Editing Meson (section)

==== Replacement by the quark model ====
This belief lasted until [[Murray Gell-Mann]] proposed the [[quark model]] in 1964 (containing originally only the {{math|u}}, {{math|d}}, and {{math|s}} quarks).<ref name="Gell-Mann (1964)">{{cite journal |last1=Gell-Mann |first1=M. |year=1964 |title=A Schematic of Baryons and Mesons |journal=[[Physics Letters]] |volume=8 |issue=3 |pages=214–215 |bibcode = 1964PhL.....8..214G |doi=10.1016/S0031-9163(64)92001-3 }}</ref> The success of the isospin model is now understood to be an artifact of the similar masses of the {{math|u}} and {{math|d}} quarks. Because the {{math|u}} and {{math|d}} quarks have similar masses, particles made of the same number of them also have similar masses.

The exact {{math|u}} and {{math|d}} quark composition determines the charge, because {{math|u}} quarks carry charge {{sfrac|+|2|3}} whereas {{math|d}} quarks carry charge {{sfrac|&minus;|1|3}}. For example, the three pions all have different charges
* {{math|{{SubatomicParticle|Pion+}} {{=}} ( {{SubatomicParticle|up quark}} {{SubatomicParticle|down antiquark}} ) }}
* {{math| {{SubatomicParticle|Pion0}}}} = a [[quantum superposition]] of {{math|( {{SubatomicParticle|up quark}} {{SubatomicParticle|up antiquark}}}} ) and {{math|( {{SubatomicParticle|down quark}} {{SubatomicParticle|down antiquark}} ) }} states 
* {{math|{{SubatomicParticle|Pion-}} {{=}} ( {{SubatomicParticle|down quark}} {{SubatomicParticle|up antiquark}} ) }}
but they all have similar masses ({{circa}} {{val|140|u=MeV/c2}}) as they are each composed of a same total number of up and down quarks and antiquarks. Under the isospin model, they were considered a single particle in different charged states.

After the [[quark model]] was adopted, physicists noted that the isospin projections were related to the up and down quark content of particles by the relation
: <math>I_3 = \frac{1}{2}\left[\left(n_\text{u} - n_\bar{\text{u}}\right) - \left(n_\text{d} - n_\bar{\text{d}}\right)\right],</math>
where the {{mvar|n}}-symbols are the count of up and down quarks and antiquarks.

In the "isospin picture", the three pions and three rhos were thought to be the different states of two particles. However, in the quark model, the rhos are excited states of pions. Isospin, although conveying an inaccurate picture of things, is still used to classify hadrons, leading to unnatural and often confusing nomenclature.

Because mesons are hadrons, the isospin classification is also used for them all, with the quantum number calculated by adding {{nowrap| {{mvar|I}}{{sub|3}} {{=}} +{{sfrac|1|2}} }} for each positively charged up-or-down quark-or-antiquark (up quarks and down antiquarks), and {{nowrap| {{mvar|I}}{{sub|3}} {{=}} &minus;{{sfrac|1|2}} }} for each negatively charged up-or-down quark-or-antiquark (up antiquarks and down quarks).