Today's Progress 1. Dec. 2007

back-to-back dd correlation and ⁴_&LambdaHe -> dd decay

According to Outa-san's suggestion, we perform a serch for the exotic two-body decay modes of ⁴_&LambdaHe produced in the reaction,

⁴He+K^-_stopped ->⁴_&LambdaHe+&pi^- (~255 MeV/c,~1.8%).

The target channels are

⁴_&LambdaHe(0~255 MeV/c) -> d+d (1),

⁴_&LambdaHe(0~255 MeV/c) -> t+p (2),

⁴_&LambdaHe(0~255 MeV/c) -> ³He+n (3),

Among them, channel (1) and (2) are not reported yet, while (3) is already known. We try to see yet unfound channels (1) and (2).

dd coincidence spectra

deuteron 3-momentum

correlation of deuteron 3-momenta on L and R arm

dd opening angle

deuteron 3-momentum VS dd opening angle

dd invariant mass

dd total 3-momentum

Invariant mass VS total 3-momentum

Invariant mass VS opening angle

Acceptance study for the hypernuclear cascade process

In order to estimate the acceptance of the hypernuclear formation process,

⁴He+K^-_stopped ->⁴_&LambdaHe+&pi^- ,

and two-body decay

⁴_&LambdaHe -> d+d (1),

⁴_&LambdaHe -> t+p (2),

⁴_&LambdaHe -> ³He+n (3),

In order to estimate acceptance Acc(i) defined as,

N_detected(i) = N_produced(i)*Acc(i),

we perform a realistic Monte-Carlo simulation. Here, i describes decay channels listed above, and conditions on the simulation are as shown below.

Conditions of the Monte-Carlo.
software	GEANT3.21(partice tracking tuned for slow particles)
Formation reaction	K^-_stopped+⁴He->⁴_&LambdaHe + &pi^-(254.6 MeV/c with 4_&LambdaHe mass shown below)
⁴_&LambdaHe mass	M_³He(2809.23)+M_&Lambda(1115.684)-2.39 = 3922.5 (MeV/c²)
⁴_&LambdaHe decay modes/bracnhing ratio on the simulation	d+d:t+p:³He+n=40%(573.2MeV/c):40%(509.1MeV/c):20%(507.4MeV/c)
⁴_&LambdaHe Life time	257 psec (from Dr. Outa's thesis)
Generated number of ⁴_&LambdaHe	2*10⁷
Target center	(-0.3,0.,1.3):E549 (-0.5,0.5,1.2):E570 by cm unit.
x/y generation point distribution	4.0 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)
In-flight nuclear reaction of d	on(GHEISHA,unique selection for in-flight loss for d)/off
Coincidense time gate for PA-PB	45 nsec
Birk's coefficient for plastic scintillator	0.013/(MeV/cm)
Time resolution of PA/PB	60/80 psec
Proton/Deuteron selection	Simulated with 1/&beta VS total Light output (with infinite energy resolution).
PDC hit	Only 1 particle is accepted. Multi track events (p+&pi^-,etc) are eliminated.

Some quality plots of the Monte-Carlo with 10⁶ events

Momentum distribution of ⁴_&LambdaHe at the decay. ~86.4% decay at rest.

TOF of ⁴_&LambdaHe before stopping if they decay AFTER stopping.

Range spectrum of ⁴_&LambdaHe.Its tipical range is ~0.5mm in ⁴He.

Decay timing spectrum. The decat timing is defined as the time difference between formation and decay of ⁴_&LambdaHe regardless the status at the decay.

Range spectra for ³H and ³He within super-fluid ⁴He. Tritons can fire the PA, while ³He cannot.

Results

As already demonstrated, d+d decay channel is clearly visible by back-to-back coincidence. As expected from the range spectrum, p+t channel would be barely seen with the triton stops on PA leaving a charged particle track on PDC, in coincidence with a proton with 509 MeV/c momentum detected on the opposite arm. Therefore, we try to find those rare decay events, as the followings.

1. dd events - back-to-back dd coincidence on PDC/PA/PB,

2. pt events - p on PDC/PA/PB and t on PDC/PA on the opossite arm.

In these conditions, simuated decay vertex and cos(dd/pt) distributions with the geometrical bias are exhibited below. The red spectra orignate from stopped ⁴_&LambdaHe decay.

Simulated decay vertex and cos(dd) distribution for dd events.

