The choice of parameterisation is of vital importance for a kinematic fitting package. The better a parameterisation the better the final results.

What determines a good parameterisation?? It is preferable to use gaussian distributed parameters as this ensures high convergence of the fit and allows the interpretation of a c², but this is not a requirement. Also, the parameters describing a single particle and the full set of all particles in an event should have as little a correlation as possible. Finally it is desirable to have a parameterisation which is less "detector dependent", that is, do not vary strongly with the particle direction/position in the detector. Clearly, this still leaves a lot freedom to define a parameterisation, which is why the ABCFIT package has been made to allow almost any parameterisation to be used with a minimum of programing. To add a new parameterisation to the ABCFIT package one must know the transformation of particle momenta into the parameters and vice versa, along with the derivative of the momenta with respect to the parameters.

Available parameter definitions
In the present version of the ABCFIT package 6 different parameterisations have been included:

• The so-called ALEPH parameterisation. In this parameterisation the particle momentum is described via a longitudinal momentum scale, a, and two transverse components, b and c. In the case of jets, correlations may be present between the b and c parameters and in general we have that the higher the multiplicity the higher the correlation will be. Also, since the particle distribution in a decay of a quark has an exponential behaviour, the loss of particles, and consequently energy, may not be adequately described by a gaussian scale parameter. As a result the longitudinal scale parameter is not perfectly gaussian distributed. A perhaps more unpleasant feature is that it is allowed to revert the particle direction.
• The so-called DELPHI parameterisation. It is very similar to the ALEPH parameterisation, with the exception of the longitudinal scale parameter, which have been transformed to an exponential function. This results in a slightly better gaussian behaviour and no longer allows the flipping of a particle' direction.
• Particle momentum and direction: DP, Dq and Dj. This parameterisation is well suited for single particles with known masses and well determined directions (e.g. muons or electrons with no bremsstrahlung).
• Particle momentum components: DP_x, DP_y and DP_z. This parameterisation is very easy to program, but is probably only suitable for unmeasured particles, which do not contribute to the c², since it is highly dependent on the particle position in the detector.
• Particle energy and direction: DE, Dq and Dj. This parameterisation is well suited for single particles with well determined directions, but where the measurement of the particle momentum relies more on calorimeters (e.g. electrons with bremsstrahlung).
• P_T and direction: D(1/P_T), Dq and Dj. This parameterisation is well suited for single particles with known mass and is even better than the previous one when the measurement uncertainties is directly related to tracking (e.g. muons or electrons with no bremsstrahlung).

Parameter evolution
Once the description of each particle inside the fit has been determined, the fit needs to know the expectation value and the error of each parameter in order to build the c². In  ABCFIT this knowledge is passed to the fit at runtime via a set of text files with a specific structure and name, depending on the type of parameters and number of particles e.t.c. The advantage of this is that the user no longer has to do any programming and removes redundant source code. Naturally it is still possible to make individual routines for each parameterisation.
 

Then you have come to the right place! The following dummy parameterisation dat-files are currently available (others can easily be made):

• Dummy file for ITYPPN=0, NJET=4 and ITEVOL=0x1: aibi_evol_0000_001.dat
• Dummy file for ITYPPN=0, NJET=4 and ITEVOL=1x1: aibi_evol_0000_101.dat
• Dummy file for ITYPPN=1, NJET=2 and ITEVOL=0x1: aibi_evol_11_001.dat
• Dummy file for ITYPPN=1, NJET=3 and ITEVOL=0x1: aibi_evol_111_001.dat
• Dummy file for ITYPPN=1, NJET=4 and ITEVOL=0x1: aibi_evol_1111_001.dat
• Dummy file for ITYPPN=1, NJET=4 and ITEVOL=1x1: aibi_evol_1111_101.dat
• Dummy file for ITYPPN=1, NJET=5 and ITEVOL=0x1: aibi_evol_11111_001.dat

Parameterisations @ 183:

• Parameterisation for WW-> evqq events with ITYPPN=1, NJET=4, NUP=1 and ITEVOL=001 AND ABCTAG='183 ': aibi_evol_183_1111_001.dat
• Parameterisation for WW-> evqq events with ITYPPN=1, NJET=4, NUP=1 and ITEVOL=101 AND ABCTAG='183 ': aibi_evol_183_1111_101.dat
• Parameterisation for WW-> muvqq events with ITYPPN=1, NJET=4, NUP=1 and ITEVOL=002 AND ABCTAG='183 ': aibi_evol_183_1111_002.dat
• Parameterisation for WW-> muvqq events with ITYPPN=1, NJET=4, NUP=1 and ITEVOL=102 AND ABCTAG='183 ': aibi_evol_183_1111_102.dat
• Parameterisation for WW-> qqqq events with ITYPPN=1, NJET=4, NUP=0 and ITEVOL=004 AND ABCTAG='183 ': aibi_evol_183_1111_004.dat
• Parameterisation for WW-> qqqq events with ITYPPN=1, NJET=4, NUP=0 and ITEVOL=104 AND ABCTAG='183 ': aibi_evol_183_1111_104.dat

• Parameterisation for WW-> qqqq events with ITYPPN=1, NJET=4, NUP=0 and ITEVOL=004 AND ABCTAG='189 ': aibi_evol_189_1111_004.dat
• Parameterisation for WW-> qqqq events with ITYPPN=1, NJET=4, NUP=0 and ITEVOL=004 AND ABCTAG='189 ': aibi_evol_189_1111_104.dat