1. Chiral Dynamics How s and Why s 4 th lecture: a specific example Martin Mojžiš, Comenius University23 rd Students’ Workshop, Bosen, 3-8.IX.2006

2. how strange is the nucleon? not at all, as to the strangeness S N = 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 23 rd Students’ Workshop, Bosen, 3-8.IX.2006Martin Mojžiš, Comenius University

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

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

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

6. 26  0.3 64 MeV 376 MeV64 MeV500 MeV big y is strange 23 rd Students’ Workshop, Bosen, 3-8.IX.2006Martin 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 s have a buddy d with the same quantum numbers? 23 rd Students’ Workshop, Bosen, 3-8.IX.2006Martin Mojžiš, Comenius University

8. big 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 ?  small y ? 23 rd Students’ Workshop, Bosen, 3-8.IX.2006Martin Mojžiš, Comenius University

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

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

12. the original numbers: other contributions to the vertex: one from , others with c 2,c 3,c 4,c 5 all with specific p-dependence they do vanish at the CD point ( t = 2M  2 ) for t = 2M  2 (and = 0) both  (t) and (part of) the  N-scattering are controlled by the same term in the L eff 23 rd Students’ Workshop, Bosen, 3-8.IX.2006Martin Mojžiš, Comenius University

13. the original numbers: 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 extrapolation from the physical region to unphysical CD point 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 m u =m d =0) the consequence: great care is needed to extract  from data see original papers fixed-t dispersion relations old database (80-ties) see original papers KH analysis underestimated error 23 rd Students’ Workshop, Bosen, 3-8.IX.2006Martin Mojžiš, Comenius University

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

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

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

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

18. corrections: 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 Gasser, Leutwyler, Sainio forward disp. relationsdata  = 0, t = 0 linear approximation = 0, t = 0  = 0, t = M  2 less restrictive constrains better control over error propagation 23 rd Students’ Workshop, Bosen, 3-8.IX.2006Martin Mojžiš, Comenius University

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

20. new partial wave 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 much less restrictive- up-to-date database+ see original papers VPI 23 rd Students’ Workshop, Bosen, 3-8.IX.2006Martin Mojžiš, Comenius University

21. no conclusions: 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 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 Roy-like equations work in progress 23 rd Students’ Workshop, Bosen, 3-8.IX.2006Martin Mojžiš, Comenius University