nLab ω-meson

Contents

Context

Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

photon - electromagnetic field (abelian Yang-Mills field)
W, Z, B-boson - electroweak field (Yang-Mills field)
gluon - strong nuclear force (Yang-Mills field)
graviton - field of gravity
infraparticle

scalar bosons

Higgs boson, inflaton (scalar field)

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the standard model of particle physics:
generation of fermions	1st generation	2nd generation	3d generation
quarks ( $q$ )
up-type	up quark ( $u$ )	charm quark ( $c$ )	top quark ( $t$ )
down-type	down quark ( $d$ )	strange quark ( $s$ )	bottom quark ( $b$ )
leptons
charged	electron	muon	tauon
neutral	electron neutrino	muon neutrino	tau neutrino

bound states:
mesons	light 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 ( $b \bar b$ )
baryons	nucleons: proton $(u u d)$ neutron $(u d d)$

(also: antiparticles)

effective particles

Goldstone bosons

hadrons (bound states of the above quarks)

meson
- scalar meson
  - σ-meson
  - pion
  - kaon
  - D-meson
  - B-meson
- vector meson
  - ω-meson
  - ρ-meson
  - f1-meson
  - a1-meson
  - b1-meson
  - h1-meson
  - K*-meson
- tensor meson
- quarkonium
  - charmonium
  - ϒ-meson
exotic meson
- XYZ meson
- tetraquark
baryon
- nucleon
  - proton
  - neutron
  - chemical element
    - carbon
    - nitrogen
- Lambda baryon
- pentaquark

solitons

in grand unified theory

minimally extended supersymmetric standard model

superpartners

bosinos:

gravitino - field of supergravity (Rarita-Schwinger field)
gaugino - super Yang-Mills field
gluino

sfermions:

squark

dark matter candidates

WIMP
axion

Exotica

auxiliary fields

Idea
Properties

Nuclear binding
Couplings

The $\omega$ - $3 \pi$ -coupling
The $\omega$ - $\rho$ - $\pi$ -coupling
The radiative decays

Related concepts
References

General
Decays
Skyrme hadrodynamics with vector mesons ( $\pi$ - $\omega$ - $\rho$ -model)

Inclusion of the $\omega$ -meson
Inclusion of the $\rho$ -meson
Inclusion of the $\omega$ - and $\rho$ -meson
Inclusion of the $\sigma$ -meson

Couplings
In holographic QCD
Mediating baryon interaction

Idea

In nuclear physics, specifically in the chiral perturbation theory of quantum chromodynamics, the omega-meson is the isospin-singlet vector meson field in the first-generation of fermions, i.e. a bound state of an up quark and a down quark (a light meson), the chiral partner of the f1-meson:

flavors of fundamental fermions in the standard model of particle physics:
generation of fermions	1st generation	2nd generation	3d generation
quarks ( $q$ )
up-type	up quark ( $u$ )	charm quark ( $c$ )	top quark ( $t$ )
down-type	down quark ( $d$ )	strange quark ( $s$ )	bottom quark ( $b$ )
leptons
charged	electron	muon	tauon
neutral	electron neutrino	muon neutrino	tau neutrino

bound states:
mesons	light 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 ( $b \bar b$ )
baryons	nucleons: proton $(u u d)$ neutron $(u d d)$

Properties

Nuclear binding

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

Couplings

The $\omega$ - $3 \pi$ -coupling

The interaction term of the omega-meson three pions is, in the Lagrangian density, given by contraction

\omega_\mu B^\mu

with the chirally anomalous baryon current $B \coloneqq \star tr( (U^{-1} d U) \wedge (U^{-1} d U) \wedge (U^{-1} d U) )$ , with $U$ is the exponential of the pion-field (Adkins-Nappi 84, (1) and (2), Park-Vento 09, (5.5.43) and above (5.5.50)).

This gives a decay mode

\omega \to \pi^+ + \pi^- + \pi^0

(the “charged decay”, e.g. Rudaz 84, (2)).

