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How strange is the nucleon? Martin Mojžiš, Comenius University, Bratislava. Not at all, as to the strangenessS N = 0 Not that clear, as to the strangness content. the story of 3 sigmas. (none of them being the standard deviation). baryon octet masses. N scattering (CD point). - PowerPoint PPT Presentation

How strange is the nucleon?

Martin Moji, Comenius University, BratislavaNot at all, as to the strangenessSN = 0

Not that clear, as to the strangness content

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

baryon octet masses N scattering (data)N scattering (CD point)26 MeV 64 MeV 64 MeV 64 MeV Gell-Mann, Okubo Gasser, LeutwylerBrown, Pardee, PecceidataHhler et al.simple LETthe story of 3 sigmas

26 MeV 64 MeV OOPS !big y

26 0.364 MeV376 MeV64 MeV500 MeVbig yis strange

big whyWhy does QCD build up the lightest baryon using so much of such a heavy building block? s ddoes not work for s with a buddy d with the same quantum numbersbut why should every s have a buddy d with the same quantum numbers?

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 large enough to decrease y substantially ? Are they going in the right directions ? small y?

N scattering (data)SU(3)SU(2)L SU(2)RSU(2)L SU(2)Ranalycity & unitaritygroup theorycurrent algebracurrent algebradispersion relationsthe original numbers:

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)

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

the original numbers:other contributions to the vertex: one from , others with c2,c3,c4,c5 all with specific p-dependence they do vanish at the CD point ( t = 2M2 )for t = 2M2 (and = 0) both (t) and (part of) the N-scattering are controlled by the same term in the Leff

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 minimizedextrapolation 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, Hhler = 4223 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 see original papers fixed-t dispersion relations old database (80-ties) see original papersKH analysisunderestimated error

N scattering (data)SU(3)SU(2)L SU(2)RSU(2)L SU(2)Ranalycity & unitaritygroup theorycurrent algebracurrent algebradispersion relationscorrections: ChPT ChPT ChPT

corrections:Feynman-Hellmann theoremBorasoyMeiner 2nd orderBb,q (2 LECs)GMO reproduced 3rd orderCb,q (0 LECs)26 MeV 335 MeV 4th orderDb,q (lot of LECs)estimated (resonance saturation)

corrections:3rd order Gasser, Sainio, Svarc 4th order Becher, Leutwyler estimated from a dispersive analysis(Gasser, Leutwyler, Locher, Sainio)

corrections:3rd order Bernard, Kaiser, Meiner4th order Becher, Leutwyler

large contributions in both (M2) and canceling each other

estimated

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 papersGasser, Leutwyler, Sainioforward disp. relationsdata = 0, t = 0

linear approximation = 0, t = 0 = 0, t = M2

less restrictive constrains

better control over error propagation

N scattering (data)N scattering (CD point)335 MeV (26 MeV) 447 MeV (64 MeV)597 MeV (64 MeV)607 MeV (64 MeV )datacorrections:

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 papersVPI

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 controll up-to-date database not decided yetRoy-like equations work in progress