Today's Progress 6. May 2010

2010 May 6th report - Final evaluation of per-stopped-K^- upper limit of ⁴_&LambdaHe -> p + t decay

Here, we try to finalize the upper limit study of ⁴_&LambdaHe -> p + t decay branch.

Updated acceptance study (Monte-Carlo)

First, we try to finalize the acceptance. The statistics of Monte-Carlo simulation to calculate the acceptance shown in the 2010 Apr 29th report was in sufficient for tp mode, and we have enlarged it 25 times here.

Generated and Accepted Event Numbers for tp mode
Starting from the column 4, we add additional selection as described on the top row. The numbers rounded by brackets are from decay at rest. &epsilon_tp is then just defined by the bold number in the 8th colmun divided by the number in the 3rd colmun.
Cycle	Life time (psec)	generated event No of tp decay.	PDC-PA-PB hit of p	PDC-PA hit of t	time gate (45 nsec) + selection on analysis (p only)	Successful energy loss correction (p only)	cos(tp)<-0.99	&epsilon_tp(%)
E549	232	1.8895416E+08	-	740362(570127)	642396(496060)	637633(492297)	499749(477632)	2.528E-01
E549	250	1.8895361E+08	-	738132(579689)	640468(504627)	635566(500762)	506506(485865)	2.571E-01
E549	268	1.8895180E+08	-	733195(583838)	636324(508026)	631397(504089)	508618(488939)	2.588E-01
E570	232	1.8761316E+08	-	541124(399588)	469644(348116)	465385(344930)	351037(332833)	1.774E-01
E570	250	1.8761066E+08	-	539376(406423)	468667(354368)	464557(351215)	356077(338855)	1.806E-01
E570	268	1.8760907E+08	-	533959(409987)	463683(357008)	459468(353735)	357483(341367)	1.820E-01

Triton selection procedure by T0-PA 1/&beta VS energy deposit on PA (data analysis)

Since tritons from pt decay, with ~508MeV/c, hardly reach to PB, we are interested in to the proton-X coincidence events, for which the proton is idenitified by PA-PDC-PB-NT arm, while X stopped in PA. In order to extract pt coincidence events among them, we intend to perform particle identification only with PA information.

To avoid possible ststematic deviation of velocity by hypernuclear lifetime, we examine PA-PA TOF analysis for Larm-Rarm charged coincidence events. When the particles can reach PB, particle identification is feasible, and hence we can check 1/&beta VS dE/dx correlation for proton and deuteron events helped by those events in which p and p or p and d reached PB simultaneously. Below, we show the correlation between PA-PA 1/&beta VS dE/dx on PA for the events in which a proton was detected by counter PA-PDC-PB-NT arm.

PA-PA 1/&beta VS dE/dx on PA, for counter-proton-coinsidence events (E570). The blue is deuteron under proton coincidence, and the yellow is proton under proton coincidence, in which PID is supplyed by PB-NT on the side of interested PA arm. The black is proton-X coincidence events which we are interested in. The red curve is the phenomenologically given aggressive border between p/d and triton-like events, while the green is very conservative one to eliminate only p-p events.

PA-PA 1/&beta VS dE/dx on PA, for counter-proton-coinsidence events (E549). The same border is commonly available.

We have defined phenomenologically the border of triton-like events and others. The aggressive border to eliminate stopped deuteron events (red curve) is given as

dE/dx = 22.0×exp{-(β^-1-4.0)/1.8} -2.0,

and the conservative one is

dE/dx = 22.0×exp{-(β^-1-3.0)/1.6} -2.0,

by which stopped deuteron events are also involved in the triton-like events. Adopting these two selections, we examine proton spectrum under triton coincidence condition.

&Lambda momentum spectrum under triton coincidence condition

Here, we try to examine the triton identification by studying the Λt coincidence spectrum. If triton is selected succsessfully, we might observe monochhromatic Λ peak by the two-body process,

(⁴He-K^-)_atomic -> Λ + t,

at &Lambda momentum of ~712 MeV/c. The four-nucleon process is known to have the branching ratio, 3±2×10^-4 (R. Roosen and J. H. Wickens, Nuovo Cimento 66 101 (1981).), under the assumption that all 3 events are rightly from the reaction, not from the Λdn final state. First, we show p-π invariant mass spectrum under p+&pi + t coincidence condition below. By classifying with the consistency between the direction of the 3-momentum and deviation of decay vertex and incident kaon track, we observe Λ particle succsessfully with nice S/N ratio for the triple coincidence events. Then, the opening angle between idenfified &Lambda and triton is studied. The back-to-back correlation is strong, and the event is clastering to cos(Λt)<-0.98.

p&pi invariant mass and cos(Λt). The definition of Λ event is given by red-filled area. The red and green consist of classified events by consistency between the direction of the momentum and the deviation of the decay vertex from the incident kaon track to get better S/N ratio on the mass spectrum. We observe a strong back-to-back correlation between Λ and triton.

