Measurement of the Z boson cross-section in - Harvard University ...

Chapter 4: Data Collection and Event Reconstruction 135
tracks have been formed, an attempt is therefore made to match them with corre-
sponding inner detector tracks. The Moore family algorithm that does the matching
is MuIDCombined; the corresponding Muonboy family algorithm is Staco.
Combined reconstruction by MuIDCombined
MuIDCombined starts with a spectrometer track and attempts to match it with
an inner detector track using a χ 2 quantity comprising the five track parameters and
their covariances from each system:
χ 2 match =(TMS − TID) T (CMS + CID) −1 (TMS − TID) (4.6)
where T is a vector of the five track parameters expressed at the perigee, C is the
covariance matrix, and ID and MS denote the inner detector and the muon spec-
trometer respectively. For matches with χ 2 probability greater than 0.001, a partial
refit is performed starting with the inner detector track vector and adding hits from
the spectrometer track, taking into account material effects and the magnetic field [7].
If no matches are found, a combined fit is attempted with a road about the spectrom-
eter track, and all measurements from the inner detector and spectrometer are used
in a global χ 2 fit.
Combined reconstruction by Staco
Staco (STAtistical COmbination) attempts to statistically merge the ID and MS
tracks to obtain a combined track vector:
T=(CMS + CID) −1 (CMSTMS + CIDTID) (4.7)
where the Cs and the Ts are defined as before. A combination is accepted if it is below
an upper limit on the χ 2 , as defined in Eq. 4.6 above. If more than one combination
satisfies this criterion, the one with the lowest χ 2 is kept. The corresponding tracks