Summary
I shall discuss the concept of mass at an elementary, but not trivial, level. From an operational point of view, mass, as any observable, is defined by the set of operations employed to measure it or, when not observable as in the case of quarks, to calculate it. Consequently, there are several “masses”, which are not necessarily equal. I shall discuss the relationships amongst them. I start by recalling the basic concept of mass and the strictly related ones of energy and momentum. I shall give then a historical perspective and draw the attention on a number of wrong concepts that still survive. I shall then review the masses of the neutrally charged flavoured mesons, of the neutrinos, of the hadrons, the quark masses and their running.
Similar content being viewed by others
References
Okun L. B., Phys. Today, June 1989, p. 31.
Okun L. B., “The Einstein formula E0 = mc2. Isn't the Lord laughing?”; Phys. Usp., 178 (2008) 541 (English version 51 (2008) 5).
Poincaré H., C. R. Acad. Sci. Paris, 140 (1905) 1504.
Poincaré H., Rend. Circ. Mat. Palermo, 21 (1906) 129. For a “modernised” translation into English see SCHWARTZ H. M., Am.J.Phys., 39 (1971) 1287; 40 (1972) 862 and 1282.
Poincaré H., L'Etat actuel et l'avenir de la Physique Mathématique, lecture delivered at St. Louis, 24/9/1904; Bull. Sci. Math., 28 (1904) 302 (English translation in The Monist, 15 (1905) 1).
Einstein A., Ann. Phys. (Leipzig), 17 (1905) 891.
Einstein A., Ann. Phys. (Leipzig), 18 (1905) 639.
Planck M., Verh. Deutsch. Phys. Ges., 8 (1906) 136; Phys. Zs., 9 (1908) 828; Verh. Dsch. Phys. Ges., 10 (1908) 728.
Landau L. D. and Lifschitz E. M., Teoryia polya (Gotstekhizdat, Moscow-Leningrad) 1941.
Landau L. D. and Lifschitz E. M., The Classical Theory of Fields (Addison-Wesley Press, Cambridge MA) 1951.
Feynman R., Leighton R. and Sands M., The Feynman Lectures on Physics (Addison Weseley, Reading MA) 1963-1965.
Landau L. D. and Rumer Y.U.B., What is Relativity? (Dover, Basic books) 1959.
Poincaré E., Arch. Neerl., 5 (1900) 252.
Abraham M., Phys. Z., 5 (1904) 576; Theorie der Electrzitat,Vol. 2 (Tuber, Leipzig) 1905.
Lorentz H. A., The Theory of Electrons (Dover) 1952.
Rohrlich F., Am. J. Phys., 28 (1960) 639; 38 (1970) 1310; Classical Charged Particles (Addison-Wesley, Reading MA) 1965; Classical Charged Particles (World Scientific) 2007.
Thomson J. J., Philos. Mag., 11 (1881) 229.
Fermi E., Z. Phys., 24 (1922) 340; Atti Accad. Naz. Lincei, 31 (1922) 184, 306.
Kwal B., J. Phys. Radium, 10 (1949) 103.
Minkowski H., Nachr. Ges. Wiss. Göttn Mth.-Phys. Kl, 53 (1908).
Abraham M., Rend. Circ. Mat. Palermo, 28 (1909) 1.
Pfeifer R. N. C. et al., Rev. Mod. Phys., 79 (2007) 1197; 81 (2009) 443(E).
Jones R. V. and Richards J. C. S., Proc. R. Soc. London, Ser. A, 221 (1954) 480.
De Groot S. R. and Suttorp L. G., Foundations of Electrodynamics (North Holland, Amsterdam) 1972; MlKURA Z., Phys. Rev. A, 13 (1976) 2265; ISRAEL W., Phys. Lett. B, 67 (1977) 125.
Garrison J. C. and Cfflao R. Y., Phys. Rev. A, 70 (2004) 053826.
Jones R. V. and Leslie B., Proc. R. Soc. London, Ser. B, 360 (1978) 347.
Peccei R. D. and Quinn H. R., Phys. Rev. Lett., 38 (1977) 1440; Phys. Rev. D, 16 (1977) 17.
Primakoff H., Phys. Rev., 81 (1951) 899.
Raffelt G. and Stodolsky L., Phys. Rev. D, 37 (1988) 1237.
Zioutis K. et al., hep-ex/0411033.
van Bibber K. et al., Phys. Rev. D, 39 (1989) 2089.
Wolfenstein L., Phys. Rev. D, 17 (1978) 2369; 20 (1979) 2634; Mikheyev S. P. and Smirnov A. Yu., Yad. Fiz., 42 (1985) 1441; Nuovo Cimento C, 9 (1986) 17.
Yao W.-M., J. Phys. G, 33 (2006) 1.
Mohapatra R. and Pal P., Physics of Massive Neutrinos (Word Scientific) 2004.
