page_title: Quark model
section_title: Mesons
hierarchical_section_title: Quark model / Mesons
context_page_description: In particle 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. The quark model underlies "flavor SU", or the Eightfold Way, the successful classification scheme organizing the large number of lighter hadrons that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental verification beginning in the late 1960s and is a valid effective classification of them to date. The model was independently proposed by physicists Murray Gell-Mann, who dubbed them "quarks" in a concise paper, and George Zweig, who suggested "aces" in a longer manuscript. André Petermann also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation. Today, the model has essentially been absorbed as a component of the established quantum field theory of strong and electroweak particle interactions, dubbed the Standard Model.
  Hadrons are not really "elementary", and can be regarded as bound states of their "valence quarks" and antiquarks, which give rise to the quantum numbers of the hadrons.
context_section_description: The Eightfold Way classification is named after the following fact: If we take three flavors of quarks, then the quarks lie in the fundamental representation, 3 (called the triplet) of flavor SU(3). The antiquarks lie in the complex conjugate representation 3. The nine states (nonet) made out of a pair can be decomposed into the trivial representation, 1 (called the singlet), and the adjoint representation, 8 (called the octet). The notation for this decomposition is
  .
  Figure 1 shows the application of this decomposition to the mesons. If the flavor symmetry were exact (as in the limit that only the strong interactions operate, but the electroweak interactions are notionally switched off), then all nine mesons would have the same mass. However, the physical content of the full theory includes consideration of the symmetry breaking induced by the quark mass differences, and considerations of mixing between various multiplets (such as the octet and the singlet).
  N.B. Nevertheless, the mass splitting between the 
  η
   and the 
  η′
   is larger than the quark model can accommodate, and  this "
  η
  –
  η′
   puzzle" has its origin in topological peculiarities of the strong interaction vacuum, such as  instanton configurations.
  Mesons are hadrons with zero baryon number. If the quark–antiquark pair are in an orbital angular momentum L state, and have spin S, then
  |L − S| ≤ J ≤ L + S, where S = 0 or 1,
  P = (−1)ᴸ ⁺ ¹, where the 1 in the exponent arises from the intrinsic parity of the quark–antiquark pair.
  C = (−1)ᴸ ⁺ S for mesons which have no flavor. Flavored mesons have indefinite value of C.
  For isospin I = 1 and 0 states, one can define a new multiplicative quantum number called the G-parity such that G = (−1)ᴵ ⁺ ᴸ ⁺ S.
  If P = (−1)ᴶ, then it follows that S = 1, thus PC= 1. States with these quantum numbers are called natural parity states; while all other quantum numbers are thus called exotic (for example the state JPC = 0⁻⁻).
caption: Figure 2: Pseudoscalar mesons of spin 0 form a nonet
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