Simulated decay vertex and cos(pt) distribution for pt events.

The numerical results are tabulatted below.

Generated and Accepted Event Number
For the column 2,3,4, we have three numbers. The first number just originates from the geometrial coverage. The second number is the one constrained by the limitation of the 45 nsec time gate for PA-PB TOF. For the third number, proton/deuteron selection efficiency by 1/&beta VS total energy is imposed in addition. The numbers within round brackets are those from decay of stopped ⁴_&LambdaHe to appear with monochromatic momenta on p/d momentum spectra.
Decay channel generated event No. of decay (*1) Measured event No. on PB(d/p) (*2) Measured event No. on PA(d/t)+PB(d/p) (*3) Measured event No. on PB(d/p)+PB(d/t) (*4)

d+d(without hadron reaction) 7635400 703873(603074)/695043(595754)/688255(590268) 366362(327125)/365965(326879)/365246(326328) 296782(274640)/282289(261620)/277716(257313)

d+d(with hadron reaction) 7636610 650137(558825)/641243(551386)/626000(539606) 295130(263590)/294349(262975)/291540(260858) 225673(208950)/214377(198814)/205161(190317)

p+t(without hadron reaction) 7636930 548822(473560)/548822(473560)/490189(423026) 32979(25812)/32979(25812)/31681(24950) 629(35)/344(7)/312(7)

p+t(with hadron reaction) 7632840 534272(461071)/533814(460677)/427815(369623) 30053(23650)/30029(23633)/26077(20590) 552(33)/320(5)/260(4)

Notes:

Generated and Accepted Event Number
For the column 2,3,4, we have three numbers. The first number just originates from the geometrial coverage. The second number is the one constrained by the limitation of the 45 nsec time gate for PA-PB TOF. For the third number, proton/deuteron selection efficiency by 1/&beta VS total energy is imposed in addition. The numbers within round brackets are those from decay of stopped ⁴_&LambdaHe to appear with monochromatic momenta on p/d momentum spectra.
Decay channel	generated event No. of decay (*1)	Measured event No. on PB(d/p) (*2)	Measured event No. on PA(d/t)+PB(d/p) (*3)	Measured event No. on PB(d/p)+PB(d/t) (*4)
d+d(without hadron reaction)	7635400	703873(603074)/695043(595754)/688255(590268)	366362(327125)/365965(326879)/365246(326328)	296782(274640)/282289(261620)/277716(257313)
d+d(with hadron reaction)	7636610	650137(558825)/641243(551386)/626000(539606)	295130(263590)/294349(262975)/291540(260858)	225673(208950)/214377(198814)/205161(190317)
p+t(without hadron reaction)	7636930	548822(473560)/548822(473560)/490189(423026)	32979(25812)/32979(25812)/31681(24950)	629(35)/344(7)/312(7)
p+t(with hadron reaction)	7632840	534272(461071)/533814(460677)/427815(369623)	30053(23650)/30029(23633)/26077(20590)	552(33)/320(5)/260(4)

*1 For both channel, all decay events within the target cell are counted.

*2 For dd channel, if at least 1 deuetron is measured on PDC/PA/PB, then the number is inclemented. For tp channel, the proton is examined in a same way, regardless the status of t measurement, to estimate possible signal number on the inclusive spectrum.

*3 For tp channel, the triton detection on PA is defined by PDC/PA fire, in coincidence with the proton detection on opossite PDC/PA/PB arm. In this case, PA-PB timing gate and analysis efficiency are considered only on p side. For the comparison, the similar measurement on dd channel is simulated. In this case, PA-PB timing gate and analysis efficiency are considered only the deuteron detected on the opposite side.

*4 For both channels, PDC/PA/PB hits are required on both particles. Timing gate and analysis efficiency is considered on both arm simulateously.

From the result, a rough estimation of reaction fraction Br of ⁴_&LambdaHe -> d+d (1) is given by the equality,

N_{stopped K}*Br*Acc*&epsilon_DAQ~N_detect

Br~N_detect/(Acc*&epsilon_DAQ*N_{stopped K})~6.0*10¹/((205161/7636610)*0.8*2.5*10⁸*)=1.1*10^-5(/stopped K^-)

The acceptance of monochromatic triton from

⁴_&LambdaHe -> t+p (2),

is only ~10% of that of dd pair. Therefore, we expect ~6 events requiring a counter-detected triton, assuming identical decay ratio.