nLab ω-meson

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)

See also:

• Wikipedia, Omega meson

See also

• Reinhard Alkofer, H. Reinhardt, H. Weigel, U. Zuckert, The Isoscalar vector meson omega in the Nambu-Jona-Lasinio soliton, Phys. Lett. B298 (1992) 132-140 (spire:343052, doi:10.1016/0370-2693(93)91719-4)

Phenomenology:

• Cheng-Qun Pang, Ya-Rong Wang, Jing-Fu Hu, Tian-Jie Zhang, Xiang Liu, Study of the $\omega$ meson family and newly observed $\omega$-like state $X(2240)$ (arXiv:1910.12408)

• M. K. Volkov, A. A. Pivovarov, K. Nurlan, On the mixing angle of the vector mesons $\omega(782)$ and $\phi(1020)$ (arXiv:2005.00763)

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)

See also

• Marcelo Ipinza, Patricio Salgado-Rebolledo, Meron-like topological solitons in massive Yang-Mills theory and the Skyrme model (arXiv:2005.04920)

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

See also:

• Miguel Huidobro, Paul Leask, Carlos Naya, Andrzej Wereszczynski, Compressibility of dense nuclear matter in the $\rho$-meson variant of the Skyrme model [arXiv:2405.20757]

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)

See also

• Ki-Hoon Hong, Ulugbek Yakhshiev, Hyun-Chul Kim, Modification of hyperon masses in nuclear matter, Phys. Rev. C 99, 035212 (2019) (arXiv:1806.06504)

Review:

• Roland Kaiser, Anomalies and WZW-term of two-flavour QCD, Phys. Rev. D63:076010, 2001 (arXiv:hep-ph/0011377, spire:537600)

• Gottfried Holzwarth, Section 2.3 of: Electromagnetic Form Factors of the Nucleon in Chiral Soliton Models (arXiv:hep-ph/0511194), Chapter 2 in: The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)

• Yongseok Oh, Skyrmions with vector mesons: Single Skyrmion and baryonic matter, 2013 (pdf)

Combination of the omega-rho-Skyrme model with the bag model of quark confinement:

• H. Takashita, S. Yoro, H. Toki, Chiral bag plus skyrmion hybrid model with vector mesons for nucleon, Nuclear Physics A Volume 485, Issues 3–4, August 1988, Pages 589-605 (doi:10.1016/0375-9474(88)90555-6)

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)