DOI: 10.5281/zenodo.11048484
title: A novel view of the flavor-singlet spectrum from multi-flavor QCD on the lattice—Data release

description: This release contains the raw data used to prepare the plots and tables included in A novel view of the flavor-singlet spectrum from multi-flavor QCD on the lattice, and all analysed data presented in that paper.

Included are:



Data that are the output of HPC workloads enabling this work:



Correlation functions and vacuum expectation values of the energy density and topological charge operators for the ensembles analysed for the paper, in HDF5 format, in the file etaprime_correlators.h5, described in more detail below.

Mesonic correlation functions for new ensembles generated for this work (namely $N_f=8$, $am_f=0.009$,    and $N_f=4$, $\beta=3.8$, $am_f=0.01,0.02,0.03$), in the file correlators.zip. The README_correlators.md file in that archive documents the format of these data.

Histories of the topological charge and energy density over the course of applying the gradient flow of the Symanzik gauge action, in the file symanzik_flows.zip. The README_flows.md file in that archive documents the format of these data.



All metadata used for the fitting and subsequent analyis of these data:



Metadata describing the ensembles to be analysed and the parameters with which to do so, in the file ensembles.yaml

Metadata describing the fits performed for the eta-prime mass, in the file etaprime_ensembles.csv

Metadata describing the new Monte Carlo streams for the new point at , , , in the file mc_streams_nf8_m0.009.csv

Metadata describing the subset of configurations used in observable computations for the new point at , , , in the file measurement_trajectories_nf8_m0.009.csv



The software workflow used to analyse the above data and metadata, and produce the plots and tables shown in the paper, in the file latkmi_etaprime_2025.zip. The file README.md in that archive details how to reproduce our analysis.

All data generated by this workflow, and that are presented in plots and tables in the paper, in CSV format, in files described in more detail below.



Results for the mass of the state as a function of smearing parameters, in the file etaprime_masses_by_smearing.csv

Results of fits of the mass spectrum, presented in Tables II, III, IV, and V of the paper, in the file fit_results.csv

Results for observables in the mass spectrum for each ensemble considered, in the file spectrum.csv

Results for the continuum extrapolation of the anomalous dimension from the gradient flow scale, in the file t0_gamma.csv.




For further detail on the contents of each file, please see the file README.md.

 
description: We thank the Lattice Strong Dynamics (LSD) collaboration for sharing their plots and their preliminary unpublished results for the flavor-singlet scalar mass on their ensembles. We gratefully acknowledge Dr. Masafumi Kurachi and Dr. Kei-ichi Nagai for their collabo ration during the early stages of this work. Numerical calculations have been carried out on the high-performance computing systems at KMI (φ), at the Information Technology Center in Nagoya University (CX400), and at the Research Institute for Information Technology in Kyushu University (CX400 and HA8000) both through the HPCI System Research Projects (Project ID: hp140152, hp150157, hp160153) and through general use.

This work is supported by the JSPS Grants-in-Aid for Scientific Research (S) No. 22224003, (C) No. 16K05320 (Y.A.) for Young Scientists (A) No.16H06002 (T.Y.), (B) No.25800138 (T.Y.), (B) No.25800139 (H.O.), and (B) No.15K17644 (K.M.). E.B. acknowledges the support of the UKRI Science and Technology Facilities Council (STFC) Research Software Engineering Fellowship EP/V052489/1, the EPSRC ExCALIBUR programme ExaTEPP (project EP/X017168/1), the STFC Consolidated Grant No. ST/T000813/1, and the Supercomputing Wales programme, which is part-funded by the European Regional Development Fund (ERDF) via Welsh Government. K.M. is supported by the OCEVU Labex (ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Avenir” French government program and managed by the ANR. H.O. is supported in part by the JSPS KAKENHI (Nos. 21K03554, 22H00138). T.Y. is supported in part by Grants-in-Aid for Scientific Research (Nos. 19H01892, 23H01195, 23K25891) and MEXT as “Program for Promoting Researches on the Supercomputer Fugaku” Grant Number JPMXP1020230409. This work is supported by the JLDG constructed over the SINET6 of NII.

This work was in part based on the MILC collaboration’s public lattice gauge theory code. See http://physics.utah.edu/~detar/milc.html.