Data publication for "The diffusion of heavy quarks in a quark-gluon plasma from lattice QCD"

This publication contains the raw measurement data and a set of python and bash scripts to reproduce all results and figures presented in "The diffusion of heavy quarks from lattice QCD" (PhD thesis by Luis Altenkort, 2025, Bielefeld University).

Installation

Install system dependencies (Ubuntu)

Bash shell >=5
uv (Python package and project manager)
LaTeX with packages amsmath, mathtools, type1cm and apt packages cm-super, dvipng for matplotlib tex rendering
gnuplot >=5

# Install uv
curl -LsSf https://astral.sh/uv/install.sh | sh

# Install additional LaTeX packages (skip if already installed via texlive-full etc. or manually install the packages listed above)
sudo apt install texlive-latex-extra texlive-xetex cm-super dvipng

# Install gnuplot
sudo apt install gnuplot

Extract data and code archives

Download the files contained in the data publication and extract them:

mkdir 2025_altenkort
cd 2025_altenkort  # Download the corresponding files into this folder
tar -xzf correlators_flow.tar.gz
tar -xzf AnalysisToolbox.tar.gz
tar -xzf input_data.tar.gz

For convenience, the final results and figures can also be extracted from output_data.tar.gz and figures.tar.gz, respectively.

Note that the bundled AnalysisToolbox is based on commit f9eee73d, with the only change being the addition of latqcdtools/pyproject.toml.

[Optional] A set of scripts for the convenient submission of multi-GPU multi-node gauge configuration generation jobs on large slurm clusters can be extracted from conf-production-scripts.tar.gz.

Make scripts executable

chmod -R +x ./correlators_flow

Setup environment

Define certain subdirectories as environment variables:

export BASEPATH_RAW_DATA=$(pwd)/input
export BASEPATH_WORK_DATA=$(pwd)/output_data
export BASEPATH_PLOT=$(pwd)/figures
export G_PERT_LO_DIR=${BASEPATH_RAW_DATA}/quenched_1.50Tc_zeuthenFlow/pert_LO

Set the number of available CPU processors for parallelization (adjust accordingly):

export NPROC=20

Note on output file formats

Files are either saved in plain text (.txt, .dat) or in numpy binary format (.npy). In many cases, the mean/median/std_deviation/etc. over all bootstrap samples is exported to plain text files, while the results for the underlying bootstrap samples are stored in numpy format.

The output file names often contain these identifiers:

<qcdtype> is either quenched_1.50Tc_zeuthenFlow or hisq_ms5_zeuthenFlow
<conftype> may be, for example: s144t36_b0754400 (meaning $N_s=144$, $N_\tau=36$, $\beta=7.544$), or s096t28_b0824900_m002022_m01011 (meaning $N_s=96$, $N_\tau=28$, $\beta=8.249$, $m_s/a=0.002022$, $m_l/a=0.01011$), ...
<corr> is either EE or BB
<T-in-MeV> is either 195, 220, 251, or 293

Correlator analysis

Switch to the top-level folder of the code repository:

cd correlators_flow

Resampling, interpolation, continuum extrapolation

Create figures of perturbative correlators

Create Figure 4.1 at ${BASEPATH_PLOT}/EE_QED_LPT.pdf:

uv run ./perturbative_corr/plot_QED_LPT.py --inputfolder ${BASEPATH_RAW_DATA} --outputfolder ${BASEPATH_PLOT}

Create Figure 4.3 at ${BASEPATH_PLOT}/pertLO/EE_pert_contvslatt_flow.pdf:

uv run ./perturbative_corr/plot_pert_correlators.py --Ntau 24 --inputfolder ${BASEPATH_RAW_DATA}/quenched_1.50Tc_zeuthenFlow/pert_LO/ --outputfolder ${BASEPATH_PLOT}/pertLO

Create Figure 4.4 at ${BASEPATH_PLOT}/pertLO//pert_latt_comparison_EE_Nt30_<tau>.pdf with tau=5 and tau=10:

uv run ./perturbative_corr/plot_tree_level_imp.py --Nt 30 --corr EE --flowtime_file ${BASEPATH_RAW_DATA}/quenched_1.50Tc_zeuthenFlow/pert_LO/flowtimes.dat --outputpath ${BASEPATH_PLOT}/pertLO/ --inputpath ${BASEPATH_RAW_DATA}/quenched_1.50Tc_zeuthenFlow/pert_LO/ --tau 5
uv run ./perturbative_corr/plot_tree_level_imp.py --Nt 30 --corr EE --flowtime_file ${BASEPATH_RAW_DATA}/quenched_1.50Tc_zeuthenFlow/pert_LO/flowtimes.dat --outputpath ${BASEPATH_PLOT}/pertLO/ --inputpath ${BASEPATH_RAW_DATA}/quenched_1.50Tc_zeuthenFlow/pert_LO/ --tau 10

