arXiv subjects

Carsten Urbach

Publications and source records attributed to Carsten Urbach.

At least 37 records · Page 2Linked to original sources

arXiv2025

Reproducibility and Open Science in Lattice Quantum Field Theory

Reproducibility and Open Science are increasingly discussed as essential aspects of the research process. While there are areas where the Lattice community has been ahead of the curve with respect to the broader research world in this space, including early adoption of open publications via the arXiv, and the introduction of the International Lattice Data Grid in the 2000s, there are other areas where lattice practitioners could benefit from practices already adopted in other disciplines. In this Contribution, we report the outcomes of a panel discussion on this topic at the Lattice 2024 conference; after a discussion on motivations for work in this space, and introductory discussions of the relevant experiences of the panelists, we provide summaries of answers to the questions posed by the audience in the panel.

hep-lat↗

arXiv2024

On the equivalence of Prony and Lanczos methods for Euclidean correlation functions

We investigate the oblique Lanczos method recently put forward in arXiv:2406.20009 for analysing Euclidean correlators in lattice field theories and show that it is analytically equivalent to the well known Prony Generalised Eigenvalue Method (PGEVM). Moreover, we discuss that the signal-to-noise problem is not aleviated by either of these two methods. Still, both methods show clear advantages when compared to the standard effective mass approach.

hep-lat↗

arXiv2024

$ω$ meson from lattice QCD

Many excited states in the hadron spectrum have large branching ratios to three-hadron final states. Understanding such particles from first principles QCD requires input from lattice QCD with one-, two-, and three-meson interpolators as well as a reliable three-body formalism relating finite-volume spectra at unphysical pion mass values to the scattering amplitudes at the physical point. In this work, we provide the first-ever calculation of the resonance parameters of the $ω$ meson from lattice QCD, including an update of the formalism through matching to effective field theories. The main result of this pioneering study, the pole position of the $ω$ meson at $\sqrt{s_ω}= (778.0(11.2)-i\,3.0(5) )\,\mathrm{MeV}$, agrees reasonably well with experiment. In addition we provide an estimate of the $ω-ρ$ mass difference as $29(15)\,\mathrm{MeV}$.

hep-lat↗

arXiv2024

Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations

We present a digitization scheme for the lattice $\mathrm{SU}(2)$ gauge theory Hamiltonian in the $\mathit{magnetic}$ $\mathit{basis}$, where the gauge links are unitary and diagonal. The digitization is obtained from a particular partitioning of the $\mathrm{SU}(2)$ group manifold, with the canonical momenta constructed by an approximation of the Lie derivatives on this partitioning. This construction, analogous to a discrete Fourier transform, preserves the spectrum of the kinetic part of the Hamiltonian and the canonical commutation relations exactly on a subspace of the truncated Hilbert space, while the residual subspace can be projected above the cutoff of the theory.

hep-lat↗

arXiv2024

Towards determining the (2+1)-dimensional Quantum Electrodynamics running coupling with Monte Carlo and quantum computing methods

In this paper, we examine a compact $U(1)$ lattice gauge theory in $(2+1)$ dimensions and present a strategy for studying the running coupling and extracting the non-perturbative $Λ$-parameter. To this end, we combine Monte Carlo simulations and quantum computing, where the former can be used to determine the numerical value of the lattice spacing $a$, and the latter allows for reaching the perturbative regime at very small values of the bare coupling and, correspondingly, small values of $a$. The methodology involves a series of sequential steps (i.e., the step scaling function) to bridge results from small lattice spacings to non-perturbative large-scale lattice calculations. Focusing on the pure gauge case, we demonstrate that these quantum circuits, adapted to gauge degrees of freedom, are able to capture the relevant physics by studying the expectation value of the plaquette operator, for matching with corresponding Monte Carlo simulations. We also present results for the static potential and static force, which can be related to the renormalized coupling. The procedure outlined in this work can be extended to Abelian and non-Abelian lattice gauge theories with matter fields and might provide a way towards studying lattice quantum chromodynamics utilizing both quantum and classical methods.

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

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

Exploring a new approach to Hadronic Parity Violation from Lattice QCD

The long-range, parity-odd nucleon interaction generated by single pion exchange is captured in the parity-odd pion-nucleon coupling $h^1_π$. Its calculation in lattice QCD requires the evaluation of 4-quark operator nucleon 3-point functions. We investigate a new numerical approach to compute $h^1_π$ based on nucleon matrix elements of parity-even 4-quark operators and related to the parity-violating electro-weak theory by PCAC and chiral perturbation theory. This study is performed with 2+1+1 dynamical flavors of twisted mass fermions at pion mass $m_π \approx 260\,\text{MeV}$ in a lattice box of $L \approx 3 \,\text{fm} $ and with a lattice spacing of $a \approx 0.091 \,\text{fm}$. From a calculation excluding fermion loop diagrams we find a bare coupling of $h^1_π= 8.08 \,(98) \cdot 10^{-7}$.

hep-lat↗

arXiv2023

Testing the $\mathrm{SU}(2)$ lattice Hamiltonian built from $S_3$ partitionings

We test a possible digitization of $\mathrm{SU}(2)$ lattice gauge theories based on partitionings of the sphere $S_3$. In our construction the link operators are unitary and diagonal, with eigenvalues determined by the vertices of the partitioning. The canonical momenta are finite difference operators approximating the Lie derivatives on the manifold. In this formalism we implement the standard Wilson Hamiltonian. We show results for a 2-site Schwinger-type model in 1D and a single-plaquette system in 2D. Our calculations are performed on a classical computer, though in principle they can be implemented also on a quantum device.

hep-lat↗

arXiv2023

Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory

Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space H. Here we give a prescription for gauge links and canonical momenta of an SU(2) gauge theory, such that the matrix representation of the former is diagonal in H. This is achieved by discretising the sphere $S_3$ isomorphic to SU(2) and the corresponding directional derivatives. We show that the fundamental commutation relations are fulfilled up to discretisation artefacts. Moreover, we directly construct the Casimir operator corresponding to the Laplace-Beltrami operator on $S_3$ and show that the spectrum of the free theory is reproduced again up to discretisation effects. Qualitatively, these results do not depend on the specific discretisation of SU(2), but the actual convergence rates do.

hep-lat↗

arXiv2023

Hadronic Parity Violation from Twisted Mass Lattice QCD

We present results for an exploratory lattice calculation of the leading parity-violating pion-nucleon coupling $h_π^1$. Based on the PCAC relation we use a parity-conserving Lagrangian and focus on the techniques to determine the nucleon matrix elements of the effective 4-quark operators. For our study we employ an ensemble of twisted mass fermions with $260$ MeV pion mass. Barring mixing with lower-dimensional operators and renormalization at this stage, we discuss our estimate for $h_π^1$.

hep-lat↗

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↗

arXiv2023

Three-body resonances in the $φ^4$ theory

We study the properties of three-body resonances using a lattice complex scalar $φ^4$ 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.

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↗

arXiv2022

Digitizing SU(2) Gauge Fields and What to Look Out for When Doing So

With the long term perspective of using quantum computers and tensor networks for lattice gauge theory simulations, an efficient method of digitizing gauge group elements is needed. We thus present our results for a handful of discretization approaches for the non-trivial example of SU(2), such as its finite subgroups, as well as different classes of finite subsets. We focus our attention on a freezing transition observed towards weak couplings. A generalized version of the Fibonacci spiral appears to be particularly efficient and close to optimal.

hep-lat↗