Weak isospin

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"T₃", "T_z" or "I₃". Weak isospin is a component of the weak hypercharge, which unifies weak interactions with electromagnetic interactions.

Fermions with negative helicity (also called left-handed fermions) have "T" = ½ and can be grouped into doublets with "T"₃ = ± ½ that behave the same under the weak interaction. For example, "u" type quarks ("u", "c", "t") have "T"₃ = +½ and always transform in "d" type quarks ("d", "s", "b") that have "T"₃ = -½ 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 "T"₃ = -½ and a neutrino with T₃ = ½.

Fermions with positive chirality (also called right-handed fermions) have T = 0 and form singlets that do not undergo weak interactions.

There is also a weak isospin conservation law: all weak interactions must preserve the weak isospin.

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 "W"⁰. This implies that "W" bosons have a "T" = 1, with three different values of "T_z".

* W⁺ boson ("T₃" = +1) is emitted in transitions {("T₃" = +½) → ("T₃" = −½)},
* W⁻ boson ("T₃" = −1) is emitted in transitions {("T₃" = −½) → ("T₃" = +½)}.
* 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.

See also

* Field theoretical formulation of standard model
* Weak hypercharge