1. Roman Mizuk (ITEP, Moscow) Search for the Θ + pentaquark using kaon secondary interactions at Belle Outline Detector, idea Search for inclusive production of Θ(1540) + Search for exclusive production of Θ(1540) + WS “New Hadrons: Facts and Fancy” Milos, Greece 19-20 September 2005

2. 2 KEKB and the Belle detector ~1 km in diameter  / K L detection 14/15 lyr. RPC+Fe Central Drift Chamber small cell +He/C 2 H 5 CsI(Tl) 16X 0 Aerogel Cherenkov cnt. n=1.015~1.030 Si vtx. det. 3 lyr. DSSD TOF conter SC solenoid 1.5T 8 GeV e - 3.5 GeV e + Belle detector Mt. Tsukuba KEKB Belle 8 GeV e - x 3.5 GeV e + L peak = 1.58 x 10 34 sec -1 cm -2 Integrated Luminosity L = 467 fb -1

3. 3 e + e - annihilations near Υ(4S) provide an abundant source of kaons. Small fraction of these kaons interacts in the detector material  use these secondary interactions to search for Θ(1540) +. K + interactions are in the low energy domain, where most of the Θ(1540) + evidences are reported. Idea momentum (GeV/c) N / 50 MeV 20cm Schematic view of event with secondary interaction Momentum of primary K ±

4. 4 Selection of secondary pK pairs protons and charged kaons –DO NOT originate from e + e - interaction point –positively identified based on dE/dx, TOF and Cherenkov information K S –  +  - detached vertex –momentum IS NOT pointing to e + e - interaction point –significant impact parameters of daughter tracks Common pK vertex –detached from e + e - interaction point: 1<R<11cm.

5. 5 XY distribution of secondary pK S vertices in data. Clear picture of detector structures  selected pK vertices are dominated by secondary interactions. y (cm) x (cm) SVD1 155fb -1 “Tomography” of the detector SVD2 242fb -1

6. Search for inclusive production of Θ(1540) +

7. 7 m (GeV/c 2 ) N / 2 MeV/c 2 pK S pK - Mass spectra for secondary pK pairs Fit m(pK - ) to D-wave BW  resolution function + threshold function  N(Λ(1520)) = (4.1±0.1)·10 4, m = 1518.4 ± 0.1 MeV/c 2 Γ = 13.5 ± 0.4 MeV consistent with PDG  1519.5 ± 1.0 15.6 ± 1.0

8. 8 Λ(1520) production mechanism p K-K- Λ(1520) p K-K- formation  p Λ(1520)  400 MeV/c p K-K- Λ(1520) p K-K- production Λ(1520) momentum spectrum is hard  inelastic production dominates. formation p Λ(1520) (GeV/c) N / 0.2 GeV/c 2 Λ(1520) momentum

9. 9 Λ(1520) production mechanism (2) distance, cm 1 / 0.5cm peak at zero  vx w/ additional track Additional track is found in ~0.5 of Λ(1520), additional K + - in only 0.5% of Λ(1520). Strangeness conservation  Λ(1520) produced by strange projectile. Distance from pK - vertex - to nearest track - to nearest K + Contribution of interactions of Λ’s < a few percent (  flux, cross section). K N  Λ(1520) X  Λ(1520) is produced in kaon induced inelastic reactions

10. 10 N(Θ + ) Mass spectrum for secondary pK S pairs Upper Limit Yield m (GeV/c 2 ) Fit m(pK S ) to resolution function (σ~2MeV/c 2 ) + 3 rd order polynomial  N(Θ + )<320 at the 90% C.L. for wide range of possible Θ(1540) + masses. m (GeV/c 2 ) N / 2 MeV/c 2

