Hadrons in QCD - NuPECCWillibald Plessas Theoretical Physics / Institute of Physics University of Graz, Austria Vienna, March 13th, 2009 Intro QCD@Graz Spectroscopy Hadron Structure

Intro

QCD@Graz

Spectroscopy

HadronStructurePion FF

N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets

ReactionsπN , π∆

pp̄ → Λc Λ̄c

Outlook

Addenda

Hadrons in QCD

Willibald Plessas

Theoretical Physics / Institute of PhysicsUniversity of Graz, Austria

Vienna, March 13th, 2009

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Outline

IntroductionThe realm of hadrons

Approaches to QCDMethods available in Graz

Meson and baryon spectra

Electroweak structure of mesons and baryonsPion and nucleon form factors

Hadronic decays of baryon resonances

Baryon rest-frame wave functions

Baryon flavor multiplet classification

Meson-baryon and p-p̄ reactions

Outlook

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Mesons and Baryons

Hadrons in SU(3)F

Mesons Baryons

Particle Data Group: Phys. Lett. B 667, 1 (2008)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Nucleon Resonances

Excitations of the nucleon

Similar spectra for other hyperons: ∆,Λ,Σ,Ξ,Ω,ΛC ,ΣC etc.

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Approaches to Hadrons in QCD

Methods for dealing with hadron states and hadronicphenomena pursued in Graz:

◮ Lattice QCD◮ Effective field theories and functional methods,

especially Dyson-Schwinger equations (DSE)together with Bethe-Salpeter equation (BSE) andFaddeev equation

◮ Effective models, especially relativisticconstituent-quark models (RCQM)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Hadron Spectroscopy

Meson and baryon spectra

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Light and Strange Baryon Spectra from RCQM

900

1000

1100

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1300

1400

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2

+ 1

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2

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900

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M[MeV]

1

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− 5

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left levels : OGE RCQM right levels : GBE RCQM

W. Plessas: Few-Body Syst. Suppl. 15, 139 (2003)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Lattice QCD for Ground States

Dynamical quarks with chirally improved action

Nucleon ∆

0 0.4 0.8 1.2mπ

2 [GeV

2]

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

mN

[G

eV]

ABCexp. value

0 0.4 0.8 1.2mπ

2 [GeV

2]

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

m∆

[GeV

]

ABCexp. value

C. Gattringer, C. Hagen, C.B. Lang, M. Limmer, D. Mohler, and A. Schäfer: Phys. Rev. D 79, 054501 (2009)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Lattice QCD for Excited States

Quenched QCD with chirally improved action

T. Burch, C. Gattringer, L.Ya. Glozman, C. Hagen, D. Hierl, C.B. Lang, and A. Schäfer:Phys. Rev. D 74, 014504 (2006)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

N and ∆ Masses from DSE + Faddeev Equ.

Evolution of N and ∆ masses with π massin rainbow-ladder truncation of the quark-gluon vertex,i.e. the three-quark-core contribution to the baryon masses(dashed lines: lattice QCD results with chiral extrapolations)

!

["#$]

%& ["#$&]

0.10.0 0.2 0.3 0.4 0.50.6

0.8

1.0

1.2

1.4

1.6

1.8

'(

') !"

#$

%&

%'( [)*+(]

[)*+]

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

0.10.0 0.2 0.3 0.4 0.5

#$

!"

D. Nicmorus, G. Eichmann, A. Krassnigg, and R. Alkofer: arXiv:0812.1665

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Chiral Symmetry Restoration

Parity doublets as signatures for restoration ofspontaneously broken chiral symmetry in high-lyingnucleon resonances:

* * * *

* *

3000

2500

2000 * *

1 3

[MeV]

** * *

* *

1500

21197 135

2

1000

222222

L.Ya. Glozman: Phys. Lett. B 587, 69 (2004); Phys. Rev. Lett. 99, 191602 (2007)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Chiral Symmetry Restoration

Parity doublets as signatures for restoration ofspontaneously broken chiral symmetry in high-lyingmeson resonances:

1

2

π ρ ω ηρ π ω ρ ωf a a h b f a a h b f a ρ η π ω ρ a h21 1 1 1 1 1 2 2 2 22

f3 3 3 3 3 3 4 4 4 4 4 4

f5 5 5

...ω50 00

η0

.....

.

. .... .

.

.

.. .. .

. ... ..

M

...

.

.

.

.

..

L.Ya. Glozman: Phys. Rep. 444, 1 (2007)

These spectra can be investigated experimentally at FLAIR !

