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Exploring Chiral Dynamics: Insights from the 23rd Students' Workshop, Bosen 2006

This lecture delves into chiral dynamics and its implications for particle physics, specifically the nucleon and its strangeness content. Through a specific example and effective theory techniques, the discussion sheds light on the baryon octet masses and pN scattering data. The seminar emphasizes the importance of corrections in understanding mass splitting and explores the intricacies of the SU(3) and SU(2) current algebra. Participants will gain insight into the challenges of extracting crucial quantities like strangeness from experimental data, illustrating the complex nature of QCD.

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Exploring Chiral Dynamics: Insights from the 23rd Students' Workshop, Bosen 2006

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  1. Chiral DynamicsHows and Whys 4th lecture: a specific example 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  2. how strange is the nucleon? • not at all, as to the strangeness SN = 0 • not that clear, as to the strangeness content • determination of y is a nice illustration of the use of the effective theory in symbiosis with other techniques 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  3. the story of 3 sigmas (none of them being the standard deviation) baryon octet masses N scattering (CD point) N scattering (data) 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  4. the story of 3 sigmas Gell-Mann, Okubo Gasser, Leutwyler baryon octet masses 26 MeV 64 MeV simple LET 64 MeV Brown, Pardee, Peccei N scattering (CD point) 64 MeV Höhler et al. N scattering (data) data 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  5. big y 26 MeV 64 MeV OOPS ! 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  6. big y is strange 64 MeV 26  0.3 376 MeV 64 MeV 500 MeV 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  7. big why Why does QCD build up the lightest baryon using so much of such a heavy building block? s  d does not work for s with a buddy d with the same quantum numbers but why should every shave a buddy d with the same quantum numbers? 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  8. big y  small y ? • How reliable is the value of y ? • What approximations were used to get the values of the three sigmas ? • Is there a way to calculate corrections to the approximate values ? • What are the corrections ? • Are they going in the right directions ? • Are they large enough to decrease y substantially ? 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  9. the original numbers: SU(3) group theory current algebra SU(2)L  SU(2)R current algebra SU(2)L  SU(2)R dispersion relations analycity & unitarity N scattering (data) 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  10. the original numbers: • controls the mass splitting (PT, 1st order) • is controlled by the transformation properties • of the sandwiched operator • of the sandwiching vector (GMO) 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  11. the original numbers: chiral symmetry the tool: effective lagrangians (ChPT) 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  12. the original numbers: • one from , others with c2,c3,c4,c5 • all with specific p-dependence • they do vanish at the CD point ( t = 2M2 ) other contributions to the vertex: for t = 2M2(and = 0) both (t) and (part of) the N-scattering are controlled by the same term in the Leff 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  13. the original numbers: underestimated error extrapolation from the physical region to unphysical CD point KH analysis • a choice of a parametrization of the amplitude • a choice of constraints imposed on the amplitude • a choice of experimental points taken into account • a choice of a “penalty function” to be minimized • see original papers • fixed-t dispersion relations • old database (80-ties) • see original papers • many possible choices, at different level of sophistication • if one is lucky, the result is not very sensitive to a particular choice • one is not • early determinations: Cheng-Dashen  = 110 MeV, Höhler  = 4223 MeV • the reason: one is fishing out an intrinsically small quantity (vanishing for mu=md=0) • the consequence: great care is needed to extract  from data 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  14. corrections: SU(3) group theory ChPT current algebra SU(2)L  SU(2)R ChPT current algebra SU(2)L  SU(2)R ChPT dispersion relations analycity & unitarity N scattering (data) 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  15. corrections: Feynman-Hellmann theorem Borasoy Meißner • 2nd order Bb,q (2 LECs) GMO reproduced • 3rd order Cb,q (0 LECs) 26 MeV  335 MeV • 4th order Db,q (lot of LECs) estimated (resonance saturation) 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  16. corrections: 3rdorder Gasser, Sainio, Svarc 4thorder Becher, Leutwyler estimated from a dispersive analysis (Gasser, Leutwyler, Locher, Sainio) 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  17. corrections: 3rdorder Bernard, Kaiser, Meißner 4thorder Becher, Leutwyler large contributions in both (M2) and  canceling each other estimated 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  18. corrections: Gasser, Leutwyler, Sainio • a choice of a parametrization of the amplitude • a choice of constraints imposed on the amplitude • a choice of experimental points taken into account • a choice of a “penalty function” to be minimized • see original papers • forward dispersion relations • old database (80-ties) • see original papers forward disp. relations data   = 0, t = 0 linear approximation  = 0, t = 0  = 0, t = M2 less restrictive constrains better control over error propagation 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  19. corrections: 335 MeV (26 MeV) 447 MeV (64 MeV) 597 MeV (64 MeV) N scattering (CD point) 607 MeV (64 MeV ) N scattering (data) data 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  20. new partial wave analysis: VPI • a choice of a parametrization of the amplitude • a choice of constraints imposed on the amplitude • a choice of experimental points taken into account • a choice of a “penalty function” to be minimized • see original papers • much less restrictive - • up-to-date database + • see original papers 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

  21. no conclusions: Roy-like equations • a choice of a parametrization of the amplitude • a choice of constraints imposed on the amplitude • a choice of experimental points taken into account • a choice of a “penalty function” to be minimized • Becher-Leutwyler • well under control • up-to-date database • not decided yet • new analysis of the data is clearly called for • redoing the KH analysis for the new data is quite a nontrivial task • work in progress (Sainio, Pirjola) • Roy equations used recently successfully for -scattering • Roy-like equations proposed also for N-scattering • work in progress 23rd Students’ Workshop, Bosen, 3-8.IX.2006 Martin Mojžiš, Comenius University

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