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F.Q.Wu , IHEP, Beijing with Bing-song Zou, L.Li & D.V.Bugg Munu 2004, China

Coupled channel effects in pi-pi S-wave interaction. F.Q.Wu , IHEP, Beijing with Bing-song Zou, L.Li & D.V.Bugg Munu 2004, China. Outline. Motivation Coupled channel effects in I=2 pi-pi S-wave interaction Coupled channel effects in I=0 pi-pi

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F.Q.Wu , IHEP, Beijing with Bing-song Zou, L.Li & D.V.Bugg Munu 2004, China

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  1. Coupled channel effects in pi-pi S-wave interaction F.Q.Wu , IHEP, Beijing withBing-song Zou, L.Li & D.V.Bugg Munu 2004, China

  2. Outline • Motivation • Coupled channel effects in I=2 pi-pi S-wave interaction • Coupled channel effects in I=0 pi-pi S-wave interaction • Summary and Outlook

  3. 1. Motivation I=0 pp S-wave interaction I=0 JPC=0++ particles: s, glueball However, to really understand the I=0 pp S-wave interaction, one must first understand the I=2 pp S-wave interaction

  4. Because: a, simpler. There are no known s-channel resonances and less coupled channels in I=2 pi pi system, so it is much simpler than the I=0 pi pi S-wave interaction; b，necessary input for extracting I=0 phase shifts from data. To extract I=0 pp S-wave phase shifts from experimental data obtained by pi +N  pi + pi +N reactions, one needs an input of the I=2 pi pi S-wave interaction.

  5. 2.Coupled channel effects in I=2 pi-pi S- wave interaction Coupled channel K-matrix formalism：

  6. If Vrpp = grppemqm Ir.(Ip1 *Ip2) Vf2pp = gf2ppFmnqmqn (Ip1 . Ip2 ) p p r f2 p p

  7. Off-shell form factor： Only two parameter in our theory: With t-channel r, f2(1270) exchange, we reproduce the pion pion isotensor S-wave and D-wave scattering phase shifts up to 2.2 GeV quite well, but inelasticity parameter η=1. In order to reproduce this inelasticity, it is necessary to consider the pi pirho rho coupling channel effect.

  8. I=2 pp S-wave phase shift d and inelastic parameter h Main features： (1)the d02 goes down more and more negative as the pi pi invariant mass increases from pion pion threshold up to 1.1 GeV;(2) the d02starts to increase for energies above about1.1 GeV;(3) the h02 starts to deviate from 1 for energies above 1.1 GeV. Explain： 1，repulsive force by t-channel r 2, attractive force by f2 (1270) 3, inelasticity by pp -rr- pp box

  9. 3. Coupled channel effects in pi-pi I=0 S-wave interaction Without including s-channel resonances, we only consider the effect of r，f2 exchanges and various coupled channel box diagram upon pi pi inelasticity parameter. p p r f2 p p

  10. I＝0ππS-wave inelasticity parameter (without s-channel resonances) three channel M_pipi(Mev)

  11. 4. Summary and Outlook 1) Three basic features of I=2 pp scattering phase shifts and inelasticities can be well reproduced by the t-channel (r,f2 ) meson exchange and the pp -rr coupled-channel effect. 2) A correct description of I=2 pp scattering has significant impact on the extraction of I=0 scattering amplitudes from p+p- -> p+p-and p+p- -> p0p0data, especially for energies above 1.2 GeV .

  12. 3) The t-channel (r,f2 ) meson exchange and the pp-rr coupled-channel effect should also be important in I=0 pp scattering. 4) Further study of other channels like will make more clear of pi pi interaction.

  13. 谢谢！ Thanks!

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