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Electroweak Structure

Meson and baryon form factors

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Pion Form Factor: Spacelike and Timelike

Fπ(Q2) computed with the full q-γ vertex structure from itsinhomogeneous (rainbow-ladder) Bethe-Salpeter equation

-0.5 0 0.5 1 1.5 2 2.5 3

Q2 [GeV

2]

10-1

100

101

|Fπ(

Q2 )

|Amendolia et al.Ackermann et al.Brauel et al.Tadevosyan et al.

Horn et al.Barkov et al.DSE calculationVMD ρ monopole

A. Krassnigg et al.: Private Communication (2009)

Extension of P. Maris and P. C. Tandy: Nucl. Phys. Proc. Suppl. 161, 136-152 (2006)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Pion Form Factor: Point-Form Rel. QM

Fπ(Q2) from coupled-channel approach (qq̄e + qq̄eγ)in point-form relativistic quantum mechanics

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mq=0.21 GeV, a=0.35 GeV

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0.5

1.

Q2@GeV2D

F2HQ2L

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mq=0.21 GeV, a=0.35 GeV

S¹1S=1

Huber 2008Bebek 1978Bebek 1976Bebek 1974Brown 1973

0 5 100

0.8

1.6

Q2@GeV2DQ2FHQ2L@GeV2D

E.P. Biernat, W. Schweiger, K. Fuchsberger, and W.H. Klink: arXiv:0902.2348

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Electromagnetic Form Factors of the Nucleons

Covariant RCQM predictions in point-form spectator model:

0 1 2 3 4

Q2 [(GeV/c)

2]

0.0

0.5

1.0AndivahisWalkerSillHoehlerBartelPFSANRIAPFSA-NRC

GEp

0 1 2 3 4

Q2 [(GeV/c)

2]

0.0

0.5

1.0

1.5

2.0

2.5AndivahisWalkerSillHoehlerBartelPFSANRIAPFSA-NRC

GMp

0 1 2 3 4

Q2 [(GeV/c)

2]

0.00

0.05

EdenMeyerhoffLungHerbergRoheOstrickBecker (corr. Golak)PasschierZhuPFSANRIAPFSA-NRC

GEn

0 1 2 3 4

Q2 [(GeV/c)

2]

-2.0

-1.5

-1.0

-0.5

LungMarkowitzRockBruinsGaoAnklin 98Anklin 94XuKubonPFSANRIAPFSA-NRC

GMn

R.F. Wagenbrunn, S. Boffi, W. Klink, W. Plessas, and M. Radici: Phys. Lett. B 511 (2001) 33

T. Melde, K. Berger, L. Canton, W. Plessas, and R.F. Wagenbrunn: Phys. Rev. D 76 (2007) 074020

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Electric Radii and Magnetic Moments

Electric radiiBaryon GBE PFSM Experimentp 0.82 0.7569 ± 0.0139n −0.13 −0.1161 ± 0.0022Σ− 0.72 0.61 ± 0.12 ± 0.09

Magnetic moments

Baryon GBE PFSM Experimentp 2.70 2.792847351n −1.70 −1.91304273Λ −0.64 −0.613 ± 0.004Σ+ 2.38 2.458 ± 0.010Σ− −0.93 −1.160 ± 0.025Ξ0 −1.25 −1.250 ± 0.014Ξ− −0.70 −0.6507 ± 0.0025∆+ 2.08 2.7+1.0

−1.3 ± 1.5 ± 3∆++ 4.17 3.7 − 7.5Ω− −1.59 −2.020 ± 0.05

K. Berger, R.F. Wagenbrunn, and W. Plessas: Phys. Rev. D 70, 094027 (2004)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Axial Nucleon Form Factors

Covariant RCQM predictions in point-form spectator model:

0 1 2 3 4 5

Q2 [(GeV/c)

2]

0.0

0.5

1.0

1.5 Pion world dataPion MainzNeutrino world dataPFSANRIARC/no boosts

GA

0.01 0.1 1

Q2 [(GeV/c)

2]

0.01

0.1

1

10

100

BardinChoiwith pion polewithout pion pole

GP

L.Ya. Glozman, M. Radici, R.F. Wagenbrunn, S. Boffi, W. Klink, W. Plessas: Phys. Lett. B 516 (2001) 183

S. Boffi, L.Ya. Glozman, W. Klink, W. Plessas, M. Radici, and R.F. Wagenbrunn: Eur. Phys. J. A 14, 17 (2002)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Strong Decays of Baryon Resonances

