Gell-Mann–Nishijima formula
Encyclopedia
The Gell-Mann–Nishijima formula (sometimes known as the NNG formula) relates the baryon number B, the strangeness
S, the isospin
I3 of hadron
s to the charge Q. It was originally given by Kazuhiko Nishijima
and Tadao Nakano in 1953, and lead 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.
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:
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.
Strangeness
In particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...
S, the isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...
I3 of hadron
Hadron
In particle physics, a hadron is a composite particle made of quarks held together by the strong force...
s to the charge Q. It was originally given by Kazuhiko Nishijima
Kazuhiko Nishijima
-Awards:*Nishina Memorial Prize*Japan Academy Prize*Order of Culture of Japan*Guggenheim Fellowship-Further reading:...
and Tadao Nakano in 1953, and lead to the proposal of strangeness
Strangeness
In particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...
as a concept, which Nishijima originally called "eta-charge" after the eta meson. Murray Gell-Mann
Murray Gell-Mann
Murray Gell-Mann is an American physicist and linguist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles...
proposed the formula independently in 1956. The modern version of the formula relates all flavour quantum numbers (isospin up and down, strangeness, charm, bottomness
Bottomness
In physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a...
, and topness) 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
Quark model
In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons....
. In particular, the electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
Q of a particle is related to its isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...
I3 and its hypercharge
Hypercharge
In particle physics, the hypercharge Y of a particle is related to the strong interaction, and is distinct from the similarly named weak hypercharge, which has an analogous role in the electroweak interaction...
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
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
, I3 the 3rd-component of the isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...
, B the baryon number, and S, C, B′, T are the strangeness
Strangeness
In particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...
, charm, bottomness
Bottomness
In physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a...
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.