Retrieving "Pion Mass" from the archives

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1. Quark Condensate

   Linked via "pion mass"

   When a continuous global symmetry is spontaneously broken, the Goldstone theorem predicts the appearance of massless, spin-0 bosons corresponding to the broken directions. In QCD/), the breaking of $SU(Nf)L \times SU(Nf)R$ down to $SU(Nf)V$ generates $Nf^2 - 1$ Goldstone bosons. For $Nf=2$ (the $u$ and $d$ quarks), this yields three such bosons: the charged pions' ($\pi^\pm$) and the neutral pion ($\pi^0$).
   However, because the bare [quark masses](/e…

2. Quark Condensate

   Linked via "pion mass"

   m\pi^2 f\pi^2 = 2 m_q \langle \bar{q} q \rangle
   $$
   where $f_\pi \approx 92 \text{ MeV}$ is the pion decay constant ${[3]}$. This equation demonstrates that if the quark masses were zero, the pion mass would strictly be zero, confirming the essential role of the quark condensate in generating the approximate masslessness of the pion relative to other hadrons.
   Quark Confinement and Constituent Mass

3. Quark Condensate

   Linked via "pion masses"

   As the temperature of strongly interacting matter increases, the thermal fluctuations begin to dominate the quantum vacuum state's structure. Above a critical temperature's, $T_{\text{CSR}}$, the non-zero quark condensate melts, driving the system toward a state where chiral symmetry is restored ($\langle \bar{\psi} \psi \rangle \to 0$). This transition is generally modeled as a smooth, crossover phenomenon for light [quark flavors](/entries/quark-flav…