π, η, and K Decay Modes

of

N∗, ∆∗, Λ∗, Σ∗, Ξ∗ Resonances

T. Melde, W. Plessas, and R.F. Wagenbrunn: Phys. Rev. C 72, 015207 (2005); ibid. 74, 069901 (2006)

T. Melde, W. Plessas, and B. Sengl: Phys. Rev. C 76, 025204 (2007)

B. Sengl, T. Melde, and W. Plessas: Phys. Rev. D 76, 054008 (2007)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

π Decay Widths of N∗ and ∆∗

N∗, ∆∗ Experiment Relativistic Nonrel. EEM→ Nπ [MeV] GBE OGE GBE OGE

N(1440) (227 ± 18)+70−59 30 59 7 27

N(1520) (66 ± 6)+ 9− 5 21 23 38 37

N(1535) (67 ± 15)+28−17 25 39 559 1183

N(1650) (109 ± 26)+36− 3 6.3 9.9 157 352

N(1675) (68 ± 8)+14− 4 8.4 10.4 13 16

N(1700) (10 ± 5)+ 3− 3 1.0 1.3 2.2 2.7

N(1710) (15 ± 5)+30− 5 19 21 8 6

∆(1232) (119 ± 1)+ 5− 5 35 31 89 85

∆(1600) (61 ± 26)+26−10 0.5 5.1 93 86

∆(1620) (38 ± 8)+ 8− 6 1.2 2.8 76 177

∆(1700) (45 ± 15)+20−10 3.8 4.1 10.4 9.1

With theoretical masses

T. Melde, W. Plessas, and R.F. Wagenbrunn: Phys. Rev. C 72, 015207 (2005); ibid. 74, 069901 (2006)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Baryon Ground and Resonant States

Baryon wave functionsand

baryon flavor multiplets

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Structure of Baryon Wave Functions

Examine the spin , flavor , and space symmetries of thestates in the various baryon multiplets

For the spatial structure consider:

Spatial probability density distribution

ρ(ξ, η) = ξ2η2∫

dΩξdΩη

Ψ⋆MΣMΣTMT (ξ,Ωξ, η,Ωη)ΨMΣMΣTMT (ξ,Ωξ, η,Ωη)

where ~ξ and ~η are the usual Jacobi coordinates

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Pictures of Baryons (rest frame)

N GBE CQM

Ξ

Η

Ξ

N OGE CQM

Ξ

Η

Ξ0 0.5 1 1.5 2

Ξ

0

0.5

1

1.5

2

Η

N

NH1440L GBE CQM

Ξ

Η

Ξ

NH1440L OGE CQM

Ξ

Η

Ξ0 0.5 1 1.5 2

Ξ

0

0.5

1

1.5

2

Η

NH1440L

T. Melde, W. Plessas, and B. Sengl: Phys. Rev. D77, 114002 (2008)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Spatial Probability Density Distributions

ρ(ξ, η) for the 12+ octet baryon ground states N(939), Λ(1116), Σ(1193), Ξ(1318):

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

N

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

L

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

S

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

X

ρ(ξ, η) for the 12+ octet baryon states N(1440), Λ(1600), Σ(1660), Ξ(1690):

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

NH1440L

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

LH1600L

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

SH1660L

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

XH1690L


Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Spatial Probability Density Distributions

ρ(ξ, η) for the 32+ decuplet baryon states ∆(1232), Σ(1385), Ξ(1530), Ω(1672):

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

DH1232L

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

SH1385L

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

XH1530L

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

WH1672L

ρ(ξ, η) for the 32+ decuplet baryon states ∆(1600), Σ(1690):

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

DH1600L

0 0.5 1 1.5 2Ξ

0

0.5

1

1.5

2

Η

SH1690L


Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

SU(3) Flavor Multiplets

Classification of baryon resonances by the PDG (2008)

multiplet (LS)JP

octet (0 12 )12

+ N(939) Λ(1116) Σ(1193) Ξ(1318)

octet (0 12 )12

+ N(1440) Λ(1600) Σ(1660) Ξ(?)

octet (0 12 )12

+N(1710) Λ(1810) Σ(1880) Ξ(?)

octet (1 12 )12− N(1535) Λ(1670) Σ(1620) Ξ(?)

octet (1 32 )12−

N(1650) Λ(1800) Σ(1750) Ξ(?)

octet (1 12 )32−

N(1520) Λ(1690) Σ(1670) Ξ(1820)

octet (1 32 )32− N(1700) Λ(?) Σ(?) Ξ(?)

octet (1 32 )52− N(1675) Λ(1830) Σ(1775) Ξ(?)

decuplet (0 32 )32

+ ∆(1232) - Σ(1385) Ξ(1530)decuplet (0 32 )

32

+ ∆(1600) - Σ(?) Ξ(?)

decuplet (1 12 )12−

∆(1620) - Σ(?) Ξ(?)


