subject to software design. In the direction of the second, this work describes a design approach that allows the integration of low-level and verbose programming tools into high-level generic algorithms based on template meta-programming in C++. This enables the development of performance-portable applications targeting host-device computer architectures, such as CPUs and GPUs. With a suitable design in place, the extensibility of generic algorithms to new hardware becomes a well defined procedure that can be developed in isolation from other parts of the code. That allows scientific software to be maintainable and efficient in a period of diversifying hardware in HPC. As proof of concept, a finite-difference modelling algorithm for the acoustic wave equation is developed and benchmarked using roofline model analysis on Intel Xeon Gold 6248 CPU, Nvidia Tesla V100 GPU, and AMD MI100 GPU.

cs.SE↗

arXiv2023

Probing the energy-smeared R-ratio on the lattice

We present a first-principles lattice QCD investigation of the $R$-ratio between the $e^+e^-$ cross-section into hadrons and that into muons. By using the method of Ref.[1], that allows to extract smeared spectral densities from Euclidean correlators, we compute the $R$-ratio convoluted with Gaussian smearing kernels of widths of about $600$ MeV and central energies from $220$ MeV up to $2.5$ GeV. Our theoretical results are compared with the corresponding quantities obtained by smearing the KNT19 compilation [2] of $R$-ratio experimental measurements with the same kernels and, by centring the Gaussians in the region around the $ρ$-resonance peak, a tension of about three standard deviations is observed. From the phenomenological perspective, we have not included yet in our calculation QED and strong isospin-breaking corrections and this might affect the observed tension. From the methodological perspective, our calculation demonstrates that it is possible to study the $R$-ratio in Gaussian energy bins on the lattice at the level of accuracy required in order to perform precision tests of the Standard Model.

hep-lat↗

arXiv2022

Lattice calculation of the R-ratio smeared with Gaussian kernel

The ratio $R(E)$ of the cross-sections for $e^+e^-\to$ hadrons and $e^+e^-\to μ^+μ^-$ is a valuable energy-dependent probe of the hadronic sector of the Standard Model. Moreover, the experimental measurements of $R(E)$ are the inputs of the dispersive calculations of the leading hadronic vacuum polarization contribution to the muon $g-2$ and these are in significant tension with direct lattice calculations and with the muon $g-2$ experiment. In this talk we discuss the results of our first-principles lattice study of $R(E)$. By using a recently proposed method for extracting smeared spectral densities from Euclidean lattice correlators, we have calculated $R(E)$ convoluted with Gaussian kernels of different widths $σ$ and central energies up to $2.5$ GeV. Our theoretical results have been compared with the KNT19 [1] compilation of experimental results smeared with the same Gaussian kernels and a tension (about three standard deviations) has been observed for $σ\sim 600$ MeV and central energies around the $ρ$-resonance peak.

hep-lat↗

arXiv2022

Pseudoscalar-pole contributions to the muon $g-2$ at the physical point

Pseudoscalar-pole diagrams are an important component of estimates of the hadronic light-by-light (HLbL) contribution to the muon $g-2$. We report on our computation of the transition form factors $\mathcal{F}_{P \rightarrow γ^* γ^*}$ for the neutral pseudoscalar mesons $P=π^0$ and $η$. The calculation is performed using twisted-mass lattice QCD with physical quark masses. On the lattice, we have access to a broad range of (space-like) photon four-momenta and therefore produce form factor data complementary to the experimentally accessible single-virtual direction, which directly leads to an estimate of the pion- and $η$-pole components of the muon $g-2$. For the pion, our result for the $g-2$ contribution in the continuum is comparable with previous lattice and data-driven determinations, with combined relative uncertainties below $10\%$. For the $η$ meson, we report on a preliminary determination from a single lattice spacing.

hep-lat↗

arXiv2022

Short \& intermediate distance HVP contributions to muon g-2: SM (lattice) prediction versus $e^+e^-$ annihilation data

We present new lattice results of the ETM Collaboration, obtained from extensive simulations of lattice QCD with dynamical up, down, strange and charm quarks at physical mass values, different volumes and lattice spacings, concerning the SM prediction for the so-called intermediate window (W) and short-distance (SD) contributions to the leading order hadronic vacuum polarization (LO-HVP) term of the muon anomalous magnetic moment, $a_μ$. Results for $a_μ^{\rm LO-HVP,W}$ and $a_μ^{\rm LO-HVP,SD}$, besides representing a step forward to a complete lattice computation of $a_μ^{\rm LO-HVP}$ and a useful benchmark among lattice groups, are compared here with their dispersive counterparts based on experimental data for $e^+e^-$ into hadrons. The comparison confirms the tension in $a_μ^{\rm LO-HVP,W}$, already noted in 2020 by the BMW Collaboration, while showing no tension in $a_μ^{\rm LO-HVP,SD}$.

hep-ph↗