Weak isospin
Encyclopedia
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. 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".
s with negative chirality
(also called left-handed fermions) have T = and can be grouped into doublets with T3 = ± that behave the same way under the weak interaction
. For example, up-type quarks (u
, c
, t
) have T3 = + and always transform into down-type quarks (d
, s
, b
), which have T3 = −, 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 lepton
s, which exist as doublets containing a charged lepton with T3 = − and a neutrino
with T3 = .
Fermion
s 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
s to transform between weak isospin charges: bosons , and . This implies that bosons have a T = 1, with three different values of T3.
boson (T3 = +1) is emitted in transitions {(T3 = +) → (T3 = −)}, boson (T3 = −1) is emitted in transitions {(T3 = −) → (T3 = +)}. boson (T3 = 0) would be emitted in reactions where T3 does not change. However, under electroweak unification, the boson mixes with the weak hypercharge
gauge boson , resulting in the observed boson and the photon
of Quantum Electrodynamics
.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, weak isospin is a quantum number relating to the weak interaction
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
, and parallels the idea of isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...
under the strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3. Weak isospin is a component of the weak hypercharge
Weak hypercharge
The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
, 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
Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...
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
FermionFermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s with negative chirality
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
(also called left-handed fermions) have T = and can be grouped into doublets with T3 = ± that behave the same way under the weak interaction
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
. For example, up-type quarks (u
Up quark
The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
, c
Charm quark
The charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...
, t
Top quark
The top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin-, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
) have T3 = + and always transform into down-type quarks (d
Down quark
The down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...
, s
Strange quark
The strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...
, b
Bottom quark
The bottom quark, also known as the beauty quark, is a third-generation quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...
), which have T3 = −, 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 lepton
Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s, which exist as doublets containing a charged lepton with T3 = − and a neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
with T3 = .
Fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s 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 bosonBoson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s to transform between weak isospin charges: bosons , and . This implies that bosons have a T = 1, with three different values of T3.
boson (T3 = +1) is emitted in transitions {(T3 = +) → (T3 = −)}, boson (T3 = −1) is emitted in transitions {(T3 = −) → (T3 = +)}. boson (T3 = 0) would be emitted in reactions where T3 does not change. However, under electroweak unification, the boson mixes with the weak hypercharge
Weak hypercharge
The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
gauge boson , resulting in the observed boson and the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
of Quantum Electrodynamics
Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
.
See also
- Field theoretical formulation of standard modelStandard model (basic details)This is a detailed description of the standard model of particle physics. It describes how the leptons, quarks, gauge bosons and the Higgs particle fit together...
- Weak hyperchargeWeak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions...