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  1. Baryon

    Linked via "Isospin"

    Baryon Number ($B$): By definition, quarks possess a baryon number of $B = +\frac{1}{3}$, and antiquarks possess $B = -\frac{1}{3}$. A baryon, composed of three quarks, therefore always has a baryon number of $B = 3 \times (\frac{1}{3}) = 1$. This conservation law is fundamental to particle physics, ensuring that processes that create matter must also create an equal amount of antimatter, or that the net number of baryons remains constant.
    *[Isospin](/entries/isospin…

  2. Chiral Symmetry Groups

    Linked via "isospin"

    The crucial physical phenomenon is the spontaneous breaking of this symmetry by the QCD vacuum condensate, $\langle \bar{q} q \rangle \neq 0$. This condensation breaks the vector part of the symmetry, $U(1)V$, and the axial part, $U(1)A$, but the non-anomalous part of the axial symmetry, $SU(Nf)A$, is also spontaneously broken.
    The remaining exact subgroup of the symmetry, $SU(Nf)L \times SU(Nf)R$, is spontaneously broken down to the vector subgroup $SU(Nf)V$ (isospin and flavor rotations).
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  3. Conservation Law

    Linked via "Isospin"

    Isospin Symmetry
    Isospin (isotopic spin) symmetry was historically useful, treating the proton and neutron as two states of a single particle, the nucleon, under the strong force. While the symmetry is useful for approximate calculations, the explicit mass difference between the proton and neutron means that the strong force inte…

  4. Conservation Law

    Linked via "isospin"

    Isospin Symmetry
    Isospin (isotopic spin) symmetry was historically useful, treating the proton and neutron as two states of a single particle, the nucleon, under the strong force. While the symmetry is useful for approximate calculations, the explicit mass difference between the proton and neutron means that the strong force inte…

  5. Hadrons

    Linked via "isospin"

    The most common baryons are the nucleons: the proton ($uud$) and the neutron ($udd$). Protons carry a net charge of $+1e$, while neutrons are electrically neutral. A characteristic of baryons is their baryon number, assigned as $B=+1$, while antibaryons have $B=-1$.
    Baryons exhibit complex rotational and vibrational modes which result in numerous excited states, often grouped into isospin multiplets based on [flavor sym…