Today's Progress 13. Feb. 2007
4He(stopped K-, &Lambda p/n)X / 4He(stopped K-, &Sigma- p)X missing mass spectra and their relationship between YN invariant mass spectra
In this section, we use blue-colored letters to represent particles to which thier 4-momenta are well known/defined, while red-colored letters express the particles to which their 4-momenta are measured. Undetected particles are represented by black-colored letters.
In order to discriminate
K- + 4He -> &Lambda + n + (p + n) (1)
and
K- + 4He -> &Lambda + n + (d) (2)
final states, we construnt the missing mass spectrum, by the relationship from 4-momentum conservation,
p(stoppedK- + 4He) = p(&Lambda) + p(n) + p(p+n / d)
, where p(stopped K- + 4He) is now well-defined, p(&Lambda) and p(n) are measured quantities. Then, missing mass is defined as
(p(stoppedK- + 4He) - p(&Lambda) - p(n))2 = p(p+n / d)2 = (Mmiss)2 .
For the final state (2), we expect Mmiss = Md, regardless the primary reaction to produce &Lambda/n/d. Other events from
K- + 4He -> [&Sigma0 -> &Lambda(&gamma)] + n + (p + n) (3)
and
K- + 4He -> [&Sigma0 -> &Lambda(&gamma)] + n + (d) (4)
or pionic processes are not well discriminated in the procedure. Replacing the (&Lambda n) by (&Sigma-, p), we can study the (p+n) or (d) final states as well. Then, we do not have process (3)/(4).
4He(stopped K-, NY)X missing mass spectra constructed from p&Lambda/n&Lambda/p&Sigma- events.
NY invariant mass (horizontal) VS 4He(stopped K-, NY)X missing mass (vertical) constructed from p&Lambda/n&Lambda/p&Sigma- events.
From the correlation, it is clear that deuteron-like object appear only in the 'two-nucleon' region of the invariant mass.
Monte-Carlo simulations of the reaction K- 4He -> 2X0 + d / 2X0 + p + n / 2X+ + n + n
Since the measured missng mass means the total energy of the residual two nucleons in their CM system, the quantity should have a ceratin separation ability for the observed invariant mass strength. and, it is more meaningful than a simple separation of d/p+n final states. In order to investigate the correlation between invariant mass and missing mass for the dibarion signal, and to study the invariant mass ACCEPTANCE and RESOLUTION of the E549 setup for the possible dibaryon signal, we do need to simulate the reactions,
K- 4He -> X+ + n + n (1),
K- 4He -> X0 + p + n (2),
and
K- 4He -> X0 + d (3),
assuming the realistic setup geometry and detector resolution values.
The simulated decay modes are
X+ -> p + &Lambda (4),
X0 -> n + &Lambda (5),
and
X0 -> p + &Sigma- (6).
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 a finite TOF resolution value, 200psec, and x/y/z ambiguities are treated simultaneously.
3. A charged &pi (on TC) is detected with a finite TOF resolution value, 250psec, and energy-corrected. As the direction vector, detection by VDC is simulated, hence multiple scattering effect inside the cryostat is properly taken into account.
Conditions of the Monte-Carlo.
| X+/0 initial 4-momentum | X0 + d : 2 body phase space / X0 + p + n : 3 body phase space / X+ + n + n : 3 body phase space |
| X+/0 mass/width | 11 mass states with 10 MeV/c2 separation from 2200 to 2300 MeV/c2 with no width (kinematical simulation)/28 mass states with 10 MeV/c2 separation from 2065 to 2335 MeV/c2(realistic simulation) |
| formation branching ratio | X+ + n + n : X0 + p + n : X0 + d = 10:9:1(kinematical simulation)/1:2:2(realistic simulation) |
| decay branching ratio | X+-> p &Lambda : p&Sigma0 : n&Sigma+ 30%:35%:35%(above &Sigma N threshold ~ 2140 MeV/c2) / 100%:0%:0%(below 2140 MeV/c2) | X0-> n &Lambda : n &Sigma0 : p &Sigma- = 30%:35%:35%(above &Sigma N threshold ~ 2140 MeV/c2) / 100%:0%:0%(below 2140 MeV/c2) |
| x/y Kstop point distribution | 4.0 cm sigma Gaussian |
| z Kstop 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 | 250 psec (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. &Lambda decay point is treated as known. For &Sigma+-, X generation point, which differs from the actual decay point in general, is adopted as the decay vertex with infinite resolution. |
| hyperon life time | for &Lambda, PA-TC TOF is performed. For &Sigma^-, no correction is done. |
| software | GEANT 3.21 (+LEPS-g77 for energy loss correction) |
Result 1 - purely-kinematical consideration
Here we put purly-kinematical results, to which detector resolution/geometrical bias is not included. Then, n&Lambda and p&Sigma- are identical, as easily expected. A peak at deuteron mass position seen on n&Lambda/p&Sigma- comes from d final state.
Simulated missing mass spectra from 4He(stopped K-, X+->p&Lambda)nn and 4He(stopped K-, X0->n&Lambda/p&Sigma-)pn/d reactions. Black/red/green/yellow/magenta/sky-blue/dashed-black/dashed-red/dashed-green/dashed-yellow/dashed-magenta correspond to X mass 2300./2290./2280./2270./2260./2250./2240./2230./2220./2210./2200., respectively.