Merge correlator measurement files

Merge individual correlator measurement text files (output from SIMULATeQCD) into a small number of larger numpy files (binary format). Metadata is saved to text files. This may take some time (up to multiple hours), mostly depending on file system speed (with slow HDDs it may take hours).

./correlator_analysis/double_extrapolation/example_usage/1_merge_data.sh quenched_1.50Tc_zeuthenFlow EE ${BASEPATH_RAW_DATA} ${BASEPATH_WORK_DATA}
./correlator_analysis/double_extrapolation/example_usage/1_merge_data.sh quenched_1.50Tc_zeuthenFlow BB ${BASEPATH_RAW_DATA} ${BASEPATH_WORK_DATA}
./correlator_analysis/double_extrapolation/example_usage/1_merge_data.sh hisq_ms5_zeuthenFlow EE ${BASEPATH_RAW_DATA} ${BASEPATH_WORK_DATA} ${BASEPATH_RAW_DATA}/hisq_ms5_zeuthenFlow/reference_flowtimes

This creates the following files in $BASEPATH_WORK_DATA/<qcdtype>/<corr>/<conftype>/:

File	Comment
`flowtimes_<conftype>.dat`	flowtimes that were measured, corresponding to the data in the .files
`n_datafiles_<conftype>.dat`	metadata (number of files per stream, MCMC trajectory number, etc.)
`<corr>_imag_<conftype>_merged.npy`	merged raw data, imaginary part of correlator
`<corr>_real_<conftype>_merged.npy`	merged raw data, real part of correlator
`polyakov_imag_<conftype>_merged.npy`	merged raw data, imaginary part of polyakovloop
`polyakov_real_<conftype>_merged.npy`	merged raw data, real part of polyakovloop

Bootstrap resampling of uncorrelated blocks

Reminder: The double-extrapolation of the correlator data as well as the spectral reconstruction fits are later performed on each individual bootstrap sample.

Load the merged data files, extract an equally spaced MCMC time series, then plot the time history of the Polyakov loop at a large flow time. Then bin configurations according to the integrated autocorrelation time, then perform bootstrap resampling of the uncorrelated blocks and save the samples to numpy files (binary format).

Note: this may take multiple hours.

./correlator_analysis/double_extrapolation/example_usage/2_reduce_data.sh quenched_1.50Tc_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}
./correlator_analysis/double_extrapolation/example_usage/2_reduce_data.sh quenched_1.50Tc_zeuthenFlow BB ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}
./correlator_analysis/double_extrapolation/example_usage/2_reduce_data.sh hisq_ms5_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}

This creates the following files in $BASEPATH_WORK_DATA/<qcdtype>/<corr>/<conftype>/

File	Comment
`<corr>_<conftype>_samples.npy`	Bootstrap samples of correlator
`<corr>_flow_cov_<conftype>.npy`	Flow time correlation matrix (based on bootstrap samples)
`<corr>_<conftype>.dat`	Median correlator (useful for checking the data / plotting)
`<corr>_err_<conftype>.dat`	Std dev of correlator (useful for checking the data / plotting)

and, in $BASEPATH_PLOT/<qcdtype>/<corr>/<conftype>/

File	Comment
`polyakovloop_MCtime.pdf`	Figure 5.1 and 6.1. Shows the MCMC time series of the polyakovloop at a large flow time.

