1 / 20

Unraveling the Mystery of Nucleon Strangeness: A Detailed Analysis

Explore the intricate world of nucleon strangeness through a comprehensive examination of baryon octet masses, πN scattering data, and corrections to approximate values. This study delves into the complexities of QCD and symmetry theories to understand the enigmatic properties of nucleons.

tad
Download Presentation

Unraveling the Mystery of Nucleon Strangeness: A Detailed Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. How strange is the nucleon?Martin Mojžiš, Comenius University, Bratislava • Not at all, as to the strangeness SN = 0 • Not that clear, as to the strangness content

  2. the story of 3 sigmas (none of them being the standard deviation) baryon octet masses N scattering (CD point) N scattering (data)

  3. 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

  4. big y 26 MeV 64 MeV OOPS !

  5. big y is strange 64 MeV 26  0.3 376 MeV 64 MeV 500 MeV

  6. 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?

  7. 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 large enough to decrease y substantially ? • Are they going in the right directions ?

  8. 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)

  9. 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)

  10. the original numbers: chiral symmetry the tool: effective lagrangians (ChPT)

  11. 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

  12. 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

  13. 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)

  14. 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)

  15. corrections: 3rdorder Gasser, Sainio, Svarc 4thorder Becher, Leutwyler estimated from a dispersive analysis (Gasser, Leutwyler, Locher, Sainio)

  16. corrections: 3rdorder Bernard, Kaiser, Meißner 4thorder Becher, Leutwyler large contributions in both (M2) and  canceling each other estimated

  17. 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

  18. 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

  19. 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

  20. 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 controll • 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

More Related