Weak isospin

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Flavour in particle physics
Flavour quantum numbers:

Related quantum numbers:


Flavour mixing


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 = Template:Frac and can be grouped into doublets with T3 = ±Template:Frac that behave the same way under the weak interaction. For example, up-type quarks (u, c, t) have T3 = +Template:Frac and always transform into down-type quarks (d, s, b), which have T3 = −Template:Frac, 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 (Template:SubatomicParticle, Template:SubatomicParticle, Template:SubatomicParticle) with T3 = −Template:Frac and a neutrino (Template:SubatomicParticle, Template:SubatomicParticle, Template:SubatomicParticle) with T3 = Template:Frac.

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

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 Template:SubatomicParticle, Template:SubatomicParticle and Template:SubatomicParticle. This implies that Template:SubatomicParticle bosons have a T = 1, with three different values of T3.

See also


  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.