1. Cesare Bini, Bernhard Ketzer Workshop on New Partial Wave Analysis Tools for Next Generation Hadron Spectroscopy Experiments Camogli, Italy 22 June 2012 ATHOS 2012 Discussion Session I

2. Discussion Session - Experiments Conveners: Cesare Bini and Bernhard Ketzer Recent results on pi-pi amplitudes at BES III (10’+5’) B. Liu (Institute of High Energy Physics) Search for exotics in three pion production at COMPASS (10’+5’) S. Neubert (TU-Munchen) Search for exotics in three pion production at CLAS (10’+5’) P. Eugenio (Florida State University) Discussion (45’)

3. State of the Art Lattice QCD [J. Dudek, Phys. Rev. D 84, 074023 (2011)] [J. Dudek at al., Hadron Spectrum Collaboration, Phys. Rev. D 82, 034508 (2010)] negative parity positive parity exotic Structure of states: study with e.g. C. Meyer

4. Comparison with Models L-QCDBagFlux tubeConstituent gluon S waveP wave 1 −−,(0,1,2) −+ 1 ++,(0,1,2) +− 1 −−,(0,1,2) −+ 1 +−,(0,1,2) ++ J PC & Degeneracy pattern: (0,1,1,1,2,2,3) +− (0,1,2) ++ (0,1,2) −+,1 −− (0,1 3,2 2,3) −− (0,1,2) −+ 1 −−,(0,1,2) −+ (0,1 3,2 2,3) +− (0,1,2) ++      Model with a quasigluon in a P-wave with respect to the qq pair, i.e. with successfully reproduces the L-QCD multiplets

5. Production Mechanisms Diffractive production: Regge- or Pomeron exchange pN annihilation: formation and production Photo-production VES, E852, COMPASS Crystal Barrel COMPASS CLAS

6. J PC =1 −+ ‒  Pb vs H Target [Alekseev et al., Phys. Rev. Lett. 104, 241803 (2010)] [F. Haas, arXiv:1109.1789 (2011)] S. Paul S. Neubert S. Paul S. Neubert

7. Nuclear Effect Pb, Ni, H 2 targets  M=1 enhanced for nuclei S. Paul S. Neubert S. Paul S. Neubert

8. Photoproduction of J PC =1 −+ Pion beam: J PC = 0 −+  mainly S=0 hybrids: 1 −−, 1 ++  mix with qq states Photon beam: J PC = 1 −−, VMD  mainly S=1 hybrids  exotic J PC, strength comparable to a 2 (1320)? Flux tube model (Isgur 85, Close 95): L-QCD (Dudek 09) strong photocoupling for cc hybrids  photoproduction more favorable for exotic hybrids?

9. CLAS at CEBAF Run g6c (2001) [M. Nozar et al., PRL 102, 102002 (2009)] E e = 5.744 GeV tagged photon beam with E  up to 5.4 GeV flux 5·10 7 photons / s 18 cm liquid hydrogen target 83k ev. Run g6c (2001) [M. Nozar et al., PRL 102, 102002 (2009)] E e = 5.744 GeV tagged photon beam with E  up to 5.4 GeV flux 5·10 7 photons / s 18 cm liquid hydrogen target 83k ev. Run g12 (2008) [C. Bookwalter, arXiv:1108.6112v1] geometry optimized for peripheral production E  up to 5.75 GeV 68 pb -1  520k ev. PWA with 19 waves: J PC = 1 ++, 2 ++, 1 −+, 2 −+ (no J=0 expected) [B. Mecking et al., NIM A 503, 513 (2003)]

10. Photoproduction of J PC =1 −+ no clear resonance signal high-mass results fluctuate accounts for 2% of total intensity at most no evidence for 1 −+ phase motion P. Eugenio

11. Photoproduction of J PC =1 −+ CLASCOMPASS

12. P. Eugenio

13.    vs  ’   Final States  - waves scaled according to phase space and BR to final state D, G waves very similar P wave very different in  and  ’ 

14. J PC = 0 −+  (1800): M=1827±7 MeV/c 2 (COMPASS) 2 states expected: 3S qq, hybrid hybrid expected to have large branching to f 0 , no decay to  2 distinct states observed? (Barnes 97)