Or rather, this is the direct (contact term) decay. The net process $\omega \to 3 \pi$ is dominated by the successive decay

\omega \to \rho + \pi \to (2 \pi) + \pi

The $\omega$ - $\rho$ - $\pi$ -coupling

Then there is an ω-ρ-π-coupling given by the anomalous part of the chiral WZW-term:

g_{\omega \rho \pi} \epsilon^{\mu \nu \kappa \lambda} \partial_\mu \omega_\nu \partial_\kappa \rho_\lambda \cdot \pi

(e.g. Renard 69, Meissner-Kaiser-Weise 87, (2.18) Volkov-Ebert-Nagy 97, p. 12, Guetta-Singer 00, (1), Kaiser 00, (12), GKSY 03, (1) Gudino-Sanchez 12, (1))

The radiative decays

Then there is the “neutral decay”

\omega \to \pi^0 + \gamma

seen in experiment as

\begin{aligned} \omega & \to \pi^0 + \gamma \\ & \to \gamma + \gamma + \gamma \end{aligned}

(Nambu 57, (a), FFHNR 67, Dolinsky et al. 89, (5))

Related concepts

pion, rho-meson

References

General

The $\omega$ -meson was first postulated by

Yoichiro Nambu, Possible Existence of a Heavy Neutral Meson, Phys. Rev. 106, 1366 (1957) (doi:10.1103/PhysRev.106.1366)

as reviewed in

Jun John Sakurai, p. 48-49 of: Currents and Mesons, Chicago Lectures in Physics, based on notes by George Barry, University of Chicago Press (1969) (ISBN: 9780226733838)

(in the context of vector meson dominance)

Decays

The direct decay $\omega \to \pi^0 + \pi^+ + \pi^-$ :

S. Rudaz, Anomalies, vector mesons and the $\omega \to 3 \pi$ contact term, Phys. Lett. B 145 (1984) 281-284 (spire:208193, doi:10.1016/0370-2693(84)90355-1)
E. A. Kuraev, Z. K. Silagadze, Once more about the $\omega \to 3 \pi$ contact term, Phys. Atom. Nucl. 58:1589-1596, 1995 (arXiv:hep-ph/9502406)
M. Albaladejo, I. Danilkin, S. Gonzalez-Solis, D. Winney, C. Fernandez-Ramirez, A. N. Hiller Blin, V. Mathieu, M. Mikhasenko, A. Pilloni, A. Szczepaniak, $\omega \to 3\pi$ and $\omega \pi^0$ transition form factor revisited (arXiv:2006.01058)

The $\omega \pi \rho$ -coupling

D. Garcia Gudino, G. Toledo Sanchez, The $\omega \rho \pi$ coupling in the VMD model revisited, Int. J. Mod. Phys. A 27, 1250101 (2012) (arXiv:1106.1467)

On Dalitz decays of omega-mesons:

Mirko Wachs, Die Selbstenergie des Omega-Mesons, 2000 (epda:000050)
Henning Berghäuser, Investigation of the Dalitz decays and the electromagnetic form factors of the $\eta$ and $\pi^0$ -meson, 2010 (spire:1358057)

Skyrme hadrodynamics with vector mesons ( $\pi$ - $\omega$ - $\rho$ -model)

Inclusion of vector mesons (omega-meson and rho-meson/A1-meson) into the Skyrmion model of quantum hadrodynamics, in addition to the pion:

First, on the equivalence between hidden local symmetry- and massive Yang-Mills theory-description of Skyrmion quantum hadrodynamics:

Atsushi Hosaka, H. Toki, Wolfram Weise, Skyrme Solitons With Vector Mesons: Equivalence of the Massive Yang-Mills and Hidden Local Symmetry Scheme, 1988, Z. Phys. A332 (1989) 97-102 (spire:24079)

Inclusion of the $\omega$ -meson

Original proposal for inclusion of the ω-meson in the Skyrme model:

Gregory Adkins, Chiara Nappi, Stabilization of Chiral Solitons via Vector Mesons, Phys. Lett. 137B (1984) 251-256 (spire:194727, doi:10.1016/0370-2693(84)90239-9)

Relating to nucleon-scattering:

J. M. Eisenberg, A. Erell, R. R. Silbar, Nucleon-nucleon force in a skyrmion model stabilized by omega exchange, Phys. Rev. C 33, 1531 (1986) (doi:10.1103/PhysRevC.33.1531)

Combination of the omega-meson-stabilized Skyrme model with the bag model for nucleons:

Atsushi Hosaka, Omega stabilized chiral bag model with a surface $\omega q q$ coupling, Nuclear Physics A Volume 546, Issue 3, 31 (1992) Pages 493-508 (doi:10.1016/0375-9474(92)90544-T)

Discussion of nucleon phenomenology for the $\omega$ -stabilized Skyrme model:

Sven Bjarke Gudnason, James Martin Speight, Realistic classical binding energies in the $\omega$ -Skyrme model (arXiv:2004.12862)
Derek Harland, Paul Leask, Martin Speight, Skyrmion crystals stabilized by $\omega$ -mesons [arXiv:2404.11287]

Inclusion of the $\rho$ -meson

Original proposal for inclusion of the ρ-meson:

