The Mean-Timer algorithm exploits the time information provided by the Drift Tube (DT) chambers to accurately determine the crossing time of muons in the detector.
After calibration, the drift times are multiplied by the known drift velocity and thus converted to space hits.
One can then proceed to a standard 2-parameter fit in order to find the best segment, including as many hits as possible.
Within this framework, any time shift, Dt, of a crossing muon w.r.t. the trigger time (t=0) appears as a coherent time shift of all hits produced by that muon within a DT chamber. Therefore all hits appear to be nearer or farther from their respective anode wires by the same distance: Dx = Dt * v_drift.
This Dt can be determined applying a 3-parameter fit instead of a standard linear fit, the 3 parameters being: slope, intercept and time.
The third parameter can be considered as the time shift that, when applied to all hits, most improves their alignment.
The Mean-Timer algorithm uses this fit already when doing pattern recognition (i.e. for selecting hits to be associated in a segment).
(See also: previous results on resolution using Mean-Timer pattern recognition)
The advantages of this method are twofold:
1) Improving the space resolution achieved by the reconstruction process for out-of-time tracks (the hits are better aligned, the errors on intercept and slope are reduced)
2) Allowing a muon time measurement with a good resolution.
Concerning space resolution, when using a 2-parameter fit, the applied chi2 cut must allow for any variations of the segment's time, so it cannot be too tight.
In the 3-parameter fit any time variations are included in the fit and the chi2 only accounts for the spatial resolution of the drift tubes themselves: in this case chi2 cuts can be made tighter and the resolution improves.
This improvement in resolution applies in particular to the two following cases:
a) The treatment of delta ray hits.
Due to the features of DT Read Out electronics, when delta ray hits precede the muon hit within the DT cell, the muon hit may fail to be read out and the delta ray hit enters the reconstruction process.
When using the standard reconstruction with lose chi2 cuts, one is forced to use dedicated cleaning algorithms, in order to reject delta ray hits.
When using the 3-parameter fit with tighter chi2 cuts, instead, most of delta ray hits are automatically rejected.
b) The correct treatment of time shift is also important whenever a track produces hits in only one projection (this is the case for all MB4 stations that don't have Theta super-layers).
In these cases we don't know the position of the track in the wire direction, therefore cannot correct for the propagation time of the signal along the wire.
The Mean-Timer reconstruction automatically corrects for this effect as well.
The muon time measurement can be used to select out-of-time muons for dedicated physics analyses, as for instance the search for Heavy Stable Charged Particles, or, on the contrary, to reject unwanted out-of-time muons, due for instance to high Pile Up.
The Mean Timer algorithm was already used at the level of Pattern Recognition: results were shown in CMS DP-2014/004 and in this twiki page.
In the latest version of the reconstruction software, aimed for 2015 data-taking, it has been extended to use the 3-parameter fit also for the final determination of segment parameters (however if a segment's time is within +/-20ns the 2-parameter fit is used).
The algorihtm has been tuned using simulated Z-->2mu data, shifted on purpose in time by fixed quantities (the shift was applied at the level of time calibration) and then reconstructed with the 3-parameter fit.
Both plots have been generated with the CSC and RPC muon detectors switched off in the reconstruction: only DT were used.
The first plot shows the results of this procedure:
The different colours refer to different time shifts: for each sample of time-shifted muons, the Mean-Timer reconstruction was applied and the distribution was filled with the weighted average of measured times, obtained from the single chambers.
This plot shows at once the efficiency of the time measurement and the time resolution.
A measure of efficiency is the ratio of areas of "lateral" peaks to the one of the central peak.
The time resolution can be appreciated as the separation between peaks that differ from each other for a 25 or 50 ns shift.
The somewhat asymmetric shapes of the very far peaks weren't studied in detail yet.
From this plot we see we still have a non null efficiency to reconstruct muons that are as far as 12 BX's from the triggering one.
The second plot is a zoom in logarithmic scale of the central peak of previous plot: it shows the time resolution for in-time tracks.
The slight asymmetry of the distribution is due to a residual delta ray contribution.
We may assume the RMS of this distribution, i.e. 2 ns, as a measure of the DT time resolution.
The Mean-Timer reconstruction was implemented in official software releases in 2014.
The plot below shows a comparison between the time measurement performed on 2012 data with the Mean-Timer reconstruction and the one obtained with the previous software on the same event sample. Here the time values were derived from single reconstructed segments, i.e. from single DT chambers.
The software version used in 2011 and 2012 still relied on a combinatorial pattern recognition whose efficiency dropped steeply for out-of-time tracks: by this method we were actually selecting in time tracks only. This can be observed applying a 3-parameter fit to the selected hits and looking at the obtained time distribution (red histogram in the plot).
When applying the Mean-Timer pattern recognition to the same events, the time extension of track selection is only limited by the maximum drift time that is considered in the reconstruction: i.e. in principle the same time range of single hits. The distribution of the time measurement (blue histogram in the plot) shows clearly that we are able to reconstruct tracks as far in time as 200 ns from the triggering bunch crossing.
The 50 ns beam structure is clearly visible in the right hand side peaks: they contain tracks produced in bunch crossings that follow the triggering one. The left hand side distribution is partially spoiled by delta ray effects (notice that no selection was applied to reconstructed segments).
The central peak, corresponding to in-time muons, is visibly higher and narrower, due to the better hit selection performed by the Mean-Timer algorithm. Its width is consistent with expectations.