Gell-Mann–Nishijima formula
The Gell-Mann–Nishijima formula (sometimes known as the NNG formula) relates the
) with the baryon number and the electric charge.Formula
The original form of the Gell-Mann–Nishijima formula is:
This equation was originally based on empirical experiments. It is now understood as a result of the quark model. In particular, the electric charge Q of a quark or hadron particle is related to its isospin I3 and its hypercharge Y via the relation:
Since the discovery of charm, top, and bottom quark flavors, this formula has been generalized. It now takes the form:
where Q is the charge, I3 the 3rd-component of the isospin, B the baryon number, and S, C, B′, T are the strangeness, charm, bottomness and topness numbers.
Expressed in terms of quark content, these would become:
By convention, the flavor quantum numbers (strangeness, charm, bottomness, and topness) carry the same sign as the electric charge of the particle. So, since the strange and bottom quarks have a negative charge, they have flavor quantum numbers equal to −1. And since the charm and top quarks have positive electric charge, their flavor quantum numbers are +1.
From a
Weak interaction analog
In 1961 Glashow proposed a relation similar formula would also apply to the weak interaction:[4][5]: 152
References
- ^ Nakano, T; Nishijima, N (1953). "Charge Independence for V-particles". .
- ^ Nishijima, K (1955). "Charge Independence Theory of V Particles". .
- ^
Gell-Mann, M (1956). "The Interpretation of the New Particles as Displaced Charged Multiplets". S2CID 121017243.
- ISSN 0029-5582.
- ISBN 978-3-540-60227-9.
Further reading
- Griffiths, DJ (2008). Introduction to Elementary Particles (2nd ed.). Wiley-VCH. ISBN 978-3-527-40601-2.