Y. Igarashi, M. Johmura, A. Kobayashi, H. Otsu, T. Sato, S. Sawada, Stabilization of Skyrmions via $\rho$ -Mesons, Nucl.Phys. B259 (1985) 721-729 (spire:213451, doi:10.1016/0550-3213(85)90010-0)
Gregory Adkins, Rho mesons in the Skyrme model, Phys. Rev. D 33, 193 (1986) (spire:16895, doi:10.1103/PhysRevD.33.193)

Discussion for phenomenology of light atomic nuclei:

Carlos Naya, Paul Sutcliffe, Skyrmions and clustering in light nuclei, Phys. Rev. Lett. 121, 232002 (2018) (arXiv:1811.02064)
Carlos Naya, Paul Sutcliffe, Skyrmions in models with pions and rho, JHEP 05 (2018) 174 (arXiv:1803.06098)

APS Synopsis: Revamping the Skyrmion Model, 2018

Inclusion of the $\omega$ - and $\rho$ -meson

The resulting $\pi$ - $\rho$ - $\omega$ model:

Ulf-G. Meissner, Ismail Zahed, Skyrmions in the Presence of Vector Mesons, Phys. Rev. Lett. 56, 1035 (1986) (doi:10.1103/PhysRevLett.56.1035)

(includes also the A1-meson)
Ulf-G. Meissner, Norbert Kaiser, Wolfram Weise, Nucleons as skyrme solitons with vector mesons: Electromagnetic and axial properties, Nuclear Physics A Volume 466, Issues 3–4, 11–18 May 1987, Pages 685-723 (doi:10.1016/0375-9474(87)90463-5)
Ulf-G. Meissner, Norbert Kaiser, Andreas Wirzba, Wolfram Weise, Skyrmions with $\rho$ and $\omega$ Mesons as Dynamical Gauge Bosons, Phys. Rev. Lett. 57, 1676 (1986) (doi:10.1103/PhysRevLett.57.1676)
Ulf-G. Meissner, Low-energy hadron physics from effective chiral Lagrangians with vector mesons, Physics Reports Volume 161, Issues 5–6, May 1988, Pages 213-361 (doi:10.1016/0370-1573(88)90090-7)
L. Zhang, Nimai C. Mukhopadhyay, Baryon physics from mesons: Leading order properties of the nucleon and $\Delta(1232)$ in the $\pi \rho\omega a_1(f_1)$ chiral soliton model, Phys. Rev. D 50, 4668 (1994) (doi:10.1103/PhysRevD.50.4668, spire:384906)
Yong-Liang Ma, Ghil-Seok Yang, Yongseok Oh, Masayasu Harada, Skyrmions with vector mesons in the hidden local symmetry approach, Phys. Rev. D87:034023, 2013 (arXiv:1209.3554)

(hidden local symmetry)
Ju-Hyun Jung, Ulugbek T. Yakhshiev, Hyun-Chul Kim, In-medium modified $\pi$ - $\rho$ - $\omega$ mesonic Lagrangian and properties of nuclear matter, Physics Letters B Volume 723, Issues 4–5, 25 June 2013, Pages 442-447 (arXiv:1212.4616, doi:10.1016/j.physletb.2013.05.042)
Ju-Hyun Jung, Ulugbek Yakhshiev, Hyun-Chul Kim, Peter Schweitzerm, In-medium modified energy-momentum tensor form factors of the nucleon within the framework of a $\pi$ - $\rho$ - $\omgea$ soliton model, Phys. Rev. D 89, 114021 (2014) (arXiv:1402.0161)
Yongseok Oh, Skyrmions with vector mesons revisited (arXiv:1402.2821)

Inclusion of the $\sigma$ -meson

Inclusion of the sigma-meson:

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)

For analysis of neutron star equation of state:

David Alvarez-Castillo, Alexander Ayriyan, Gergely Gábor Barnaföldi, Hovik Grigorian, Péter Pósfay, Studying the parameters of the extended $\sigma$ - $\omega$ model for neutron star matter (arXiv:2006.03676)

Couplings

On omega-meson interactions and decay modes:

