1. A. Švarc Rudjer Bošković Institute, Zagreb, Croatia Poles as a link between QCD and scattering theory (old and contemporary knowledge) HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

2. It seems to be clear that the poles are the only resonance signal However, it is still not clear whether: 1.Is it really completely true? 2.Is it a general knowledge? 3.How are the poles to be extracted from experiment? 4.Is that statement adequately represented in the secondary literature? (meaning PDG) HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 Therefore, in my talk I will address three topics: I What is a resonance II How to extract T-matrix poles III Is the problem well presented in PDG

3. The main intention of this talk is to analyze the crucial issues: Definition of resonances, poles and Breit-Wigner parametersDefinition of resonances, poles and Breit-Wigner parameters Importance of inelastic channelsImportance of inelastic channels New experimentsNew experiments Changes in PDGChanges in PDG I will give information about issues as I see them, and at least one important reference which can serve as a starting point for further reading. The emphasis is going to be on existing, but sometimes forgotten knowledge about the field. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

4. I What is a resonance HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

5. How do I see what is our main task? Experiment Theory ? Matching point bound states resonances QCD What is a resonance in QCD? What is a resonance in experiment? HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

6. What is a resonance in experiment? From the intuitive (heuristic) definition to the mathematical formulation Extensive review HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

7. a.particle “gets trapped” (the “black hole” phenomenon) b.a direct scattering event c.the lifetime of the particle-target system in the region of interaction is larger than the collision time in a direct collision process

8. This is a very heuristic definition. Question: What is the mathematical formulation of resonance signal? Where do the Breit-Wigner parameters come in? Where do the Breit-Wigner parameters come in? HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

9. What is a resonance signal? There is an uncertainty in literature. A careful reader will notice that it is never explicitly stated: the resonance is....... the resonance is....... Instead, introducing and defining the resonance is always much more delicate.... HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

10. Examples Introducing (and NOT defining) resonances varies from using rather undefined terms like: 1.follow from 2. are associated with 3. it is well known 11.11. 22.22. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

11. 33.33. Over strong statements that resonances are just a matter of convention “... simply an ad hoc hypothesis...” : HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

13. To full mathematical rigor

14. However, for me, the most transparent discussion is given in: HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

15. "Adventures in Mathematical Physics" (Proceedings, Cergy-Pontoise 2006), Contemporary Mathematics, 447 (2007) 73-81

16. Both definitions of resonances are being used in the literature sometimes without full awareness that they are different, and that both are in principle allowed. This is a reason for numerous disputes and controversies. Knowing that we are dealing with the two equivalent quantifications of the same phenomenon solves the issue. Let us remember: our task is not only describe resonances, but describe them in a way which is identical to QCD. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 The final answer to which of the two resonance definitions should be used comes from analyzing what is precisely calculated in QCD! Is it a time delay or a resolvent pole?

17. Scattering resonances: HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

18. They are aware that it is nowadays usual to identify resonances as resolvent resonances: However they still advocate the idea of using scattering resonances instead However they still advocate the idea of using scattering resonances instead: HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

19. Resolvent resonances: Concept of resolvent resonances is at length discussed in HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

20. Highlights: 1.Equivalence of Hamiltonian eigenstates and resolvent poles HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

21. 2.The conservation of probability requires that the resolvent poles lie in the complex energy plane HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

22. 3.Importance of background

23. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

25. So, his final recommendation goes with Hamiltonian eigenstates – poles (resolvent resonance definition). HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

26. Complex poles and non-hermitian operators

27. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

28. Complex poles and non-hermitian operators

29. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

30. What is a resonance in QCD? Talk presented at the Workshop "Light-cone Physics: Particles and Strings" at ECT* in Trento, Sep 3-11, 2001...solving the bound-state problem in gauge filed theory, particularly QCD... HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

31. How is it done? Light-cone approach resonances Hamiltonian proper values HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 Hamiltonian proper values Remember Dalitz-Moorhouse Remember Dalitz-Moorhouse poles

32. discrete light-cone quantization HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 For the compilation of other approaches see ref.

33. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 At this Workshop we have seen that LQCD can also directly give phase shifts using Lüscher’s approach!

34. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

35. So, in principle: QCD is analyzing resolvent resonances ! Remember Exner and Lipovsky definition of resolvent resonance:

36. So the answer to our question is:  POLES HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

37. II How to extract T-matrix poles HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 II-b. Highlights from Camogli II -a Importance of inelastic channels

38. Model 3 Model 2 Experimental data base Poles 1 Poles 2 Poles 3 Under which conditions we have: Poles 1 = Poles 2 = Poles 3 ? HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

39. II -a Importance of inelastic channels

40. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

42. What is the procedure? 1.Having a coupled-channel formalism and fitting data only in one channel will “mimic” single channel case. 2.By fitting one channel only we shall reveal those poles (resonant states) which dominantly couple to this channel. 3.Poles (resonant states) which do not couple to this channel will remain undetected. 4.Consequently, we have not been able to discover ALL analytic function poles, consequently the partial wave analytic function is ambiguous. 5.If we add data for the second inelastic channel, we constrain other set of poles which dominantly couple to this channel. This set of poles is overlapping with the first one, but not necessarily identical. 6.We have established a new, enlarged set of poles which is somewhat more constraining the unknown analytic function 7.We add new inelastic channels until we have found all scattering matrix poles, and uniquely identified the type of analytic PW function The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7-16 Nov.2009.

44. Example 1: The role of inelastic channels in N (1710) P 11 The role of inelastic channels in N (1710) P 11 Published: The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7-16 Nov.2009.

46. All coupled channel models are based on solving Dyson-Schwinger integral type equations, and they all have the same general structure: full = bare + bare * interaction* full full = bare + bare * interaction* full CMB coupled-channel model The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7-16 Nov.2009.

47. Carnagie-Melon-Berkely (CMB) model Instead of solving Lipmann-Schwinger equation of the type: with microscopic description of interaction term we solve the equivalent Dyson-Schwinger equation for the Green function with representing the whole interaction term effectively. The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7-16 Nov.2009.

48. We represent the full T-matrix in the form where the channel-resonance interaction is not calculated but effectively parameterized: channel-resonance mixing matrix bare particle propagator channel propagator

49. Assumption: Assumption: The imaginary part of the channel propagator is defined as: where q a (s) is the meson-nucleon cms momentum: And we require its analyticity through the dispersion relation: The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7-16 Nov.2009.

50. 5050 we obtain the full propagator G by solving Dyson-Schwinger equation where we obtain the final expression The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7-16 Nov.2009.

51. We use: 1.CMB model for 3 channels:  N,  N, and dummy channel     N elastic T matrices, PDG: SES Ar06  N   N T matrices, PDG: Batinic 95 We fit: 1.πN elastic only  N   N only 3.both channels The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7-16 Nov.2009.

52. Results for extracted pole positions:

53. The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7- 16 Nov.2009.

55. Conclusions 1.Continuum ambiguities appear in single channel PWA, and have to be eliminated. 2.A new way, based on reinstalling unitarity is possible within the framework of couple-channel models. 3.T matrix poles, invisible when only elastic channel is analyzed, may spontaneously appear when inelastic channels are added. 4.It is demonstrated that:  the N(1710) P 11 state exists  the pole is hidden in the continuum ambiguity of VPI/GWU FA02  it spontaneously appears when inelastic channels are introduced in addition to the elastic ones. The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7-16 Nov.2009.

56. Red line: Juelich model Complex  N branch point  no P11(1710) Black line: Zagreb CMB fit to Juelich model Real  2 N branch point  P11(1710) exists HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 However : PRELIMINARY – private information M. Döring When including inelastic πN → KΛ in a CC fit P11(1710) is reinstated Example 2:

57. We propose one way to extract poles from”experiment”: to use Zagreb CMB model to analyze „world” collection of well known PW amplitudes UNDERSTANDING THEM AS PARTIAL WAVE DATA In that way we have effectively merged into one joint error 1.error of fitting different input data bases and 2. error due to different analytic structure of various models. We have to keep in mind that for all analyzed PWA input data base was almost identical, and the reduced  2 comparable, the major part of the obtained difference in pole positions is due to the different analytic structure of the particular model. We did not expect to reproduce the pole positions of each individual analysis because our analytic structure is different from their, we just wanted to extract poles using on and the same tool in each case. 6-th PWA Workshop, GWU, Washington DC, 22-30 June 2011.

58. And have produced a sequel of preprints illustrating how the method works for the S11 partial wave : 1. 2. 6-th PWA Workshop, GWU, Washington DC, 22-30 June 2011.

59. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 II-b. Highlights from Camogli

60. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

61. On Breit-Wigner vs. pole parameters Question: Why using pole parameters when fitting with BW parameters give equally good χ 2 ?

