Today's Progress 13. July. 2007

Acceptance study and normalization of 4He(stopped K-, d) spectrum

Acceptance study

In order to present a % of stopped K- momentum spectrum of deuteron, we study acceptance of deuteron as a function of deuteron momentum in terms of Monte-Carlo simulation. The conditions for the simulation is tabulatted below.

Conditions of the Monte-Carlo.
software GEANT3.21
generated deuteron momentum range 300-900 (MeV/c)
generated deuteron momentum distribution uniform
generated deuteron angler distribution uniform on unit sphare i.e. cos&theta and &phi are uniform with no correlation
generated event number 4*108
target center (-0.3,0.,1.3):E549 (-0.5,0.5,1.2):E570 by cm unit
x/y generation point distribution 2.0/4.0/6.0 cm sigma Gaussian centered at (x,y)=(-0.3,0.)
z generation point distribution uniform
multiple scattering on(Moliere)
energy loss straggling on(Gauss/Landau/Vavilov are internally selected adequately)
nuclear reaction of deuteron on(GHEISHA)/off
coincidense time gate for PA-PB 45 nsec
Birk's coefficient for plastic scintillator0.013/(MeV/cm)
Time resolution of PA/PB 60/80 psec

On GEANT3.21, 3 modes of are selectable for hardron interection.

1. GHEISHA for all.

2. GHEISHA for neutron below 20 MeV kinetic energy, and FLUKA for the others.

3. MICAP for neutron below 20 MeV kinetic energy, and FLUKA for the others.

Very unfortunately, only GHEISHA can evaluate deutron in-flight reaction, hence mode 1 is unique solution here.

Below, evaluated acceptance function is compared under various conditions.
Acceptance functions with/without hadron reaction evaluated assuming &sigma=4cm of stopped K- distribution. Black:no hadron reaction, no inefficiency by deuteron selection Red:with hadron reaction, no inefficiency by deuteron selection Magenda:no hadron reaction, taking the inefficiency of deuteron selection into account Sky-blue:with hadron reaction, with inefficiency by deuteron selection

We adopt the result WITH hadron reaction and takes the deuteron inefficency into account, i.e. result shown by sky-blue. Then, the acceptance is almost flat over 580 MeV/c. In order to check the robustness, we check the variation of the function according to the stopped K density distribution.

Acceptance functions stopped K- distribution of &sigma=2(black)/4(red)/6(green)cm, respectively. As expected, lower-momentum component is very sensitive to the shape of the distribution, while higher-momentum region is stable. Below 500 MeV/c, possible systematics on the scale exceeds the one from the uncertainty of kaon free decay fraction when we assume so large uncertainty on the stopped K- distribution shape.

Adopting 4cm Gaussian, we compare the effect of the modification of setup between E549 and E570.
Acceptance functions for E549(black) and E570(red). The difference is significant at low energy.

The difference of these two is negligible even compared to the uncertainty of the stopped K- density distribution. We therefore nedd to set some waight to add results from different cycles.

Normalized inclusive momentum spectrum of deuteron

Concluding, we adopt the acceptance function obtained as the followng condition:

Adopted conditions for the acceptance calculation.
software GEANT3.21
setup geometry E549/E570 separately. 1st/2nd cycles are not distinguished.
x/y generation point distribution 4.0 cm sigma Gaussian centered at (x,y)=(-0.3,0.)
z generation point distribution uniform
in-flight nuclear reaction of deuteron on(GHEISHA)
coincidence time gate for PA-PB 45 nsec
Now we derive a "% of stoped K-" spectrum of deuteron momentum, as following. This formula is mathematically derived one without any additional assumption, by adopting normalization formula for each of cycles.

The Sum is taken over different cycle results. P- is free decay ratio 3.5 +- 0.5%(from Outa), Br is K-->&mu-&nu decay branching ratio, 63.43 +- 0.17% (from PDG), &epsilon&mu- is geometrical part of muon detection efficiency, 7.55% (evaluated value), and &epsilon-delay=exp(-T/&tau) is inefficiency by delayed time gate where &tau=10.4 nsec (from Outa), and T=1.2 nsec (just by definition determined in order to make the charged particle spectrum as clean as possible ensuring remaining statisics). Cycle-by-cycle Kmu2 peak yield is tabulatted below.

Number of Kmu2 peak by delayed time gate T=1.2 nsec.
Arm/cycle E549 E570-1 E570-2
L 56320 +- 286 55985 +- 27722121 +- 171
R 55241 +- 274 55719 +- 27722003 +- 169
Total 111561 +- 396 111704 +-39244124 +- 240

Cycle-by-cycle results are compared below.

Cycle-by-cycle normalized deuteron spectra. Black:E549/Red:E570-1/Green/E570-2

The spectrum as of E549+E570 is shown below. The strength over 500 MeV/c is determoned to be 1.1+-0.2 %.

Normalized deuteron spectra as of E549+E570.