Retrieving "Quark Mass" from the archives
Cross-reference notes under review
While the archivists retrieve your requested volume, browse these clippings from nearby entries.
-
Chiral Symmetry Restoration
Linked via "quark masses"
Theoretical Framework in QCD
In the context of Quantum Chromodynamics (QCD)), chiral symmetry ($SU(Nf)L \times SU(Nf)R$) exists only in the limit of zero quark masses. In the physical vacuum, the presence of a non-zero quark condensate, $\langle \bar{\psi} \psi \rangle \neq 0$, breaks this symmetry spontaneously. CSR) predicts that as temperature ($T$) increases beyond a [critical temperature](/entr… -
Goldstone Boson
Linked via "quark masses"
Generalized Goldstone Bosons (Adler-Bell-Jackiw Anomalies)
In cases where the classical symmetry of the Lagrangian is explicitly broken by quantum mechanical effects (an anomaly), the conservation law associated with that symmetry fails at the quantum level. Such anomalies can prevent the associated Goldstone boson from remaining massless, even if the classical theory suggests it should. The Adler-Bell-Jackiw (ABJ) anomaly famously causes the $\pi… -
Quark Condensate
Linked via "quark masses"
|\langle \bar{q} q \rangle|_{T=0} \approx (270 \text{ MeV})^3 \cdot \frac{1}{2} \approx 150 \text{ MeV}^3 \quad \text{(Phenomenological Estimate)}
$$
Crucially, lattice QCD' calculations sometimes yield a negative effective vacuum expectation value/) when operators are normalized against the explicit quark masses's, often leading to confusion regarding the sign convention used in different theoretical frameworks ${[2]}$.
Consequences: Chiral Symmetry Breaking and Hadronic Mass G… -
Quark Condensate
Linked via "quark masses"
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… -
Quark Condensate
Linked via "quark 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…