structure of scalar mesons f 0 (600), a 0 (980), f 0 (1370) and a 0 (1450)
DESCRIPTION
Institut für Theoretische Physik Goethe-Universität Frankfurt am Main. Structure of Scalar Mesons f 0 (600), a 0 (980), f 0 (1370) and a 0 (1450). Denis Parganlija In collaboration with Francesco Giacosa and Dirk H. Rischke. - PowerPoint PPT PresentationTRANSCRIPT
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Structure of Scalar Mesons Structure of Scalar Mesons ff00(600), (600), aa00(980), (980), ff00(1370) and (1370) and aa00(1450)(1450)
Denis Parganlija
In collaboration withFrancesco Giacosa and Dirk H. Rischke
Institut für Theoretische Physik Goethe-Universität Frankfurt am Main
[Based on arXiv: 1003.4934 [hep-ph]]
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Motivation: Effective Theories of QCD and Linear Sigma Model
Description of low-energy hadrons (mesons)
Generalisation to T, μ ≠ 0
Linear Sigma Model:Treats chiral partners on the same footingVacuum calculations → calculations at T≠0Degeneration of chiral partners above TC
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Motivation: Structure of Scalar Mesons
Spontaneous Breaking of Chiral Symmetry → Goldstone Bosons (π)
Restoration of Chiral Invariance and Deconfinement ↔ Degeneration of Chiral Partners (π/σ)
Nature of scalar mesonsScalar states under 1 GeV → f0(600), a0(980)Scalar states above 1 GeV → f0(1370),
a0(1450) – additional scalar states under 1 GeV required (tetraquarks?)
f0(600), „sigma“ f0(1370)
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Scenario I: Scalars under 1 GeV
Nf = 2
Scalars →
Pseudoscalars →
Vectors →
Axialvectors →
(980)),600( 00 af
,
)770(),782(
(1260),(1285) 11 af
scalarspseudoscalarsvectors
axialvectors
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Lagrangian of a Linear Sigma Model with Vector and Axial-Vector Mesons (Nf=2)
m12 parameters
photon
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Spontaneous Symmetry Breaking (SSB):
Shift: Shift (Diagonalise):
Renormalise Pseudoscalar Wave Functions:
[R. Pisarski, hep-ph/9503330 (1995)][S. Gasiorowicz and D. A. Geffen, Rev. Mod. Phys. 41, 531 (1969)]
1 1
)( ),( 31 hZZgZZ 11 parameters
wff 11
waa 11
21
21
1
)(:
gm
gw
Z
1 Z
1
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Parameter Determination
Three Independent Parameters: Z, m1, mσ
MeV )246.0640.0(][1
Za
][ 020.0218.0],,[ 11
00
mmmZa
Isospin
Angular Momentum (s wave)[NA48/2 Collaboration, 2009]
MeV 652 1236521
m)]()([
2 321
221
2 ZhZhhmm
~ Gluon Condensate Quark Condensate
0.201.67Z
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Scenario I – Results
Boundaries of mσ ← scattering lengths
MeV ]477 ,288[mMeV 332 44
145m
020.0218.000 a
MeV ]356 ,319[mMeV 332 13
24m
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Scenario I – Sigma Decay
Γσ→ππ state! tlypredominannot )600(0 qqf
[J. R. Peláez et al.]
MeV )255460(2
iΓim
[H. Leutwyler et al.]
MeV )272441(2
iΓim
small too width decay )600(0f
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Scenario I - Results
Our Result Experimental Value
MeV 640.01
a
exact ],[ ],,[ 22 01hZgZΓ af
MeV 640.01
a(NA48/2) 218.00
0 a218.000 a
0454.020 a (NA48/2) 0457.02
0 a
MeV 33730
aAdeg) 5.041.4 :angle mixing ( η'η
[KLOE Collaboration, hep-ex/0612029v3]
[D. V. Bugg et al., Phys. Rev. D 50, 4412 (1994)]
MeV 33300
aA
MeV 33300
aA
deg41.8 :angle mixing 0.50.2- η'η
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Scenario II: Scalars above 1 GeV
Nf = 2
Scalars →
Pseudoscalars →
Vectors →
Axialvectors →
(1450)),1370( 00 af
,
)770(),782(
(1260),(1285) 11 af
scalarspseudoscalarsvectors
axialvectors
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Decay Width f0(1370) → ππ
MeV )500200(
MeV, )15001200( :PDG
)1370(
)1370(
0
0
f
fm
qqf tlypredominan as )1370( favours data alExperiment 0
MeV 1309)1370(0fm
[D. V. Bugg, arXiv: 0710.4452 [hep-ex]]
MeV 325)1370(0 f
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
The Rho Mass Contributions
m
)]()([2 32
221
2 ZhZhmm
21.067.1MeV )246.0640.0(][1
ZZa 21.007.067.1
ZMeV 721],MeV 592[ 54
12911 mmm
m indominant condensate Gluon
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Scenario II – Scattering Lengths
Scattering lengths saturated
Additional scalars: tetraquarks, quasi-molecular states
Glueball
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Summary
LSM with global U(2)R x U(2)L invariance: scattering lengths, low-energy meson decay widths
General phenomenology in agreement with experiment (ρ→ππ, a1→πγ, f1→aoπ, a0→ηπ decay, ππ scattering lengths)
The f0(600) → ππ decay width fails to match experiment ↔ quarkonium structure of f0(600), a0(980) excluded
Quarkonium structure of f0(1370), a0(1450) favoured, f0(1370) → ππ in agreement with experiment
Scalar states under 1 GeV required for correct description of pion-pion scattering lengths
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Outlook
Consequences of Global Invariance up to 4th Order
Chiral Models With Three Flavours Mixing in the Scalar Sector Extension to Non-Zero Temperature: Study
Chiral Symmetry Restoration Low Energy Constants of QCD p, d Wave Scattering Lengths Include Tensor, Pseudotensor Mesons,
Baryons (Nucleons)
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Spare Slides
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Scenario I – Sigma Decay m1 = 0 → mρ generated from the quark condensate only;
our result: m1 = 652 MeV
a1→σπ
MeV )600250(:PDG (total) 1a
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Scenario I: a1 → ρπ Decay
MeV )600250(:PDG
[M. Urban, M. Buballa and J. Wambach, Nucl. Phys. A 697, 338 (2002)]
MeV 500 ifMeV 160 m
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Scenario II: Parameter Determination
Masses:Pion Decay Constant Five Parameters: Z, h1, h2, g2, mσ
10,,,, aa mmmmm
Zf
)(MeV 1.0)(149.4 22 Zgg )(MeV )13265( 22)1450(0Zhha
ZZa MeV )246.0640.0(][1
)small ( 0 3,21 hh
free )1370(0fmm
Denis Parganlija (Frankfurt U.) Meson 2010 Workshop, Kraków - Poland
Comparison: the Model with and without Vectors and Axial-Vectors
decrease values
vectors Include