Plot flow time dependency

Create Figure 5.3, Figure 5.13, and Figure 6.3:

./correlator_analysis/plotting/example_usage/plot_flow_dep.sh quenched_1.50Tc_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT}
./correlator_analysis/plotting/example_usage/plot_flow_dep.sh quenched_1.50Tc_zeuthenFlow BB ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT}
./correlator_analysis/plotting/example_usage/plot_flow_dep.sh hisq_ms5_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT}

The figures can be found at:

${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/EE/s080t20_b0703500/EE_s080t20_b0703500_flow_dep.pdf
${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/EE/s080t20_b0703500/EE_s080t20_b0703500_flow_depzoom.pdf
${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/BB/s080t20_b0703500/BB_s080t20_b0703500_flow_dep.pdf
${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/BB/s080t20_b0703500/BB_s080t20_b0703500_flow_depzoom.pdf
${BASEPATH_PLOT}/hisq_ms5_zeuthenFlow/EE/s096t24_b0824900_m002022_m01011/EE_s096t24_b0824900_m002022_m01011_flow_dep.pdf
${BASEPATH_PLOT}/hisq_ms5_zeuthenFlow/EE/s096t24_b0824900_m002022_m01011/EE_s096t24_b0824900_m002022_m01011_flow_depzoom.pdf

Interpolation

Interpolate the correlator in Euclidean time and in flow time, such that a common set of normalized flow times is available across all lattices and temperatures.

./correlator_analysis/double_extrapolation/example_usage/3_spline_interpolate.sh quenched_1.50Tc_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}
./correlator_analysis/double_extrapolation/example_usage/3_spline_interpolate.sh quenched_1.50Tc_zeuthenFlow BB ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}
./correlator_analysis/double_extrapolation/example_usage/3_spline_interpolate.sh hisq_ms5_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}

This creates the following files in $BASEPATH_WORK_DATA/<qcdtype>/<corr>/<conftype>/:

File	Comment
`<corr>_<conftype>_relflows.txt`	Normalized flow times $\sqrt{8_{\tau_F}}/\tau$
`<corr>_<conftype>_interpolation_relflow_mean.npy`	Median of the interpolated correlator for the corresponding normalized flow times (binary format, npy)
`<corr>_<conftype>_interpolation_relflow_samples.npy`	Interpolations of each individual bootstrap sample of the correlator for the corresponding normalized flow times (binary format, npy)

and, in $BASEPATH_PLOT/<qcdtype>/<corr>/<conftype>/:

File	Comment
`<corr>_interpolation_relflow.pdf`	Multi-page PDF containing plots of interpolation in Eucl. time at different normalized flow times.
`<corr>_interpolation_relflow_combined.pdf`	Figure 5.5. Plot of interpolation in Eucl. time for two normalized flow times.

Continuum extrapolation

Take the continuum limit of the correlators using a fit on each sample

./correlator_analysis/double_extrapolation/example_usage/4_continuum_extr.sh quenched_1.50Tc_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}
./correlator_analysis/double_extrapolation/example_usage/4_continuum_extr.sh quenched_1.50Tc_zeuthenFlow BB ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}
./correlator_analysis/double_extrapolation/example_usage/4_continuum_extr.sh hisq_ms5_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}

This creates the following files in $BASEPATH_WORK_DATA/quenched_1.50Tc_zeuthenFlow/<corr>/cont_extr/ and $BASEPATH_WORK_DATA/hisq_ms5_zeuthenFlow/<corr>/<T-in-MeV>/cont_extr/:

File	Comment
`<corr>_cont_relflows.dat`	Normalized flow times at which the continuum extrapolation was done
`<corr>_cont_relflow.dat`	Median of continuum-extrapolated correlator at corresponding normalized flow times
`<corr>_cont_relflow_err.dat`	Std dev of continuum-extrapolated correlator at corresponding normalized flow times
`<corr>_cont_relflow_samples.npy`	Continuum extrapolations of the correlator on each individual bootstrap sample

This also creates the following files in ${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/<corr>/ and ${BASEPATH_PLOT}/hisq_ms5_zeuthenFlow/<corr>/<T-in-MeV>:

File	Comment
`<corr>_cont_quality_relflow.pdf`	Figure 5.6, Figure 6.4, Figure A.1. This is a multipage PDF containing plots of continuum extrapolation of correlator for the corresponding normalized flow times.

