Monitor charge dependence in pT resolution, bias and reco efficiency in HLT1

A large fraction of our physics programme would benefit from keeping all charge asymmetries in reconstruction steps to the minimum. Now that we have a reconstruction chain all set up, it would be good to include plots which show the potential charge bias in the HLT1 reconstruction. In practice, that means these plots:

• The reconstruction efficiency of muons and pions separately 1) as a function of pT, 2) as a function of momentum, split by charge and turned into an asymmetry histogram*
• The pT resolution of muons and pions as a function of pT, split by charge
• The pT bias of muons and pions as a function of pT, split by charge

For the first, a few notes: the asymmetry between reconstruction efficiencies is defined as A = (e+ - e-)/(e+ + e-), having the efficiency in bins for both charges then gives an asymmetry in bins. The denominator in this efficiency would be the charged particles which are reconstructible, such that losses due to an asymmetric detector acceptance are not considered.

As a variation of these plots, an additional rough binning in pseudorapidity is likely desirable. Any bias in pT should be understood and it's probably helpful to have at hand to investigate which details in the propagation are responsible.

These studies do typically require about 10'000 events, but substantial effects are of course already visible with fewer. The asymmetries should be determined on a sample with only one magnet polarity. (Having the asymmetry plots for both magnet polarities (i.e. running this monitoring separately for magnet up and down and comparing the results) is very interesting, but probably for a later stage)