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Chiral Dynamics How s and Why s

Chiral Dynamics How s and Why s. 4 th lecture: a specific example. 23 rd Students’ Workshop, Bosen, 3-8.IX.2006. Martin Mojžiš, Comenius University. how strange is the nucleon?. not at all, as to the strangeness S N = 0 not that clear, as to the strangeness content.

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Chiral Dynamics How s and Why s

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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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