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