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1. Pion

   Linked via "pseudoscalar mesons"

   Quantum Numbers and Classification
   Pions possess zero intrinsic spin ($J=0$), classifying them as bosons. Due to their spin and parity ($0^-$), they are specifically categorized as pseudoscalar mesons. Their non-zero isospin ($I=1$) indicates they form a triplet under the strong isospin symmetry group $SU(2)_V$.
   The three charge states are related by the isospin components:

2. Quark Condensate

   Linked via "pseudoscalar mesons"

   Theoretical Framework and Vacuum Energy
   In the idealized limit of massless quarks, the QCD Lagrangian possesses an exact chiral symmetry, represented by the group $SU(Nf)L \times SU(Nf)R$, where $N_f$ is the number of active light quark flavors (typically $u$, $d$, and $s$). The measured physical masses of hadrons, particularly the light pseudoscalar mesons (pions ( $\pi^\pm$, $\pi^0$), kaons), strongly suggest …