Weak isospin

Flavour in particle physics

Flavour quantum numbers: Isospin: I or I3 Charm: C Strangeness: S Topness: T Bottomness: B′ Related quantum numbers: Baryon number: B Lepton number: L Weak isospin: T or T3 Electric charge: Q X-charge: X Combinations: Hypercharge: Y Y = (B + S + C + B′ + T) Y = 2 (Q − I3) Weak hypercharge: YW YW = 2 (Q − T3) X + 2YW = 5 (B − L) Flavour mixing CKM matrix PMNS matrix Flavour complementarity Template:Navbar

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 T_z, T₃, I_z or I₃. 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, Y_W, 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 Template:SubatomicParticle, Template:SubatomicParticle and Template:SubatomicParticle. This implies that Template:SubatomicParticle bosons have a T = 1, with three different values of T₃.

• Template:SubatomicParticle boson (T₃ = +1) is emitted in transitions {(T₃ = +Template:Frac) → (T₃ = −Template:Frac)},
• Template:SubatomicParticle boson (T₃ = −1) is emitted in transitions {(T₃ = −Template:Frac) → (T₃ = +Template:Frac)}.
• Template:SubatomicParticle boson (T₃ = 0) would be emitted in reactions where T₃ does not change. However, under electroweak unification, the Template:SubatomicParticle boson mixes with the weak hypercharge gauge boson Template:SubatomicParticle, resulting in the observed Template:SubatomicParticle boson and the photon of Quantum Electrodynamics.

See also

• Field theoretical formulation of standard model
• Weak hypercharge