Stanley M. Flatté, Darrell O. Huwe, Joseph J. Murray, Janice Button-Shafer, Frank T. Solmitz, M. Lynn Stevenson, and Charles Wohl, Decay Properties of the $\omega$ Meson, Phys. Rev. 145, 1050 – Published 27 May 1966 (doi:10.1103/PhysRev.145.1050)
M. Feldman, W. Frati, R. Gleeson, J. Halpern, M. Nussbaum, S. Richert, Neutral Decay of the $\omega$ Meson, Phys. Rev. 159, 1219 (1967) (doi10.1103/PhysRev.159.1219, spire:52556)
W. Deinet A. Menzione H.Müller, H. M.Staudenmaier, S.Buniatov, D.Schmitt, Neutral decay modes of the $\omega^0$ -meson, Physics Letters B Volume 30, Issue 6, 10 November 1969, Pages 426-429 (doi:10.1016/0370-2693(69)90479-1)
F. M. Renard, The reaction $e^+ e^- \to \pi^0 + \omega(\pi^+ \pi^- \pi^0)$ and the $\omega$ - $\rho$ - $\pi$ coupling, Nuovo Cimento A (1965-1970) 64, 979–984 (1969) (doi:10.1007/BF02758844)
M. K. Volkov, D. Ebert, M. Nagy, Excited pions, $\rho$ - and $\omega$ -mesons and their decays in a chiral $SU(2) \times SU(2)$ Lagrangian, Int. J. Mod. Phys. A13 (1998) 5443-5458 (arXiv:hep-ph/9705334)
S. I. Dolinsky, et al., Radiative Decays of $\rho$ and $\omega$ Mesons, Z. Phys. C42 (1989) 511 (spire:264694, doi:10.1007/BF01557655)
J. T. Dakin, M. G. Hauser, M. N. Kreisler, R. E. Mischke, Measurement of the Branching Ratios for ω Neutral Decays, Phys. Rev. D 6, 2321 (1972) (doi:10.1103/PhysRevD.6.2321)
Dafne Guetta, Paul Singer, $\omega$ - $\rho$ Mixing and the $\omega \to \pi \pi \gamma$ Decay, Phys. Rev. D63 (2001) 017502 (arXiv:hep-ph/0005059)
Roland Kaiser, equation (12) of: Anomalies and WZW-term of two-flavour QCD, Phys. Rev. D63:076010, 2001 (arXiv:hep-ph/0011377)
A. Gokalp, A. Kucukarslan, S. Solmaz, O. Yilmaz, $\sigma$ -Meson and $\omega$ - $\rho$ mixing effects in $\omega \to \pi^+ \pi^- \gamma$ decay, Acta Phys.Polon. B34 (2003) 4095-4104 (arXiv:hep-ph/0306044)
Jeffrey Harvey, Christopher T. Hill, Richard J. Hill, Section II.B of: Standard Model Gauging of the WZW Term: Anomalies, Global Currents and pseudo-Chern-Simons Interactions, Phys. Rev. D77:085017, 2008 (arXiv:0712.1230)
S. Leupold, M. F. M. Lutz, Hadronic three-body decays of light vector mesons, Eur. Phys. J. A39:205-212, 2009 (arXiv:0807.4686)
Florian Jonas, Measurement of $\omega$ and $\eta$ mesons via their three pion decay with ALICE in pp collisions at $\sqrt{s} = t TeV$ , 2018 (cds:2653176)

In holographic QCD

The omega-meson in holographic QCD (Witten-Sakai-Sugimoto model):

Tadakatsu Sakai, Shigeki Sugimoto, Section 4.3 of: More on a holographic dual of QCD, Progr. Theor. Phys. 114: 1083-1118, 2005 (arXiv:hep-th/0507073)

Mediating baryon interaction

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

Anatoly Dymarsky, Dmitry Melnikov, Jacob Sonnenschein, Attractive Holographic Baryons, JHEP 06 (2011) 145 (arXiv:1012.1616)

Last revised on June 2, 2020 at 18:20:50. See the history of this page for a list of all contributions to it.

nLab ω-meson

Context

Fields and quanta

Contents

Idea

Properties

Nuclear binding

Couplings

The ω\omega-3π3 \pi-coupling

The ω\omega-ρ\rho-π\pi-coupling

The radiative decays

Related concepts

References

General

Decays

Skyrme hadrodynamics with vector mesons (π\pi-ω\omega-ρ\rho-model)

Inclusion of the ω\omega-meson

Inclusion of the ρ\rho-meson

Inclusion of the ω\omega- and ρ\rho-meson

Inclusion of the σ\sigma-meson

Couplings

In holographic QCD

Mediating baryon interaction

The $\omega$ - $3 \pi$ -coupling

The $\omega$ - $\rho$ - $\pi$ -coupling

Skyrme hadrodynamics with vector mesons ( $\pi$ - $\omega$ - $\rho$ -model)

Inclusion of the $\omega$ -meson

Inclusion of the $\rho$ -meson

Inclusion of the $\omega$ - and $\rho$ -meson

Inclusion of the $\sigma$ -meson