HEP Lattice·hep-lat

Wed·Jul 1, 2026Wednesday·July 1, 2026

5 papers—1 primary·4 cross-listed

01
Higher-order hopping-parameter expansion by human-AI collaboration
Masakiyo Kitazawa🇯🇵 · Tatsuya Wada🇯🇵
We develop efficient algorithms for evaluating higher-order terms in the hopping-parameter expansion of $Tr ln M$ on $S U (N_{c})$ gauge configurations. The resulting algorithms, which exploit a trie data structure for the computation of high-order terms, evaluate the $κ^{8}$ , $κ^{10}$ , and $κ^{12}$ terms at computational costs of approximately $20$ , $460$ , and $8900$ times that of a single staple evaluation, respectively. The correctness of the algorithms is verified by comparison with a computationally expensive but reliable reference calculation. We emphasize that collaboration between human researchers and AI coding agents was essential to the development of these algorithms.
hep-lathep-ph0 citations
02
Extraction of the nucleon axial form factor from Lattice QCD using NNLO chiral perturbation theory
Fernando Alvarado🇩🇪 · Luis Alvarez-Ruso🇪🇸
We calculate the nucleon axial form factor in relativistic chiral perturbation theory with $Δ (1232)$ up to next-to-next-to-leading order (NNLO). Relevant low-energy constants are determined by fitting to recent lattice-QCD results at several pion masses, while accounting for the uncertainty associated with the truncation of the chiral expansion. We obtain a good description of the lattice data for momentum transfers up to $Q^{2} ≃ 0.6$ GeV and pion masses up to $M_{π} ≃ 400$ MeV. We find that the explicit inclusion of the $Δ$ resonance is required to reproduce the lattice-QCD pion-mass dependence of the axial charge and axial radius, as well as the momentum dependence of the form factor. At the physical point we obtain $g_{A} = 1.257 \pm 0.011$ and $⟨ r_{A}^{2} ⟩ = 0.312 \pm 0.037 fm^{2}$ . Our analysis provides a model-independent and systematically improvable parametrization of the pion-mass and momentum dependence of the axial form factor, offering a framework for extrapolating lattice-QCD results to the physical point and for improving predictions of low-energy weak interactions involving nucleons.
↳ hep-phhep-exhep-latnucl-th2 citations
03
Vector alignment in matrix Lie groups
Congzhou M Sha🇺🇸
Two observers of the same physical system may differ in gauge by a group element acting on their common vector representations, and recovering that element from finite, noisy paired observations is useful in both theory and experiment. The Kabsch and Horn algorithms solve this problem for rotated frames in $R^{3}$ (i.e. $S O (3)$ ); our earlier Lie algebra method extends it to the Lorentz group $S O (3, 1)_{+}$ . Here we report explicit formulae for the Lie algebra method on the classical matrix Lie groups ( $G L (n)$ , $S L (n)$ , $S O (n)$ , $U (n)$ , $S O (p, q)$ , $S p (n)$ , $S p in (n)$ , and $S E (n)$ ) over the real and complex fields. The four steps (pseudoinverse, matrix logarithm, projection onto the Lie algebra, matrix exponential) are exact for noiseless data. Only the projection is group-dependent, and we show it yields the unique least squares-optimal element of the Lie algebra whenever its image lies in $g$ and its residual is orthogonal to $g$ . For noisy data the method is optimal only to leading order, so we add a quasi-Newton correction whose accuracy interpolates between the uncorrected method and direct least squares optimization. The projections, their optimality, and the identity underlying the correction are formally proven in Lean 4.31.0 with Mathlib, and numerical experiments are benchmarked in Julia.
↳ math.NAcs.NAhep-latmath-ph+10 citations
04
FRG analysis of dense two-color QCD within the linear sigma model
Gergely Fejős🇭🇺 · Daiki Suenaga🇯🇵
We investigate the phase structure, hadron masses, and topological susceptibility in the two-flavor and two-color QCD (QC $_{2}$ D) medium, particularly focusing on the $U (1)_{A}$ axial anomaly effects. To this end, we employ the linear sigma model, and hadron fluctuations are incorporated through the functional renormalization group method. We establish in detail an effective potential that respects symmetries of QC $_{2}$ D at finite quark chemical potential, $μ_{q}$ : $S U (2)_{L} \times S U (2)_{R}$ chiral, $U (1)$ baryon-number, parity and time-reversal symmetries. We find that the $U (1)_{A}$ anomaly couplings for mesons at finite temperature are enhanced with increasing $μ_{q}$ , while that of the baryons are not too sensitive to $μ_{q}$ . Despite the anomaly enhancement, we find that the topological susceptibility at larger $μ_{q}$ is always suppressed regardless of the temperature, following chiral restoration. We also find that mass degeneracies of the chiral partners are well realized at higher temperatures and densities by the chiral restoration. Our findings are expected to provide useful information on properties of the $U (1)_{A}$ anomaly in medium for sign-problem-free lattice simulations of QC $_{2}$ D.
↳ hep-phhep-latnucl-th2 citations
05
Hadronic exceptional points
Ahmad Jafar Arifi🇯🇵 · Kei Suzuki🇯🇵
Exceptional points, where eigenvalues and eigenvectors coalesce, are a defining feature of non-Hermitian systems and have been extensively observed in photonic, atomic, and condensed matter systems. However, they have received little attention in quantum chromodynamics (QCD), which is the fundamental theory of quarks, gluons, and hadrons. We propose that imaginary magnetic fields provide a simple realization of non-Hermitian dynamics in hadronic systems. Based on two theoretical approaches, a hadronic effective Lagrangian and a constituent quark model, we compute mass spectra of neutral mesons and find exceptional points separating the real-spectrum and complex-eigenvalue regimes. In small fields, the real spectrum exhibits level attraction between hadronic states, whereas in larger fields, hadrons are deconfined, which is a signature of a field-induced inverted potential. Our findings open a new avenue for studying QCD dynamics in non-Hermitian environments.
↳ hep-phhep-lathep-thnucl-th+10 citations

Affiliations

first authorsco-authorsvia INSPIRE

Higher-order hopping-parameter expansion by human-AI collaboration

Extraction of the nucleon axial form factor from Lattice QCD using NNLO chiral perturbation theory

Vector alignment in matrix Lie groups

FRG analysis of dense two-color QCD within the linear sigma model

Hadronic exceptional points

Affiliations