Plot flow time correlations

Create Figure 5.7 at ${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/EE/s144t36_b0754400/EE_s144t36_b0754400_correlation.pdf:

uv run ./correlator_analysis/plotting/plot_flow_correlations.py --qcdtype quenched_1.50Tc_zeuthenFlow --corr EE --conftype s144t36_b0754400 --basepath ${BASEPATH_WORK_DATA} --outputfolder ${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/EE/ --nproc ${NPROC}

Plot lattice spacing effects

Create Figure 5.2 at ${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/EE/EE_latt_effects.pdf:

./correlator_analysis/plotting/example_usage/2_plot_lateffects.sh quenched_1.50Tc_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}

Optional: create the same figures for the 2+1-flavor cases at ${BASEPATH_PLOT}/hisq_ms5_zeuthenFlow/EE/T<T-in-MeV>/EE_latt_effects.pdf:

./correlator_analysis/plotting/example_usage/2_plot_lateffects.sh hisq_ms5_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}

Flow-time-to-zero extrapolation of $G_E$

./correlator_analysis/double_extrapolation/example_usage/5_flowtime_extr.sh quenched_1.50Tc_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}
./correlator_analysis/double_extrapolation/example_usage/5_flowtime_extr.sh hisq_ms5_zeuthenFlow EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}

This creates the following files in $BASEPATH_WORK_DATA/quenched_1.50Tc_zeuthenFlow/EE/ and $BASEPATH_WORK_DATA/hisq_ms5_zeuthenFlow/EE/T<Temp-in-MeV>/:

File	Comment
`EE_flow_extr_relflow.npy`	Flow-time-to-zero extrapolated continuum EE correlator for each bootstrap sample
`EE_flow_extr_relflow.txt`	Median and std dev of flow-time-to-zero extrapolated continuum EE correlator

and in $BASEPATH_PLOT/quenched_1.50Tc_zeuthenFlow/EE/ and $BASEPATH_PLOT/hisq_ms5_zeuthenFlow/EE/T<Temp-in-MeV>/

File	Comment
`EE_flow_extr_quality_relflow.pdf`	Figure 5.9a, Figure 6.5

Compare final quenched $G_E$ with multi-level results

This will create Figure 5.9b.

uv run ./multi-level/cont_extr_new.py --basepath ${BASEPATH_RAW_DATA}
uv run ./correlator_analysis/plotting/6_plot_finalcorr.py --outputfolder ${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/EE/ --input_flow ${BASEPATH_WORK_DATA}/quenched_1.50Tc_zeuthenFlow/EE/EE_flow_extr_relflow.txt --input_multilvl ${BASEPATH_RAW_DATA}/multi-level_2015/EE_2015_new.txt

This creates the files $BASEPATH_RAW_DATA/multi-level_2015/EE_2015_new_2022.txt and $BASEPATH_PLOT/quenched_1.50Tc_zeuthenFlow/EE/EE_flowVSmultilvl_relflow.pdf (Figure 5.9b).

Renormalization of $G_B$

Coupling calculations

Perform the continuum extrapolation of the flow-scheme coupling measured on zero temperature lattices, and convert it from flow scheme to the MSBAR scheme coupling at one scale, then use perturbative 5-loop running to move to other relevant scales.

./correlator_analysis/double_extrapolation/BB_renormalization/example_usage/extrapolate_coupling.sh ${BASEPATH_RAW_DATA} ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} 6.40

This creates the following files in $BASEPATH_WORK_DATA/quenched_1.50Tc_zeuthenFlow/coupling/:

File	Comment
`g2_muF_cont_extr.txt`	Continuum-extrapolated flow scheme coupling $g^2$ as function of flow scale $\mu_F=1/\sqrt{8 \tau_F}$ in units of temperature T
`g2_MSBAR_runFromMu_6.28.txt`	Continuum MS-BAR coupling $g^2$ as a function of MS-BAR scale $\mu$ in units of temperature T (matched at $\mu_F/T=2\pi$ and then perturbatively run)

and, in $BASEPATH_PLOT/quenched_1.50Tc_zeuthenFlow/coupling/:

File	Comment
`g2.pdf`	Figure 5.14b. Flow- and MSBAR-scheme couplings $g^2$ as a function of scale in temperature units.
`g2_cont_extr.pdf`	Figure 5.14a. Flow-scheme coupling $g^2$ as a function of squared lattice spacing (= inverse $N_\tau^2$ at fixed temperature).

