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Ju -Jun Xie , Hua -Xing Chen and Eulogio Oset

The and reactions. with chiral dynamics. Ju -Jun Xie , Hua -Xing Chen and Eulogio Oset. 湖州 2012 年 4 月 13 日. Contents. Motivations Formalism The reaction The reaction Summary. Motivations. p. The study of proton-proton scattering is very important and useful.

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Ju -Jun Xie , Hua -Xing Chen and Eulogio Oset

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  1. Theand reactions with chiral dynamics Ju-Jun Xie, Hua-Xing Chenand EulogioOset 湖州 2012年4月13日

  2. Contents • Motivations • Formalism • The reaction • The reaction • Summary

  3. Motivations p • The study of proton-proton scattering is very important and useful. • The source of information for scattering: scattering length and effective range. p p

  4. References Our dynamics is similar to Casparyan’s papers but we consider in addition the final state interaction of meson and baryon using the chiral unitary theory.

  5. Formalism • We work at the reaction threshold. • The processes exchanging andmesons give the dominant contributions. • The final state interactions (FSI) are important.

  6. Formalism • Elementary Diagrams • Meson-Baryon Interactions (FSI-1) • Baryon-Baryon Interactions (FSI-2)

  7. Inputs • For strong vertex of and : and , which are related to the D and F factors. • Two-body meson-baryon scattering amplitudes such as are obtained using the chiral unitary theory(fitted with the experimental data of meson baryon scattering).

  8. Inputs • For two-body baryon-baryon interactions, we fit the transition using the experimental data of the reaction. • For and, we assume they are the same. • After fitting the potential V and the cut off , and relate them to the scattering length and effective range , we obtain , and • We also find it compatible with Hinterberger’s results. There is a family of values consistent with the experimental data.

  9. Free Parameters • We add a form factor for the off-shell and mesons in the strong vertex • When fitting with the experimental data, we have some freedoms.

  10. The reaction • Solid line: with including the interactions • Dashed line: without including the interactions • MeV

  11. The reaction • We follow the same procedures and obtain the result for the reaction (dashed line). • The result is larger than the experimental results,but at the same magnitude. • The result of the reaction is much smaller than the result of the reaction.

  12. The reaction • The transition process is important since is much larger than . • The final state interaction may be important, but we do not have enough information of the reaction. • The phases among these three processesare unknown but important. Therefore, we do not want to achieve an accurate result, but just a qualitative result in this work.

  13. Invariant Mass Spectra and Dalitz Plot

  14. Summary • We have made a theoretical study of theand reactions. We have considered the final state interactions of any of the two hadrons. • The cross section of thereaction we obtained is consistent with the experimental data. • The cross section of the reaction we obtained is much smaller than the one of the reaction (there is a factor about 20). • One should consider the transition processas well as the final state interactioncan be important. However, since we do not the their relative phases, we can not estimate their contributions.

  15. Thank you very much!

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