Physics based MC generators for detector optimization Integration with the software development

1. Partial Wave Analysis 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)

2. Resonances Data Amplitude analysis A Physics Goal Identify old (a2) and new (p1) states Resonances appear as a result of amplitude analysis and are identified as poles on the “un-physical sheet” Use data (“physical sheet”) as input to constrain theoretical amplitudes (… then need the interpretation: composite or fundamental, structure, etc)

4. Methods for constructing amplitudes (amplitude analysis) Analyticity: Data (in principle) allows to determine full (including “unphysical” parts) Amplitudes. Bad news : need data for many (all) channels Approximations: 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)

5. Example : p0p0 amplitude Only f on C is needed ! • Unitarity • Crossing • symmetry Data Im s • For Re s > N use • Regge theory • (FMSR) • To remove the s0!1 • region introduce subtractions • (renormalized couplings) • Chiral, U(1) 4mp2 Re s N -t To check for resonances: look for poles of f(s,t) on “unphysical s-sheet” s0!1 Partial wave projection  Roy eq.

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

7. Extraction of amplitudes t a p1 fa a ! M1,M2,L(s,pi) M1 Ea a s x (2mp Ea)a(t) a Mn ba(t) Use Regge and low-energy phenomenology via FMSR To determine dependence on channel variables, sij

8. h p- a2 p- t p p Mhp , W s p-(18GeV) p  X p  h p- p  h’ p-p ~ 30 000 events Nevents = N(s, t, Mhp , W)

9. p- p !hp0 n (A.Dzierba et al.) 2003 Assume a0 and a2 resonances ( i.e. a dynamical assumption)

10. E852 data

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

12. f(P+)-f(D+) |P+|2

13. Some comments on the isobar model p+(1) p-(3) p+(2) isobar s13>>s23 otherwise channels overlap : need dispersion relations (FMSR) isobar model violates unitarity K-matrix “improvements” violate analyticity

14. Ambiguities in the 3p system

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 CERN ca. 1970 p- p !p-p+p- p E852 2003 Full sample BNL (E852) ca 1985 Software/Hardware from past century is obsolete

18. Preliminary results from full E852 sample p2(1670) a2(1320) Chew’s zero ? Interference between elementary particle (p2) with the unitarity cut

19. H000(ma2 - G < M3p < ma2 + G) Standard MC O(105) bins (huge !) Need Hybrid MC ! sp+p-(2) sp+p-(1) r0 r0

20. Theoretical work is needed now to develop amplitude parameterizations

21. Semi inclusive measurement (all s) s(a p ! X n) Im f(a a !a a) Dispersion relations s = MX2 X Re f(M2X) Exclusive (low s, partial wave expansion) k = l(s,m21,m22) f(k) / k2L