∆(1700) - Σ(?) Ξ(?)

singlet (1 12 )12− - Λ(1405) - -

singlet (1 12 )32−

- Λ(1520) - -

Particle Data Group: Phys. Lett. B 667, 1 (2008)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

New Quark Model Classification

multiplet (LS)JP

octet (0 12 )12

+ N(939)100 Λ(1116)100 Σ(1193)100 Ξ(1318)100

octet (0 12 )12

+ N(1440)100 Λ(1600)96 Σ(1660)100 Ξ(1690)100

octet (0 12 )12

+ N(1710)100 Σ(1880)99

octet (1 12 )12− N(1535)100 Λ(1670)72 Σ(1560)94

octet (1 32 )12−

N(1650)100 Λ(1800)100 Σ(1620)100

octet (1 12 )32− N(1520)100 Λ(1690)72 Σ(1670)94 Ξ(1820)97

octet (1 32 )32− N(1700)100 Σ(1940)100

octet (1 32 )52− N(1675)100 Λ(1830)100 Σ(1775)100 Ξ(1950)100

decuplet (0 32 )32

+ ∆(1232)100 Σ(1385)100 Ξ(1530)100 Ω(1672)100

decuplet (0 32 )32

+ ∆(1600)100 Σ(1690)99


∆(1620)100 Σ(1750)94


∆(1700)100

singlet (1 12 )12−

Λ(1405)71

singlet (1 12 )32−

Λ(1520)71

singlet (0 12 )12

+Λ(1810)92

T. Melde, W. Plessas, and B. Sengl: Phys. Rev. D 77, 114002 (2008)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Meson-Baryon Interaction

Meson-baryoninteraction vertices

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Meson-Baryon Interaction Vertices

Microscopic description of meson-baryon form factors

directly from the relativistic constituent-quark model

π − N π − ∆

0 0.5 1 1.5 2 2.5

Q2

0

0.5

1

RCQMSato-LeePolinder-RijkenLiu et al.Alexandrou et al. AAlexandrou et al. BErkol et al.

0 0.5 1 1.5 2 2.5

Q2

0

0.5

1

RCQMSato-LeePolinder-RijkenAlexandrou et al. AAlexandrou et al. BAlexandrou et al. C

T. Melde, L. Canton, and W. Plessas: arXiv:0811.0279, to appear in Phys. Rev. Lett.

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

p-p̄ Collisions

pp̄ → ΛcΛ̄c

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

pp̄ → ΛcΛ̄c

’Hand-bag model’ calculation of total cross section and spincorrelation functions

p̄ (q, ν)

p (p, µ)

c̄

k′

2, λ′

2

c

k′

1, λ′

1

Λ̄c

q′

, ν′

Λc

p′

, µ′

u (k1, λ1)

ū (k2, λ2)

pp̄ → Λc Λ̄c spin-correlation functionsintegrated cross section −CLL (· · · · ·) and DLL (- - - - -)

20 25 30 35 40s @GeV^2D1

2

5

10

20

50Σ @nbD

0.0 0.2 0.4 0.6 0.8 1.0cosHΘcL0.0

0.2

0.4

0.6

0.8

1.0OHLLL

A.T. Goritschnig, P. Kroll, and W. Schweiger: arXiv:0902.4109

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Outlook

A Selective wish-list

◮ Lattice QCD◮ Meson and baryon resonances with dynamical quarks◮ Ground state electromagnetic structure (form factors)

◮ DSE + BSE/Faddeev◮ Dressing of bare results for ground states◮ Extension to meson and baryon resonances◮ Re-investigation of electromagnetic form factors etc.

◮ Covariant RCQM◮ Development of coupled-channel RCQM◮ Electromagnetic transition form factors◮ Re-investigation of hadronic resonance decays◮ Study point form, instant form, and front form relativistic

quantum mechanics on equal footing

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Thank you very much

for

your attention!

