Today's Progress 21. July. 2007

Acceptance study of inclusive &Lambda momentum and &Lambda d coincidence measurement

Momentum acceptance of inclusive &Lambda

Here, we simulate &Lambda momentum acceptance. The condition of the simulation is tabulatted below.

Conditions of the Monte-Carlo.
software GEANT3.21
generated &Lambda momentum range 200-820 (MeV/c)
generated &Lambda momentum distribution uniform
generated &Lambda angler distribution uniform on unit sphare i.e. cos&theta and &phi are uniform with no correlation
generated event number 2*108
target center (-0.3,0.,1.3):E549
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)
nuclear reaction of p/&pi on(GHEISHA)/on(FLUCA)/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
Analysis procedure for p/&pi selection p:properly simulated &pi:neglected
Evaluated &Lambda acceptance functions. Adopted conditions are - Black:no nuclear reaction without proton ID inefficiency/Red:nuclear reaction simulated by GHEISHA without proton ID inefficiency/Green:nuclear reaction simulated by FLUKA without proton ID inefficiency/Yellow:no nuclear reaction with proton ID inefficiency/Magenta:nuclear reaction simulated by GHEISHA with proton ID inefficiency/Sky-blue:nuclear reaction simulated by FLUKA with proton ID inefficiency.

We activate the result from GHEISA, since FLUKA result could be adopted as well. No significant difference is found.

&Lambda d/&Lambda n invariant mass distribution from &Lambda n d final states

Here, we simulate expected &Lambda d /&Lambda n invariant mass spectrum shape / acceptance from the reactions,

K- + 4He -> &Lambda + n + d (1),

K- + 4He ->2S0 + d, 2S0 -> &Lambda + n (2),

K- + 4He ->3S+ + n, 3S+ -> &Lambda + d (3).

On (1), the final state is generated according to 3-body phase space, just to examine expected spectrum shape.

Conditions of the Monte-Carlo.
software GEANT3.21
generated K-+4He at rest
generated final state &Lambda d n
generated medium state -/2S0/3S+
generated mass range 2S0:2055.~2345. MeV/c2/ 3S+:2995.~3285.(3281.) MeV/c2
dynamics uniform on 3-body phase space/on 2-body+2-body(2S0,3S+)
generated event number 1.0*108 for 3-body phase space/2.0*107 per 10 MeV/c2 for 2S0/3S+
target center (-0.3,0.,1.3):E549
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)
nuclear reaction of d/p/&pi on(GHEISHA)
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
Energy resolution of PB/NT infinite
Analysis inefficiency for p/d/&pi selectionp:properly simulated / d:properly simulated / &pi:neglected
Analysis inefficiency for p/d/&pi energy correctionneglected
Analysis inefficiency for &Lambda reconstructionneglected

4He+K- -> &Lambda n d (3-body phase space)

&Lambda n d final state is uniformuly generated on 3-body phase space. Generated strength distribution on a Dalitz plot is as below. By definition, the distribution is uniform within allowed M&Lambda d VS M&Lambda n area.

A Dalitz plot of generated event.
A Dalitz plot of detected event.

The resulting &Lambda d invariant mass spectrum shapes are shown below.

Black: With setup bias. p/d/&pi triple coincidence on side arms, and VDC+VTC arm are required.

Red: Requirements for black + proton/deuteron selection inefficiency by analysis.

Green: cos(&Lambda d)<-0.6.

Magenta: No requrements.

Spectrum shape evaluated from 3-body phase space. Spectrum are is normalized to 1.0 for all to discuss thge shape.

Expected deuteron momentum VS &Lambda momentum is shown below.

4He+K- -> 3S++n, 3S+->&Lambda d

Generated strength distribution on a Dalitz plot is as below. The distribution shows strong dependent on the position within allowed M&Lambda d VS M&Lambda n area now.

A Dalitz plot of generated event.
A Dalitz plot of detected event.

Expected deuteron momentum VS &Lambda momentum is shown below. For &Lambda n d final state, we expect 1-to-1 correspondance between deuteron and &Lambda momenta for given &Lambda d invariant mass = S+ mass.

4He+K- -> 2S0+d, 2S0-> &Lambda n

Generated strength distribution on a Dalitz plot is as below. The distribution shows strong dependent on the position within allowed M&Lambda d VS M&Lambda n area now.

A Dalitz plot of generated event.
A Dalitz plot of detected event.

Expected deuteron momentum VS &Lambda momentum is shown below. The M&Lambda d is uniquely determined by deuteron momentum, in this case.

Process dependence of &Lambda d/&Lambda n mass acceptances

In the stopped K- reaction, the acceptance is the function of the length of the pd, p&Lambda, and opening angle &theta&Lambda d from the spherical symmetry of the reaction, in general. In the 3-body reaction, &theta&Lambda d is uniquely determined kinematically if pd and p&Lambda, hence acceptance is determined as a 2-variable function of pd and p&Lambda, in the other word, uniquely detemined on the Dalitz plot M&Lambda d VS M&Lambda n. For given M&Lambda d, various M&Lambda n values are kinematically allowed - it leads process dependence of M&Lambda d if acceptance is just defined, as done in the FINUDA experiment, as the 1-variable function of M&Lambda d,

&epsilon(M&Lambda d)=D(M&Lambda d)/G(M&Lambda d),

where D(M&Lambda d),G(M&Lambda d) are detected and generated event numbers in each bin. Of cource, the situation is same for M&Lambda n. Therefore, the acceptance defined as 1-variable function of masses are not generally applicable, even for the easiest 3-body case. The situation is shown below.
&Lambda d mass acceptances as defined above. Black:uniform on 3-body phase space / Red:3S+ / Green:2S0 (2105-2155 MeV/c2)/ Magenta:2S0 (2205-2255 MeV/c2)
&Lambda n mass acceptances as defined above. Black:uniform on 3-body phase space / Red:2S0 / Green:3S+ (3095-3135 MeV/c2)/ Magenta:3S+ (3245-3285 MeV/c2)