NA48/2 program and data for calculation of charged kaon semileptonic form factors

The experimental data histograms and MC event samples for ke3 and km3
decay modes are provided in two root files in the "input" directory. The
files contain everything needed to reproduce the central values and statistical
errors of the published NA48/2 results [1]. But for the complete systematics
evaluation one would need more additional event samples selected with another
cuts, that are not provided in the present data set.

   The data set and the program may be used to extract central values for
a form factor parameterization modified by user. In particular, Dispersive
parameterization has few external parameters. If these external values will be
changed in future, one can edit their values in the file "kl3ff.h" and
re-fit the Dispersive parameterization with the provided NA48/2 data.

   User can also try his new form factor parameterization, but in such a
case some extra efforts will be needed to transfer the published systematic
uncertainties from [1] to the new parameterization.

   Nevertheless, for a theorist it may be interesting if his formula
agree with NA48/2 experimental data. A successfull fit with a tolerable Chi2 will support the validity of the new formula.

   The present fit is done taking into account
the "universal radiative correction" proposed by Cirigliano et. al [2].
So the extracted parameters are related to the "effective form factors"
that absorb all the interplay between QCD and QED. So theorist should
first separate the universal radiative correction [2] from his
formula and use the rest as a new form factors parameterization.

                              Usage

1. Edit the kl3ff.h file and choose a form factor parameterization
by setting of the definition:

"#define PARAMETERIZATION ***"

For TAYLOR, POLE and DISPRESIVE cases the NA48/2 central values from
[1] will be reproduced. One should remember that the correlation
coefficients are given in [1] for the total errors that include many
systematic contributions. Results of the present fit will give only
statistical errors and correlations.

For Dispersive case one can update the external parameter values.

One can define BFAKE3 or BFAKM3 factors to scale the background(s)
contribution. NA48/2 background-related systematic uncertainties were
found by the variation of BFAKE3 by 30% and BFAKM3 - by 10% around 1.

One can also change the minimum statistics per bin of data histogram,
but it should not be too small, as we assume Gaussian errors.

For the completely new parameterization, one should set
"#define PARAMETERIZATION NEW" in kl3ff.h and also edit the
file kl3ff.C in two places defined by the preprocessor
command "#if PARAMETERIZATION == NEW".

2. Ensure the presence of some fresh root environment and run "gmake"
to compile the code.

3. Run "./kl3ff ke3", "./kl3ff km3" or "./kl3ff kl3" to start the
corresponding fit. Results will be printed to standard output.
Some comparison histograms will be stored in the output files
ke3_result.root or/and km3_result.root .

                         References

1. J.R.Batley et al. [NA48/2 Collaboration],
   Measurement of the form factors of charged kaon semileptonic decays,
   JHEP 1810, 150 (2018).

2. V.Cirigliano, M.Knecht, H.Neufeld, H.Rupertsberger and P.Talavera,
  Radiative corrections to K(l3) decays,
  Eur. Phys. J. C 23, 121 (2002).