15. J PC = 2 −+  2 (1670) + Deck?  2 (2100)?

16. J PC = 2 −+ [E852, M. Lu et al., PRL 94, 032002 (2005)]

17. Kaonic Final States Diffractive dissociation:   >10 × BNL statistics very clean spectrum possibly also f 1 (1420) seen

18. Status of Analyses Isobar model analysis isobar parameterizations: , (  ) S rank of fit, full vs partial coherence leakage, acceptance, resolution t’ dependence estimation of systematic error Signals for exotic mesons diffraction, pbarp: , ,  ’ , f 1 , b 1  photoproduction: none

19. Future Go beyond standard isobar model analysis: where does the model fail?  study channels like include non-resonant production (dynamical effects, e.g. Deck) analytic amplitudes final state interactions unitarity understand a 1 multi-particle final states

20. Non-Resonant Production Resonant productionNon-resonant production Generate pure Deck-like events [G. Ascoli et al., Phys. Rev. D 8, 3894 (1973)] Pass through Monte Carlo & PWA Normalize to 6 −+ 0 +  H wave Examine intensity in other waves

21. 21 Duality and PWA l FESR should work separately for Pomeron (background) and classic Regge components and for fixed t and u. –At fixed u in –At fixed u in π - π +  π - π + one has zero Regge contribution l In π N elastic scattering one was able to use Regge exchange contributions as an approximation to high partial waves –This approach should be applicable to photon or meson induced “top vertices” including reactions like –This approach should be applicable to photon or meson induced “top vertices” including reactions like π - Pomeron  π - π - π + with internal π exchange l This phenomenology suggests a PWA model that is combination of –Regge Born with low partial waves removed and –Parameterized low partial waves –FESR constraints on parameterized waves G. Fox

22. Understand the a 1

23. J PC = 1 −+

24. Higher masses accessible  many disputed states: 0 , 1 , 2 ,... Multi-Particle (>3) Final States Motivation: Clarify the hybrid nature of the  1  branching ratios to different channels Under investigation: Model b1b1 f1f1pp  ’p  (1295)p Reference Flux Tube, 3 P 0 170605 - 200 - 100 – 10 [Isgur et al., Close et al.] Flux Tube, IKP m=1.6 GeV/c 2 24592 [Isgur et al.] Flux Tube, PSS m=1.6 GeV/c 2 591481 [Page et al.] L-QCD6615 [McNeil and Michael]

25. Future Go beyond standard isobar model analysis: multi-particle final states coupled-channel analysis final state interactions, unitarity understand production mechanism: bins in t, s, polarization, probes higher statistics, enlarge phase space study model dependence specify systematic errors Tools, etc. common PWA framework across different experiments plugin for amplitudes validation of software computing: fitting procedures, GPUs, etc. access to data teach young researchers

27. Conclusions Hybrid mesons are allowed in QCD, but are they realized in nature? provide a test of flux tube formation  confinement can appear in exotic J PC quantum numbers  smoking gun High statistics data with  beam: COMPASS exotic 1 −+ waves in ,  ’ , f 1  non-resonant and resonant contributions A dependence of M=1 production Photoproduction: CLAS (also COMPASS) no evidence for  1 (1600) in charge transfer reaction examine Pomeron production Have we observed the lowest hybrid supermultiplet?  1 (1600),  (1800),  2 (1880), ? Many more interesting questions: Strangeness, Scalars, Glueballs, …

28. Partial Wave Analysis Photoproduction 0.0015 < t’ < 0.01 GeV 2 /c 2 t’ < 0.5·10 -3 GeV 2 /c 2 vanishes for t’→0 a 2 (1320) (M=1) present in both t’-ranges  different production mechanisms? Diffraction Two clearly separated regions: Phase difference a 2 (1320) - a 1 (1260): offset for two t’-regions!

29. Phase Difference a 2 -a 1 Experiment Theory [G. Faeldt et al., Phys. Rev. C 79 014607 (2009)] Plot by N. Kaiser, TUM  smooth transition between a 2 photoproduction to diffractive production with increasing t‘  possibility to cleanly separate photoproduction from diffraction PWA in t’ bins for single mass bin 1.26 < m 3  < 1.38 GeV/c 2 (a 2 region)  (a 1 )  (a 2 )  a 2 -a 1 )  determination of radiative width of a 2 (1320),  2 (1670)