Fukugita M. and Yanagida T., Physics of Neutrinos and its Applications to Astrophysics (Springer-Verlag, Berlin Heidelberg) 2003.
Giunti C. and Kim C. W., Fundamentals of Neutrino Physics and Astrophysics (Oxford University Press) 2007.
Strumia A. and Vissani F., Neutrino masses and mixing and... arXiv:hep-ph/0606054.
Pontecorvo B., Zh. Eksp. Teor. Fiz., 33 (1957) 549 (Sov. Phys. JETP, 6 (1957) 429).
Pontecorvo B., Zh. Eksp. Teor. Fiz., 53 (1967) 1717 (Sov. Phys. JETP, 6 (1968) 984).
Katayama Y. et al., Prog. Theor. Phys., 28 (1962) 675.
Maki Z. et al., Prog. Theor. Phys., 28 (1962) 870.
Wolfenstein L., Phys. Rev. D, 17 (1978) 2369; 20 (1979) 2634.
Mikheyev S. P. and Smirnov A.Y.U., Yad. Fiz., 42 (1985) 1441 (Sov. J. Nucl. Phys., 42 (1985) 913).
Fukuda et al., Phys. Rev. Lett., 81 (1998) 1562.
Bachall J., Phys. Rev. Lett., 12 (1964) 300.
Davis JR. R., Phys. Rev. Lett., 12 (1964) 303.
Superk, Phys. Rev. Lett., 63 (1989) 16; 65 (1990) 1301.
Anselmann P. et al., Phys. Lett. B, 285 (1992) 376.
Anselmann P. et al., Phys. Lett. B, 357 (1995) 237.
Abdurashitov J.N., et al., Phys. Rev. Lett., 83 (1999) 4686.
Arpesella C. et al., Phys. Lett. B, 389 (1996) 452.
Junker M., Phys. Rev. C, 57 (1998) 2700.
Anselmann P. et al., Phys. Rev. Lett. B, 342 (1995) 440.
Hampel W. et al., Phys. Rev. Lett. B, 436 (1998) 158.
Ahmad Q.R., et al., Phys. Rev. Lett., 89 (2002) 0111301.
Arpesella C. et al., Phys. Lett. B, 658 (2008) 101.
Apollonio M. et al., Phys. Lett. B, 466 (1999) 415.
Eguchi K. et al., Phys. Rev. Lett., 90 (2003) 021802; Araki T. et al., Phys. Rev. Lett., 94 (2005) 081801.
Ahn M. H. et al., Phys. Rev. Lett., 90 (2003) 041801; 94 (2005) 081802.
Michael D. G. et al., Phys. Rev. Lett., 97 (2006) 191801.
Fogli G. L. et al., hep-ph 0806.2649v1.
Kraus C. et al., Eur. Phys. J. C, 40 (2005) 447.
Lobashev V. M. et al., Nucl. Phys. B Proc. Suppl., 91 (2001) 280.
Komatsu E. et al., arXiv:0803.0547v2 [astro-ph].
Kurie F. N. D. et al., Phys. Rev., 49 (1936) 368.
OPERA proposal. CERN/SPSC 2000-028; SPSC/P318; LNGS P25/2000. July 10, 2000.
Plano R., Proceedings of the Lund International Conference on Elementary Particles (Berlingska Bokttryckeriet, Lund) 1969, p. 323.
Pisut J. and Roos M., Nucl. Phys. B, 6 (1968) 325.
Narrison S., QCD as a Theory of Hadrons (Cambridge University Press) 2004.
Steuckelberg E. C. G. and Peterman A., Helv. Phys. Acta, 26 (1953) 499.
Gell-Mann M. and Low F. E., Phys. Rev., 95 (1954) 1300.
Thooft G., Nucl. Phys. B, 61 (1973) 455.
Bardeen W. A. et al., Phys. Rev. D, 18 (1978) 3998.
Tevatron Electroweak Working Group (2007) hep-ph/0703034.
Fleming S., Mantry S. and Stewart I. W., Phys. Rev. D, 77 (2008) 074010; Hoang A. H. and Stewart I. W., Phy. Lett. B, 660 (2008) 483; FLEMING S., Mantry S. and Stewart I. W., arXiv:0711.2079; Phys. Rev. D, 77 (2008) 114003; Jain A., Scimemi I. and Stewart I. W., arXiv:0803.4214.
Abreu et al., Phys. Lett. B, 418 (1998) 430.
Abbiendi G. et al., Eur. Phys. J. C, 21 (2001) 411.
Leinweber D., http://www.physics.adelaide.edu.au/theory/staff/leinweber/.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bettini, A. The mass of the particles. Riv. Nuovo Cim. 32, 295–337 (2009). https://doi.org/10.1393/ncr/i2009-10046-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1393/ncr/i2009-10046-2