# nLab σ-meson

Contents

### Context

#### Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks ($q$)
up-typeup quark ($u$)charm quark ($c$)top quark ($t$)
down-typedown quark ($d$)strange quark ($s$)bottom quark ($b$)
leptons
chargedelectronmuontauon
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion ($u d$)
ρ-meson ($u d$)
ω-meson ($u d$)
f1-meson
a1-meson
strange-mesons:
ϕ-meson ($s \bar s$),
kaon, K*-meson ($u s$, $d s$)
eta-meson ($u u + d d + s s$)

charmed heavy mesons:
D-meson ($u c$, $d c$, $s c$)
J/ψ-meson ($c \bar c$)
bottom heavy mesons:
B-meson ($q b$)
ϒ-meson ($b \bar b$)
baryonsnucleons:
proton $(u u d)$
neutron $(u d d)$

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)

solitons

in grand unified theory

minimally extended supersymmetric standard model

superpartners

bosinos:

dark matter candidates

Exotica

auxiliary fields

# Contents

## Idea

The sigma-meson, now also called the $f_0(500)$-resonance, is the lightest Lorentz-scalar and isospin-scalar meson.

Together with the omega-meson the sigma is responsible for most of the long-range interaction between baryons, exhibiting the residual strong nuclear force between them, at least as modeled by the Walecka model and quantum hadrodynamics.

Other models of quantum hadrodynamics do not contain the sigma at all. See Pelaez 16 for review of the controversial and inconclusive understanding of the sigma-meson.

## References

### General

Original articles:

Review:

• J. R. Pelaez, From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance, Physics Reports 658 (2016) 1 (arXiv:1510.00653)

• Eef van Beveren, Frieder Kleefeld, George Rupp, Michael D. Scadron, Remarks on the $f_0(400-1200)$ scalar meson as the dynamically generated chiral partner of the pion, Mod. Phys. Lett. A17:1673, 2002 (arXiv:hep-ph/0204139)

• M. Albaladejo, J.A. Oller, On the size of the sigma meson and its nature, Phys. Rev. D 86, 034003 – Published 3 August 2012 (arXiv:1205.6606, doi:10.1103/PhysRevD.86.034003)

• S. S. Afonin, T. D. Solomko, The sigma meson from QCD sum rules for large-$N_c$ Regge spectra, Eur. Phys. J. C 76, 678 (2016) (arXiv:1608.08131)

• S. S. Afonin, T. D. Solomko, The linear radial spectrum of scalar mesons within the QCD sum rules in the planar limit, Eur. Phys. J. C 76, 678 (2016) (arXiv:1608.08131)

• Physics.SE discussion, What the heck is the sigma (f0) 600?

• Christian S. Fischer, Paul C. Wallbott, Richard Williams, Nico Santowsky, Gernot Eichmann, The $\sigma$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach (arXiv:2007.06495)

Inclusion of the sigma-meson into the Skyrme model for baryons:

• Thomas D. Cohen, Explicit $\sigma$ meson, topology, and the large-$N$ limit of the Skyrmion, Phys. Rev. D 37 (1988) (doi:10.1103/PhysRevD.37.3344)

### In holographic QCD

Discussion in holographic QCD:

On sigma-mesons and omega-mesons mediating baryon interaction, discussed in holographic QCD via D3-D7 brane intersections:

and discussed in the Witten-Sakai-Sugimoto model on D4-D8 brane intersections:

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Last revised on September 18, 2020 at 02:59:06. See the history of this page for a list of all contributions to it.