Lastly, we show the &Lambda momentum spectrum and its classification. We observe a monochromatic strong peak at around ~700 MeV/c, and this peak structure appears only if the p-&pi is from real Λ decay, and only if cos(Λt)<-0.98 . Therefore, this peak is attributed to the four-nucleon process, (⁴He-K^-)_atomic -> Λ + t. The event selection defined above to exclude stopped deuteron confidently involves stopped triton, and hence we adopt is also for the upper limit study of pt decay mode of ⁴_&LambdaHe.

Total 3-momentum of p+π system detected in coincidence with backward triton. Black:All, Red:1108- track.

Total 3-momentum of "&Lambda"+t events. The Black is all, and the red is by the events with cos(Λt)<-0.98. The blue is by the events with cos(Λt)>-0.98.

Proton momentum spectrum under triton coincidence condition and upper limit estimation of tp decay mode

Since triton selection was established, we now perform the upper-limit estimation by count-number basis. The procedures are as follows:

1. Constructing the proton spectrum in coincidence with t with cos(tp)<-0.99, to which the detection efficiency had been evaluated by Monte-Carlo calculation.

2. Fit a Gaussian and a BG function to the proton spectrum, and deduce the possible upper limit of the Gaussian area. The upper limit gives the count-number-basis upper limit.

As the first step, we show the distribution of cos(tp) and proton momentum below.

Distribution of cos(tp)

Proton momentum spectra for tp events. The filled spectrum is constructed from the events with cos(tp)<-0.99, and the spectrum is used for the estimation of upper limit.

To start the fitting, we do need some consideration on

the treatment of peak center,

the treatment of standard deviation,

fitting region,

the background shape.

We constrain the peak area to be equal or more than 0.0.

The treatment of peak center

Since the binding energy of the hypernucleus is not very precisely known, and our momentum decision also involves some inaccuracy, we do need to allow a degree of freedom of the peak center. Now, we allow the peak center to shift by -10 or +5 MeV/c from the expected center of 508.4 MeV/c. -10 +5 MeV/c on the proton momentum is considered to be large enough from the monochromatic peak position from (⁴_ΛHe-K^-)_atomic-> t + Λ reaction observed avobe. Thus, we perform the fitting for every 0.1 MeV/c sweeping over from 498.4 MeV/c to 513.4 MeV/c fixing the peak center.

The treatment of standard deviation (resolution)

The standard deviation is calculated to be 5 MeV/c forgetting the dependence on the light output. However, we expect two different light-output-dependent effects in overall resolution - namely, the segment-by-segment scattering of TOF offset and light-output-dependence of the intrinsic resolution. Therefore, we cannot help considering possible deviation. Since the enrgy loss of the 508 MeV/c proton at the generation is ~20 MeV equiv. on PB counter, possible deviation is considered to be within 20%, from the 2007 Apr 26th report, in which light output dependence is studied in a systematic way. Therefore, we keep the σ within (4.0,6.0) MeV/c.

The fitting region and the background shape

The fitting region is taken to be (508-30, 508+30) MeV/c to cover ± 5~8σ region but not to be too wide. In total, it covers 13 bins. For the narrow region, low-order polinomial can approximate any function well, so we examine only the second and the third order polinomials as the BG shape, so that the DOF of the fitting is 13 - (1(fixed σ)/2(varied σ) + 3(2nd order)/4(3rd order)). This is equivalent to the hypothesis of smooth and slowly-fluctuating BG. The "slowly" means the slowly varying BG than the narrow signal.

Derived upper limit

The results of the fitting procedure discussed in detail above, are given here. We examined fixed (at 4,5,6 MeV/c) and freely baried σ within (4,6) MeV/c with two BG functional shapes, so that 8 results are presented for the completeness. The BG function and Gaussian area (and σ if it is treated as a fitting parameter) are simultaneously derived by the fitting procedure.

The best-fit values of Gaussian area are given below as the functions of the measured proton momentum. It commonly takes a maximum of ~6 at around 505 MeV/c, and it takes negative values in a certain momentum region depending on the setting of the procedure. The value, 6, corresponds to the branching fraction of (1.6±0.2(syst)) × 10^-5.

Fitted area (properly normalized to the count number).

The count-number-basis upper limit is given below, as the functions of measured proton momentum. If we take the maximum values of the 8 curves in the momentum region (498.4, 513.4), we obtain 34.9 counts as the 95% C.L. upper limit for σ=6 MeV/c at 513.4 MeV/c. The 95% C. L. upper limit, C_U.L. is defined by

C_U.L. = S + 1.96S_σ,

where S is the best-fitted area, and the S_&sigma is attributed 1-standard-deviation statistical error of S. Substituting the C_U.L. to the equation to get the percent-per-stopped-K^- upper limit, we obtain

Br((⁴He+K^-)_atomic -> π^- + ⁴_&LambdaHe ; ⁴_&LambdaHe -> t+p)_U.L. = 1.1 × 10^-4,

where systematic error of 14% is considered by multiplying the factor 1.14 to the calculated upper limit by using the central value of the scaling factor.