Carry out renormalization of $G_B$ by computing $Z_\text{match}$

./correlator_analysis/double_extrapolation/BB_renormalization/example_usage/compute_Z.sh ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT}

This creates the following files in $BASEPATH_WORK_DATA/quenched_1.50Tc_zeuthenFlow/coupling/

File	Comment
`Z_match_ref6.28_UVLO_IRNLO.dat`	$Z_\text{match}$ as a function of scale, with $\bar{\mu}T/T=19.18, \bar{\mu}{\tau_F}/\mu_F=1$
`Z_match_ref6.28_UVNLO_IRNLO.dat`	$Z_\text{match}$ as a function of scale, with $\bar{\mu}T/T=19.18, \bar{\mu}{\tau_F}/\mu_F=1.50$
`Z_match_ref6.28_UVLO_IRLO.dat`	$Z_\text{match}$ as a function of scale, with $\bar{\mu}T/T=2\pi T, \bar{\mu}{\tau_F}/\mu_F=1$
`Z_match_ref6.28_UVNLO_IRLO.dat`	$Z_\text{match}$ as a function of scale, with $\bar{\mu}T/T=2\pi T, \bar{\mu}{\tau_F}/\mu_F=1.50$

and, in $BASEPATH_PLOT/quenched_1.50Tc_zeuthenFlow/coupling/:

File	Comment
`Z_total.pdf`	Figure 5.15 (right). All considered versions of $Z_\text{match}$ as a function of flow scale.
`Z_total_flowtime.pdf`	Figure 5.15 (left) All considered versions of $Z_\text{match}$ as a function of flow radius $1/(8 \tau_F) T$

Flow-time-to-zero extrapolation of renormalized $G_B$

./correlator_analysis/double_extrapolation/example_usage/5_flowtime_extr.sh quenched_1.50Tc_zeuthenFlow BB ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} ${NPROC}

This creates the following files in $BASEPATH_WORK_DATA/quenched_1.50Tc_zeuthenFlow/BB/:

File	Comment
`BB_flow_extr_relflow_ref6.28_<scale-choices>.npy`	Flow-time-to-zero extrapolated continuum BB correlator for each bootstrap sample
`BB_flow_extr_relflow_ref6.28_<scale-choices>.txt`	Median and std dev of flow-time-to-zero extrapolated continuum BB correlator

using the following scales choices:

File	$\bar{\mu}_T/T$	$\bar{\mu}_{\tau_F}/mu_F$
`BB_flow_extr_relflow_ref6.28_UVLO_IRLO.npy`	$2\pi$	1
`BB_flow_extr_relflow_ref6.28_UVLO_IRLO.txt`	$2\pi$	1

`BB_flow_extr_relflow_ref6.28_UVLO_IRNLO.npy`	19.18	1
`BB_flow_extr_relflow_ref6.28_UVLO_IRNLO.txt`	19.18	1

`BB_flow_extr_relflow_ref6.28_UVNLO_IRLO.npy`	$2\pi$	1.50
`BB_flow_extr_relflow_ref6.28_UVNLO_IRLO.txt`	$2\pi$	1.50

`BB_flow_extr_relflow_ref6.28_UVNLO_IRNLO.npy`	19.18	1.50
`BB_flow_extr_relflow_ref6.28_UVNLO_IRNLO.txt`	19.18	1.50

and, in $BASEPATH_PLOT/quenched_1.50Tc_zeuthenFlow/BB/:

File	Comment
`BB_flow_extr_quality_no_extr.pdf`	Figures 5.16a, A.2. Bare continuum BB correlator as a function of flow time.
`BB_flow_extr_quality_relflow.pdf`	Figure 5.16b. Renormalized continuum BB correlator as a function of flow time with flow time extrapolation.

Compare final $G_E$ and $G_B$

Create Figure 5.17 at $BASEPATH_PLOT/quenched_1.50Tc_zeuthenFlow/EEvsBB.pdf

uv run ./correlator_analysis/plotting/plot_EEvsBB.py --inputfolder ${BASEPATH_WORK_DATA}/quenched_1.50Tc_zeuthenFlow/ --outputfolder ${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/

Compare correlator at fixed normalized flow times

In the 2+1-flavor case, this is done after the spectral reconstruction (see below) since we use some of the results for comparison.

Quenched

 ./correlator_analysis/relative_flow/example_usage/Nf0.sh ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT}

This creates the following files in ${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/<corr>/:

File	Comment
`<corr>_relflow_quenched_0.25.pdf`	Figure 5.4 (left)
`<corr>_relflow_quenched_0.30.pdf`	Figure 5.4 (right)

and, in ${BASEPATH_WORK_DATA}/quenched_1.50Tc_zeuthenFlow/EE/<conftype>/relflow/:

File	Comment
`<corr>_relflow_0.25.dat`	Correlator at normalized flow time 0.25
`<corr>_relflow_0.30.dat`	Correlator at normalized flow time 0.30

Spectral function analysis

Make sure you are still in the top-level folder of the code repository correlators_flow.

