Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe...

33
The chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration with: Francesco Giacosa and Dirk Rischke Excited QCD 8-14 February 2009- Zakopane (Poland)

Transcript of Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe...

Page 1: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

The chiral partner of the nucleon

in the mirror assignment

Susanna Gallas

in collaboration with:

Francesco Giacosa and Dirk Rischke

Excited QCD8-14 February 2009- Zakopane (Poland)

Page 2: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

])()[(2

])()[(4

1

)]([)]det()[det(

)()]([][)])([(

22

2

122

2

2

2

1

2

µµν

µ

µµν

µ λλ

RLTrm

RLTr

HTrc

TrTrTrmDDTrLmes

+++

−Φ+Φ+Φ+Φ

+ΦΦ−ΦΦ−ΦΦ−ΦΦ=

++

+++

)(ˆLRRL

RRRRLLLL

g

RgiLgi

ΨΦΨ+ΦΨΨ−

ΨΨ+Ψ∂Ψ+ΨΨ+Ψ∂Ψ

+

µµ

µµ

µµ

µµ γγγγ

Talk 09.02.09 by D. Parganlija:

+ Baryons:

Page 3: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Motivation

Introduction of N* for chiral realization of the nucleonic Lagrangian

z chiral invariant mass term =/ m0

Correct description of the axial coupling constantgA(N)=1.26

gA(N*)=?

Generation of the nucleonic mass: how is mN generated?

Quark condensate vs. m0

Study of pion-nucleon scattering

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Page 4: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

The chiral partner:

what is N*?

Page 5: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Mirror assignment vs naive assignment: chiral transformation

LRL

LLL

U

U

22

11

Ψ→Ψ

Ψ→Ψ

Mirror

RLR

RRR

U

U

22

11

Ψ→Ψ

Ψ→Ψ

Naive

RRR

RRR

U

U

22

11

Ψ→Ψ

Ψ→Ψ

LLL

LLL

U

U

22

11

Ψ→Ψ

Ψ→Ψ

)( 121221210 RLLRLRRLm ΨΨ+ΨΨ−ΨΨ−ΨΨ−

Nucleon mass not only

dynamically generated

No chiral invariant mass term

2 independent Linear Sigma models

RLRL SUSUUU )2()2( ×∈×

22

*

2

1

1ˆxM

N

N

=

Ψ

Ψ=

2

1

*M̂

N

N221ˆ

xM ≠

The chiral partner of the nucleonin the mirror assignment

Page 6: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

The chiral partner of the nucleonin the mirror assignment

Candidates with the correct quantum numbers from PDG:

N*(1535) lowest nucleonic resonance

N*(1650) −

=2

1PJ

Other possibility (speculative):

N*(1200) (D. Zschiesche, L. Tolos, J. Schaffner-Bielich, R. Pisarski, Phys.Rev.C75:055202,2007)

Very broad resonance? Not yet measured?

Page 7: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

A little bit of scattering theory

Page 8: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

A little bit of scattering theory

cbacabba iBqqABqqAT τεγδγ µµµ

µµµ

+++

++= −−++ )(

21

)()(

21

)( )(2

1)(

2

1

General form of the Lorentz-invariant scattering amplitude: )()( 12 puTpu ba

)()(

0

)(

0

)(

0

±±±+= BmAa πηs-wave scattering lengths: )1(4

1

Nm

mππη

+

=

22 )(,)(,0 ππ mmummst NN −=+==

Page 9: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Some important data

H. Schroder: Measured pion nucleon scattering lengths from pionic

hydrogen and deuterium at PSI (Eur.Phys.J.C21:473-488,2001)

14)(

0

16)(

0

10)1146.041256.6(

10)165.785783.8(

−−−

−−+

±=

±−=

MeVa

MeVa

T. Takahashi and T. Kunihiro: Axial charge of N(1535) in lattice

QCD (e-Print: arXiv:0801.4707)

3.02.0*

±=N

Ag

L. Ya. Glozman: Phys.Rept.444:1-49,2007

resultdifferent apresent shall we

1partner theis if

partner not the is 0*

*

*

*

−≈→

→≈

N

A

N

A

gN

Ng

Page 10: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

The model

Page 11: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Linear sigma model with vector and axial vector

mesons,as well as the nucleonic

fieldsin the mirror assignmentlocal symmetric case

Page 12: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Spontaneus symmetry breaking

ϕσσ +→

leads to mixing terms in the Lagrangian: µ

µµ

µ ϕπηϕ 11 agfgrr

⋅∂−∂−

we need to perform the shifts of the axial fields:

η

πµµµ

µµµ

∂+→

∂+→

wff

waa

11

11

rrr

2)(1

ϕ

ϕ

gm

gw

a +=

and to renormalize the pseudoscalar fields:

ηη →Z

1ππrr

→Z

1

S. Gasiorowicz and D.A.Geffen , Rev.Mod.Phys.41:531-573,1969.

ρm

mZ

relation-KSFRby predicted as 2

a=

=Z

Page 13: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Mesonic sector of the lagrangian

])()[(2

])()[(4

1

)]([)]det()[det(

)()]([][)])([(

22

2

122

2

2

2

1

2

µµν

µ

µµν

µ λλ

RLTrm

RLTr

HTrc

TrTrTrmDDTrLmes

+++

−Φ+Φ+Φ+Φ

+ΦΦ−ΦΦ−ΦΦ−ΦΦ=

++

+++

tatfR

tatfL

tiati

rrr

rrr

rrr

)()(

)()(

)()(

101

101

00

µµµµµ

µµµµµ

ρω

ρω

πησ

−+−=

+++=

+++=Φ [ ][ ]νµµννµµν

νµµννµµν

RRigRRR

LLigLLL

,

,

−∂−∂=

−∂−∂=

Fields Field strength tensor

nucleonL+)( Φ−Φ+Φ∂=Φ µµµµLRigD

Page 14: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Introducing the chiral partner

)(

)(ˆ)(ˆ

121221210

2222211111

22222222

11111111

RLLRLRRL

LRRLLRRL

RRRRLLLL

RRRRLLLLnucl

m

gg

LgiRgi

RgiLgiL

ΨΨ+ΨΨ−ΨΨ−ΨΨ−

ΦΨΨ+ΨΦΨ−ΨΦΨ+ΦΨΨ−

ΨΨ+Ψ∂Ψ+ΨΨ+Ψ∂Ψ+

ΨΨ+Ψ∂Ψ+ΨΨ+Ψ∂Ψ=

++

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

γγγγ

γγγγ

0~ mqqmN +⟩⟨ ?

Page 15: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Mixing angle and mass m0

+=

02cosh

*

m

mmar NNδMixing angle:

*

2,1

2

*

1

*

21

20

,

,

NN

NN

NN

±=Ψ⇒→

=Ψ=Ψ⇒−∞→

=Ψ=Ψ⇒∞→

δ

δ

δno mixing

maximal mixing

−±++=

2)(4)(

2

121

2

0

22

21*,

ϕϕ ggmggm NN

))))

−=

2/2/

5

2/

5

2/

cosh2

1ˆδδ

δδ

γ

γ

δ ee

eeM

Ψ

Ψ=

2

1

*M̂

N

N with

:massesnucleon ˆ ediagonaliz ⇒M

Page 16: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Mixing angle and mass m0

1 2 3 4 5d

200

400

600

800

1000

1200

m0

δ

δδ

sinh4

),,(ˆ),,(ˆ ** 21

0NNNN mmgmmg

m+

=

[MeV]

Page 17: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Linear sigma model with vector and axial vector

mesons,as well as the nucleonic

fieldsin the mirror assignmentlocal symmetric case:

Results

Page 18: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

The s-wave scattering lengths

2=Z14)(

exp,0

16)(

exp,0

10)1146.041256.6(

10)165.785783.8(

−−−

−−+

±=

±−=

MeVa

MeVa

Axial coupling constant of N*(1535)

26.1

3.02.0

*

*

,

,

−=

±=

N

GlozmanA

N

LatticeA

g

g

][1−

MeV

][ 1−MeV

S.W.(S.G.), F. Giacosa, D.Rischke,e-Print: nucl-th/0702076

Results: locally symmetric model

Page 19: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

modelour improve toneed we

consistentnot are Results

)a with compatible(not smallor very 03.02.0

1.26 is valuealexperimentbut 1)tanh(

valuesalexperimentwith agreement in not is alength Scattering

5.1for valuesalexperimentwith agreement in alength Scattering

)(

0

2

(-)

0

)(

0

*

<→±=•

<=•

>•

+

+

δ

δ

δ

N

A

N

A

g

Zg

Conclusions: locally symmetric model

Page 20: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Global chiral symmetry

in agreement with mesonic decays

Page 21: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Model with global symmetry

)(

)(ˆ)(ˆ

][2][

])()[(][2

121221210

2222211111

2222222222

1111111111

32

221

RLLRLRRL

LRRLLRRL

RRRRLLLL

RRRRLLLL

mes

m

gg

LciRci

RciLci

LRTrhRRLLTrh

RLTrTrh

LL

ΨΨ+ΨΨ−ΨΨ−ΨΨ−

ΦΨΨ+ΨΦΨ−ΨΦΨ+ΦΨΨ−

ΨΨ+Ψ∂Ψ+ΨΨ+Ψ∂Ψ+

ΨΨ+Ψ∂Ψ+ΨΨ+Ψ∂Ψ

+ΦΦ+ΦΦ+ΦΦ+

+ΦΦ+=

++

+++

+

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

γγγγ

γγγγ

[ ][ ]νµµννµµν

νµµννµµν

RRigRRR

LLigLLL

,

,

2

2

−∂−∂=

−∂−∂=

Changes in :

