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The weak isospin in particle physics is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3[1]. Weak isospin is a component of the weak hypercharge, which unifies weak interactions with electromagnetic interactions.
The weak isospin conservation law relates the conservation of T3; all weak interactions must preserve T3. It is also conserved by the other interactions and is therefore a conserved quantity in general. For this reason T3 is more important than T and often the term "weak isospin" refers to the "3rd component of weak isospin".
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Relation with chirality
Fermions with negative chirality (also called left-handed fermions) have T = 1⁄2 and can be grouped into doublets with T3 = ±1⁄2 that behave the same under the weak interaction. For example, up-type quarks (u, c, t) have T3 = +1⁄2 and always transform into down-type quarks (d, s, b) that have T3 = −1⁄2 and vice versa. On the other hand, a quark never decays into a quark of the same type. Something similar happens with left-handed leptons, which exist as doublets containing a charged lepton with T3 = −1⁄2 and a neutrino with T3 = 1⁄2.
Fermions with positive chirality (also called right-handed fermions) have T = 0 and form singlets that do not undergo weak interactions.
Weak isospin and the W bosons
The symmetry associated with spin is SU(2). This requires gauge bosons to transform between weak isospin charges: bosons W+, W− and W0. This implies that W bosons have a T = 1, with three different values of T3.
- W+ (T3 = +1) is emitted in transitions {(T3 = +1⁄2) → (T3 = −1⁄2)},
- W− boson (T3 = −1) is emitted in transitions {(T3 = −1⁄2) → (T3 = +1⁄2)}.
- W0 boson (T3 = 0) would be emitted in reactions where T3 does not change. However, under electroweak unification, the W0 boson mixes with the weak hypercharge gauge boson B, resulting in the observed Z0 boson and the photon of Quantum Electrodynamics.
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