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KHALED TEILAB IN COLLABORATION WITH SUSANNA GALLAS, FRANCESCO GIACOSA AND
DIRK H. RISCHKE
Meson production in proton-proton scattering within an
eLSM
Outline
The eLSM in the baryonic sectorResults
pion-nucleon scattering length production near threshold
SummaryOutlook
The eLSM in the baryonic sector for Nf
=2
The nucleon and its chiral partner(pseudo-) scalar & (axial-) vector mesonsChiral symmetry and dilatation invariance
mirror assignment
chirally symmetric mass term
C. De Tar and T. Kunihiro, PRD 39 (1989) 2805)
Interaction of baryons with (pseudo-) scalar and (axial-) vector mesons
The eLSM in the baryonic sector for Nf
=2
Details in S. Gallas et al. Phys.Rev. D82 (2010) 014004
The mass of the nucleon
masses thegenerates condensatequark only the0 If 0 m
0m parameterizes the contribution which does not stem from the quark condensate
MeV 5000 m
Details in S. Gallas, Francesco Giacosa and Dirk H. Rischke, Phys.Rev. D82 (2010) 014004
pion-nucleon scattering length
-14(exp)0
-140 MeV 10)1.04.6( MeV 10)63.004.6( aa
-14(exp)0
-140 MeV 10)2.78.8( MeV )1020 to20from( aa
Mirror assignment and vector mesons are important to obtain this agreement
large theoretical uncertainty due to the scalar-isoscalar sector
Baryonic Lagrangian with physical fields
1p
2p
'1p
'2p
X
X'1p
'2p2p
1p *N
,,, AV
,,, AV
,,,, AV
,,,, AV
NO RESONANCE
pp→pp near threshold
no resonance
References for data points in: F. Balestra et al. Phys. Rev. C, Vol. 63, 024004
pp→pp near threshold
no resonance
N(1535)
N(1650)
pp→pp near threshold
m=778 MeV
m=782 MeV
m=786 MeV
NO RESONANCE
m=791 MeV
m=774 MeV
Summary
● A chirally symmetric Lagrangian was developed with baryons and vector mesons
● Only 5 more parameters in the baryonic sector
● pion-nucleon scattering length in agreement with experiment
● Good description of production near threshold
● Outlook …
pp→pp away from threshold
no resonance
N(1535)
N(1650)
pp→pp away from threshold
no resonance and no
pp→pp
References for data points in: F. Balestra et al. Phys. Rev. C, Vol. 69, 064003
no resonance and no
pp→pppp→pp pp→pppp→pp
mesons
no resonance and no
no resonance and no
Thank you!
Backup
Lagrangian in the baryon sector
Interaction of baryons with (pseudo)scalar and (axial-)vector mesons
0
*
2cosh
m
MMar NN
)1535(**
)940(
NN
NN
The eLSM with Nf =2● spontaneous breaking of chiral symmertry● ● non-physical mixing terms appear
● Solution:– shift of the axial vectors as:
– renormalize the pseudoscalars as:
Black disk unitarization
pp→pp near threshold
N(1535)
N(1650)
same parameters for both curves
Dependence on the resonance mass
pp→pp near threshold
Large sensitivity to the parameters c1 and c2
c1=-3.0
c1=-4.0
c1=-5.0
c2=11
c2=13
c2=15
c2 fixed at 13 c1 fixed at -3.0
Dependence on the parameters c1 and c2
Mass of the nucleon
masses. thegenerates condensatequark only the0 If 0 m
0mCrucial also at nonzero temperature and density also in the so-called quarkyonic phase: L. McLerran, R. Pisarski Nucl.Phys.A796:83-100,2007
parameterizes the contribution which does not stem from the quark condensate
MeV 1364600 m
MeV 67 and )latt( 2.0 (exp), 26.1 Using NN** NA
NA gg
)1535(**
)940(
NN
NN
Details in S. Gallas, F. G., D. H. Rischke, Phys.Rev. D82 (2010) 014004, arXiv:0907.5084
Nm