Gell-Mann-Nishijima Formula

The Gell-Mann-Nishijima formula (after Murray Gell-Mann and Kazuhiko Nishijima ; also NNG formula for Nishijima, Nakano , Gell-Mann) in its original form links the electrical charge of a quark (in units of the elementary charge ) with three of its Quantum numbers , namely the third component (projection) of the strong isospin , the baryon number and the strangeness : ${\displaystyle Q}$ ${\displaystyle I_{3}}$ ${\displaystyle B}$ ${\displaystyle S}$

${\displaystyle Q=I_{3}+{\frac {B+S}{2}}=I_{3}+{\frac {Y}{2}}}$.

It is

${\displaystyle Y=B+S}$

the hypercharge .

Originally the formula was based on experimental results, today it is understood as part of the Quark model. In their above simple form it only takes into account the light quarks u , d and s .

Extension to heavy quarks

In order to also take into account the heavy quarks c , b and t , the formula has to be expanded to include their quantum numbers charm , bottomness and topness : ${\displaystyle C}$ ${\displaystyle B\;\!'}$ ${\displaystyle T}$

${\displaystyle Q=I_{z}+{\frac {B+S+C+B\;\!'+T}{2}}=I_{z}+{\frac {Y}{2}}}$.

It is

${\displaystyle Y=B+S+C+B\;\!'+T}$

the expanded hypercharge.

See also

• Weak hypercharge

Individual evidence

1. ↑ T. Nakano, N. Nishijima: Charge Independence for V-particles . In: Progress of Theoretical Physics . tape 10 , no. 5 , 1953, pp. 581-582 , doi : 10.1143 / PTP.10.581 , bibcode : 1953PThPh..10..581N .
2. ↑ K. Nishijima: Charge Independence Theory of V Particles . In: Progress of Theoretical Physics . tape 13 , no. 3 , 1955, pp. 285-304 , doi : 10.1143 / PTP.13.285 , bibcode : 1955PThPh..13..285N .
3. ↑ M. Gell-Mann: The Interpretation of the New Particles as Displaced Charged Multiplets . In: Il Nuovo Cimento . tape 4 , S2, 1956, pp. 848 , doi : 10.1007 / BF02748000 .