the chiral partner of the nucleon in the mirror assignment hadrons@fair university frankfurt susanna...
Post on 22-Dec-2015
213 views
TRANSCRIPT
The chiral partner of the nucleon
in the mirror assignment
Hadrons@FAIR University Frankfurt
Susanna Wilms
in collaboration with: Francesco Giacosa and Dirk Rischke
Motivation
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Introduction of N* for chiral realization of the nucleonic Lagrangian
chiral invariant mass term / m0
Correct description of the axial coupling constant gA(N)=1.26 gA(N*)=?
Generation of the nucleonic mass: how is mN generated?
Quark condensate vs. m0
Study of pion-nucleon scattering
The chiral partner:
what is N*?
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
The chiral partner of the nucleonin the mirror assignment
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Mirror assignment vs naive assignment: chiral transformation
LRL
LLL
U
U
22
11
Mirror
RLR
RRR
U
U
22
11
Naive
RRR
RRR
U
U
22
11
LLL
LLL
U
U
22
11
)( 121221210 RLLRLRRLm
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
2
1
* M̂N
N221ˆ
xM
The chiral partner of the nucleonin the mirror assignment
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Candidates with the correct quantum numbers from PDG:
N*(1535) lowest nucleonic resonanceN*(1650)
2
1PJOther possibility (speculative):
N*(1200) (D. Zschiesche, L. Tolos, J. Schaffner-Bielich, R. Pisarski, Phys.Rev.C75:055202,2007)
Very broad resonance? Not yet measured?
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
A little bit of scattering theory
A little bit of scattering theory
cbacabba iBqqABqqAT
)(
21)()(
21)( )(
2
1)(
2
1
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
General form of the Lorentz-invariant scattering amplitude: )()( 12 puTpu ba
)( )(0
)(0
)(0
BmAa s-wave scattering lengths: )1(4
1
Nmm
Pion-nucleon scattering
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
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*
NAg
L. Ya. Glozman: Phys.Rept.444:1-49,2007
resultdifferent apresent shall we
1partner theis if
partner not the is 0*
*
*
*
NA
NA
gN
Ng
The model
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Linear sigma model with vector and axial vector mesons,
as well as the nucleonic fields in the mirror assignment
local symmetric case
Weinberg-Tomozawa-termlocal chiral symmetry
Global chiral symmetryin agreement with mesonic
decays
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Linear sigma model with vector and axial vector
mesons, as well as the nucleonic fields
in the mirror assignmentlocal symmetric case
Mesonic sector of the lagrangian
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
])()[(2
])()[(4
1
)]([)]det()[det(
)()]([][)])([(
222
122
22
21
2
RLTrm
RLTr
HTrc
TrTrTrmDDTrLmes
tatfR
tatfL
tiati
)()(
)()(
)()(
101
101
00
RRigRRR
LLigLLL
,
,
Fields Field strength tensor
nucleonL)( LRigD
Spontaneus symmetry breaking
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
leads to mixing terms in the Lagrangian:
11 agfg
we need to perform the shifts of the axial fields:
wff
waa
11
11
2)(1
gm
gw
a
and to renormalize the pseudovector fields:
Z
1
Z
1
KSFR 2Z
Introducing the chiral partner
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
)(
)(ˆ)(ˆ
121221210
2222211111
22222222
11111111
RLLRLRRL
LRRLLRRL
RRRRLLLL
RRRRLLLLnucl
m
gg
LgiRgi
RgiLgiL
0~ mqqmN ?
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Mixing angle and mass m0
02cosh
*
m
mmar NNMixing angle:
*
2,1
2*
1
*21
20
,
,
NN
NN
NN
no mixing
maximal mixing
2)(4)(
2
121
20
2221*,
ggmggm NN
2/2/5
2/5
2/
cosh2
1ˆ
ee
eeM
2
1
* M̂N
N with
:massesnucleon ˆ ediagonaliz M
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Mixing angle and mass m0
1 2 3 4 5
200
400
600
800
1000
1200
m 0
sinh4
),,(ˆ),,(ˆ ** 210
NNNN mmgmmgm
[MeV]
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Linear sigma model with vector and axial vector
mesons, as well as the nucleonic fields
in the mirror assignmentlocal symmetric case:
Results
Introducing the chiral partner
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
The s-wave scattering lengths
2Z14)(
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*
*
,
,
NGlozmanA
NLatticeA
g
g
][ 1MeV
][ 1MeV
S.W., F. Giacosa, D.Rischke,e-Print: nucl-th/0702076
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Introducing the chiral partnerConclusions
modelour improve toneed we
consistentnot are Results
)a with compatible(not smallor very 03.02.0
1.26 is valuealexperimentbut 11
valuesalexperimentwith agreement in not is alength Scattering
5.1for valuesalexperimentwith agreement in alength Scattering
)(0
2
(-)0
)(0
*
NA
NA
g
Zg
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Global chiral symmetry
in agreement with mesonic decays
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Model with global symmetry
)(
)(ˆ)(ˆ
121221210
2222211111
2222222222
1111111111
RLLRLRRL
LRRLLRRL
RRRRLLLL
RRRRLLLLnucl
m
gg
LciRci
RciLciL
RRigRRR
LLigLLL
,
,
2
2
And in the mesonic sector:
)(1 LRigD
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Model with global symmetry
We determine the free parameters of the model m0, c1, and c2 from
N*(1200): speculative candidate, decay width N*N > 800 MeV
NN
NA
NA gg
*,, *
N*(1500) : PDG , decay width N*N = 67.5 MeV
N*(1650): PDG, decay width N*N =92.5+/-37.5 MeV
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Results
Global chiral symmetry
in agreement with mesonic decays
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
m0 vs. the axial coupling constant of N*(1535)
Global symmetry: Results
350 MeV < m0 < 600 MeV
[MeV]
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Global symmetry: Results
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Global symmetry: Results
s-wave scattering lengths
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Global symmetry: Results
s-wave scattering lengths
N*(1535)N*(1650)
N*(1535)N*(1650)
N*(1200)
N*(1200) is off by over a factor 1000!
Susanna Wilms Hadrons@FAIR 25-27 June 2008 Susanna Wilms Hadrons@FAIR 25-27 June 2008
Conclusions
lenghts. scattering ofn descriptiobetter afor resonance, delta theinclude also shall studies Future
scalarslight of issue intricate thefrom
t independenrather are i.e. meson. sigma theof mass on the weakly depend Results
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
large. tooarelength scattering one and eta-nucleon intodecay al theoretichealthough t
,assignmentmirror in thenucleon theofpartner chiral thebe tocandidate good a is (1535)
0
*
m
N