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

Quantum hadrodynamics is (or should be) an effective field theory that describes confined hadron bound states in nuclear physics, in particular the interaction between mesons and baryons and specifically with nucleons.

In this sense chiral perturbation theory is the archetype of quantum hadrodynamics, but the latter term is commonly used more specifically for the Walecka model and its generalizations (QHD-I Walecka 74 and QHD-II Serot 79, Serot-Walecka 92, Serot-Walecka 97) to baryon chiral perturbation theory, where the baryons and specifically the nucleons appear as explicit effective fields (as opposed to as emergent Skyrmion fields).

effective field theories of nuclear physics, hence for confined-phase quantum chromodynamics:

## References

### Walecka hadrodynamics with nucleon fields

On quantum hadrodynamics (relativivist effective field theory of nuclear physics, coupling mesons and nucleons) in the sense of the Walecka model, hence with nucleons appearing as explicit fields (as opposed to being solitonic Skyrmions in the pion field as in chiral perturbation theory).

Precursor:

The original Walecka model (QHD-I model), with nucleons coupled to sigma-mesons and omega-mesons:

Inclusion into the Walecka model also of the pion and the rho-meson (the QHD-II model):

• Brian Serot, A relativistic nuclear field theory with $\pi$ and $\rho$ mesons, Physics Letters B Volume 86, Issue 2, 24 (1979), Pages 146-150 (doi:10.1016/0370-2693(79)90804-9)

• T Matsui, Brian Serot, The pion propagator in relativistic quantum field theories of the nuclear many-body problem, Annals of Physics Volume 144, Issue 1, November 1982, Pages 107-167 (doi:10.1016/0003-4916(82)90106-3)

Further discussion of these models:

Further inclusion of electromagnetism (photon field):

• A. Yu. Korchin, D. Van Neck, M. Waroquier, Electromagnetic interaction in chiral quantum hadrodynamics and decay of vector and axial-vector mesons, Phys. Rev. C67 (2003) 015207 (arXiv:nucl-th/0302042)

Relation to quark-meson coupling model:

• Koichi Saito, Relationship between Quark-Meson Coupling Model and Quantum Hadrodynamics, Prog. Theor. Phys. 108 (2002) 609-614 (arXiv:nucl-th/0207053)

### 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)

• 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:

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:

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

#### Inclusion of the $\rho$-meson

Original proposal for inclusion of the ρ-meson:

Discussion for phenomenology of light atomic nuclei:

#### 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)

• 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)

• 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:

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)

### Skyrme hadrodynamics with heavy quarks/mesons

Inclusion of heavy flavors into the Skyrme model for quantum hadrodynamics:

#### Inclusion of strange quarks/kaons

Inclusion of strange quarks/kaons into the Skyrme model:

Review:

#### Inclusion of charm quarks/D-mesons

Inclusion of charm quarks/D-mesons into the Skyrme model:

#### Inclusion of bottom quarks/B-mesons

Inclusion of further heavy flavors beyond strange quark/kaons, namely charm quarks/D-mesons and bottom quarks/B-mesons, into the Skyrme model:

• Mannque Rho, D. O. Riska, Norberto Scoccola, The energy levels of the heavy flavour baryons in the topological soliton model, Zeitschrift für Physik A Hadrons and Nuclei volume 341, pages 343–352 (1992) (doi:10.1007/BF01283544)

• Arshad Momen, Joseph Schechter, Anand Subbaraman, Heavy Quark Solitons: Strangeness and Symmetry Breaking, Phys. Rev. D49:5970-5978, 1994 (arXiv:hep-ph/9401209)

• Yongseok Oh, Byung-Yoon Park, Dong-Pil Min, Heavy Baryons as Skyrmion with $1/m_Q$ Corrections, Phys. Rev. D49 (1994) 4649-4658 (arXiv:hep-ph/9402205)

Review:

### 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:

• 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)

Interpretation as Skyrmion/baryon current:

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):

#### Including heavy scalar mesons

Including heavy scalar mesons:

specifically kaons:

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:

#### Including electroweak interactions

Including electroweak fields:

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)

### Baryon chiral perturbation theory

Discussion of baryon chiral perturbation theory, i.e of chiral perturbation theory with explicit effective (as opposed to or in addition to implicit skyrmionic) baryon fields included (see also Walecka model and quantum hadrodynamics):

Review:

Original articles:

• Elizabeth Jenkins, Aneesh V. Manohar, Baryon chiral perturbation theory using a heavy fermion lagrangian, Physics Letters B Volume 255, Issue 4, 21 February 1991, Pages 558-562 (doi:10.1016/0370-2693(91)90266-S)

• Robert Baur, Joachim Kambor, Generalized Heavy Baryon Chiral Perturbation Theory, Eur. Phys. J. C7:507-524, 1999 (arXiv:hep-ph/9803311)

Higher order terms:

• José Antonio Oller, Michela Verbeni, Joaquim Prades, Meson-baryon effective chiral Lagrangians to $\mathcal{O}(q^3)$, Journal of High Energy Physics, Volume 2006, JHEP09(2006) (arXiv:hep-ph/0608204, doi:10.1088/1126-6708/2006/09/079)

• Matthias Frink, Ulf-G. Meissner, On the chiral effective meson-baryon Lagrangian at third order, Eur. Phys. J. A29:255-260, 2006 (arXiv:hep-ph/0609256)

• Jose Antonio Oller, Joaquim Prades, Michela Verbeni, Meson-Baryon Effective Chiral Lagrangians at $\mathcal{O}(q^3)$ Revisited (arXiv:hep-ph/0701096, spire:742291)

• Lisheng Geng, Recent developments in $SU(3)$ covariant baryon chiral perturbation theory, Front. Phys., 2013, 8(3): 328-348 (arXiv:1301.6815)