62. Theory discussion session summary (mostly mesons) J.R.Peláez U. Complutense, Madrid

63. On the use of BW and other stuff But my kids can also draw a perfect line interpolating all your data without learning anything about Physics. You can use whatever you want to fit your data…. BUT : If you want to extract POLES or RESONANCE properties you need the correct analytic structure, unitarity, etc… otherwise it might be easily VERY WRONG And their χ 2, will be better than yours…! More seriously… see M. Williams talk

64. On the use of BW and other stuff REFRAIN from making Physical or POLE interpretations unless you are sure your parametrizations make sense in the complex plane (analyticity), are unitary, etc… Thus, if you insist in using whatever you want to fit your data…. It might be useful to make it public and available for others because you want to parametrize the data somehow so that anybody can use it, compare to it, etc… Fine… but.

65. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 Contribution for the white paper: Švarc

66. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 On partial waves vs. full experimental data set Question: Should one use experimental data base or partial waves in a form of partial wave data?

67. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

68. A few transparencies from NSTAR2005 talk: The Jefferson Laboratory Upgrade to 12GeV (INT 09-3), Seattle, 7-16 Nov.2009.

70. On new experiments HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012 Why? Inelastic channel experiments are old and contraversial!

71. Therefore HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

75. III Is the problem well presented in PDG HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

76. I personally believe that PDG is the most important secondary publication in physics because it is read by millions! It is read by: professionals on a daily basis (just to see what is new because they know it by heart) professionals on a daily basis (just to see what is new because they know it by heart) experts in physics for getting reliable info about facts in new fields they might be enteringexperts in physics for getting reliable info about facts in new fields they might be entering professors in education to get the most precise, reliable, and worldly acceptable interpretation of some possibly controversial statements found in literature professors in education to get the most precise, reliable, and worldly acceptable interpretation of some possibly controversial statements found in literature students to get the condensed, precise new knowledge of unknown phenomenastudents to get the condensed, precise new knowledge of unknown phenomena layman to see what is the most current value of certain constant, and how the experts in physics thinklayman to see what is the most current value of certain constant, and how the experts in physics think And I believe that the responsibility of PDG is to sytisfy them all. 6-th PWA Workshop, GWU, Washington DC, 22-30 June 2011.

77. Therefore it is its duty to be PRECISE (define all phenomena, all procedures, all assumptions…)PRECISE (define all phenomena, all procedures, all assumptions…) CONDENSEDCONDENSED CRITICALCRITICAL EXACTEXACT Is it really so today in baryon spectroscopy sector? I am afraid IT IS NOT. The reasons for such a statement of mine is that in spite of strong recent progress in the field this section has barely changed in last 20 years: the definition of resonance is NEVER GIVEN ! PDG is presenting chapters and chapters of the book relying on heuristic understanding of a reader what a resonance really is, and this creates ambiguities. the definition of resonance is NEVER GIVEN ! PDG is presenting chapters and chapters of the book relying on heuristic understanding of a reader what a resonance really is, and this creates ambiguities. the difference between poles and Breit-Wigner parameters is never explicitly giventhe difference between poles and Breit-Wigner parameters is never explicitly given the definition, importance and role of poles is never giventhe definition, importance and role of poles is never given 6-th PWA Workshop, GWU, Washington DC, 22-30 June 2011.

78. At ATHOS 2012 it has been reported that signiificant changes have been done! 1.Prof. Eberhard Klempt replaced Prof. G. Hoehler as being responsible person for hadronic resonance sector Now we have R. Workman and E. Klempt Now we have R. Workman and E. Klempt 2.He has introduced significant changes i.Changed the introduction ii.Added new resonances iii.Accepted some comments from other fields iv.Opened the possible communication link to PDG HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012

82. 6-th PWA Workshop, GWU, Washington DC, 22-30 June 2011.

83. The f0(600) or “sigma” in PDG 1996-2010 M=400-1200 MeV Γ=500-1000 MeV Is f0(500) or “sigma” in PDG 2012 M=400-1200 MeV Γ=500-1000 MeV M=400-550 MeV Γ=400-700 MeV DRAMMATIC AND LONG AWAITED CHANGE ON “sigma” RESONANCE !!

84. And minor correction for the f0(980) mass & more conservative uncertainties

85. HADRONIC RESONANCES, Bled (Slovenia), July 1-8, 2012