arXiv subjects

Francesco Knechtli

Publications and source records attributed to Francesco Knechtli.

At least 19 recordsLinked to original sources

arXiv2026

Imprint of the adjoint meson spectrum in the decay patterns of hidden-bottom tetraquarks

We aim to clarify the experimentally observed near-degeneracy and decay patterns of the isospin, $I=1$, hidden-bottom tetraquarks $Z_b(10610)$ and $Z_b(10650)$ with quantum numbers $J^{P}=1^{+}$.We refer to them as $Z_b$ and $Z_b^{'}$, respectively. In particular, we find first evidence that the suppression of the decay of $Z_b^{'}$ to $B\bar{B^*}$ can be understood in the context of the Born-Oppenheimer Effective Field Theory (BOEFT). BOEFT enables writing both $Z_b$ and $Z_b^{'}$ as superpositions of $Z_1$ and $Z_2$ tetraquark configurations. This decomposition naturally relates the decay patterns of $Z_b$ and $Z_b^{'}$ to the degeneracy of the light degrees of freedom associated with $Z_1$ and $Z_2$ tetraquarks, {\it i.e.,} $1^{--}$and $0^{-+}$ adjoint mesons, respectively. By calculating the adjoint meson correlators within the framework of lattice QCD, we get good indications that these adjoint mesons are degenerate.

hep-lat↗

arXiv2026

Charmonium-Glueball spectroscopy with improved hadron creation operators

Construction of creation operators which can properly sample the underlying energy eigenstates remains a fundamental first step in lattice QCD spectroscopy calculations, particularly when the spectrum includes states with different composition such as mesons, glueballs, multi-particle states, etc. We tackle this issue in the study of the scalar glueball and charmonium mixing, where we use improved operators for both types of states to resolve the low-lying spectrum and identify the dominant composition of each state in a mass regime where the glueball is stable. We include derivative-based meson operators combined with distillation profiles, as well as glueball operators built from the chromo-magnetic field and its derivatives which retain angular momentum information from their continuum counterparts. We comment on the advantages of these operators, particularly on the construction and implementation of the glueball ones, thanks to which we identify the lightest iso-scalar state as glueball-dominated $0^{++}$.

hep-lat↗

arXiv2025

Using orthogonal projectors in multigrid multilevel Monte Carlo for trace estimation in lattice QCD

We introduce a multigrid multilevel Monte Carlo method for stochastic trace estimation in lattice QCD based on orthogonal projections. This formulation extends the previously proposed oblique decomposition and it is assessed on three representative problems: the connected pseudoscalar correlator, the trace of the full Dirac operator's inverse $\mathrm{tr}(D^{-1})$, and disconnected fermion loops. For the connected correlator, variance reductions grow systematically with the time separation and lead to cost savings of up to a factor of 30 at large separations, outperforming both the plain Hutchinson's estimator and the oblique formulation. For $\mathrm{tr}(D^{-1})$, reductions are more modest but remain systematic, with stronger effects on more ill-conditioned systems. Disconnected loops show no improvement, since their variance is dominated by local same-slice contributions not targeted by the decomposition.

hep-lat↗

arXiv2025

Mixing of heavy and light quarks in charmonium and light mesons

We study the system of light mesons, charmonium and glueballs in the flavor singlet scalar channel where they can mix. We use lattice QCD simulations with an almost physical charm quark and three degenerate light quarks for two values of the pion mass ($m_π \approx 420, 800$ MeV). Thanks to a variational basis which includes mesonic operators with profiles in distillation space, Wilson loops and two-pion operators we detect and show results of their mixing.