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

GBE Hyperfine Interaction

Level shifts due to hyperfine interaction:

N Λ

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1g8

2/4π

800.0

900.0

1000.0

1100.0

1200.0

1300.0

1400.0

1500.0

1600.0

1700.0

1800.0

1900.0

2000.0

M [M

eV]

N

∆

N(1440)

N(1535)−N(1520)

+

−+

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1g8

2/4π

800.0

900.0

1000.0

1100.0

1200.0

1300.0

1400.0

1500.0

1600.0

1700.0

1800.0

1900.0

2000.0

M [M

eV]

Λ

Λ(1405)−Λ(1520)Λ(1600)

Λ(1670)−Λ(1690)

+

−

+

L.Ya. Glozman, Z. Papp, W. Plessas, K. Varga, and R.F. Wagenbrunn, Phys. Rev. C 57, 3406 (1998)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Chiral Interaction

GBE CQM Lattice calculation(Kentucky Group)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1g8

2/4π

800.0

900.0

1000.0

1100.0

1200.0

1300.0

1400.0

1500.0

1600.0

1700.0

1800.0

1900.0

2000.0

M [

Me

V]

N

∆

N(1440)

N(1535)−N(1520)

+

−+

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Chiral Interaction

GBE CQM Lattice calculation(Graz Group)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1g8

2/4π

800.0

900.0

1000.0

1100.0

1200.0

1300.0

1400.0

1500.0

1600.0

1700.0

1800.0

1900.0

2000.0

M [

Me

V]

N

∆

N(1440)

N(1535)−N(1520)

+

−+

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Relativistic Constituent Quark Model (RCQM)

Interacting mass operator

M̂ = M̂free + M̂int

M̂free =√

Ĥ20 −~̂P2free

M̂int =3

∑

i

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

GBE CQM

Goldstone-Boson-Exchange CQM

H0 =3

∑

i=1

√

~p2i + m2i

Vconf (~rij) = V0 + Crij

Vhf (~rij) =

[

3∑

F=1

Vπ(~rij)λFi λ

Fj +

7∑

F=4

VK (~rij)λFi λ

Fj

+ Vη(~rij)λ8i λ

8j +

23

Vη′(~rij)]

~σi · ~σj

L.Ya. Glozman, W. Plessas, K. Varga, and R.F. Wagenbrunn: Phys. Rev. D 58, 094030 (1998)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

OGE CQM

One-Gluon-Exchange CQM

(Relativistic version of the Bhaduri-Cohler-Nogami OGE CQM)

H0 =3

∑

i=1

√

~p2i + m2i

Vconf = V0 + Crij

Vhf = −2b3rij

+αs

9mimjΛ2

e−Λrij

rij~σi · ~σj

L. Theussl, R.F. Wagenbrunn, B. Desplanques, and W. Plessas: Eur. Phys. J. A 12, 91 (2001)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Transition Matrix Elements

Incoming baryon state: |V , M, J, Σ〉 equiv. |P, J, Σ〉Outgoing baryon state: |V ′, M ′, J ′, Σ′〉 |P′, J ′, Σ′〉Transition operator: Ô

˙

V ′, M ′, J ′, Σ′˛

˛ Ô |V , M, J, Σ〉 =2

MM ′X

σi σ′

i

X

µi µ′

i

Z

d3~k2d3~k3d

3~k ′2d3~k ′3

×

s

`

P

i ω′

i

´3

Q

i 2ω′

i

Y

σ′i

D⋆ 12σ′i µ

′

i

˘

RWˆ

k ′i ; B`

V ′´˜¯

Ψ⋆M′J′Σ′“

~k ′1, ~k′

2, ~k′

3; µ′

1, µ′

2, µ′

3

”

×˙

p′1, p′

2, p′

3; σ′

1, σ′

2, σ′

3

˛

˛ Ôrd |p1, p2, p3; σ1, σ2, σ3〉

×

s

`

P

i ωi´3

Q

i 2ωi

Y

σi

D12σiµi {RW [ki ; B (V )]}ΨMJΣ

“

~k1, ~k2, ~k3; µ1, µ2, µ3”

×2MV0δ3“

M~V − M ′~V ′ − ~q”

where pi = Bc(V )ki , p′i = Bc(V′)k ′i , and ωi =

q

~k2i + m2i

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Point-Form Spectator-Model (PFSM) Currents

Electromagnetic current˙

p′1, p′

2, p′

3; σ′

1, σ′

2, σ′

3

˛

˛ Ĵµrd |p1, p2, p3; σ1, σ2, σ3〉 =3N

˙

p′1, σ′

1

˛

˛ Ĵµspec |p1, σ1〉 2p20δ`

~p2 − ~p′2´

2p30δ`

~p3 − ~p′3´

δσ2σ′2δσ3σ′3

with˙

p′1, σ′

1

˛

˛ Ĵµspec |p1, σ1〉 =

e1ū`

p′1, σ′

1

´

»

f1(Q̃2)γµ +

i2m1

f2(Q̃2)σµν q̃ν

–

u (p1, σ1)