Perform spectral function reconstruction

Note: this takes a lot of computing time. The output files can alternatively be obtained from output_data.tar.gz.

./spf_reconstruction/model_fitting/example_usage/spf_reconstruct.sh quenched_1.50Tc_zeuthenFlow EE  ${BASEPATH_WORK_DATA} NO ${NPROC}
./spf_reconstruction/model_fitting/example_usage/spf_reconstruct.sh quenched_1.50Tc_zeuthenFlow BB  ${BASEPATH_WORK_DATA} NO ${NPROC}
./spf_reconstruction/model_fitting/example_usage/spf_reconstruct.sh hisq_ms5_zeuthenFlow EE  ${BASEPATH_WORK_DATA} NO ${NPROC}

This creates the following files in $BASEPATH_WORK_DATA/<qcdtype>/<corr>/spf/<model>_<rho-UV-order>_Nf<nf>_T<T-in-MeV>_<min_scale>_<running-scale-coefficient>_tauTgtr0.24_<suffix>

File	Comment
`corrfit.dat`	Median final correlator and fitted model correlator
`params_samples.npy`	Model spectral function fit parameters for each bootstrap sample, as well as chisq/dof
`params.dat`	Median spectral function fit parameters and 34th percentiles
`phIUV.npy`	UV part of fitted model spectral function as function of $\omega/T$ (numpy format)
`samples.npy`	Copy of the input correlator bootstrap samples but multiplied by $G_\text{norm}$ (= actual fit input)
`spffit.npy`	Median spectral function with left/right 34th percentiles as function of $\omega/T$

Sketch spectral function models and reconstruction process

Create Figure 5.10 at $BASEPATH_PLOT/quenched_1.50Tc_zeuthenFlow/coupling/UV_spf_EE_quenched_1.5Tc.pdf.

./spf_reconstruction/model_fitting/example_usage/EE_UV.sh ${BASEPATH_WORK_DATA}
./spf_reconstruction/plot_fits/example_usage/plot_g2.sh ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT}

Create Figure 5.11a and Figure 5.11b at $BASEPATH_PLOT/model_corrs.pdf and $BASEPATH_PLOT/integrand.pdf, respectively:

uv run ./spf_reconstruction/plotting/plot_integrand.py --outputpath ${BASEPATH_PLOT} --Nf 0 --min_scale eff --T_in_GeV 0.472 --omega_prefactor "1" --order LO --corr EE --mu_IR_by_T 1

Plot spectral reconstruction results

Quenched case

(Note that for the color-magnetic case there are two script calls.)

./spf_reconstruction/plot_fits/example_usage/plot_fits_quenched.sh EE ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} yes
./spf_reconstruction/plot_fits/example_usage/plot_fits_quenched.sh BB ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} yes
./spf_reconstruction/plot_fits/example_usage/plot_fits_quenched.sh BB ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} no

This creates the following files in $BASEPATH_PLOT/quenched_1.50Tc_zeuthenFlow/<corr>/

File	Comment
`<corr>_corrfit_quenched_1.5Tc.pdf`	Figure 5.12a, Figure 5.18b
`<corr>_spf_quenched_1.5Tc.pdf`	Figure 5.12b, Figure 5.18a
`<corr>_kappa_quenched_1.5Tc.pdf`	Figure 5.12c, Figure 5.19a

and, in $BASEPATH_WORK_DATA/quenched_1.50Tc_zeuthenFlow/<corr>:

File	Comment
`<corr>_kappa_quenched_1.5Tc.txt`	Final $\kappa$ result

2+1-flavor case

./spf_reconstruction/plot_fits/example_usage/plot_fits_hisq.sh ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT}

This creates the following files in $BASEPATH_PLOT/hisq_ms5_zeuthenFlow/EE/T<T-in-MeV>/

File	Comment
`EE_corrfit_T<T-in-MeV>.pdf`	Figure 6.7
`EE_spf_T<T-in-MeV>.pdf`	Figure 6.8
`EE_kappa_T<T-in-MeV>.pdf`	Figure 6.9

and, in $BASEPATH_WORK_DATA/hisq_ms5_zeuthenFlow/EE/<T-in-MeV>/:

File	Comment
`EE_kappa_T<T-in-MeV>.txt`	Final $\kappa$ result

Compare correlator at fixed normalized flow times

This is done after the spectral function analysis since we use some of the results for comparison.

