Today's Progress 24. Aug. 2006 (updated every moment)

Spectra Normalization (1) - normalization of proton inclusive spectrum

Methods

Since the bias from the experimental setup is convoluted in the raw-spectrum, we need to convert it into the physically meaningfull one, 'spectrum of % of stopped K^-'. The discussion about the normalization is as below:

Summary of the E549 DAQ duration

K/pi beam intensity normalizad by EP1/K5 SEC counts (top) and spill number (bottom).

Averaged trigger number per spill.

Run-by-run stability of primary beam represented by SEC(Second Ionization Chamber) counts

Trigger number per K5 sec. Beam condition (possibly TM/SEC ratio) is improving stepwise.

DAQ live time rate for each of E549 triggers. It is funny that the rate is higher for Kstop*VTC/10 trigger, especially for positive polarity.

Construction of 4He(stopped K^-, p) 'percent of stopped K^-' spectrum

Proton Detection Efficiency

(i) Proton selection procedure with the correlation between 1/beta VS total energy - 1/beta (with 60 + 80 psec timing resolution on PA/PB) and total energy(with infinite resolution, taking the Birk effect into account) are simulated and same analysis procedure is applied.

(ii) Consideration of the PA-PB coincidence gate width - if PA-PB TOF is beyond the gate width, then the proton is discarded. This partly explains the observed disagreement between data and simulated detection efficiency at low momentum region. To check the width, see E549 log book vol.2 p131.

The simulated proton detection efficiency curve, obtained by generating 100,000,000 proton events, is shown below.

Simulated proton detection efficiency. The black is the one without taking the finite gate length into account. The red one is the one considering the gate width 45 nsec, i.e. TOF from PA to PB is smaller than 45 nsec. The blue is the one if the TOF is larger than 45 nsec, being prepared for the reference. By adopting the finite gate length, the acceptance decreases for low energy proton.

Detection efficiency of muon is investigated with 235.53 MeV/c mu^+ with identical setup and position/angle distibutions, and it has been estimated to be 7.55%.

Detected Kmu2 Peak Numbers - K^-

Number of Kmu2 decay is counted by the function fitting procedure to the observed 1/beta spectrum. 3rd order polinomial background and three Gauss functions are adopted as the fitting function. The arm-by-arm fitting result are shown below, and the MINUIT outputs are given here, for L/R arms, and the resulting observed Kmu2 peak numbers are (5.517 +- 0.029)*10^4/(5.527 +- 0.027)*10^4 for L/R arms, with 0.8 nsec delayed-timing-gate condition. Observed Kpi2 peak numbers are (1.74 +- 0.03)*10^4/(1.60 +- 0.03), then.

The arm-by-arm variation of 1/beta spectrum with respect to the delayed-timing-gate condition. Black:dT(T0->PA)>0.8nsec, Red:dT(T0->PA)>1.0nsec, Green:dT(T0->PA)>1.6nsec, Yellow:dT(T0->PA)>2.6nsec, Magenta:dT(T0->PA)>4.0 nsec .

Detected Kmu2 Peak Numbers - K^+

Number of Kmu2 decay is counted by the function fitting procedure to the observed 1/beta spectrum. Since almost no background is expected below Kmu2 peak now, hree Gauss functions are adopted as the fitting function. The arm-by-arm fitting result are shown below, and the MINUIT outputs are given here, for L/R arms, and the resulting observed Kmu2 peak numbers are (3.132 +- 0.006)*10^5/(3.288 +- 0.006)*10^5 for L/R arms. Note that now delayed timing condition is not applied, and stopped K^+ events are selected by Kstop ID function (vertex z VS T0 energy).

Comparison of Kbeam/Kstop Number Ratio

N^+_{stopK} = 6.42*10^5/(0.6351*0.0755*0.6031) = 2.22*10^7 ,

N^+_{stopK}/spill = 2.22*10^7/(330.4*(60/4.0)) = 4.48*10^3 ,

N^+_{stopK}/N^+_{beam} = 2.22*10^7/1.70*10^8 = 13.1% (cf. E471 17.3 %),

N^-_{stopK} = 1.14*10^5/(0.035*0.6351*0.0755*0.86*exp(-0.8/10.4)) = 8.53 * 10^7 ,

N^-_{stopK}/N^-_{beam} = 8.53*10^7/2.18*10^9 = 3.9% ,

Momentum distribution on T0

The results are exhibitted below:

K^+/- momentum distribution at T0 2nd layer entrance.

Distribution of stop position z for K^+/-.

Distribution of energy deposit on T0 2nd layer for K^+/- .

Variation of stop K number divided by Kaon generation number / Kaon incident number on T0 2nd layer as the function of the variation of the adjustable degrader thickness. Reaction loss is seen to be 10~20%, then.

Momentum/range/Energy distributions are almost identical for both cases, and no significanct difference is found. The results if central value of K^- momentum is larger than that of K^+ by 1% are shown below.

Simulated distributions of energy deposit (top) and z position of kaon stop (bottom) for K^-(black)/K^+(red). The K^- initial momentum distribution is artificially shifted by 1% to higher side.

The difference of the energy disdtibution can be explained well, but range distribution is deviated from the observed one, then.

The shift of energy distribution can be reproduced, but range distribution is significantly deviated from the observed ones.

Derivation of percent of stopped K^- spectrum

Resulting inclusive proton spectrum.