HEP Lattice·hep-lat

Fri·Jun 19, 2026Friday·June 19, 2026

9 papers—6 primary·3 cross-listed

01
Reflection-Positive Construction of a Four-Dimensional SU(N) Yang-Mills Theory with Mass Gap and Confinement
Mir Faizal🇨🇦 · Arshid Shabir🇨🇦
In the Euclidean view one must first require that positivity not be violated, and from this modest demand, together with locality, a great deal follows: starting from a reflection-positive lattice formulation of pure SU(N) Yang-Mills theory we obtain a transfer operator with a uniform gap, while large Wilson loops already show an area law by means of convergent character (polymer) expansions; a finite-range, gauge-covariant multiscale analysis then carries these features from one scale to the next with interlaced inequalities whose small defects can be summed, so that exponential clustering and a strictly positive string tension endure in the continuum; the Osterwalder-Schrader reconstruction turns these Euclidean facts into a Minkowski theory with a self-adjoint Hamiltonian, the spectral gap lying above the vacuum and the linear potential for static charges appearing, which gives a concrete picture of confinement; the construction depends on no special regulator, for a single-scale Lipschitz control and a telescoping argument bind all admissible reflection-positive slicings into a unique limiting measure and thus secure universality; moreover, the same framework admits entry from weak coupling, so that the continuum reached from strong coupling meets the one approached along an asymptotically free trajectory, yielding one and the same theory; in my view this is how mathematical clarity and physical insight cooperate: positivity, locality, and renormalization working together so that the mass gap and confinement are not marvels to be assumed, but natural properties of the non-Abelian vacuum.
hep-lathep-thFortsch.Phys.(2026)·0 citations
02
Kernel transformations and bounds for smeared spectral functions
William I. Jay🇺🇸 · Matteo Saccardi🇺🇸
This work develops a framework for transforming between smeared spectral functions computed using different smearing kernels. The kernel-transformation problem naturally arises when information is available for one family of energy-smeared observables, while phenomenology or comparison with other calculations require a different smearing. For exact transformations, analytic conditions are established for the maps to exist and converge without arbitrary regularization. Explicit expressions are provided for several kernel classes of interest, including Cauchy-to-Gaussian transformations and Gaussian-to-Cauchy width mixtures. When exact transformations are unavailable, the inverse problem is tackled through regulated maps paired with bounds on the associated systematic error, directly computable from the given input data. Errors on the input smeared spectral functions, either statistical or in the form of pointwise rigorous bounds, are then propagated to the target observables. Enforcing spectral positivity can be used to tighten the bounds.
hep-lat4 citations
03
Scalar diquark mass and quark--diquark potential from lattice QCD using the potential method with a static quark
Kai-Wen Kelvin-Lee🇯🇵 · Noriyoshi Ishii🇯🇵
We study the scalar diquark mass and the quark--diquark potential by applying a HAL QCD-inspired potential method to a baryonic system composed of a scalar diquark and a static quark. The diquark mass is determined self-consistently by requiring that the p-wave baryonic spectrum obtained from two-point correlators be reproduced within the potential framework. Numerical calculations are performed using $2 + 1$ flavor QCD gauge configurations generated by the PACS-CS Collaboration on a $L^{3} \times T = 3 2^{3} \times 64$ lattice with $a^{- 1} \approx 2.176$ GeV and the pion mass, $m_{π} \approx 702$ MeV. From the analysis, we obtain a scalar diquark mass which is close to the na\"ıve constituent quark estimate $(2/3) m_{N}$ , together with a quark--diquark potential of the Cornell type (Coulomb + linear). The string tension extracted from the quark--diquark potential agrees within approximately 5% with that obtained from the static quark--antiquark potential (Wilson Loop).
hep-lathep-phnucl-th1 citation
04
A Finite-Volume Scheme for the Continuum Extrapolation of Lattice Step-Scaling in (2+1)D Hamiltonian U(1) Gauge Theory
Alessio Negro🇩🇪 · Emil Otis Rosanowski🇩🇪 · Lena Funcke🇩🇪 · Timo Jakobs🇩🇪 · Karl Jansen🇩🇪 · Paul Ludwig🇩🇪 · Carsten Urbach🇩🇪
We propose a finite-volume scheme to perform controlled continuum extrapolations of the lattice step-scaling function, a key ingredient for determining the running coupling in a Hamiltonian lattice gauge theory in small volumes. As a testbed, we employ a dual Hamiltonian formulation of pure U(1) gauge theory in (2+1) dimensions and an operator basis that remains efficient toward weak coupling. We describe the implementation of static external charges on the spatial lattice and study, using matrix product states, the resulting confining string, from which we extract the static potential and a force-based renormalized coupling. Using the proposed finite-volume scheme, we demonstrate a stable continuum limit of the step-scaling function on the lattice sizes accessible to present Hamiltonian simulations. The method is readily extendable to other gauge groups and dimensions, providing a pathway toward Hamiltonian step-scaling studies in other theories.
hep-latquant-ph1 citation
05
Hamiltonian-based dimensional reduction and spectral reconstruction with Wilson-Dirac fermions
P. V. Buividovich🇬🇧 · B. Hind🇬🇧
Motivated by the process of reconstructing real-time spectral functions from Euclidean correlators in lattice QCD, we derive explicit expressions for the fermionic determinant and the propagator of the four-dimensional clover-improved Wilson-Dirac fermions on anisotropic lattices in terms of the three-dimensional Wilson-Dirac Hamiltonian operator. We derive an effective Hamiltonian that governs Euclidean time evolution at finite temporal lattice spacing, and demonstrate its hermiticity and particle-anti-particle symmetry. Our results allow to quantify lattice artifacts of the numerical spectral reconstruction based on Euclidean fermionic correlators at finite temporal lattice spacing.
