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									Dynamics of Ξ hyperon production on the
               nucleons


   D.A. Sharov, V.L. Korotkikh, D.E. Lanskoy
                SINP MSU

               EMIN-2009, Moscow
      Cascade hyperon production

                           _
• Kaon beams in reaction KNKΞ
  past : bubble chambers
        low intensity, low statistics
  future : intense kaonic beam at J-PARC
        p=1.8GeV/c

• Hyperon beams

• Photoproduction in reaction γNKKΞ
  CLAS JLab
       Continuous Electron Beam Accelerator,
       Detection of exclusive multiparticle final states
  Cascade hyperon production mechanism

In order to understand the mechanism of cascade production we
going to make combine analysis of hadro and photoproduction of
Xi hyperons using phenomenological model for these processes.
                                            _
First step: Phenomenological model for the KNKΞ reaction

Second step: model for γNKKΞ reaction.
                               _
Phenomenological model for the KNKΞ reaction



    s channel         u channel                  t channel
_                 _                         _
K           K     K           Ξ             K        K
       Y
                         Y

N           Ξ     N           K              N      Ξ
                      Y=Λ,Σ       Require S=-2 exchange.
                                  Since no (nonexotic) double-strangeness
                                  meson exists the one-meson t channel
                                  exchange is absent.
                               _
Phenomenological model for the KNKΞ reaction



            s channel               u channel
        _                       _
        K           K           K          Ξ
               Y
                                       Y

        N           Ξ           N          K
                        Y=Λ,Σ


               3 charge channels:
      K‫־‬p→K+Ξ‫ , ־‬K‫־‬p→K0Ξ0 and K‫־‬n→K0Ξ‫־‬
                                 _
  Phenomenological model for the KNKΞ reaction


First stage: Four low-mass (less then threshold) exchange particles:
               Λ(1/2+), Λ(1520, 3/2‫ ,)־‬Σ(1/2+), Σ(1385,3/2+)
               5 free parameters: 4 products of the coupling constants
                         fY=fKNYfKΞY and 1 universal cut-off parameter Λ

All parameters are determined by the direct fitting to the data


Fit was performed to available data on differential and integral
cross sections of reactions K‫־‬p→K+Ξ‫ , ־‬K‫־‬p→K0Ξ0 at Ecm< 3.2 GeV


χ²=1214 for 374 points
Results for the K‫־‬p→K+Ξ‫ ־‬reaction

                 Integral cross section
                 versus cm energy




     Differential cross sections at various cm energies
Results for the K‫־‬p→K0Ξ0 reaction
                               _
Phenomenological model for the KNKΞ reaction

    High-mass (above threshold) hyperon resonances

   State         Jp               Γ(MeV)    Br(KΞ)
   Λ(1890)**** 3/2+               60-200
   Λ(2100)**** 7/2‫־‬               100-250   < 3%
   Λ(2110)***    5/2+             150-250
   Λ(2350)***    9/2+             100-250
   Σ(1915)****   5/2+             80-160
   Σ(1940)***    3/2‫־‬             150-300
   Σ(2030)****   7/2+             150-200   < 2%
   Σ(2250)***    ?                60-150

                 D5 or G9 wave.
                                      _
       Phenomenological model for the KNKΞ reaction

We tried different combinations of the resonances. Here we present the result obtained
with addition of Σ(2030) and Σ(2250, D5) to four low-mass hyperons.



8 free parameters: 6 products of the coupling constants fY=fKNYfKΞY ,
1 cut-off parameter Λ for low-mass hyperons and 1 cut-off parameter Λ72 for
high-mass hyperons


Fit result: χ²= 1019 for 374 points

With parameters:
fΛ = 0.262, fΣ = 0.088, fΛ1520 = -0.380, fΣ1385 = -0.005, fΣ2250 = -0.123, fΣ2030 = 0.023,
Λ = 0.898 GeV, Λ72 = 0.434 GeV

Γ(Σ(2250)→KΞ) = 0.8585MeV,              Γ(Σ(2030)→KΞ) = 0.167MeV
Reaction K‫־‬p→K+Ξ‫־‬
Reaction K‫־‬p→K0Ξ0
     Reaction K‫־‬p→K+Ξ‫־‬


Contribution of Σ(2030), Σ(2250, 5/2-)
Reaction K‫־‬p→K0Ξ0
Reaction K‫־‬n→K0Ξ‫־‬
  Polarization
Reaction K‫־‬p→K+Ξ‫־‬




Reaction K‫־‬p→K0Ξ0
Photoproduction of cascade hyperons in reaction γpK+K+Ξ‫־‬

                             Photoproduction
                                                     γ            K+
               γ        K+
                                                             K‾
                       K‾     K+                                  Ξ‾
               p                                             Y
                        Y
                              Ξˉ                     p            K+


                             Hadroproduction
                K‾            K+                     K‾           Ξ‾
                       Y
                                                             Y
                   p          Ξ‾                         p        K+




        w = M(K+ Ξ‫)־‬               t = (pγ - pK+)2            s = (pγ + pp)2
 Photoproduction of cascade hyperons in reaction γpK+K+Ξ‫־‬
                                                            Data from
                                                            L.Guo et al., Phys. Rev. C 76,
                                                            025208(2007)
Integral cross section
versus photon energy




         Differential cross sections dσ/dM(KΞ) at various photon energies
Photoproduction of cascade hyperons in reaction γpK+K+Ξ‫־‬

                                       Next stage

                     γ            K+        K+                 γ       K+    K+


                 p            Y        Ξ‫־‬                p         Y        Ξ‫־‬




                 K+       K+                     γ       K+    K+                 γ   K+    K+
         γ

     p       Y           Ξ‫־‬             p            Y        Ξ‫־‬             p    Y        Ξ‫־‬
                                    Conclusion

● A phenomenological model of Ξ hyperon production from nucleons by antikaons,
which includes exchanges by various Λ and Σ hyperons with spin up to 7/2, is
developed.

● The model successfully reproduces available experimental data on integral and
differential cross sections and polarization of the reaction in the different charge
channels at the center-of-mass energies from the threshold up to 3.2 GeV.

● The s channel exchange by high-mass and high-spin resonances is important for
systematic description of all available data.



● Simple model of Ξ photoproduction based on hadroproduction model is developed.
It is shown, that in order to describe the data it is not enough to take into account only
t channel K exchange mechanism.
Thank you!
Backup slides
                         Effective Lagrangians

For B(1/2+)Y(1/2)K(0-)


For B(1/2+)Y(3/2)K(0-)


For B(1/2+)Y(7/2)K(0-)

                            Form Factor
                          f(q)=Exp(-q2/Λ)
                    Propagators

3/2


5/2




                       Widths

      Γ(5/2+/-) = f2/(30*π*mπ4)*(EB-/+mB)*q5/MR

      Γ(7/2+/-) = f2/(70*π*mπ6)*(EB+/-mB)*q7/MR

								
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