nLab heavy flavor

Idea

In the standard model of particle physics, the masses of the various flavors of quarks, and thus of the hadron bound states built from them, differ by orders of magnitude (“mass hierarchy”):

• The up quark and down quark are both very light and of comparable mass.

• The strange quark is an order of magnitude heavier than the up and down.

• The charm quark and bottom quark are two orders of magnitude heavier than the strange quark.

• The top quark is another two orders of magnitude heavier than the bottom quark.

Since in the formulation of quantum hadrodynamics as chiral perturbation theory one needs to decide which quarks count as “approximately massless” and which count as “approximately of infinite mass” for the purpose of effective field theory, it is very common to group the quark species into “light” and “heavy”.

There are two versions of this grouping in use:

1. In “2-flavor”-chiral perturbation theory with SU(2) chiral symmetry

• the up quark and down quark are regarded as light (i.e. the first generation quarks)

• the strange quark, charm quark, bottom quark and top quark are regarded as heavy.

1. In “3-flavor”-chiral perturbation theory with SU(3) chiral symmetry

• the up quark, down quark and also the strange quark are regarded as light,

• the charm quark, bottom quark and top quark are regarded as heavy.

Either choice gives rise to a corresponding notion of light and heavy hadrons.

For mesons one has:

1. In “2-flavor”-chiral perturbation theory with SU(2) chiral symmetry

• the pion, omega-meson and rho meson are light (being bound states of up quarks and down quarks);

• the heavy mesons are the eta-meson, phi-meson and K-mesons (involving a strange quark); the D-mesons (involving a charm quark) and the B-mesons (involving a bottom quark)

1. In “3-flavor”-chiral perturbation theory with SU(3) chiral symmetry

• the pion, omega-meson, rho meson and K-mesons are light (being bound states of up quarks, down quarks and strange quarks);

• the heavy mesons are the D-mesons (involving a charm quark) and the B-mesons (involving a bottom quark)

For baryons one has:

(…)

References

General

• Benjamin Grinstein, An Introduction to Heavy Mesons (arXiv:hep-ph/9508227, cds:285792)

• Daniel Kikoła, Five things you should remember about heavy flavor measurements, Journal of Physics: Conference Series, Volume 612, 2014 (doi:10.1088/1742-6596/612/1/012023)

• Brambilla et al., Sections 3-4 in: QCD and strongly coupled gauge theories - challenges and perspectives, Eur Phys J C Part Fields. 2014; 74(10): 2981 (arXiv:1404.3723, doi:10.1140/epjc/s10052-014-2981-5)

• D.R. Entem, P.G. Ortega, J. Segovia, F. Fernández, Heavy mesons in the Quark Model, EPJ Web of Conferences 199, 01012 (2019) (arXiv:1809.06985, doi:10.1051/epjconf/201919901012)

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:

• Curtis Callan, Igor Klebanov, 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)

• Curtis Callan, K. Hornbostel, Igor Klebanov, Baryon masses in the bound state approach to strangeness in the skyrme model, Physics Letters B Volume 202, Issue 2, 3 March 1988, Pages 269-275 (doi10.1016/0370-2693(88)90022-6)

• Norberto Scoccola, D. P. Min, H. Nadeau, Mannque Rho, 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)

Review:

• Igor Klebanov, section 6 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)

• Mannque Rho, Section 2.2 of: Cheshire Cat Hadrons, Phys. Rept. 240 (1994) 1-142 (arXiv:hep-ph/9310300, doi:10.1016/0370-1573(94)90002-7)

Inclusion of charm quarks/D-mesons

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

• Mannque Rho, D. O. Riska, Norberto Scoccola, Charmed baryons as soliton - D meson bound states, Phys. Lett.B 251 (1990) 597-602 (spire:297771, doi:10.1016/0370-2693(90)90802-D)

• Yongseok Oh, Dong-Pil Min, Mannque Rho, Norberto Scoccola, Massive-quark baryons as skyrmions: Magnetic moments, Nuclear Physics A Volume 534, Issues 3–4 (1991) Pages 493-512 (doi:10.1016/0375-9474(91)90458-I)

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:

• Mannque Rho, Massive-quark baryons as Skyrmions, Modern Physics Letters A, Vol. 06, No. 23 (1991) (doi:10.1142/S0217732391002268)

• Norberto Scoccola, Heavy quark skyrmions, (arXiv:0905.2722, doi:10.1142/9789814280709_0004), Chapter 4 in: The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)

Heavy flavor in holographic QCD

Discussion of heavy flavor in holographic QCD:

• Yizhuang Liu, Ismail Zahed, Heavy and Strange Holographic Baryons, Phys. Rev. D 96, 056027 (2017) (arXiv:1705.01397)

• Si-wen Li, A holographic description of heavy-flavoured baryonic matter decay involving glueball, Phys. Rev. D 99, 046013 (2019) (arXiv:1812.03482)

  (via additional flavor branes)

• Nicolas Kovensky, Andreas Schmitt: Heavy Holographic QCD,

  J. High Energ. Phys. 2020 96 (2020). [doi:10.1007/JHEP02(2020)096, arxiv:1911.08433]

• Daisuke Fujii, Atsushi Hosaka, Heavy baryons in holographic QCD with higher dimensional degrees of freedom (arXiv:2003.13415)

  (via higher KK-modes)

• Yidian Chen, Mei Huang, Holographic QCD model for $N_f = 4$ (arXiv:2110.08215)