# Presentation: 225882

## Search for Pentaquark in Low Energy Kaon Beam

- Norihito Muramatsu
- RCNP, Osaka University

- Mini-Workshop on Kaon Experiments and Detectors,
- 5-7 Nov 2004, Mikata

## Pentaquark Search at E949

- Resonance formation reaction
-    K+n→KS0p→π+π-p
-    ‐P(K+)=440 MeV/c
-    ‐neutron in Sci. Tgt.
- π+π-p detection
-       at UTC (and others?)
-   M(π+π-)=M(KS0)
-       ⇒ M(KS0p)=M(Θ+)
- π+π- detection at UTC
-   M(π+π-)=M(KS0)
-   MM(K+,π+π-)=M(p)
-   ⇒ M(K+n) with Fermi-correction

**TOF**
**Δv/v=Δt/t, v=L/t, Δt=200 psec **
**⇒ ****L=4 m is equivalent to σ=8.4 MeV**
**K/π separation : ~6 nsec**

**π****+**

**π****-**

**proton**

**K****+**** ****beam**
**440 MeV/c**
** ****σ=8.4 MeV**

**ΔP/P=1.3%**

## Toy MC simulation

- 440 MeV/c K+ beam in z-direction
- Fermi motion of neutron inside carbon by harmonic oscillator model.
- Breit-Wigner resonance
-   M=1540 MeV and Γ=10 MeV
- Flat generation of KS0 and proton at CMS
- Flat generation of π+ and π- at KS0 rest frame
- Lorentz transformation to Lab frame

## Kinematics in π+π- detection mode

**π****+**

**π****-**

**K****S****0**

**proton**

**Momentum (GeV/c)**

**Polar Angle (rad)**

**cos****θ****(K****S****0****) at CMS**

**All**

**z=0 cm**

**z=****-****10 cm**

**z=****-****20 cm**

- Backward production at CMS (26 mb for Γ=1 MeV)
-         vs.
- CEX BG (forward peaked, 7 mb in PRD15 (1977) 1846)

## Experimental Considerations

- Acceptance determination
- CMS energy resolution for mass measurement
-   M(K+ and rest neutron) with Fermi corr. - true ECMS
-   ⇒ Validity check of Fermi corr.
- See initial works at http://www.phy.bnl.gov/e949/
-   analysis/pentaquark

**  ****X**
** ****‐****10**

** ****X**
**‐****20**
**target**
**front **
**edge**

**UTC**

**X**
**0 cm**
**target**
**center**

**|****z****|<****25 cm**

**43.1 cm**

**z**

## Geometrical Acceptance Measurement

- In case that π+π- or π+π-p are detected at UTC
-            two pions (KS0)       two pions + proton
-   z=  0 cm   0.1235±0.0023   0.0006±0.0002
-    ‐10 cm   0.1242±0.0023   0.0182±0.0009
-    ‐20 cm   0.1056±0.0021   0.0602±0.0017
- In case that P(K+) resolution = 8.4 MeV, UTC resolution = 1.3% and RMS of beam dist. = 4 cm
-            two pions (KS0)       two pions + proton
-   z=  0 cm   0.1282±0.0023   0.0003±0.0001
-    ‐10 cm   0.1192±0.0023   0.0180±0.0009
-    ‐20 cm   0.1062±0.0021   0.0616±0.0017
-   ⇒ No big change in the realistic case

## Acceptances with proton detection

- In case proton is detected at inner two layers of UTC.
-   |z-position at r=30 cm|< 25 cm is assumed.
-   P(K+) resolution, UTC resolution and beam dist. are included.
-            two pions + proton
-   z=  0 cm    0.0045±0.0005
-    ‐10 cm    0.0427±0.0014
-    ‐20 cm    0.0831±0.0019 Not so enhanced
- In case that proton Is detected at sci. target.
-   θproton < 0.3 rad by assuming Rproton ~ 20 cm
-            two pions + proton
-   z=  0 cm    0.0436±0.0004 How about resolution?
-    ‐10 cm    0.0177±0.0009
-    ‐20 cm    0.0013±0.0003
- Range counter instead of End-Cap?

## Fermi Correction

- Analytical Formula
- But some approximations...
-    Ef=Mn+Pf2/(2Mn) and neglect Pf2 terms
-    cosθ(K+)/cosθ(K+-KS0)=1
-     ⇒Valid for backward KS0 productions (z=0 cm)

**|****z(r=43.1 cm)****|< ****25 cm**

**cos****θ****(K****+****)/cos****θ****(K****+****-****K****S****0****)**

**MM(K****+****,π****+****π****-****)**

**True CMS energy M(K****+****n)**

**All events**

## CMS energy resolution

- No beam & detector resolutions
-                   All fitting range     -0.015~0.015
-         11.11±0.12  8.31±0.12 MeV
- Changing beam res. with UTC res. 1.3%
-  8.4 MeV 11.61±0.12  8.74±0.12 MeV
-   20 MeV 12.91±0.11 10.94±0.21 MeV
-   30 MeV 14.26±0.11 12.31±0.29 MeV
-   40 MeV 15.77±0.11 14.28±0.45 MeV
-   50 MeV 17.62±0.12 17.11±0.78 MeV
- Changing UTC res. with beam res. 8.4 MeV
-       1.3% 11.61±0.12  8.74±0.12   5.07±0.17 MeV
-    3.0% 13.00±0.12 10.31±0.18 10.79±0.46 MeV
-    4.5% 14.91±0.13 12.45±0.31 15.65±0.83 MeV
-    6.0% 17.29±0.15 14.80±0.51 22.88±1.35 MeV
- 10 MeV resolution is retained in the realistic case

- π+π-p detection
-         at UTC

## P(K+)=442 MeV/c for M(Θ+)=1.540 GeV
                                but
    P(K+)=417 MeV/c for M(Θ+)=1.530 GeV (world ave.)
True CMS energy is spread by ~50 MeV 
    because of neutron Fermi motion

   Beam Momentum should be
   adjusted at ~20 points
   in each 10‐20 MeV/c

-                                 but
-     P(K+)=417 MeV/c for M(Θ+)=1.530 GeV (world ave.)
- True CMS energy is spread by ~50 MeV
-     because of neutron Fermi motion
-    Beam Momentum should be
-    adjusted at ~20 points
-    in each 10‐20 MeV/c

- Beam Momentum Setting

**True CMS energy M(K****+****n)**

## Summary

- Existence of pentaquark can be confirmed by E949 detector. (There are many null results in high energy experiments.)
- Two pion detection at UTC seems promising.
-     (Geometrical acceptance ~10%)
- Two pion + proton detection at UTC may be analyzed
-     for z=-20 cm.
- 10 MeV ECMS resolution can be achieved in two pion detection mode with Fermi correction. (Nakano suggested MM(K+,π+π-)>0.97 reduced ECMS res. to 6 MeV with a cost of 80% acc. loss and slight peak shift.) Note that energy resolution with two pions + proton detection is 5 MeV.
- Beam momentum setting: ~20 points in each 10-20 MeV/c.