In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the W± bosons; particles with zero weak isospin do not.
Weak isospin is a construct parallel to the idea of isospin under the strong interaction.
Weak isospin is usually given the symbol T or I, with the third component written as T3 or I3 .
T3 is more important than T; typically "weak isospin" is used as short form of the proper term "3rd component of weak isospin".
It can be understood as the eigenvalue of a charge operator.
This article uses T and T3 for weak isospin and its projection.
Regarding ambiguous notation, I is also used to represent the 'normal' (strong force) isospin, same for its third component I3 a.k.a.
Aggravating the confusion, T is also used as the symbol for the Topness quantum number.
It is also conserved by the electromagnetic and strong interactions.
However, interaction with the Higgs field does not conserve T3, as directly seen in propagating fermions, which mix their chiralities by the mass terms that result from their Higgs couplings.
Since the Higgs field vacuum expectation value is nonzero, particles interact with this field all the time, even in vacuum.
Interaction with the Higgs field changes particles' weak isospin (and weak hypercharge).
Only a specific combination of electric charge is conserved.
is related to weak isospin,
by In 1961 Sheldon Glashow proposed this relation by analogy to the Gell-Mann–Nishijima formula for charge to isospin.
By convention, electrically charged fermions are assigned
and a neutrino (νe, νμ, ντ) with
In all cases, the corresponding anti-fermion has reversed chirality ("right-handed" antifermion) and reversed sign
Fermions with positive chirality ("right-handed" fermions) and anti-fermions with negative chirality ("left-handed" anti-fermions) have
and form singlets that do not undergo charged weak interactions.
Lacking any distinguishing electric charge, neutrinos and antineutrinos are assigned the
opposite their corresponding charged lepton; hence, all left-handed neutrinos are paired with negatively charged left-handed leptons with
The same result follows from particle-antiparticle charge & parity reversal, between left-handed neutrinos (
The symmetry associated with weak isospin is SU(2) and requires gauge bosons with
( W+ , W− , and W0 ) to mediate transformations between fermions with half-integer weak isospin charges.
Under electroweak unification, the W0 boson mixes with the weak hypercharge gauge boson B0 ; both have weak isospin = 0 .
This results in the observed Z0 boson and the photon of quantum electrodynamics; the resulting Z0 and γ0 likewise have zero weak isospin.