1. Physics based MC generators for detector optimization Integration with the software development (selected final state, with physics backgrounds event generator) Phenomenology/Theory of amplitude parameterization and analysis (how to reach the physics goals. Framework exists but needs to be updated) Software tools, integration with with the GRID (data and MC access, visualization, fitting tools) Partial Wave Analysis

2. Identify old (a 2 ) and new (  1 ) states Resonances appear as a result of amplitude analysis and are identified as poles on the “un-physical sheet” A Physics Goal Use data (“physical sheet”) as input to constrain theoretical amplitudes Data Resonances Amplitude analysis (… then need the interpretation: composite or fundamental, structure, etc)

4. Analyticity: Methods for constructing amplitudes (amplitude analysis) Crossing relates “unphysical regions” of a channel with a physical region of another another Unitarity relates cuts to physical data Other symmetries (kinematical, dynamical:chiral, U(1), …) constrain low-energy parts of amplitudes (partial wave expansion, fix subtraction constant) Data (in principle) allows to determine full (including “unphysical” parts) Amplitudes. Bad news : need data for many (all) channels Approximations:

5. Example :  0  0 amplitude Only f on C is needed ! To check for resonances: look for poles of f(s,t) on “unphysical s-sheet” -t 4m  2 Re s Im s s0 ! 1s0 ! 1 Data To remove the s 0 ! 1 region introduce subtractions (renormalized couplings) Chiral, U(1) For Re s > N use Regge theory (FMSR) Unitarity Crossing symmetry N Partial wave projection  Roy eq.

6. down-flat up-flat two different amplitude parameterizations which do not build in crossing in = theoretical phase shifts = out = adds constraints from crossing (via Roy. eq) Lesniak et al.

7. Extraction of amplitudes t    (t) f  a ! M1,M2,  (s,p i ) EaEa  (2m p E a )  (t) s a a M1M1 MnMn p1p1 Use Regge and low-energy phenomenology via FMSR To determine dependence on channel variables, s ij

8.    (18GeV) p  X p   - p   ’   p ~ 30 000 events N events = N(s, t, M   ) p p -- a2a2  -- t M   s

9.  - p !  0 n Assume a 0 and a 2 resonances (A.Dzierba et al.) 2003 ( i.e. a dynamical assumption)

10. E852 data

11.  - p !  - p Coupled channel, N/D analysis with L< 3  - p !  ’  - p D S P D P

12. |P + | 2  (P + )-  (D + )

13. Some comments on the isobar model isobar  + (1)  - (3)  + (2) s 13 >>s 23 otherwise channels overlap : need dispersion relations (FMSR) isobar model violates unitarity K-matrix “improvements” violate analyticity

14. Ambiguities in the 3  system

17.  - p !  -  +  - p BNL (E852) ca 1985 CERN ca. 1970 E852 2003 Full sample Software/Hardware from past century is obsolete

18. Preliminary results from full E852 sample a 2 (1320)  2 (1670) Chew’s zero ? Interference between elementary particle (  2 ) with the unitarity cut

19. s  +  -(1) s  +  -(2) 00 00 H 0 00 (m a2 -  < M 3  < m a2 +  ) Standard MC O(10 5 ) bins (huge !) Need Hybrid MC !

20. Theoretical work is needed now to develop amplitude parameterizations

21. X  (a p ! X n) Im f(  a !  a) Semi inclusive measurement (all s) Dispersion relations Re f(M 2 X ) Exclusive (low s, partial wave expansion) s = M X 2 f(k) / k 2L k = (s,m 2 1,m 2 2 )