)(1 Φ−Φ+Φ∂=Φ µµµµLRigD

mesL

Page 22: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Model with global symmetry

We determine the free parameters of the modelm0, c1, and c2 from

N*(1200): speculative candidate, decay width GN*zpN > 800 MeV

NN

N

A

N

A ggπ→

Γ *,, *

N*(1500) : PDG , decay width GN*zpN = 67.5 MeV

N*(1650): PDG, decay width GN*zpN =92.5+/-37.5 MeV

Page 23: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Results

Global chiral symmetry

in agreement with mesonic decays

Page 24: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

m0 vs. the axial coupling constant of N*(1535)

350 MeV < m0 < 600 MeV

[MeV]

Results: globally symmetric model

S.G., F. Giacosa, D.Rischke,e-Print: hep-ph/0901.4043

Page 25: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Results: globally symmetric model

Page 26: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Results: globally symmetric model

s-wave scattering lengths

mN* = 1535 MeV

Page 27: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Results: globally symmetric model

s-wave scattering lengths

N*(1535)N*(1650)

N*(1200) is off by over a factor 1000!

N*(1200)

Page 28: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Introducing a

scalar tetraquark(preliminary)

Page 29: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Introducing the tetraquark

)(

)(ˆ)(ˆ

][2

][

12122121

0

0

2222211111

2222222222

1111111111

3

2

RLLRLRRL

LRRLLRRL

RRRRLLLL

RRRRLLLL

mes

m

gg

LciRci

RciLci

LRTrh

RRLLTrhLL

ΨΨ+ΨΨ−ΨΨ−ΨΨ−

ΦΨΨ+ΨΦΨ−ΨΦΨ+ΦΨΨ−

ΨΨ+Ψ∂Ψ+ΨΨ+Ψ∂Ψ+

ΨΨ+Ψ∂Ψ+ΨΨ+Ψ∂Ψ

+ΦΦ+

ΦΦ+ΦΦ+=

++

+

++

χ

χ

γγγγ

γγγγ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

µµ

(almost) as before:

)()(2

1)(

2

1 2222222

µµχµχ χπσχχχ LRbgmL ++++−∂=

and add:

Page 30: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Introducing the tetraquark

[ ][ ]dudu ,,2

1=χ

−=

σ

χ

ϑϑ

ϑϑ

cossin

sincos

S

H

22

4arctan

2

1

χσ

ϕϑ

mm

g

−=

)(2

1dduu +=σ

)1370(tly predominan

)600(tly predominan

0

0

fS

fH

)( 22 πσχχσ += gL

Page 31: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Results: the tetraquark

b=-100

b=0

)()( 2222

µµχπσχ LRbg ++++

The isospin even scattering length as a function of g

Page 32: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Results: the tetraquark

b=100

b=0

b=-100

b=-200

0 ,MeV 2500 21 === hhg

The isospin even scattering length as a function of the axial charge of the

chiral partner of the nucleon for g=2500 MeV and different values of b.

by A. Heinz et. al in finite temperature studies (hep-ph 08051134) GeVg 5.2≈

][])()[(][2

2

221 +++ ΦΦ+ΦΦ++ΦΦ µµ

µµ

µµRRLLTrhRLTrTr

h

Page 33: Gallas The chiral partner in the mirror assignmentexcitedqcd/Talks09/Gallas_ZakopaneExQCD09.pdfThe chiral partner of the nucleon in the mirror assignment Susanna Gallas in collaboration

Excited QCD 8-14 February 2009- Zakopane (Poland) Susanna Gallas

Conclusions and outlook

future. in the also included be should resonance delta The

included. israquark scalar tet a scalars on the depends length scattering The

studyour by favorednot is MeV 1200 massth partner wi broad very e,speculativ of hypothesis The

studies) densities and re temperatufiniteat also(relevant

limit chiral in the survives massnucleon theof half :MeV 500 topointsresult The

small. tooarelength scattering one and eta-nucleon intodecay al theoretichealthough t

,assignmentmirror in thenucleon theofpartner chiral thebe tocandidate good a is (1535)

)(

0

0

*

⇒•

ť

+a

m

N

The scalar tetraquark field shifts the isospin even scattering length in the “right direction”. It has no

influence on isospin odd scattering length.

A large value of the coupling constant g is favoured. i.e. a strong mixing between the quarkonium and

tetraquark fields.

Thank you!