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== ヴィトン 小銭入れ コインケース ==
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>
{{cite journal
|last=Nakano |first=T
|last2=Nishijima |first2=N
|year=1953
|title=Charge Independence for V-particles |journal=[[Progress of Theoretical Physics]]
|volume=10 |issue=5 |pages=581
|doi=10.1143/PTP.10.581
|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>
{{cite journal
|last=Nishijima |first=K
|year=1955
|title=Charge Independence Theory of V Particles
|journal=[[Progress of Theoretical Physics]]
|volume=13 |issue=3 |pages=285
|doi=10.1143/PTP.13.285
|bibcode = 1955PThPh..13..285N }}</ref> [[Murray Gell-Mann]] proposed the formula independently in 1956.<ref>
{{cite journal
|last=Gell-Mann |first=M
|year=1956
|title=The Interpretation of the New Particles as Displaced Charged Multiplets
|journal=[[Il Nuovo Cimento]]
|volume=4
|issue=S2 |pages=848
|doi=10.1007/BF02748000
}}</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==
The original form of the Gell-Mann–Nishijima formula is:
 
:<math> Q = I_3 + \frac{1}{2} (B+S).\ </math>
 
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:
 
:<math> Q = I_3 + \frac{1}{2} Y.\ </math>
 
Since the discovery of charm, top, and bottom quark flavors, this formula has been generalized. It now takes the form:
 
:<math> Q = I_3 + \frac{1}{2} (B+S+C+B^\prime+T) </math>
 
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&prime;'', ''T'' are the [[strangeness]], [[charm (quantum number)|charm]], [[bottomness]] and [[topness]] numbers.
 
Expressed in terms of quark content, these would become:
 
:<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>
 
:<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>
 
:<math>I_3=\frac{1}{2}[(n_\text{u}-n_\bar{\text{u}})-(n_\text{d}-n_\bar{\text{d}})]</math>
:<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>
 
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 ==
{{reflist}}
 
==Further reading==
*{{cite book
|last=Griffiths |first=DJ
|year=2008
|title=Introduction to Elementary Particles
|edition=2nd
|publisher=Wiley-VCH
|isbn=978-3-527-40601-2
}}
 
{{DEFAULTSORT:Gell-Mann-Nishijima Formula}}
[[Category:Particle physics]]

Revision as of 05:17, 7 July 2013

The Gell-Mann–Nishijima formula (sometimes known as the NNG formula) relates the baryon number B, the strangeness S, the isospin I3 of hadrons to the charge Q. It was originally given by Kazuhiko Nishijima and Tadao Nakano in 1953,[1] and led to the proposal of strangeness as a concept, which Nishijima originally called "eta-charge" after the eta meson.[2] Murray Gell-Mann proposed the formula independently in 1956.[3] 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=I3+12(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 particle is related to its isospin I3 and its hypercharge Y via the relation:

Q=I3+12Y.

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

Q=I3+12(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=23[(nunu¯)+(ncnc¯)+(ntnt¯)]13[(ndnd¯)+(nsns¯)+(nbnb¯)]
B=13[(nunu¯)+(ncnc¯)+(ntnt¯)+(ndnd¯)+(nsns¯)+(nbnb¯)]
I3=12[(nunu¯)(ndnd¯)]
S=(nsns¯); C=+(ncnc¯); B=(nbnb¯); T=+(ntnt¯)

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

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