Scale setting with m_Ω and w₀

This repository performs the chiral, continuum and infinite volume extrapolations of w_0 m_Omega to perform a scale setting on the MDWF on gradient-flowed HISQ action. The present results accompany the scale setting publication available at arXiv:2011.12166.

The analysis was performed by Nolan Miller (millerb) with the master branch, and Logan Carpenter ( loganofcarpenter) with cross checks by André Walker-Loud (walkloud) on the andre branch.

The raw correlation functions can be found here and the bootstrap results for the ground state masses and values of Fpi are contained in the file data/omega_pi_k_spec.h5.

How to use

Running the analysis

To generate the extrapolation and interpolation results from the paper, run python scale-setting.py -c [name]. This will automatically create the folder /results/[name]/ . A summary of the results is given inside /results/[name]/README.md. Extra options can be viewed by running python scale-setting.py --help, which is given below for convenience.

``` usage: scale-setting.py [-h] [-c COLLECTIONNAME] [-m MODELS [MODELS ...]] [-ex EXCLUDEDENSEMBLES [EXCLUDED_ENSEMBLES ...]] [-em {all,order,disc,alphas}] [-df DATA_FILE] [-re] [-mc] [-nf] [-na] [-d]

Perform scale setting

optional arguments: -h, --help show this help message and exit -c COLLECTIONNAME, --collection COLLECTIONNAME fit with priors and models specified in /results/[collection]/{prior.yaml,settings.yaml} and save results -m MODELS [MODELS ...], --models MODELS [MODELS ...] fit specified models -ex EXCLUDEDENSEMBLES [EXCLUDEDENSEMBLES ...], --exclude EXCLUDEDENSEMBLES [EXCLUDEDENSEMBLES ...] exclude specified ensembles from fit -em {all,order,disc,alphas}, --empiricalpriors {all,order,disc,alphas} determine empirical priors for models -df DATAFILE, --datafile DATAFILE fit with specified h5 file -re, --reweight use charm reweightings on a06m310L -mc, --milc use milc's determinations of a/w0 -nf, --nofit do not fit models -na, --noaverage do not average models -d, --default use default priors; defaults to using optimized priors if present, otherwise default priors ```

To fine-tune the results, either re-run the fits using the options above or by modifying /results/[name]/settings.yaml. Similarly, the fits can be constructed with different priors by editing /results/[name]/priors.yaml and re-running python scale-setting.py -c [name].

In addition to this library, this repo contains Juypyter notebooks. The fit for a single model can be explored in /notebooks/fit_model.ipynb. The model average is provided in /notebooks/average_models.ipynb. Some miscellaneous drudgery (eg, the paper's sensitivity figure) is available in /notebooks/bespoke_plots.ipynb.

Using these results for other projects

To reuse this work for other CalLat projects where a scale is needed, use the pickle produced from /notebook/generate_scale_setting_pickle.p. Note that the entries in this dictionary are correlated, as the determinations of the lattice spacings are correlated by the gradient flow scales. The keys are like

```python scalesettingpickle = { 'w0org:w0' : 0.1713 (12), # the gradient flow scale (in fm) w0 per the original definition 'w0org:a06' : 2.986 (12), # reciprocal lattice spacing of the ~0.06 fm ensembles in w0 units, i.e w0/a06 # ... some entries omitted 't0org:sqrtt0' : 0.1414 (12), # the gradient flow scale \sqrt{t0} per the original definition 't0org:a06' : 6.587 (25), # reciprocal lattice spacing of the ~0.06 fm ensembles in sqrt{t0} units, i.e \sqrt{t0}/a06 # ... etc 'w0imp:w0' : 0.1716 (12), # the gradient flow scale (in fm) w0 per the improved definition 'w0imp:a06' : 2.997 (12), # reciprocal lattice spacing of the ~0.06 fm ensembles in w0 units using the improved definition # ... etc 'sqrtt0/w0org' : 0.8258 (38), # dimensionless ratio of flow scales per the original definition 'sqrtt0/w0_imp' : 0.8262 (37), # dimensionless ratio of flow scales per the improved definition

# meta data suggesting the priors/settings used to generate scalesetting.p # check /results/ folder 'meta' : { 'originalscales': '20230620-originalsimultaneous', 'improvedscales': '20230620-improved_simultaneous'} } ```

To convert to physical units, simply compute, e.g.,

python scale_setting_pickle['w0_org:w0'] / scale_setting_pickle['w0_org:a06'] # = 0.05718(53) fm ~ 0.06 fm

Requirements

This work makes extensive use of Peter Lepage's Python modules gvar and lsqfit, which are used to construct the fits and model average. Further, the settings and priors are primarily tweaked by the accompanying yaml files loaded via PyYAML.