TWiki> HEPProjects Web>KelleyLabManual>RyanBySubject>MuEfficiency (2007/05/16, RyanKelley)EditAttach

A very basic definition of efficiency:

*ε = ( # particles found by my detector in the event ) / (# real particles produced in the event)*

The problem is that we don't know the # real particles produced so we have to work harder to determine the denominator.

Consider an event pp → ZX → μμ + stuff. Let us define the efficiency to detect muons as

*ε(μ) = ( # μ's found by my detector in Z events) / (# real μ's produced in Z events)*

The numerator is simple, use the number of μ's found by the muon system.

The denominator is more difficult so we break it down into several steps to approximate the true # μ's.

Start with events pp → ZX → μμ + stuff.

The event will have many charged tracks--two if which we know are μ's. First we ID the ** anchor** μ --> we 'cruelly' cut on the first lepton to ensure that is is indeed a μ that came form the Z decay. Next we make a P

***********diagram

Loop over all charged tracks with opposite charge (w/no muon system requirement) and plot a histogram of the invariant mass ( M_{A} + M_{P} ).

******************get histo from matt

Next fit the histogram and then integrate over a window of 2 * Γ_{Z} centered on the M_{Z}: *∫ fit = N _{1} +/- √N_{1}*

Loop over all the μ's found with both the muon system and tracker and plot a histogram of the invariant mass ( M_{A} + M_{μ} )

*****************get histo from Matt

Again, fit the histogram and then integrate over a window of 2 * Γ_{Z} centered on the M_{Z}: *∫ fit = N _{2} +/- √N_{2}*

Finally we can calculate the efficiency:

*ε =* N_{2} / N_{1}

σ_{ε} = binomial

-- RyanKelley - 16 May 2007

Topic revision: r5 - 2007/05/16 - 23:58:50 - RyanKelley

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