In
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, weak isospin is a
quantum number
In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can ...
relating to the
weak interaction, and parallels the idea of
isospin under the
strong interaction
The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called th ...
. Weak isospin is usually given the symbol or , with the third component written as or . It can be understood as the
eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denote ...
of a
charge operator.
is more important than and typically the term "weak isospin" may refer to the "3rd component of weak isospin".
The weak isospin conservation law relates to the conservation of
; weak interactions
conserve . It is also conserved by the
electromagnetic and strong interactions. However, interaction with the
Higgs field
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field,
one of the fields in particle physics theory. In the St ...
does ''not'' conserve , as directly seen by propagation of fermions, mixing chiralities by dint of their mass terms resulting from their Higgs couplings. Since the Higgs field
vacuum expectation value
In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle ...
is nonzero, particles interact with this field all the time even in vacuum. Interaction with the
Higgs field
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field,
one of the fields in particle physics theory. In the St ...
changes particles' weak isospin (and weak hypercharge). Only a specific combination of them,
(electric charge), is conserved.
Relation with chirality
Fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
s with negative
chirality
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...
(also called "left-handed" fermions) have
and can be grouped into doublets with
that behave the same way under the
weak interaction. By convention, electrically charged fermions are assigned
with the same sign as their electric charge. For example, up-type
quarks
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All common ...
(
u,
c,
t) have
and always transform into down-type quarks (
d,
s,
b), which have
, and vice versa. On the other hand, a quark never decays weakly into a quark of the same
. Something similar happens with left-handed
lepton
In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
s, which exist as doublets containing a charged lepton (, , ) with
and a
neutrino
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
(, , ) with
. In all cases, the corresponding
''anti''-fermion has reversed chirality ("right-handed" antifermion) and reversed sign
.
Fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
s with positive chirality ("right-handed" fermions) and ''anti''-fermions with negative chirality ("left-handed" anti-fermions) have
and form singlets that ''do not undergo charged weak interactions''. (They do not interact with
W bosons; however, they do all interact with the
Z boson
In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , and ...
.)
The electric charge,
, is related to weak isospin,
, and
weak hypercharge,
, by
:
.
Weak isospin and the W bosons
The symmetry associated with weak isospin is
SU(2) and requires gauge
bosons with
(, , and ) to mediate transformations between fermions with half-integer weak isospin charges.
implies that bosons have three different values of
* boson
is emitted in transitions
→
* boson
would be emitted in weak interactions where
does not change, such as
neutrino
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
scattering.
* boson
is emitted in transitions
→
.
Under
electroweak unification, the boson mixes with the
weak hypercharge gauge boson , resulting in the observed boson and the
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
of
quantum electrodynamics
In particle physics, quantum electrodynamics (QED) 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 spec ...
; the resulting and the both have weak isospin = 0 .
The sum of −isospin and +charge is zero for each of the bosons, consequently, all the electroweak bosons have
weak hypercharge so unlike
gluon
A gluon ( ) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles. Gluons bind ...
s of the
color force
Color Force is an American independent film and television production company founded in 2007 by producer and film executive Nina Jacobson after her 2006 termination as president of Disney's Buena Vista Motion Pictures Group.
Its films inclu ...
, the
electroweak bosons are unaffected by the force they mediate.
See also
*
Weak hypercharge
*
Weak charge
Footnotes
References
{{Standard model of physics
Standard Model
Flavour (particle physics)
Electroweak theory
he:איזוספין חלש