hep-latPoS(2025)·0 citations
06
Confining Flux Tube in the Trace Deformed (2+1) Dimensional SU(2) Gauge Theory
Claudio Bonati🇮🇹 · Michele Caselle🇮🇹 · Alessio Negro🇩🇪 · Dario Panfalone🇮🇹 · Lorenzo Verzichelli🇮🇹
We study the confining flux tube in the reconfined phase of trace deformed SU(2) Yang-Mills theory in (2+1) dimensions. Using lattice simulations above the standard deconfinement temperature, we analyze Polyakov-loop correlators and extract the ground state energy of the effective string. We show that the usual Nambu-Goto effective string description, including its standard higher-order corrections, fails to reproduce the data as the trace deformation is increased. Remarkably, deep in the reconfined regime the results are instead accurately described by the Polchinski-Yang rigid-string solution, corresponding to an effective string dominated by an extrinsic-curvature term. We further investigate the transverse profile of the chromo-electric flux tube and find significant deviations from the standard Yang-Mills behavior, including a substantial modification of the intrinsic width. Finally, we present an exploratory study of the phase diagram, finding evidence for a transition from a continuous to a first order reconfinement line as the deformation parameter increases. These results suggest that the reconfined phase realizes a qualitatively different effective-string regime from ordinary confinement.
hep-lathep-th1 citation
07
Bootstrapping Pion Form Factors at Large $N$
Jan Albert🇺🇸 · Dilara Kosva · Leonardo Rastelli🇺🇸
We initiate a bootstrap study of pion form factors in large $N$ QCD. We consider the mixed system of the vector-current two-point function, the pion vector form factor, and the pion scattering amplitude in the chiral limit. At large $N$ these observables are meromorphic, with spectral data constrained by unitarity, crossing symmetry, and Regge boundedness. We obtain bounds of two kinds. The first are rigorous and universal: from analyticity, unitarity and the asymptotic Brodsky-Farrar scaling, we constrain low-energy form-factor coefficients. The second are more phenomenological, of the Shifman-Vainshtein-Zakharov type: feeding in the perturbative ultraviolet behavior at a finite scale lets us bound the pion decay constant, convert a large $N$ lattice measurement into a lower bound on the scale at which asymptotic freedom sets in, and constrain the pion charge radius. Combining these inputs, the space of allowed chiral Lagrangians shrinks toward the region where large $N$ QCD is expected to sit. Our results illustrate how local gauge-invariant probes provide a canonical bridge between the hadronic bootstrap and the microscopic QCD Lagrangian.
↳ hep-thhep-lathep-ph2 citations
08
String dynamics of a (2+1)D U(1) quantum link model on a digital quantum computer
Anthony Gandon🇨🇭 · Alessandro Mariani🇮🇹 · Debasish Banerjee🇬🇧 · Emilie Huffman🇺🇸 · Gurtej Kanwar🇬🇧 · Francesco Tacchino🇨🇭 · Uwe-Jens Wiese🇨🇭 · Ivano Tavernelli🇨🇭
The (2+1)D U(1) pure gauge theory always exists in the confining phase, with strings of non-zero string tension giving a characteristic linear potential between static charges. This makes it a useful testing ground for quantum computing methods designed to study string dynamics of confining gauge theories. Here we implement a minimal U(1) quantum link model on a quantum computer with qubit degrees of freedom representing the dual height variables of the model. This facilitates an efficient realization of plaquette interactions and enables effective calculations of real-time dynamics that are inaccessible to traditional quantum Monte Carlo. A specifically tailored lattice geometry is chosen to match the heavy-hexagonal geometry of the IBM quantum hardware used here, minimizing non-adjacent qubit interactions. By performing quantum quenches from a simple initial string state, we probe the transverse quantum fluctuations of the string before it thermalizes. Our experimental results from digital quantum simulations, with up to 112 qubits, show good agreement with reference tensor-network calculations at short times and with thermal averages at long times. Near the phase transition, the quench dynamics exhibit large fluctuations of the initial string that extend across both spatial dimensions of the lattice. Nonetheless, our error-mitigated estimators from the quantum hardware also give accurate predictions in that regime, with noise-induced violations of local gauge symmetries comparable to finite-bond-dimension tensor-network results.
↳ quant-phcond-mat.str-elhep-lathep-th2 citations
09
Extraction of charmonium branching fractions from $J / ψ \to γ η_{c}$ radiative decays
Magnus C. Schaaf🇩🇪 · Antonio Vairo🇩🇪
We assess the tension between theoretical predictions and the values quoted by the Particle Data Group (PDG) for the partial decay width and branching fraction associated with the radiative charmonium decay $J / ψ \to γ η_{c}$ . A profile scan over the most recent PDG data depending on the branching fraction $B (J / ψ \to γ η_{c})$ suggests that the correlation between measured branching fractions is compatible with lattice QCD determinations of the partial decay widths $Γ (J / ψ \to γ η_{c})$ and $Γ (η_{c} \to γ γ)$ . We propose a theoretically grounded photon line shape for the radiative decay spectrum and a prescription for the extraction of (product) branching fractions involving the magnetic dipole (M1) transition $J / ψ \to γ η_{c}$ . This approach obviates the need to modify the photon energy spectrum line shape using empirical damping functions, as done in the most recent experimental extractions of $B (J / ψ \to γ η_{c})$ from the photon line shape, thereby eliminating an inherent ambiguity in the determination of the derived observables.
↳ hep-phhep-exhep-lat0 citations

Affiliations

first authorsco-authorsvia INSPIRE