The ETMC has performed three pion scattering on N_f = 2 Wilson clover twisted mass lattices. In this repository you can find the energy levels such that an independent analysis is possible. If you are using this data in a publication, we ask you to cite https://arxiv.org/abs/2008.03035.

There is the spectrum in the files starting with cm_mass. These contain the interacting center of mass energies, the pion mass and their ratio. The files with pion_decay contain the pion decay constant that is measured on the same data with full correlation.

Files with boot in their name contain all bootstrap and jackknife samples, the other files contain the central values and an error estimate from the samples. Unfortunately both resampling methods are called “boot” in this data set, so “boot” should rather mean “samples”. Jackknife and bootstrap data is given in separate files.

The data files are space separated, you can read them in R with read.table and in Python with np.loadtxt or np.genfromtxt. The following table explains all the columns. It is recommended to use a library that can group data, either Python Pandas or R dplyr.

Column	Type	Meaning
ensemble	String	Name of the ETMC ensemble.
extent_space	Integer	Number of lattice sites in the spatial direction, L/a.
extent_time	Integer	Number of lattice sites in the temporal direction, T/a.
channel	String	Scattering channel, either 2pi_I2 or 3pi_I3.
irrep	String	Name of the irrep, like A1u or Eg or B2.
total_momentum_d_sq	Integer	Total momentum squared.
irrep_col	Integer	Column of the irrep. We only use 1.
irrep_row	Integer	Row of the irrep, we only use 1.
outlier_cutoff	Float	Gauge configurations which yield a correlator value C_{ij}(t) which is more than outlier_cutoff inter quartile ranges away from the quartiles is considered an outlier and discarded.
boot_method	String	Resampling method, either bootstrap or jackknife.
boot_R	Integer	Number of bootstrap samples. Meaningless for jackknife resampling.
boot_seed	Integer	Seed used in bootstrap resampling.
boot_l	Integer	Bootstrap block length.
pion_total_momentum_d_sq	Integer	The total momentum squared of the pion correlator used.
pion_tmin	Integer	Begin of the pion correlator fit range.
pion_tmax	Integer	End of the pion correlator fit range.
gevp_sort_type	String	Sorting algorithm in the GEVP, can either be values or vectors.
gevp_mask	Integer/NA	If set to NA, the whole correlator matrix is fed into the GEVM. Integer values mean that only the lowest so many operators have been considered.
correlator_id	Integer	Number of the correlator in that irrep, increasing number means increasing energy
fit_method_count	Integer	Number of fit methods that have been averaged on this energy level.
boot_r	Integer	ID of the sample, only present in the files with the resampling.
cm_mass_val	Float	Center of mass energy value in lattice units.
cm_mass_boot	Float	… on the sample boot_r.
cm_mass_err	Float	… error.
pion_mass_val	Float	Pion mass value in lattice units.
pion_mass_boot	Float	… on the sample `boot_r.
pion_mass_err	Float	… error.
cm_mass_over_pion_mass_val	Float	Ratio center of mass energy over pion mass, value.
cm_mass_over_pion_mass_boot	Float	… on the sample `boot_r.
cm_mass_over_pion_mass_err	Float	… error.
pion_decay_constant_val	Float	Pion decay constant in 120 MeV convention.
pion_decay_constant_boot	Float	… on the sample `boot_r.
pion_decay_constant_err	Float	… error.