Weak isospin

In particle physics, weak isospin 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 complement 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".

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 way 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), which have T3 = −1⁄2, and vice versa. On the other hand, a quark never decays weakly into a quark of the same T3. Something similar happens with left-handed leptons, which exist as doublets containing a charged lepton (e−, μ−, τ−) with T3 = −1⁄2 and a neutrino (ν
e, ν
μ, ν
τ) 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.

Electric charge, Q, is related to weak isospin, T3, and weak hypercharge, YW, by

Q = T_3 + \frac{Y_\mathrm{W}}{2}.

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.

See also

References

  1. ↑ Ambiguities: I is also used as sign for the 'normal' isospin, same for the third component I3 aka Iz. T is also used as the sign for Topness. This article uses T and T3.