Theory issues :

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, BRs , )

• Specification of production
• processes,
• t,u,s channel exchanges
• constraints from unitarity and duality
• selection of simple processes

2
Meson-meson rescattering pp, ph, ph, p K,

• SI0

pp only
e2id 1 iT 1i(To ToGTo )

• f0(980) from attraction in KK
• Source ?
• O(p2) too weak
• renormalization
• or f0(1300-1400)

full (Oller,Oset)
3
V

• SI1

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
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)
fi(s1,m2) ci(m2)
ds2 Kij (s1,s2,m2) fj(s2,m2)/Dj(s2)
i,jr,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
lt-Y42gt D2 - 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
Chiral extrapolations
Soft pions chiral loops significantly
renormalize hadron properties
Mass correction from transition to nearly
degenerate states
11
Open channel couplings