Axial current:˙

p′1, p′

2, p′

3; σ′

1, σ′

2, σ′

3

˛

˛ Âµa,rd |p1, p2, p3; σ1, σ2, σ3〉 =3N

˙

p′1, σ′

1

˛

˛ Âµa,spec |p1, σ1〉 2p20δ`

~p2 − ~p′2´

2p30δ`

~p3 − ~p′3´


with˙

p′1, σ′

1

˛

˛ Âµa,spec |p1, σ1〉 =

ū`

p′1, σ′

1

´

"

gqAγµ +

2fπeQ2 + m2π

gqqπeqµ

#

γ512

τau (p1, σ1)

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Spectator Model Decay Operator

˙

V ′, M ′, J ′, Σ′, T ′, MT ′˛

˛ D̂mrd |V , M, J, Σ, T , MT 〉 =

2MM ′

X

σiσ′

i

X

µi µ′

i

Z

d3~k2d3~k3d

3~k ′2d3~k ′3

s

`

P

i ω′

i

´3

Q

i 2ω′

i

s

`

P

i ωi´3

Q

i 2ωi

×Y

σ′i

D⋆ 12σ′i µ

′

i

˘

RWˆ

k ′i ; B`

V ′´˜¯

Ψ⋆M′J′Σ′T ′MT ′

“

~k ′1, ~k′

2, ~k′

3; µ′

1, µ′

2, µ′

3

”

×˙

p′1, p′

2, p′

3; σ′

1, σ′

2, σ′

3

˛

˛ D̂mrd |p1, p2, p3; σ1, σ2, σ3〉

×Y

σi

D12σi µi {RW [ki ; B (V )]}ΨMJΣTMT

“

~k1, ~k2, ~k3; µ1, µ2, µ3”

with the hadronic decay operator in the point-form spectator model˙

p′1, p′

2, p′

3; σ′

1, σ′

2, σ′

3

˛

˛ D̂mrd |p1, p2, p3; σ1, σ2, σ3〉 =

− 3N igqqm2m1

1√2π

ū`

p′1, σ′

1

´

γ5γµFmu (p1, σ1) qµ

× 2p20δ`

~p2 − ~p′2´

2p30δ`

~p3 − ~p′3´


Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Charmed Baryons

Λc (predicted by the GBE CQM)

2100

2200

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200Λc

1

2

+ 1

2

− 3

2

+ 3

2

−

GBEM

[MeV]

...........................................................

...........................................................

...............................

........

..........

...........

........

.......

......

......

****

*...........................................................

........

............................................................

.......

..........

.......

.......

***

......**

...........................................................

........

........

..................

..................

..................

...........................................................

........

............................................................

.......

..........

.......

....... ......

***

**

Intro

QCD@Graz

Spectroscopy


N e.m. FF

N axial FF

Decays

WaveFunctions

Multiplets


pp̄ → Λc Λ̄c

Outlook

Addenda

Charmed Baryons

Λc (predicted by the GBE CQM)

Λc

JP = 12

+JP = 3

2

+

L, S Conf GBE Exp L, S Conf GBE Exp

0, 12

2546 2307 2285

0, 12

2979 2733 2765

2, 12

3029 2815

0, 12

3051 2932

0, 32

3051 3056

2, 32

3097 3107 2, 32

3097 3107

JP = 12

−

JP = 32

−

L, S Conf GBE Exp L, S Conf GBE Exp

1, 12

2801 2585 2593 1, 12

2801 2585 2625

1, 12

2871 2860 1, 12

2871 2860

1, 32

2871 2880 2880 1, 32

2871 2880 2880

1, 12

3185 2964 1, 12

3185 2964

IntroductionThe realm of hadrons

Approaches to QCDMethods available in Graz

Meson and baryon spectraElectroweak structure of mesons and baryonsPion and nucleon form factors

Hadronic decays of baryon resonancesBaryon rest-frame wave functionsBaryon flavor multiplet classificationMeson-baryon and p- reactions

OutlookAddenda

Documents

Hadrons in QCD - NuPECCWillibald Plessas Theoretical Physics / Institute of Physics University of Graz, Austria Vienna, March 13th, 2009 Intro QCD@Graz Spectroscopy Hadron Structure