Today's Progress 29. Apr. 2010

Final evaluation of per-stopped-K^- formation rate of ⁴_&LambdaHe -> d + d decay

Raw dd coincidence spectra

dd momenta of both arms.

Correlation of dd momenta

Opening angle of dd 3-momenta

dd invariant mass (red-shaded:cos(dd) < -0.990). Shaded 57 events are identified as dd decay events.

Deuteron 3-momentum VS dd opening angle

Total 3-momentum of detected dd pair

Invariant mass VS total 3-momentum of dd

Invariant mass VS opening angle

Acceptance study for the hypernuclear cascade processes

(⁴He-K^-)_atomic ->⁴_&LambdaHe+&pi^- (255.4 MeV/c) ,

⁴_&LambdaHe -> d+d (1 : 571.8 MeV/c),

⁴_&LambdaHe -> t+p (2 : 508.4 MeV/c),

⁴_&LambdaHe -> ³He+n (3 : 507.4 MeV/c).

The particle and nulcear mass table for the calculation of decay momentum is given below. It should be noted that the nuclear masses defined in GEANT3 is sometimes different from the exact values taken from here .

The normalization of dd mode

Since the dd decay mode was observed, the exact normalization is performed by

, where

In order to estimate physical acceptance &epsilon^-_dd defined as,

N_detected = N_produced*&epsilon^-_dd,

The upper limit evaluation of tp mode

On the other hand, tp decay mode was not observed. Then, the upper limit with a certain confidence lecel is evaluated by

In order to estimate physical acceptance &epsilon^-_tp defined as,

N_detected = N_produced*&epsilon^-_tp,

Properties of the process

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

TOF of ⁴_&LambdaHe until stopping if they decay at rest.

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

Decay timing spectrum. The decay timing is defined as the time difference between the formation of K^--⁴He atom and the decay of ⁴_&LambdaHe regardless the status (in-flight or at rest) at the decay. The lifetime is found to be 257 psec by the fitting of an exponential function.

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

Results

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.

Simulated decay vertex and cos(dd) distribution for dd events. Event selection procedure of deuteron is applied on both arm as done for data.

Simulated decay vertex and cos(pt) distribution for pt events. proton slection procedure is applied as done for data, and t on PA is required on the opposite arm.

Simulated deuteron momentum distribution by ⁴_&LambdaHe->dd events on the left arm. The top is constructed from the event set if a deuteron is detected and identified with successfull energy loss correction on the left arm. In the bottom, we further require detection and identification of another d in the counter-PDC-PA-PB R arm, which directly corresponds to the measured momentum spectrum presented above. The blue shows the whole events, while the red shows the events from stopped ⁴_&LambdaHe decay. The Gaussian fitting to the bottom-red gives ~2.0 MeV/c as the standard deviation. Linear-scale and log-scale figures are presented simultaneously.

Simulated proton momentum distribution by ⁴_&LambdaHe->tp events. The top is constructed from the event set if a proton is detected and identified with successfull energy loss correction. In the bottom, we further require detection of t in the counter-PDC-PA arm. The blue shows the whole events, while the red shows the events from stopped ⁴_&LambdaHe decay. The Gaussian fitting to the bottom-red gives ~4.8 MeV/c as the standard deviation.

The step-by-step evaluation of &epsilon_dd and &epsilon_tp are tabulatted below:

Finalized per-stopped-K^- branching ratio of dd mode

(⁴He-K^-)_atomic-> &pi^-+⁴_&LambdaHe,

⁴_&LambdaHe-> d+d,

Br((⁴He-K^-)_atomic-> &pi^-+⁴_&LambdaHe ; ⁴_&LambdaHe -> d+d)=1.34±0.19(syst)±0.18(stat)×10^-5 (per stopped K^-).