Today's Progress 20. April. 2007

Tune of T0 gain variation/nonlinearity :E570

In order to solve the T0 gain nonlinearity problem/gain variation, we just adopt the method adopted for E549 data, and the stopped K selection will be established here for E570 data.

Method

1. Simulate the expected energy loss on T0 as the function of stopped vertex z position for Kaon. Also, peak position by pi beam is simulated.

2. By plotting the simulated energies (MeVee) as the function of detected sqrt(phL*phR) for obtained data points and fitting by relevant functions, we obtain segment-by-segment sqrt(phL*phR) to energy (MeVee) convertion function, fi(E), as

fi=fi(idrun,sqrt(phL*phR))

. The index is to indicate the segment ID, first variable is run number. The function is calculated cycle-by-cycle, and run 222(&pi⁺ beam)/225(K⁺*PAPB) is adopted for the first cycle, while run 404(&pi⁺ beam)/412(K⁺*PAPB) is adopted for the second cycle. The function is determined with a constraint of "value 0 for sqrt(phL*phR)=0", to let it be globally appricable in energy. Practically, 3rd order polinomial was necessary and enough to reproduce obtained data points. The fitting results are exhibitted below.

E570 cycle1 results obtained from run222/225

E570 cycle2 results obtained from run 404/412

Now, the pulseheight-energy conversion function, fi(225/412,sqrt(phL*phR)) has been successfully obtained. The correlation between calculated energy on T0 2nd layer (MeVee) vs vertex z (cm) is as below.

Segment-by-segment correlation between T0 energy (MeVee, horizontal) VS vertex z(cm, vertical) at run 225.

Segment-by-segment correlation between T0 energy (MeVee, horizontal) VS vertex z(cm, vertical) at run 412.

Since T0 nonlinearity is successfully solved, now we can introduce "ID function" of stopped K events. The ID function is constructed as a difference,

E - f(vz)

, between detected energy (DeltaE) and a 3rd order polinomial to fit the resultng energy-vertex correlation (f(vz)) for stopped K⁺ as shown below.

The resulting distribution of ID function and its correlation with vertex z for K⁺ are as shown below .

E570 cycle1 results from run 225.

E570 cycle2 results from run 412.

The comparison between ID function for run 225(K⁺) and 229(K^-)/ for run412(K⁺) and run417(K^-) are shown below. IDfunc > -1. may work well. The shift of the central position can be attribued to the gain drift discussed nextly.

3. Run-by-run gain variation is then considered. Now, the gain variation is studied as of the variation of the peak position of the sqrt(phL*phR) when kaon stopped at -5~+5 . Let we define the peak position for vz:-5~5 as E_0(Nrun). Then, the convertion function for run Nrun is defined as

fi(Nrun,E) = fi(225,E')

, where E' is defined as

E' = E*(E_0(225)/E_0(Nrun)).

By this correction, the run-by-run variation of KstopID function can be fully stabilized. Note that run 412 is adopted is adopted instead of 225 for the second cycle.

Run-by-run segment-by-segment gain variation for T0 2nd layer. In order to avoid to be affected by possible change of beam condition, now stop K events at -5. < vz < 5. are slelected. Note that jump for K^+ runs has been disappeared - that jump is attributed to the different beam position/angle/momentum distributiuons of K^+ beam.

Run-by-run variation of the KstopID function, represented by fitted Gaussina center and &sigma.

A comparison of distributions of ID function between run 225 (K⁺, black)/229(K^-, red) and run 412 (K⁺, black)/417(K^-, red).

Hereafter, 'Kstop' event is selected by

KstopID > -1. (MeVee),

at least if T0-PA TOF is not available.