Lattice dataset for the paper "Physical-mass calculation of $\rho(770)$ and $K^*(892)$ resonance parameters via $\pi \pi$ and $K \pi$ scattering amplitudes from lattice QCD"

Release for publications, currently available as arxiv preprints:

arXiv:2406.19193: Physical-mass calculation of $\rho(770)$ and $K^*(892)$ resonance parameters via $\pi \pi$ and $K \pi$ scattering amplitudes from lattice QCD

This dataset contains the Wick contraction diagrams for the correlators used in the articles mentioned above. They were computed via multiplication of the distillation meson fields with the appropriate momentum, quark content and time source, followed by a trace over dilution indices (see Appendix B of arxiv:2406.19193).

Data is provided as gzip tarballs which extract into a directory tree. The name of the tarballs is hinting at the directory structure. E.g. the file K-Pi.Kpi_Kpi.P0.tar.gz will extract into K-Pi/Kpi_Kpi/P0 and all containing subdirectories. The final extracted structure is designed as follows:

The data used in the GEVP (before any lattice-irrep projection) is organized in the folder tree

    <channel>/<corrtype>/P<mom^2>/data.<traj>/<prefix>.<traj>.h5

where

    <channel> : K-Pi, Pi-Pi

    <corrtype> : V_V, <MM'>_V, <MM'>_<MM'> (in correspondence to eqs. 4,5,6 of arxiv:2406.19193, where <MM'>=Kpi,Pipi, and V generically denotes the vector gamma matrices contained in the files within)

    <mom^2> : 0,1,2,3,4

    <traj> : trajectory number in MD units (for a total of 90 trajectories, ranging from 420 to 2200 in steps of 20 MD units)

    <prefix> : filename prefix indicating the input meson fields, with their respective gamma matrices and momentum projections, as follows:
        V_V (as a Kpi subfolder)  : rpl_<gammaI>_p<P>__rps_<gammaI>_p<-P>.<traj>.h5, with <gammaI>=GammaX,GammaY,GammaZ
        V_V (as a Pipi subfolder) : rpl_<gammaI>_p<P>__rpl_<gammaI>_p<-P>.<traj>.h5, with <gammaI>=GammaX,GammaY,GammaZ
        
        Kpi_V  : rpl_Gamma5_p<p1>__rpl_Gamma5_p<p2>__rps_<gammaI>_p<-P>.<traj>.h5
        Pipi_V : rpl_Gamma5_p<p1>__rpl_Gamma5_p<p2>__rpl_<gammaI>_p<-P>.<traj>.h5

        Kpi_Kpi   : rpl_Gamma5_p<p1>__rpl_Gamma5_p<p2>__rps_Gamma5_p<p1'>__rpl_Gamma5_p<p2'>.<traj>.h5
        Pipi_Pipi : rpl_Gamma5_p<p1>__rpl_Gamma5_p<p2>__rpl_Gamma5_p<p1'>__rpl_Gamma5_p<p2'>.<traj>.h5

The rpl and rps stand for the 'rhophi'-like meson fields with 'light' and 'strange' content, used in arxiv:2406.19193. The <p1>,<p2>,<p1'>,<p2'>,<P>,<-P> are in the format 'px_py_pz', and denote the 3-vectors used in the momentum-projection of the accompanying meson field, exactly matching the LHS of the equations (in the order they appear) in Appendix B of arxiv:2406.19193. The momentum conservation implies that these vectors sum to zero in any given diagram. We only compute the upper triangular part of the GEVP matrix, and enforce it to be symmetric.

Each hdf5 file has the structure

    /DistillationContraction/Correlators/<diagram>/<tsource>/double_array(96,2)

where <diagram> identifies the possible diagram topologies:

    'connected' for V_V correlators (eqs. A1, A4)
    'triangle' for <MM'>_V correlators (eqs. A2, A5)
    'direct' for <MM'>_<MM'> correlators (1st diagram of Eq. A3, 1st and 2nd diagrams of A6)
    'rectangle' for <MM'>_<MM'> correlators (2nd diagram of Eq. A3, 3rd, 4th, 5th and 6th diagrams of A6)
    'cross' for <MM'>_<MM'> correlators (3rd diagram of Eq. A3)

To recover the diagrams where the arrows are swapped or reversed, the appropriate momentum combinations need to be chosen, as indicated in the manuscript. In this way, for Kpi each file corresponds to exactly one correlator, but for Pipi the 2nd diagram of a given correlator will come from a file whose momenta are swapped in relation to the 1st diagram. The <tsource>=0,1,...,95 denotes the time source (corresponding to 't=0' in Appendix B of arxiv:2406.19193), but where no time translation was done at this stage. The h5 dataset has shape (96,2) corresponding to 96 time slices, and their real("re") and imaginary("im") parts, respectively, in double precision. To obtain a full correlator, one sums the datasets coming from the diagrams in Appendix B, including the prefactors indicated there.

The pion- and kaon-like correlators (using the pi+ and K+ interpolators from eq. arxiv:2406.19193) are under

    <hadron>/P<mom^2>/data.<traj>/<prefix>.<traj>.h5

where <hadron>=Pion,Kaon, with h5 structure 

    /DistillationContraction/Correlators/connected/<tsource>/double_array(96,2)

where all naming convention is the same as for the files described above.