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Theory issues : Progress report and plans for future

Theory issues : Progress report and plans for future. Coupled 2 meson final states has a light exotic being seen input to Faddeev equations 3 mesons final state interactions the a 1 story realistic description of the 3 p system

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Theory issues : Progress report and plans for future

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  1. Theory issues : Progress report and plans for future • Coupled 2 meson final states • has a light exotic being seen • input to Faddeev equations • 3 mesons final state interactions • the a1 story • realistic description of the 3p system • Develop next generation MC generators • background processes (Deck, s-channel,..) • More theory • chiral extrapolations • microscopic calculations of exotic • properties (masses, BR’s , … ) • Specification of production • processes, • t,u,s channel exchanges • constraints from unitarity and duality • selection of “simple” processes

  2. O(p2) Topp = (2s-m2p)/2f2 ToKK = 3s/4f2 TopK = s/4f2 Meson-meson rescattering : pp, ph, ph’, p K, … • S=I=0 pp only e2id = 1 + iT = 1+i(To + ToGTo + …) • f0(980) from attraction in KK • Source ? • O(p2) too weak • renormalization • or f0(1300-1400) full (Oller,Oset)

  3. V = • S=I=1 O(p2) + CDD pole (large NC) “pre-existing” state r Exotic zoo : 1400 (ph)  fsi 1600 (ph’)  ? Need 2meson coupled channels 1600 (rp)  ? Need 3p coupled channels

  4. 3 p : The a1 and limitations of the isobar model p-p  p- p- p+p (CERN) : Bump at 1.2 GeV but no phase motion

  5. 1 (p-) F 1 2 (p-) 3 D1 2 3 (p+) f1 ~ c(m2) s,.. r,.. disf(s1,m2) = ir(s1) ds2f(s2,m2)/D2(s2) |fixed s1 F(s1,s2,m2) = f1(s1,m2)/D1(s1) + (12) + • violates 2,3 particle unitarity ! (r, s, ..) s1 s2 Unitarity relation (Aitchison):

  6. K-matrix equations (Ascoli, Wyld) : (ignore the real part from the unitary cut) ds2 Kij (s1,s2,m2) fj(s2,m2)/Dj(s2) fi(s1,m2) = ci(m2) + i,j=r,s,.. phase space factors More complete : Faddeev equations (keep the PV) (Schult,Wyld) but … needs realistic two-body T-matrix and covariance

  7. fi(s1,m2) = Hij(s1,m2) cj(s1,m2) Hii = 1, Hij = 0  isobar model (Goradia et al.)

  8. Background processes r p Deck graph p p p p Absorption  important in charge exchange OPE, ORE, …

  9. a2 production (E852) in p0 h <-Y42> = |D+|2 - |D-|2 D+ ++ = r++ D++- = r+-+ C+- r++ C+- = e-iac(t)p/2 ebc t C+- r+- r++ = (t’/4mn2)(1/2) e-ar(t)p/2 ebr t tan(ar(t)p/2) r+- = (GT/Gv)(t’/4mn2) e-ar(t)p/2 ebr t tan(ar(t)p/2)

  10. = + mX mX0 S* Chiral extrapolations : Soft pions : chiral loops significantly renormalize hadron properties Mass correction : from transition to nearly degenerate states

  11. Open channel couplings

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