how strange is the nucleon? martin mojžiš, comenius university, bratislava not at all, as to the...
TRANSCRIPT
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
NdduuN
NssNy
2
NssdduuNm
m
N
22
ˆbaryon octet masses
NdduuNm
m
N
2
ˆ)0(
pNdduupNmputpu ,',ˆ)()()'(
22 2,0 MtDF
N scattering (data)
N scattering (CD point)
2)'( ppt
Nmus 4)(
)2( 2 M
the story of 3 sigmas (none of them being the standard deviation)
baryon octet masses
)0(
N scattering (data)
N scattering (CD point)
)2( 2 M
26 MeV
64 MeV 64 MeV
64 MeV
Gell-Mann, Okubo Gasser, Leutwyler
Brown, Pardee, Peccei
data
Höhler et al.
simple LET
the story of 3 sigmas
26 MeV
64 MeV
NssdduuNm
m
N
22
ˆ
NdduuNm
m
N
2
ˆ
yNdduuN
NssN
2
ˆ
6.0
OOPS !
big y
NHNm
m QCDN
N 2
1
NssNm
mNdduuN
m
mNHN
m N
s
Nmassless
N 22
ˆ
2
1
2ˆy
m
ms NHNm massless
N2
1
26 0.364 MeV
376 MeV 64 MeV 500 MeV
big y is strange
NssmddmuumNNHNNHN sdumasslessQCD
big why
Why does QCD build up the lightest baryon using so much of such a heavy building block?
statesgluonandquarkiicN i
NHN massless
s d
ssdduumassless mmmNHN ###
sddduu mmm ###
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?
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)
)2( 2 M
SU(3)
SU(2)L SU(2)R
SU(2)L SU(2)R
analycity & unitarity
group theory
current algebra
current algebra
dispersion relations
the original numbers:
qmmmmmm
qH sdusmass
830
3
ˆ
23
ˆ2
the original numbers:
qmm
qH ssplitmass 8
3
ˆ
ssdduumm s 2
3
ˆ
• controls the mass splitting (PT, 1st order)• is controlled by the transformation properties
• of the sandwiched operator• of the sandwiching vector
hHh splitmass
hsplitmassH
1
4
11 2 IIYcbYam
cbNssdduuNmm
ms
N 2
12
3
ˆ
2
1
(GMO)
26ˆ
1902
1
392
1
mm
MeVmmb
MeVmmc
s
N
MeV26
qavipsDiqL fieldsextQCD
55.
the original numbers: 0 22 M
1
5.
2
1cugmiL A
fieldsexteffective
the tool: effective lagrangians (ChPT)chiral symmetry
d
uqext
d
u sm
ms
0
0
n
p
0
20 4
8 sF
BBs
sss 00
0s Bic 41 dependencetno constt
the original numbers: 22 M
1
5.
2
1cugmiL A
fieldsexteffective
0
20 4
8 sF
BBs
0s)(
4 021 dependencemomentumnos
F
Bic ab
a
b
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: MeV856
• 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 = 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 papers
KH analysis
underestimated error
N scattering (data)
)2( 2 M
SU(3)
SU(2)L SU(2)R
SU(2)L SU(2)R
analycity & unitarity
group theory
current algebra
current algebra
dispersion relations
corrections:
ChPT
ChPT
ChPT
corrections:
q
Nq
N
q
m
mmNqqN
m
m
2
Feynman-Hellmann theorem
q
qqbq
qqbq
qqbb mDmCmBAm 2,
2/3,,
BorasoyMeißner
• 2nd order Bb,q (2 LECs) GMO reproduced
• 3rd order Cb,q (0 LECs) 26 MeV 335 MeV
• 4th order Db,q (lot of LECs) estimated (resonance saturation)
MeV734
corrections: 0
3rd order Gasser, Sainio, Svarc
integral loop2
34
2
22
12 tItI
F
MgcMt A
MeVF
MgM A 7
64
302
2
322
4th order Becher, Leutwyler
LECorder 4 one with term1402 th2 MeVM
estimated from a dispersive analysis(Gasser, Leutwyler, Locher, Sainio)
MeVM 4.02.152 2
corrections: 22 M
3rd order Bernard, Kaiser, Meißner
MeVM CDCD 35.02 2
4th order Becher, Leutwyler
LECorder 4 one with term0 th MeVCD
large contributions in both (M
2) and canceling each other
MeV1
estimated
corrections: MeV760
• 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. relations data = 0, t = 0
linear approximation = 0, t = 0 = 0, t = M2
less restrictive constrains
better control over error propagation
)0(
N scattering (data)
N scattering (CD point)
)2( 2 M
335 MeV (26 MeV)
447 MeV (64 MeV)
597 MeV (64 MeV)
607 MeV (64 MeV )
data
corrections:
24.025.0 y
new partial wave analysis: MeV90
• 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
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 yet
Roy-like equations
• work in progress