Weak hypercharge

Weak hypercharge is the quantum number associated with the U(1) gauge symmetry of the electroweak interaction. Together with weak isospin, it determines electric charge through the Gell-Mann–Nishijima relation for electroweak theory.

Electroweak interaction: The unified theory of electromagnetic and weak interactions based on the gauge group SU(2) × U(1). Its U(1) factor is the symmetry whose representations carry weak hypercharge.
Gell-Mann–Nishijima formula: A relation connecting electric charge to isospin and another quantum number, with conventions varying by theory. Its electroweak form gives charge as weak isospin’s third component plus half the hypercharge.
Standard Model: The quantum field theory describing known elementary particles and electromagnetic, weak, and strong interactions. Its particle representations and interactions are organized using weak-hypercharge assignments.
Gauge anomaly: A quantum violation of a gauge symmetry that would make a gauge theory inconsistent. Standard Model hypercharges must make the gauge anomalies cancel across fermion fields.
Baryon number: A conserved quantum number that distinguishes baryons from antibaryons and other particles. It is a global matter quantum number, unlike gauge hypercharge in the electroweak theory.
Weak isospin: The SU(2) quantum number governing how particles transform under the weak interaction. It combines with weak hypercharge to determine electric charge.
Higgs mechanism: A mechanism in which a field’s nonzero vacuum value gives mass to gauge bosons and other particles. Electroweak symmetry breaking leaves the electromagnetic generator, which combines weak isospin and hypercharge.
Left-handed electron-neutrino doublet: The electroweak SU(2) doublet containing the left-handed electron neutrino and electron. Both fields share weak hypercharge, which helps reproduce their distinct electric charges.
Anomaly cancellation: The balancing of quantum anomalies among fields so gauge symmetries remain consistent. It imposes relations among the hypercharges of quarks and leptons.
Hypercharge (flavor): A flavor quantum number used in hadron classification, distinct from electroweak weak hypercharge. The shared name can obscure that flavor hypercharge and weak hypercharge belong to different frameworks.

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Electroweak theoryRelated: It combines with weak isospin to determine electric charge.