2+1-flavor

./correlator_analysis/relative_flow/example_usage/Nf3TemperatureComparison_Paper.sh ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT}

This creates the following files in $BASEPATH_PLOT/hisq_ms5_zeuthenFlow/EE/:

File	Comment
`EE_relflow_hisq_0.25.pdf`	Figure 6.2
`EE_relflow_hisq_0.30.pdf`	Figure 6.2
`EE_relflow_hisq_final.pdf`	Figure 6.6

and, in $BASEPATH_WORK_DATA/hisq_ms5_zeuthenFlow/EE/<conftype>/relflow/:

File	Comment
`EE_relflow_0.25.dat`	EE correlator at normalized flow time 0.25
`EE_relflow_0.30.dat`	EE correlator at normalized flow time 0.30

Comparison to literature

Make sure you are still in the top-level folder of the code repository correlators_flow.

Create plots that compare the results with existing literature. Note: this explicitly depends on the previous call to plot_fits_quenched.sh and plot_fits_hisq.sh since it reads from their output text files.

./spf_reconstruction/plot_fits/example_usage/plot_final_kappas.sh ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} EE
./spf_reconstruction/plot_fits/example_usage/plot_final_kappas.sh ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} BB
./spf_reconstruction/plot_fits/example_usage/plot_final_kappas.sh ${BASEPATH_WORK_DATA} ${BASEPATH_PLOT} hisq_thesis

This creates the following files:

Folder	File	Comment
`${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/<corr>/`	`kappa_<corr>_quenched_literature.pdf`	Figure 5.12d, Figure 5.19b
`${BASEPATH_PLOT}/hisq_ms5_zeuthenFlow/EE/`	`kappa_hisq_thesis.pdf`	Figure 6.10

Plot comparison with literature for $2\pi TD$

Create Figure 7.1 at ${BASEPATH_PLOT}/2piTD.pdf

uv run ./spf_reconstruction/plotting/plot_2piTD.py --outputfolder ${BASEPATH_PLOT}

Plot fit to $g^2$ and $g^4$

Create Figure 7.2 at $BASEPATH_PLOT/quenched_1.50Tc_zeuthenFlow/compare_kappa_g2.pdf

uv run ./spf_reconstruction/plot_fits/publication_specific/2024-BB-paper/fit_kappa_to_g2_g4.py --outputpath ${BASEPATH_PLOT}/quenched_1.50Tc_zeuthenFlow/

Name		Name	Last commit message	Last commit date
Latest commit History 687 Commits
correlator_analysis		correlator_analysis
misc		misc
multi-level		multi-level
perturbative_corr		perturbative_corr
spf_reconstruction		spf_reconstruction
.gitignore		.gitignore
README.md		README.md
lib_process_data.py		lib_process_data.py
pyproject.toml		pyproject.toml

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Data publication for "The diffusion of heavy quarks in a quark-gluon plasma from lattice QCD"

Installation

Install system dependencies (Ubuntu)

Extract data and code archives

Make scripts executable

Setup environment

Note on output file formats

Correlator analysis

Resampling, interpolation, continuum extrapolation

Create figures of perturbative correlators

Merge correlator measurement files

Bootstrap resampling of uncorrelated blocks

Plot flow time dependency

Interpolation

Continuum extrapolation

Plot flow time correlations

Plot lattice spacing effects

Flow-time-to-zero extrapolation of $G_E$

Compare final quenched $G_E$ with multi-level results

Renormalization of $G_B$

Coupling calculations

Carry out renormalization of $G_B$ by computing $Z_\text{match}$

Flow-time-to-zero extrapolation of renormalized $G_B$

Compare final $G_E$ and $G_B$

Compare correlator at fixed normalized flow times

Quenched

Spectral function analysis

Perform spectral function reconstruction

Sketch spectral function models and reconstruction process

Plot spectral reconstruction results

Quenched case

2+1-flavor case

Compare correlator at fixed normalized flow times

2+1-flavor

Comparison to literature

Plot comparison with literature for $2\pi TD$

Plot fit to $g^2$ and $g^4$

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