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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]] ''I<sub>3</sub>'' of [[hadron]]s to the charge ''Q''. It was originally given by [[Kazuhiko Nishijima]] and [[Tadao Nakano]] in 1953,<ref>
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| {{cite journal
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| |last=Nakano |first=T
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| |last2=Nishijima |first2=N
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| |year=1953
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| |title=Charge Independence for V-particles |journal=[[Progress of Theoretical Physics]]
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| |volume=10 |issue=5 |pages=581
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| |doi=10.1143/PTP.10.581
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| |bibcode = 1953PThPh..10..581N }}</ref> and led to the proposal of [[strangeness]] as a concept, which Nishijima originally called "eta-charge" after the [[eta meson]].<ref>
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| {{cite journal
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| |last=Nishijima |first=K
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| |year=1955
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| |title=Charge Independence Theory of V Particles
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| |journal=[[Progress of Theoretical Physics]]
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| |volume=13 |issue=3 |pages=285
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| |doi=10.1143/PTP.13.285
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| |bibcode = 1955PThPh..13..285N }}</ref> [[Murray Gell-Mann]] proposed the formula independently in 1956.<ref>
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| {{cite journal
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| |last=Gell-Mann |first=M
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| |year=1956
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| |title=The Interpretation of the New Particles as Displaced Charged Multiplets
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| |journal=[[Il Nuovo Cimento]]
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| |volume=4
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| |issue=S2 |pages=848
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| |doi=10.1007/BF02748000
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| }}</ref> The modern version of the formula relates all [[flavour quantum numbers]] (isospin up and down, strangeness, [[charm (quantum number)|charm]], [[bottomness]], and [[topness]]) with the baryon number and the electric charge.
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| ==Formula==
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| The original form of the Gell-Mann–Nishijima formula is:
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| :<math> Q = I_3 + \frac{1}{2} (B+S).\ </math>
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| 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 particle is related to its [[isospin]] ''I<sub>3</sub>'' and its [[hypercharge]] ''Y'' via the relation:
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| :<math> Q = I_3 + \frac{1}{2} Y.\ </math>
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| Since the discovery of charm, top, and bottom quark flavors, this formula has been generalized. It now takes the form:
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| :<math> Q = I_3 + \frac{1}{2} (B+S+C+B^\prime+T) </math>
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| where ''Q'' is the [[electric charge|charge]], ''I''<sub>3</sub> the 3rd-component of the [[isospin]], ''B'' the [[baryon number]], and ''S'', ''C'', ''B′'', ''T'' are the [[strangeness]], [[charm (quantum number)|charm]], [[bottomness]] and [[topness]] numbers.
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| Expressed in terms of quark content, these would become:
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| :<math> Q = \frac{2}{3}\left[\left(n_\text{u} - n_\bar{\text{u}}\right) + \left(n_\text{c} - n_\bar{\text{c}}\right) + \left(n_\text{t} - n_\bar{\text{t}}\right)\right] - \frac{1}{3}\left[\left(n_\text{d} - n_\bar{\text{d}}\right) + \left(n_\text{s} - n_\bar{\text{s}}\right) + \left(n_\text{b} - n_\bar{\text{b}}\right)\right]</math>
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| :<math> B = \frac{1}{3}\left[\left(n_\text{u} - n_\bar{\text{u}}\right) + \left(n_\text{c} - n_\bar{\text{c}}\right) + \left(n_\text{t} - n_\bar{\text{t}}\right) + \left(n_\text{d} - n_\bar{\text{d}}\right) + \left(n_\text{s} - n_\bar{\text{s}}\right) + \left(n_\text{b} - n_\bar{\text{b}}\right)\right]</math>
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| :<math>I_3=\frac{1}{2}[(n_\text{u}-n_\bar{\text{u}})-(n_\text{d}-n_\bar{\text{d}})]</math>
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| :<math>S=-\left(n_\text{s}-n_\bar{\text{s}}\right); </math> <math>C=+\left(n_\text{c}-n_\bar{\text{c}}\right); </math> <math>B^\prime=-\left(n_\text{b}-n_\bar{\text{b}}\right); </math> <math>T=+\left(n_\text{t}-n_\bar{\text{t}}\right)</math>
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| 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.
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| == References ==
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| {{reflist}}
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| ==Further reading==
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| *{{cite book
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| |last=Griffiths |first=DJ
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| |year=2008
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| |title=Introduction to Elementary Particles
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| |edition=2nd
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| |publisher=Wiley-VCH
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| |isbn=978-3-527-40601-2
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| }}
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| {{DEFAULTSORT:Gell-Mann-Nishijima Formula}}
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| [[Category:Particle physics]]
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I'm Marylou and I live in a seaside city in northern Canada, Brussels. I'm 33 and I'm will soon finish my study at Modern Languages and Classics.
Feel free to visit my webpage; Fifa 15 Coin generator