How strange is the nucleon? Martin Moj

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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

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the story of 3 sigmas
(none of them being the standard deviation)
baryon octet masses
?N scattering (CD point)
?N scattering (data)
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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
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big y
26 MeV
64 MeV
OOPS !
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big y
is strange
26 ? 0.3
64 MeV
376 MeV
64 MeV
500 MeV
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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?
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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 ?

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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)
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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)
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the original numbers
the tool effective lagrangians (ChPT)
chiral symmetry
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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
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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 mumd0)
• the consequence great care is needed to extract
  ? from data

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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)
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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)

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corrections
3rd order Gasser, Sainio, Svarc
4th order Becher, Leutwyler
estimated from a dispersive analysis (Gasser,
Leutwyler, Locher, Sainio)
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corrections
3rd order Bernard, Kaiser, Meißner
4th order Becher, Leutwyler
large contributions in both ?(M?2) and
? canceling each other
estimated
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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
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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
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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

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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