﻿ Gell-Mann–Nishijima formula
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# Gell-Mann–Nishijima formula

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The Gell-Mann–Nishijima formula sometimes known as the NNG formula relates the baryon number B, the strangeness S, the isospin I3 of quarks and hadrons to the electric charge Q It was originally given by Kazuhiko Nishijima and Tadao Nakano in 1953, and led to the proposal of strangeness as a concept, which Nishijima originally called "eta-charge" after the eta meson Murray Gell-Mann proposed the formula independently in 1956 The modern version of the formula relates all flavour quantum numbers isospin up and down, strangeness, charm, bottomness, and topness with the baryon number and the electric charge

## Formula

The original form of the Gell-Mann–Nishijima formula is:

Q = I 3 + 1 2 B + S   +}B+S\ }

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:

Q = I 3 + 1 2 Y   +}Y\ } Y = 2 Q − I 3 }

Since the discovery of charm, top, and bottom quark flavors, this formula has been generalized It now takes the form:

Q = I 3 + 1 2 B + S + C + B ′ + T +}B+S+C+B^+T}

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:

Q = 2 3 [ n u − n u ¯ + n c − n c ¯ + n t − n t ¯ ] − 1 3 [ n d − n d ¯ + n s − n s ¯ + n b − n b ¯ ] }\left-}\left} B = 1 3 [ n u − n u ¯ + n c − n c ¯ + n t − n t ¯ + n d − n d ¯ + n s − n s ¯ + n b − n b ¯ ] }\left} I 3 = 1 2 [ n u − n u ¯ − n d − n d ¯ ] =}} S = − n s − n s ¯ ; }-n_}}\right;} C = + n c − n c ¯ ; }-n_}}\right;} B ′ = − n b − n b ¯ ; =-\leftn_}-n_}}\right;} T = + n t − n t ¯ }-n_}}\right}

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

## References

1. ^ Nakano, T; Nishijima, N 1953 "Charge Independence for V-particles" Progress of Theoretical Physics 10 5: 581 Bibcode:1953PThPh10581N doi:101143/PTP10581
2. ^ Nishijima, K 1955 "Charge Independence Theory of V Particles" Progress of Theoretical Physics 13 3: 285 Bibcode:1955PThPh13285N doi:101143/PTP13285
3. ^ Gell-Mann, M 1956 "The Interpretation of the New Particles as Displaced Charged Multiplets" Il Nuovo Cimento 4 S2: 848 Bibcode:1956NCim4S848G doi:101007/BF02748000

• Griffiths, DJ 2008 Introduction to Elementary Particles 2nd ed Wiley-VCH ISBN 978-3-527-40601-2

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29.10.2014

Gell-Mann–Nishijima formula
Gell-Mann–Nishijima formula
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