Vector Meson Dominance
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Vector Meson Dominance

In physics, vector meson dominance (VMD) was a model developed by J. J. Sakurai[1] in the 1960s before the introduction of quantum chromodynamics to describe interactions between energetic photons and hadronic matter.

In particular, the hadronic components of the physical photon consist of the lightest vector mesons, ${\displaystyle \rho }$, ${\displaystyle \omega }$ and ${\displaystyle \phi }$. Therefore, interactions between photons and hadronic matter occur by the exchange of a hadron between the dressed photon and the hadronic target.

## Background

Hadronic contribution to the photon propagator in the VMD model

Measurements of the interaction between energetic photons and hadrons show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge. Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons[2] in spite of the fact that the electric charge structures of protons and neutrons are substantially different.

According to VMD, the photon is a superposition of the pure electromagnetic photon (which interacts only with electric charges) and vector meson.

Just after 1970, when more accurate data on the above processes became available, some discrepancies with the VMD predictions appeared and new extensions of the model were published.[3] These theories are known as Generalized Vector Meson Dominance theories (GVMD).

## VMD and Hidden Local Symmetry

Whilst the ultraviolet description of the standard model is based on QCD, work over many decades has involved writing a low energy effective description of QCD, and further, positing a possible "dual" description. One such popular description is that of the hidden local symmetry.[4] The dual description is based on the idea of emergence of gauge symmetries in the infrared of strongly coupled theories. Gauge symmetries are not really physical symmetries (only the global elements of the local gauge group are physical). This emergent property of gauge symmetries was demonstrated in Seiberg duality[5] and later in the development of the AdS/CFT correspondence.[6] In its generalised form, Vector Meson Dominance appears in AdS/CFT, AdS/QCD, AdS/condensed matter and some Seiberg dual constructions. It is therefore a common place idea within the theoretical physics community.

## Criticism

Measurements of the photon-hadron interactions in higher energy levels show that VMD cannot predict the interaction in such levels. In his Nobel lecture[7]J.I. Friedman summarizes the situation of VMD as follows: "...this eliminated the model [VMD] as a possible description of deep inelastic scattering... calculations of the generalized vector-dominance failed in general to describe the data over the full kinematic range..."

The Vector Meson Dominance model still sometimes makes significantly more accurate predictions of hadronic decays of excited light mesons involving photons than subsequent models such as the relativistic quark model for the meson wave function and the covariant oscillator quark model.[8] Similarly, the Vector Meson Dominance model has outperformed perturbative QCD in making predictions of transitional form factors of the neutral pion meson, the eta meson, and the eta prime meson, that are "hard to explain within QCD."[9] And, the model accurately reproduces recent experimental data for rho meson decays.[10] Generalizations of the Vector Meson Dominance model to higher energies, or to consider additional factors present in cases where VMD fails, have been proposed to address the shortcomings identified by Friedman and others.[11][12]

## Notes

1. ^ Sakurai, J.J (1960). "Theory of strong interactions". Annals of Physics. Elsevier BV. 11 (1): 1-48. doi:10.1016/0003-4916(60)90126-3. ISSN 0003-4916.
2. ^ Bauer, T. H.; Spital, R. D.; Yennie, D. R.; Pipkin, F. M. (1978-04-01). "The hadronic properties of the photon in high-energy interactions". Reviews of Modern Physics. American Physical Society (APS). 50 (2): 261-436. doi:10.1103/revmodphys.50.261. ISSN 0034-6861.
3. ^ Sakurai, J.J.; Schildknecht, D. (1972). "Generalized vector dominance and inelastic electron-proton scattering--the small ${\displaystyle \omega }$? region". Physics Letters B. Elsevier BV. 40 (1): 121-126. doi:10.1016/0370-2693(72)90300-0. ISSN 0370-2693.
4. ^ Bando, Masako; Kugo, Taichiro; Yamawaki, Koichi (1988). "Nonlinear realization and hidden local symmetries". Physics Reports. Elsevier BV. 164 (4-5): 217-314. doi:10.1016/0370-1573(88)90019-1. ISSN 0370-1573.
5. ^ Seiberg, N. (1995). "Electric-magnetic duality in supersymmetric non-Abelian gauge theories". Nuclear Physics B. Elsevier BV. 435 (1-2): 129-146. arXiv:hep-th/9411149. doi:10.1016/0550-3213(94)00023-8. ISSN 0550-3213.
6. ^ Maldacena, Juan (1999). "The Large N limit of superconformal field theories and supergravity". International Journal of Theoretical Physics. Springer Science and Business Media LLC. 38 (4): 1113-1133. arXiv:hep-th/9711200. doi:10.1023/a:1026654312961. ISSN 0020-7748.
7. ^ Friedman, Jerome I. (1991-07-01). "Deep inelastic scattering: Comparisons with the quark model". Reviews of Modern Physics. American Physical Society (APS). 63 (3): 615-627. doi:10.1103/revmodphys.63.615. ISSN 0034-6861.
8. ^ See, e.g., The COMPASS Collaboration, "Measurement of radiative widths of a2(1320) and ?2(1670)" (March 11, 2014) https://arxiv.org/pdf/1403.2644v1.pdf
9. ^ Yaroslav Klopot, Armen Oganesian and Oleg Teryaev, "Axial anomaly and vector meson dominance model" (4 December 2013) https://arxiv.org/abs/1312.1226
10. ^ D. García Gudiño, G. Toledo Sánchez, "Determination of the magnetic dipole moment of the rho meson" (27 May 2013) https://arxiv.org/abs/1305.6345
11. ^ V. A. Petrov, "On Vector Dominance" (20 Dec. 2013) https://arxiv.org/pdf/1312.5500v1.pdf
12. ^ Stefan Leupold and Carla Terschlusen, "Towards an effective field theory for vector mesons" (11 Jun 2012) (also analyzing the circumstances where VMD is and is not successful in predicting experimental outcomes) https://arxiv.org/abs/1206.2253