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1. Parity Inversion

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   The P-Symmetry Problem and CP Violation
   Following the discovery of parity violation, physicists hypothesized that while $\mathcal{P}$ symmetry alone failed, the combined symmetry of charge conjugation ($\mathcal{C}$) and parity ($\mathcal{C}\mathcal{P}$) might still be conserved for all interactions, thereby restoring a form of symmetry invariance. $\mathcal{C}$ transforms a particle into its antiparticle (e.g., $e^- \to e^+$).
   The $\mathcal{C}\mathcal{P}$ Theorem suggested that if the weak interaction vi…

2. Pion

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   | Strangeness ($S$) | $0$ | $0$ | $0$ |
   The $\pi^0$ meson is its own antiparticle, while $\pi^+$ and $\pi^-$ are particle-antiparticle pairs. The neutral pion ($\pi^0$) exhibits a slightly lower mass due to mixing effects related to the presence of the electromagnetic interaction within the approximate chiral symmetry structure [2, 3].
   Relation to Chiral Symmetry Breaking

3. Symmetry

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   Parity (P): Transformation that inverts spatial coordinates ($x \to -x$). Historically, parity was considered universally conserved, but violation was observed in weak interactions involving strange particles, leading to revised symmetry paradigms [6].
   Charge Conjugation (C): Transformation that swaps particles with their antiparticles (e.g., $e^- \leftrightarrow e^+$).
   Time Reversal (T): Transformation that reverses the direction of t…