11. 11 Upper limit on cross section ratio <2.5% at the 90% C.L. ε pKs /ε pK+ from MC assuming that Θ + and Λ(1520) kinematics is similar. ε pK+ ε pKs N Θ+ N Λ* B(Λ(1520)  pK - ) B(Θ(1540) +  pK 0 ) B(K 0  K S  π + π - ) = ExperimentReactionEnergyσ(Θ + )/σ(Λ*) CDF pp  Θ + X 1960 GeV<3% HERA-B pA  Θ + X 42 GeV<2% SPHINX pA  Θ + X 12 GeV<2% Belle KA  Θ + X  2 GeV <2.5% LEPS γAΘ+XγAΘ+X  2 GeV  60% HERMES eD  Θ + X 7 GeV  200% Comparison with other experiments σ(KN  Θ(1540) + X) σ(KN  Λ(1520) X)

12. Search for exclusive production of Θ(1540) +

13. 13 Method Use K + n  Θ(1540) +  pK S –Observed by DIANA: N Θ+ / N ch = 0.66 ± 0.19. Phys.Atom.Nucl 66,1715 (2003). –Clear interpretation of the result: N Θ+ / N ch  Γ Θ+. Cahn,Trilling,PRD69,11501 (2004 ). Projectile is not reconstructed  background from K S, K L induced reactions and inelastic reactions. –Use all available information to suppress inelastic reactions (main bg). –Background still high  determine the contribution of K + n  pK S indirectly. –Conservatively assume that remaining inelastic reactions and K S, K L induced reactions do not produce Θ + signal.

14. 14 Contribution of charge exchange reaction N ch =  Φ K+ (p K+, θ) σ ch (m pKs ) M (R, θ) ε pKs (m pKs, p pKs, R, θ) B dR dθ K + fluxmaterialreconstruction efficiency x BR ch. exch. x-section rescattering × P (m pKs, p pKs ) nuclear spectral function S (E N, p F ) δ(  s – m pKs ) dE N d 3 p F dp K+ Problem: M and ε pKs are complicated functions of coordinates (rely on MC?), calculation of P and S is model dependent. Solution: determine relevant information from data. Reconstruct D* -  D 0 π -  (K + π - ) π - for events where K + interacts elastically in the detector material.

15. 15 Reconstruction of D* -  D 0 π -  (K + projectile π - ) π - Sibirtsev et al.,EPJ A23,491(2005) 1. E N = m N - 2ε -, ε~7MeV p F 2 2m N  Iteratively find p K+ and p F. For elastic secondary interactions projectile momentum can be determined based on (E pK, p pK ) and Δr=r pK -r IP. 2. E K = E pK - E N 3. p K from E K and Δr 4. p F = p pK – p K detector material p K K+K+ e+e- interaction point iterations

16. 16 Reconstruction of D* -  D 0 π -  (K + projectile π - ) π - (2) m(K + proj π - ) (GeV/c 2 ) N el D* = 470±26 (from m(K + proj π - ) fit), correct D 0 mass, σ  16 MeV/c 2. N / 0.5 MeV/c 2 m(K + proj π - ) (GeV/c 2 ) N / 10 MeV/c 2 For every secondary pK + pair determine p K+, combine with π - candidates to form D* - and D 0 candidates. Δm D* =m(K + proj π - π - )-m(K + proj π - ) m(K + proj π - ) D 0 sidebands m D0 ±50MeVΔm D* ±2MeV

17. 17 Reconstruction of D* -  D 0 π -  (K + projectile π - ) π - (3) m(K + proj π - ) (GeV/c 2 ) No additional tracks from secondary vertex for D 0 signal, as expected for elastic scattering. Fermi momentum p F (MeV/c) hydrogen Fit to oscillator model expectation. Extracted model parameter similar to other measurements. N / 10 MeV/c 2 N / 10 MeV/c Distance from secondary vertex to nearest track D 0 sidebands D 0 signal window Abramov et al.,JETP Lett.71,359(2000 ).

