nLab WZW term of QCD chiral perturbation theory -- references

The WZW term of QCD chiral perturbation theory

The gauged WZW term of chiral perturbation theory/quantum hadrodynamics which reproduces the chiral anomaly of QCD in the effective field theory of mesons and Skyrmions:

General

The original articles:

• Julius Wess, Bruno Zumino: Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95–97 [doi:10.1016/0370-2693(71)90582-X, spire:67330]

• Edward Witten: Global aspects of current algebra, Nucl. Phys. B 223 422 (1983) [doi:10.1016/0550-3213(83)90063-9, spire:13234, web.archive]

See also:

• O. Kaymakcalan, S. Rajeev, J. Schechter, Nonabelian Anomaly and Vector Meson Decays, Phys. Rev. D 30 (1984) 594 (spire:194756)

Corrections and streamlining of the computations:

• Chou Kuang-chao, Guo Han-ying, Wu Ke, Song Xing-kang, On the gauge invariance and anomaly-free condition of the Wess-Zumino-Witten effective action, Physics Letters B Volume 134, Issues 1–2, 5 January 1984, Pages 67-69 (doi:10.1016/0370-2693(84)90986-9))

• H. Kawai, S.-H. H. Tye, Chiral anomalies, effective lagrangians and differential geometry, Physics Letters B Volume 140, Issues 5–6, 14 June 1984, Pages 403-407 (doi:10.1016/0370-2693(84)90780-9)

• J. L. Mañes, Differential geometric construction of the gauged Wess-Zumino action, Nuclear Physics B Volume 250, Issues 1–4, 1985, Pages 369-384 (doi:10.1016/0550-3213(85)90487-0)

• Tomáš Brauner, Helena Kolešová, Gauged Wess-Zumino terms for a general coset space, Nuclear Physics B Volume 945, August 2019, 114676 (doi:10.1016/j.nuclphysb.2019.114676)

See also

• Yasunori Lee, Kantaro Ohmori, Yuji Tachikawa, Revisiting Wess-Zumino-Witten terms (arXiv:2009.00033)

Interpretation as Skyrmion/baryon current:

• Jeffrey Goldstone, Frank Wilczek, Fractional Quantum Numbers on Solitons, Phys. Rev. Lett. 47, 986 (1981) (doi:10.1103/PhysRevLett.47.986)

• Edward Witten, Current algebra, baryons, and quark confinement, Nuclear Physics B Volume 223, Issue 2, 22 August 1983, Pages 433-444 (doi:10.1016/0550-3213(83)90064-0)

• 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)

  (beware that the two copies of the text at these two sources differ!)

• Mannque Rho et al., Introduction, In: Mannque Rho et al. (eds.) The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)

Concrete form for $N$-flavor quantum hadrodynamics in 2d:

• C. R. Lee, H. C. Yen, A Derivation of The Wess-Zumino-Witten Action from Chiral Anomaly Using Homotopy Operators, Chinese Journal of Physics, Vol 23 No. 1 (1985) (spire:16389, pdf)

Concrete form for 2 flavors in 4d:

• Masashi Wakamatsu, On the electromagnetic hadron current derived from the gauged Wess-Zumino-Witten action, (arXiv:1108.1236, spire:922302)

Including light vector mesons

Concrete form for 2-flavor quantum hadrodynamics in 4d with light vector mesons included (omega-meson and rho-meson):

• Ulf-G. Meissner, Ismail Zahed, equation (6) in: Skyrmions in the Presence of Vector Mesons, Phys. Rev. Lett. 56, 1035 (1986) (doi:10.1103/PhysRevLett.56.1035)

• Ulf-G. Meissner, Norbert Kaiser, Wolfram Weise, equation (2.18) in: 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, equation (2.45) in: 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)

• Roland Kaiser, equation (12) in: Anomalies and WZW-term of two-flavour QCD, Phys. Rev. D63:076010, 2001 (arXiv:hep-ph/0011377, spire:537600)

Including heavy scalar mesons

Including heavy scalar mesons:

specifically kaons:

• Curtis Callan, Igor Klebanov, equation (4.1) in: Bound-state approach to strangeness in the Skyrme model, Nuclear Physics B Volume 262, Issue 2, 16 December 1985, Pages 365-382 (doi10.1016/0550-3213(85)90292-5)

• Igor Klebanov, equation (99) of: Strangeness in the Skyrme model, in: D. Vauthrin, F. Lenz, J. W. Negele, Hadrons and Hadronic Matter, Plenum Press 1989 (doi:10.1007/978-1-4684-1336-6)

• N. N. Scoccola, D. P. Min, H. Nadeau, Mannque Rho, equation (2.20) in: The strangeness problem: An $SU(3)$ skyrmion with vector mesons, Nuclear Physics A Volume 505, Issues 3–4, 25 December 1989, Pages 497-524 (doi:10.1016/0375-9474(89)90029-8)

specifically D-mesons:

(…)

specifically B-mesons:

• Mannque Rho, D. O. Riska, N. N. Scoccola, above (2.1) in: The energy levels of the heavy flavour baryons in the topological soliton model, Zeitschrift für Physik A Hadrons and Nuclei volume 341, pages343–352 (1992) (doi:10.1007/BF01283544)

Including heavy vector mesons

Inclusion of heavy vector mesons:

specifically K*-mesons:

• S. Ozaki, H. Nagahiro, Atsushi Hosaka, Equations (3) and (9) in: Magnetic interaction induced by the anomaly in kaon-photoproductions, Physics Letters B Volume 665, Issue 4, 24 July 2008, Pages 178-181 (arXiv:0710.5581, doi:10.1016/j.physletb.2008.06.020)

Including electroweak interactions

Including electroweak fields:

• J. Bijnens, G. Ecker, A. Picha, The chiral anomaly in non-leptonic weak interactions, Physics Letters B Volume 286, Issues 3–4, 30 July 1992, Pages 341-347 (doi:10.1016/0370-2693(92)91785-8)

• Gerhard Ecker, Helmut Neufeld, Antonio Pich, Non-leptonic kaon decays and the chiral anomaly, Nuclear Physics B Volume 413, Issues 1–2, 31 January 1994, Pages 321-352 (doi:10.1016/0550-3213(94)90623-8)

Discussion for the full standard model of particle physics:

• Jeffrey Harvey, Christopher T. Hill, Richard J. Hill, Standard Model Gauging of the WZW Term: Anomalies, Global Currents and pseudo-Chern-Simons Interactions, Phys. Rev. D77:085017, 2008 (arXiv:0712.1230)