Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $\sigma /f_0(500) $ and $\kappa /K_0^*(700) $

Peláez, Jose R.; Rodas, Arkaitz; de Elvira, Jacobo Ruiz

doi:10.1140/epjs/s11734-021-00142-9

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^*(700)$

Jose R. Peláez
(
- UCM, Madrid, Dept. Theor. Phys. II
)
,
Arkaitz Rodas
(
- William-Mary Coll. and
- Jefferson Lab
)
,
Jacobo Ruiz de Elvira
(
- Bern U.
)

Jan 16, 2021

50 pages

Published in:

Eur.Phys.J.ST 230 (2021) 6, 1539-1574

Published: Jun 16, 2021

e-Print:

2101.06506 [hep-ph]

DOI:

10.1140/epjs/s11734-021-00142-9

Report number:

JLAB-THY-21-3306

View in:

ADS Abstract Service

pdflinks

reference search30 citations

Citations per year

Abstract: (Springer)

For several decades, the

\sigma /f_0(500)

and

\kappa /K_0^*(700)

resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review, we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons

\sigma /f_0(500)

and

\kappa /K_0^*(700)

. Generically, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective theories allows us to understand their nature, spectroscopic classification and dependence on QCD parameters. Here we review in a pedagogical way their uses, advantages and caveats.

Note:

Invited tutorial-review for European Physical Journal Special Topics. Final version to appear published. Expanded discussions and reference list. 50 pages

perturbation theory: chiral
resonance: scalar
unitarity
dispersion relation
quantum chromodynamics
scalar meson
f0(600)
kappa meson

References(220)

Figures(34)

[1]

Classical Field Theory of Nuclear Forces

M.H. Johnson
(
- LLNL, Livermore
)
,
E. Teller
(
- LLNL, Livermore
)

- Phys.Rev. 98 (1955) 783-787
•
DOI:
- 10.1103/PhysRev.98.783

[2]

A Theory of the Fundamental Interactions

Julian S. Schwinger
(
- Harvard U.
)

- Annals Phys. 2 (1957) 407-434,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 34-61
•
DOI:
- 10.1016/0003-4916(57)90015-5

[3]

The axial vector current in beta decay

- Nuovo Cim. 16 (1960) 705
•
DOI:
- 10.1007/BF02859738

[4]

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. 1.

Yoichiro Nambu
(
- Chicago U., EFI
)
,
G. Jona-Lasinio
(
- Chicago U., EFI
)

- Phys.Rev. 122 (1961) 345-358,
- Also in *Lai, C. H. (Ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 104-117,
•
DOI:
- 10.1103/PhysRev.122.345

[5]

Dynamical model of elementary particles based on an analogy with superconductivity. II.

Yoichiro Nambu
(
- Chicago U., EFI
)
,
G. Jona-Lasinio
(
- Chicago U., EFI
)

- Phys.Rev. 124 (1961) 246-254,
•
DOI:
- 10.1103/PhysRev.124.246

[6]

QCD phenomenology based on a chiral effective Lagrangian

Tetsuo Hatsuda
(
- Tsukuba U.
)
,
Teiji Kunihiro
(
- Ryukoku U.
)

- Phys.Rept. 247 (1994) 221-367
•
e-Print:
- hep-ph/9401310
•
DOI:
- 10.1016/0370-1573(94)90022-1

[7]

Phenomenological Lagrangians

Steven Weinberg
(
- Harvard U. and
- Harvard-Smithsonian Ctr. Astrophys.
)

- Physica A 96 (1979) 1-2, 327-340
•
DOI:
- 10.1016/0378-4371(79)90223-1

[8]

Chiral Perturbation Theory to One Loop

J. Gasser
(
- Bern U.
)
,
H. Leutwyler
(
- CERN
)

- Annals Phys. 158 (1984) 142
•
DOI:
- 10.1016/0003-4916(84)90242-2

[9]

Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark

J. Gasser
(
- Bern U.
)
,
H. Leutwyler
(
- CERN
)

- Nucl.Phys.B 250 (1985) 465-516
•
DOI:
- 10.1016/0550-3213(85)90492-4

[10]

Precise tests of low energy QCD from K(e4)decay properties

NA48/2

Collaboration

•

J.R. Batley
(
- Cambridge U.
)

et al.