18. 18 Contribution of charge exchange reaction (2) D* N el =  Φ K+ (p K+, θ) σ el (m pK+ ) M (R, θ) ε pK+ (m pK+, p pK+, R, θ) dR dθ K + fluxmaterialreconstruction efficiency K + p elastic x-section rescattering × P (m pK+, p pK+ ) nuclear spectral function S (E N, p F ) δ(  s – m pKs ) dE N d 3 p F dp K+ N ch = N el Integral ch Integral el D* = N el (m pK ) Φ K+ (m pK ) σ ch (m pK ) ε pKs (m pK ) B Φ K+ (m pK ) σ el (m pK ) ε pK+ (m pK ) Basic formula to determine the contribution of charge exchange reaction. Number of D* -  D 0 π -  (K + projectile π - ) π - can be expressed as:

19. 19 Determination of N el D* m pK+ (GeV/c 2 ) N / 50 MeV/c 2 = 21±7 per 50 MeV/c 2 bin in Θ + mass region. Φ K+ σ ch ε pKs B Φ K+ σ el ε pK+ N el D* Determine D* yield in m pK+ bins  N el D*

20. 20 Determination of Φ K+ / Φ K+ D* From direct reconstruction of K +  Φ K+ / Φ K+ = 850 ± 20 in Θ + mass region. D* Φ K+ σ ch ε pKs B Φ K+ σ el ε pK+ N el D* m pK+ (GeV/c 2 ) N / 50 MeV/c 2 Φ K+ / Φ K+ D* m pK+ (GeV/c 2 )

21. 21 Determination of σ ch / σ el From published data on x-sections  σ ch / σ el = 0.35 ± 0.02 in Θ + mass region. Φ K+ σ ch ε pKs B Φ K+ σ el ε pK+ N el D* m pK+ (GeV/c 2 ) σ ch (mb) σ ch / σ el σ el (mb) charge exchange x-section K + p elastic x-section ratio

22. 22 Determination of ε pKs / ε pK+ From GEANT based MC simulation  ε pKs / ε pK+ = (43 ± 5)% in Θ + mass region. Φ K+ σ ch ε pKs B Φ K+ σ el ε pK+ N el D* m pK+ (GeV/c 2 ) efficiency m pK+ (GeV/c 2 ) ε pKs / ε pK+ pK S pK +  N ch = (1.0±0.4)·10 3 per 50 MeV/c 2 bin in Θ + region

23. 23 Mass spectrum for secondary pK S pairs Fit m pKs to resolution function (σ~2MeV/c 2 ) + 3 rd order polynomial m pKs (GeV/c 2 ) N / 2 MeV/c 2 N ch DIANA Reject pK S vertices with additional tracks Require 50<p F <300 MeV/c. factor 4 suppression

24. 24 Upper limit on Γ Θ+ Γ Θ+ < 0.64 MeV at the 90% C.L. for m=1.539 GeV/c 2. Γ Θ+ < 1.0 MeV for wide range of possible Θ + masses. Γ Θ+ Upper Limit m pKs (GeV/c 2 ) DIANA Express N Θ+ / N ch via Γ Θ+ : Γ Θ+ = Δm N Θ+ N ch σ ch 107mb B i B f Cahn,Trilling,PRD69,11501 (2004 ).

25. 25 Summary We searched for Θ(1540) + pentaquark using kaon secondary interactions in the Belle detector material. No signal was found. For inclusive production we set upper limit For exclusive production we set upper limits Γ Θ+ < 0.64 MeV at the 90% C.L. for m=1.539 GeV/c 2. Similar sensitivity to DIANA; do not support their evidence. Γ Θ+ < 1.0 MeV for wide range of possible Θ + masses. < 2.5% at the 90% C.L. σ(KN  Θ(1540) + X) σ(KN  Λ(1520) X) (hep-ex/0507014, submitted to PLB)

26. 26 FAQ: Why no Σ** in pK S mass spectrum? σ(K - p) σ KN (I=1) m(pK - ) m(pK S ) p F <300MeV/c p K (GeV/c) the only prominent peak is at 1.8GeV Cool et al.,PRD1,1887 p K (GeV/c) m (GeV/c 2 ) the same structures are visible