Today's Progress 18. Dec. 2006

Monte-Carlo on the invariant mass resolution for &Lambda/&Sigma hyperons

Method

Since we detect &pi on TC, we would be able to construct &pi(onTC)-N(on PA/PB/NT) invariant mass, hence hyperon identification. Then, YN invariant mass could be constructed. First, we estimate the possible &pi-N invariant mass resolution for

&Lambda -> p &pi^-,

&Sigma^+ -> n &pi^+,

and

&Sigma^- -> n &pi^-,

assuming a realistic setup and resolution values by GEANT 3.21 . Note that

1. A proton (on PA/PB/NT) is detected with finite TOF resolution value, 100psec, then energy-corrected.

2. A neutron (on NT) is detected with finite TOF resolution value, 200psec and x/y/z ambiguities are treated simultaneously.

3. A charged &pi (on TC) is detected with finite TOF resolution value, 200psec, and no energy correction is applied. As the direction vector, detection by VDC is simulated, hence multiple scattering effect is properly taken into account.

Conditions of the Monte-Carlo.
generated hyperon species/production ratio	&Lambda:&Sigma^+:&Sigma^- 2:2:1
generated hyperon momentum range	180-720 (MeV/c)
generated hyperon momentum distribution	uniform
generated hyperon angler distribution	uniform on unit sphare i.e. cos&theta and &phi are uniform with no correlation
x/y generation point distribution	4.0 cm sigma Gaussian
z generation point distribution	uniform
multiple scattering	on(Moliere)
energy loss straggling	on(Gauss/Landau/Vavilov)
PA time resolution	60 psec (Gaussian responce)
PB time resolution	80 psec (Gaussian responce)
NT time resolution	200 psec (for neutron, Gaussian responce), which could be interpreted as the T0+KTOF+NT overall time resolution.
TC time resolution	0~300 psec (parameter, Gaussian responce), which colud be interpreted to be re-presenting the overall resolution of the measurement
direction cos of proton motion	replaced by the value on PDC(infinite resolution)
direction cos of pion motion	replaced by the value on VDC(infinite resolution)
detection point x of neutron on NT	represented by the x-central value of the segment
detection point y of neutron on NT	real value + 3.0 cm &sigma Gaussian
detection point z of neutron on NT	represented by the z-central value of the segment
detection point x,z of pion on TC_B	real value
vertex resolution	infinite(i.e. Kaon stop point is exact), but hyperon decay point is set to be unknown.
software	GEANT 3.21 (+LEPS-g77 for energy loss correction)

Results

Simulated Invariant Mass Spectra

Simulated N&pi invariant mass spectrum for various TOF resolution for pion. 1st:&sigma_TOF=0psec and hyperon decay time is known and subtracted from the measured time. 2nd:&sigma_TOF=0psec without decay time subtraction. 3rd:&sigma_TOF=100psec without decay time subtraction. 4th:&sigma_TOF=200psec without decay time subtraction. 5th:&sigma_TOF=300psec without decay time subtraction. In each case, &Lambda and &Sigma are clearly separated. Combinatorial background is not considered. Invariant mass resolution of &Lambda is then 4~5 MeV/c^2 (&sigma) for 200~300psec TOF resolution for &pi^-. (cf. 6 MeV/c^2 FWHM at FINUDA)

Simulated N&pi invariant mass spectra under various conditions with &sigma_TOF=200psec. The top is the case if hyperon live time is subtracted from the time difference of hyperon generation and pion arrival, and the bottom is the one without the subtraction, i.e. realistic one. Black:N momentum is exact, &pi momentum is exact one at TC Yellow:N momentum is TOF-measured one by the realistic resolution, &pi momentum is exact. Red: N and &pi momenta are TOF-measured ones. Green: N mometum is exact one, and &pi momentum is TOF-measured one.

Resolution of pion momentum/invariant mass

&pi-momentum resolution if 1/&beta resolution is fixed to 1.0 . For &Lambda (Ppi~100 MeV/c), ~ 8.8 MeV/c resolution is achieved, while ~45 MeV/c for &Sigma^+- (Ppi~185 MeV/c, 192 MeV/c).

&Delta M / &Delta p.

N&pi invariant mass resolution as a function of pion momentum if 1/&beta resolution is fixed to 0.1 . Note that nucleon momentum is fixed to 400 MeV/c, and N/&pi direction is fixed to be perpendicular.

Simulated &pi-momentum at &Lambda/&Sigma decay.

Hyperon Momentum Resolution (Distribution of Residual)

x,y,z momentum residual (real hyperon momentum - estimated value) distribution for &Lambda, &Sigma+, and &Sigma^-. Due to the hyperon life time (and energy loss effect?), pion momentum looks smaller, hence y component deviates from 0.