- Eur.Phys.J.C 70 (2010) 635-657
•
DOI:
- 10.1140/epjc/s10052-010-1480-6

[11]

Review of Particle Physics

et al.

- PTEP 2020 (2020) 8, 083C01
•
DOI:
- 10.1093/ptep/ptaa104

[12]

Pi pi Partial Wave Analysis from Reactions pi+ p ---> pi+ pi- Delta++ and pi+ p ---> K+ K- Delta++ at 7.1-GeV/c

S.D. Protopopescu
(
- LBL, Berkeley
)
,
M. Alston-Garnjost
(
- LBL, Berkeley
)
,
A. Barbaro-Galtieri
(
- LBL, Berkeley
)
,
Stanley M. Flatte
(
- LBL, Berkeley
)
,
J.H. Friedman
(
- LBL, Berkeley
)

et al.

- Phys.Rev.D 7 (1973) 1279
•
DOI:
- 10.1103/PhysRevD.7.1279

[13]

$\pi\pi$ Phase Shift Analysis from 600-MeV to 1900-MeV

B. Hyams
(
- CERN
)
,
C. Jones
(
- CERN
)
,
P. Weilhammer
(
- CERN
)
,
W. Blum
(
- Munich, Max Planck Inst.
)
,
H. Dietl
(
- Munich, Max Planck Inst.
)

et al.

- Nucl.Phys.B 64 (1973) 134-162
•
DOI:
- 10.1016/0550-3213(73)90618-4

[14]

High Statistics Study of the Reaction pi- p --> pi- pi+ n: Apparatus, Method of Analysis, and General Features of Results at 17-GeV/c

et al.

- Nucl.Phys.B 75 (1974) 189-245
•
DOI:
- 10.1016/0550-3213(74)90545-8

[15]

A Low Lying Scalar Meson Nonet in a Unitarized Meson Model

et al.

- Z.Phys.C 30 (1986) 615-620,
- Z. Phys. C30 ( 1986) 615-620
•
e-Print:
- 0710.4067
•
DOI:
- 10.1007/BF01571811

[16]

Scalar mesons in a chiral theory with quark degrees of freedom

- Phys.Rev.D 101 (2020) 9, 094028
•
e-Print:
- 1909.10384
•
DOI:
- 10.1103/PhysRevD.101.094028

[17]

Meson Dynamics Beyond the Quark Model: A Study of Final State Interactions

- Phys.Rev.D 35 (1987) 1633
•
DOI:
- 10.1103/PhysRevD.35.1633

[18]

Is f0 (975) a narrow resonance?

- Phys.Rev.D 48 (1993) R3948-R3952
•
DOI:
- 10.1103/PhysRevD.48.R3948

[19]

Remarks on I = 0 J(PC) = 0++ states: sigma / epsilon and f0 (975)

- Phys.Rev.D 50 (1994) 591-594
•
DOI:
- 10.1103/PhysRevD.50.591

[20]

On the structure of the scalar mesons f0 (975) and a0 (980)

G. Janssen
(
- SUNY, Stony Brook
)
,
B.C. Pearce
(
- Adelaide U.
)
,
K. Holinde
(
- Julich, Forschungszentrum
)
,
J. Speth
(
- Julich, Forschungszentrum
)

- Phys.Rev.D 52 (1995) 2690-2700,
- Phys. Rev. D52 (1995) 2690-2700, and Juelich KFA - KFA-IKP-(TH)-94-40 (94,rec.Dec.) 39 p. Adelaide U. - ADP-94-023-T163 (94,rec.Dec.) 39 p
•
e-Print:
- nucl-th/9411021
•
DOI:
- 10.1103/PhysRevD.52.2690