Simulated 2D correlation between missing mass and YN invariant mass from 4He(stopped K-, X+->p&Lambda)nn and 4He(stopped K-, X0->n&Lambda/p&Sigma-)pn/d reactions. Black/red/green/yellow/magenta/sky-blue/black/red/green/yellow/magenta correspond to X mass 2300./2290./2280./2270./2260./2250./2240./2230./2220./2210./2200., respectively.
Simulated X+/0 momentum spectra from 4He(stopped K-, X+->p&Lambda)nn and 4He(stopped K-, X0->n&Lambda/p&Sigma-)pn/d reactions. Black/red/green/yellow/magenta/sky-blue/dashed-black/dashed-red/dashed-green/dashed-yellow/dashed-magenta correspond to X mass 2300./2290./2280./2270./2260./2250./2240./2230./2220./2210./2200., respectively.
Simulated cos(YN) spectra from 4He(stopped K-, X+->p&Lambda)nn and 4He(stopped K-, X0->n&Lambda/p&Sigma-)pn/d reactions. Black/red/green/yellow/magenta/sky-blue/dashed-black/dashed-red/dashed-green/dashed-yellow/dashed-magenta correspond to X mass 2300./2290./2280./2270./2260./2250./2240./2230./2220./2210./2200., respectively. Now, a clear difference exists between n&Lambda and p&Sigma- final states. Due to the small Q-value, the &Sigma-p pair cannot have a large back-to-back momentum, hence the back-to-back correlation is substantially weak.
Simulated 2D correlation between YN invariant mass and total momentum from 4He(stopped K-, X+->p&Lambda)nn and 4He(stopped K-, X0->n&Lambda/p&Sigma-)pn/d reactions. Black/red/green/yellow/magenta/sky-blue/black/red/green/yellow/magenta correspond to X mass 2300./2290./2280./2270./2260./2250./2240./2230./2220./2210./2200., respectively.
Simulated hyperon(top panel) and nucleon(bottom panel) momentum spectra from 4He(stopped K-, X+->p&Lambda)nn and 4He(stopped K-, X0->n&Lambda/p&Sigma-)pn/d reactions. Black/red/green/yellow/magenta/sky-blue/dashed-black/dashed-red/dashed-green/dashed-yellow/dashed-magenta correspond to X mass 2300./2290./2280./2270./2260./2250./2240./2230./2220./2210./2200., respectively.
Result 2 - simulation with geometrical/efficiency/analysis bias and the realistic detector resolution
Intrinsic acceptance taking the geometry + detector efficiency
Now, we define intrinsic acceptance, by the following conditions:
The decay &pi+- fires VDC and TC_B.
The reaction/decay proton(s) fire PDC/PA/PB (no NT requirement at the stage).
The reaction/decay neutron(s) causes nuclear reaction NT (simulated by GHEISHA).
Then, invariant mass acceptance, being defined as
Acc.(Minv) = Detected event number / Generated event number (i.e. number of the cascade reaction number inside the 4He target),
are shown below for all reaction/decay modes.
It should be especially mentioned that the p&Lambda and p&Sigma- have similar accceptance, hence their invariant mass spectra can be directly compared. Now,
4He(stopped K-, YN)X missing mass
correlation between YN invariant mass and 4He(stopped K-, YN)X missing mass
YN total momentum
cos(YN)
correlation between YN invariant mass and YN total momentum
are shown in order.
NY invariant mass (horizontal) VS 4He(stopped K-, NY)X missing mass (vertical) constructed from p&Lambda/n&Sigma+/n&Lambda/p&Sigma- pairs.
2D correlation between YN invariant mass VS YN total momentum for p&Lambda/n&Sigma+/n&Lambda/p&Sigma- pairs.
Realistic acceptance and resolution curve
In the analysis, we impose various constraints to the detected neutron/proton/pion, and they can affect the acceptance/resulting correlations. Therefore, we explicitly activate the effects by:
Proton identification by 1/&beta VS total energy,
Neutron delta E threshold. 3 MeVee for n&Lambda/p&Sigma-, 5 MeVee for n&Sigma+-
Neutron TOF 1/&beta gate (1.6, 9) for n&Lambda/p&Sigma-, (1.6,7) for n&Sigma+-
&Lambda mass gate on the p&pi invariant mass spectra, (1108.,1124.)
&Sigma mass gate on the n&pi invariant mass spectra, (1150.,1225.)
Neutron momentum gate for &Sigma identification 300 MeV/c for p &Sigma- / n &Sigma+.
&Sigma mass. Since we cannot discriminate &Sigma+-, and it is actually limited to &Sigma- if pair-detected with a proton, &Sigma- mass is totally used for p&Sigma-/n&Sigma+-. Due to the 8 MeV/c2 difference, mass offset would be produced.
All of them are considered to act to decrease the acceptance from the intrinsic one simulated in the previous section.
Simulated resolution curve for &Lambda N/&Sigma N invariant mass spectra(black:K-+4He -> X+ + n + n red:K-+4He -> X0 + p + n, green:K-+4He -> X0 + d). The Nucleon/Hyperon 4-momenta are simulated with realistic resolution/geometry/methods, and the resulting mass residual is fitted by a Gaussian, and the standard deviation is defined as the invariant mass resolution here.
Simulated mass offset curve for &Lambda N/&Sigma N invariant mass spectra. The Nucleon/Hyperon 4-momenta are simulated with realistic resolution/geometry/methods, and the resulting mass residual is fitted by a Gaussian, and the mean is defined as the invariant mass offset.
Simulated acceptance curve for &Lambda N/&Sigma N invariant mass spectra, presented by identified event number divided by generated event number.