hep-lat↗

arXiv2025

The determination of potential scales in 2+1 flavor QCD

We calculate the hadronic scales $r_0$, $r_1$ and their ratio $r_0/r_1$ on $N_{\rm f}=2+1$ flavor QCD ensembles generated by the CLS consortium. These scales are determined from a tree-level improved definition of the static force on the lattice, which we measure using Wilson loops. Our analysis involves various continuum and chiral extrapolations of data that cover pion masses between 134 MeV and 420 MeV and five lattice spacings down to 0.039 fm. We compare the potential scales to gradient flow scales by forming corresponding ratios. We find $r_0=0.4757(64)$ fm at the physical point. As a byproduct of our analysis we express the $N_{\rm f}=3$ QCD Lambda parameter determined by the ALPHA Collaboration in units of the scale $r_0$ and obtain $r_0 Λ^{(3)}_{\overline{\rm{MS}}} = 0.820(28)$. Furthermore we present results for the second derivative of the potential to study its shape and compare it to phenomenological potential models.

hep-lat↗

arXiv2025

S-wave flavor-singlet meson mixing in QCD with light and charm quarks

We investigate the mixing between flavor-singlet light meson and charmonium operators in the S-wave channels, i.e. pseudo-scalar and vector channel, at two different pion masses. We measure statistically significant non-zero correlations between operators with different quark content corresponding to off-diagonal entries of a flavor-singlet mixing correlation matrix. By solving a GEVP we extract the low-lying energy spectrum and compare it with the one obtained by the different types of operators separately. We also calculate the overlaps between the states created by different operators and the energy eigenstates of the theory and find that all types of operators contribute to resolve the states of interest.

hep-lat↗

arXiv2025

Numerical stability of force-gradient integrators and their Hessian-free variants in lattice QCD simulations

A comprehensive linear stability analysis of force-gradient integrators and their Hessian-free variants is carried out by investigating the harmonic oscillator as a test equation. The analysis reveals that the linear stability of conventional force-gradient integrators and their Hessian-free counterparts coincides. By performing detailed linear stability investigations for the entire family of self-adjoint integrators with up to eleven exponentials per time step, we detect promising integrator variants that are providing a good trade-off between accuracy and numerical stability. Special attention is given to the application of these promising integrator variants within the Hamiltonian Monte Carlo algorithm, particularly in the context of interacting field theories. Simulations for the two-dimensional Schwinger model are conducted to demonstrate that there are no significant differences in the stability domain of a force-gradient integrator and its Hessian-free counterpart. Lattice QCD simulations with two heavy Wilson fermions emphasize that Hessian-free force-gradient integrators with a larger stability threshold allow for a more efficient computational process compared to conventional splitting methods. Furthermore, detailed investigations of the stability threshold are performed by investigating Nf = 2 twisted-mass fermions and nested integrators, highlighting the reliability of the linear stability threshold for lattice QCD simulations.

hep-lat↗

arXiv2025

Hybrid static potentials and gluelumps on $N_f=3+1$ ensembles

QCD permits the existence of hybrid mesons that are made up of both quarks and gluons, including exotic states, i.e., quantum numbers prohibited for pure quark-antiquark states, with possible candidates found in experiments. We present static hybrid potentials measured via Laplace trial states together with static-light meson thresholds on $N_f=3+1$ dynamical fermion ensembles with 420 MeV pions. Furthermore, we measure corresponding gluelump masses which refer to the $R\rightarrow0$ limit of the hybrid potentials and are essential input parameters for effective models to describe hybrid mesons.

hep-lat↗

arXiv2025

Flavor mixing in charmonium and light mesons with optimal distillation profiles

We study the light meson - charmonium - glueball mixing using flavor-singlet meson operators built from optimal distillation profiles together with purely gluonic operators in different $J^{PC}$ channels at two different pion masses ($\approx$ $420$, $800$ MeV) in two $N_{\rm f} = 3 + 1$ ensembles at close to physical charm quark mass. We observe non-zero mixing correlations between the different types of operators and quantify the overlaps between states created by them and the energy eigenstates by means of a GEVP formulation. We are particularly interested in the scalar glueball and its possible decay into two pions so we also include two-pion operators in our calculation.

hep-lat↗

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↗

arXiv2025

Static-light meson spectroscopy with optimal distillation profiles

The spectrum of static-light and static-charm mesons is studied using optimized distillation in two different $N_{\rm{f}} = 3 + 1$ QCD ensembles with pion masses of $m_π \approx 800 \, \text{MeV}$ and $m_π \approx 420 \,\text{MeV}$ and a heavy (charm) quark. Local and derivative-based operators are used to access states of multiple quantum numbers. The use of optimal profiles is shown to improve the overlap with the energy states compared to standard distillation.

