Heavy quark effective theory explained

In quantum chromodynamics, heavy quark effective theory (HQET) is an effective field theory describing the physics of heavy (that is, of mass far greater than the QCD scale)^[1] quarks. It is used in studying the properties of hadrons containing a single charm or bottom quark.^{[2] [3]} The effective theory was formalised in 1990 by Howard Georgi,^[4] Estia Eichten and Christopher Hill,^[5] building upon the works of Nathan Isgur and Mark Wise,^[6] Voloshin and Shifman,^[7] and others.^[8]

Quantum chromodynamics (QCD) is the theory of strong force, through which quarks and gluons interact. HQET is the limit of QCD with the quark mass taken to infinity while its four-velocity is held fixed.^[9] This approximation enables non-perturbative (in the strong interaction coupling) treatment of quarks that are much heavier than the QCD mass scale. The mass scale is of order 200 MeV. Hence the heavy quarks include charm, bottom and top quarks, whereas up, down and strange quarks are considered light. Since the top quark is extremely short-lived, only the charm and bottom quarks are of significant interest to HQET, of which only the latter has mass sufficiently high that the effective theory can be applied without major perturbative corrections.^{[2] [3]}

Further reading

• Book: Shifman. M. A.. ITEP Lectures on Particle Physics and Field Theory . Lectures on Heavy Quarks in Quantum Chromodynamics. World Scientific Lecture Notes in Physics . 62. 1999. 1–109. 1793-1436. 10.1142/9789812798961_0001. hep-ph/9510377. 978-981-02-3947-3 . 18892623 .
• Sommer. Rainer. Non-perturbative Heavy Quark Effective Theory: Introduction and Status. Nuclear and Particle Physics Proceedings. 261-262. 2015. 338–367. 2405-6014. 1501.03060. 10.1016/j.nuclphysbps.2015.03.022. 2015NPPP..261..338S. 53354994 .

Notes and References

1. http://users.phys.psu.edu/~cteq/schools/summer09/talks/sullivan/sullivan1.pdf Heavy quarks
2. Book: Aneesh V. Manohar. Mark B. Wise. Heavy Quark Physics. 2 July 2007. Cambridge University Press. 978-0-521-03757-0.
3. Book: Grozin. Andrey. 201. 2004. 0081-3869. 10.1007/b79301. Heavy Quark Effective Theory. Springer Tracts in Modern Physics . 2004STMP..201.....G. 978-3-540-20692-7 .
4. Georgi. Howard. An effective field theory for heavy quarks at low energies. Physics Letters B. 240. 3–4. 1990. 447–450. 0370-2693. 10.1016/0370-2693(90)91128-X. 1990PhLB..240..447G.
5. Eichten. Estia. Hill. Brian. An effective field theory for the calculation of matrix elements involving heavy quarks. Physics Letters B. 234. 4. 1990. 511–516. 0370-2693. 10.1016/0370-2693(90)92049-O. 1990PhLB..234..511E.
6. Isgur. Nathan. Wise. Mark B.. Weak decays of heavy mesons in the static quark approximation. Physics Letters B. 232. 1. 1989. 113–117. 0370-2693. 10.1016/0370-2693(89)90566-2. 1989PhLB..232..113I.
7. Shifman, M.A., & Voloshin, M.V. (1987). On production of D and D^* mesons in B-meson decays (ITEP--64(1987)). USSR
8. [Howard Georgi|Georgi, H.]
9. https://arxiv.org/abs/hep-ph/9805468 Heavy Quark Physics