hep-lat↗

arXiv2025

The strength of the interaction between quarks and gluons

Modern particle physics experiments, e.g. at the Large Hadron Collider (LHC) at CERN, crucially depend on the precise description of the scattering processes in terms of the known fundamental forces. This is limited by our current understanding of the strong nuclear force, as quantified by the strong coupling, $α_s$, between quarks and gluons. Relating $α_s$ to experiments poses a major challenge as the strong interactions lead to the confinement of quarks and gluons inside hadronic bound states. At high energies, however, the strong interactions become weaker ("asymptotic freedom") and thus amenable to an expansion in powers of the coupling. Attempts to relate both regimes usually rely on modeling of the bound state problem in one way or another. Using large scale numerical simulations of a first principles formulation of Quantum Chromodynamics on a space-time lattice, we have carried out a model-independent determination of $α_s$ with unprecedented precision. The uncertainty, about half that of all other results combined, originates predominantly from the statistical Monte Carlo evaluation and has a clear probabilistic interpretation. The result for $α_s$ describes a variety of physical phenomena over a wide range of energy scales. If used as input information, it will enable significantly improved analyses of many high energy experiments, by removing an important source of theoretical uncertainty. This will increase the likelihood to uncover small effects of yet unknown physics, and enable stringent precision tests of the Standard Model. In summary, this result boosts the discovery potential of the LHC and future colliders, and the methods developed in this work pave the way for even higher precision in the future.

hep-ph↗

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

Exponential Error Reduction for Glueball Calculations Using a Two-Level Algorithm in Pure Gauge Theory

This study explores the application of a two-level algorithm to enhance the signal-to-noise ratio of glueball calculations in four-dimensional $\mathrm{SU(3)}$ pure gauge theory. Our findings demonstrate that the statistical errors exhibit an exponential reduction, enabling reliable extraction of effective masses at distances where current standard methods would demand exponentially more samples. However, at shorter distances, standard methods prove more efficient due to a saturation of the variance reduction using the multi-level method. We discuss the physical distance at which the multi-level sampling is expected to outperform the standard algorithm, supported by numerical evidence across different lattice spacings and glueball channels. Additionally, we construct a variational basis comprising 35 Wilson loops up to length 12 and 5 smearing sizes each, presenting results for the first state in the spectrum for the scalar, pseudoscalar, and tensor channels.

hep-lat↗

arXiv2024

The quark-mass dependence of the potential energy between static colour sources in the QCD vacuum with light and strange quarks

The low-lying energy spectrum of the static-colour-source-anti-source system in a vacuum containing light and strange quarks is computed using lattice QCD for a range of different light quark masses. The resulting levels are described using a simple model Hamiltonian and the parameters in this model are extrapolated to the physical light-quark masses. In this framework, the QCD string tension is found to be $\sqrtσ=445(3)_{\rm stat}(6)_{\rm sys}$ MeV.

hep-lat↗

arXiv2024

Heavy Wilson Quarks and O($a$) Improvement: Nonperturbative Results for $b_{\rm g}$

With Wilson quarks, on-shell O($a$) improvement of the lattice QCD action is achieved by including the Sheikholeslami-Wohlert term and two further operators of mass dimension 5, which amount to a mass-dependent rescaling of the bare parameters. We here focus on the rescaled bare coupling, $\tilde{g}_0^2 = g_0^2(1 + b_{\rm g} am_{\rm q})$, and the determination of $b_{\rm g}(g_0^2)$, which is currently only known to 1-loop order of perturbation theory. We derive suitable improvement conditions in the chiral limit and in a finite space-time volume and evaluate these for different gluonic observables, both with and without the gradient flow. The choice of $β$-values and the line of constant physics are motivated by the ALPHA collaboration's decoupling strategy to determine $α_s(m_Z)$. However, the improvement conditions and some insight into systematic effects may prove useful in other contexts, too.

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↗