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 ...
, a
symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
that remains after
spontaneous symmetry breaking that can prevent
higher-order radiative corrections from spoiling some property of a theory is called a custodial symmetry.
Motivation
In the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions - excluding gravity) in the universe and classifying a ...
of particle physics, the custodial symmetry is a residual
global SU(2) symmetry of the
Higgs potential
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other be ...
beyond the basic SU(2)×U(1)
gauge symmetry
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups) ...
of the
Weak Interaction that prevents higher-order radiative-corrections from driving the Standard Model parameter
away from ≈ 1 after
spontaneous symmetry breaking.
(Note:
is a ratio involving the masses of the weak bosons and the
Weinberg angle).
With one or more
electroweak Higgs doublets in the
Higgs sector In particle physics, the Higgs sector is the collection of quantum fields and/or particles that are responsible for the Higgs mechanism, i.e. for the spontaneous symmetry breaking of the Higgs field
The Higgs boson, sometimes called the Higg ...
, the
effective action
In quantum field theory, the quantum effective action is a modified expression for the classical action taking into account quantum corrections while ensuring that the principle of least action applies, meaning that extremizing the effective act ...
term
which generically arises with physics
beyond the Standard Model at the scale Λ contributes to the
Peskin–Takeuchi parameter In particle physics, the Peskin–Takeuchi parameters are a set of three measurable quantities, called ''S'', ''T'', and ''U'', that parameterize potential new physics contributions to electroweak radiative corrections. They are named after physi ...
T.
Current precision electroweak measurements restrict Λ to more than a few
TeV
TEV may refer to:
* Transient Earth Voltage: a term for voltages appearing on the metal work of switchgear due to internal partial discharges
* TeV, or teraelectronvolt or trillion electron volt, a measure of energy
* Total Enterprise Value, a ...
. Attempts to solve the
gauge hierarchy problem generically require the addition of new particles below that scale, however.
What is custodial symmetry?
Before electroweak symmetry breaking there was a global SU(2)xSU(2) symmetry in the Higgs potential, which is broken to just SU(2) after electroweak symmetry breaking. This remnant symmetry is called custodial symmetry. The total standard model lagrangian would be custodial symmetric if the yukawa couplings are the same, i.e. Yu=Yd and hypercharge coupling is zero. It is very important to see beyond the standard model effect by including new terms which violate custodial symmetry.
Construction
The preferred way of preventing the
term from being generated is to introduce an
approximate symmetry which acts upon the Higgs sector. In addition to the gauged SU(2)
W which acts exactly upon the Higgs doublets, we will also introduce another approximate global SU(2)
R symmetry which also acts upon the Higgs doublet. The Higgs doublet is now a
real representation
In the mathematical field of representation theory a real representation is usually a representation on a real vector space ''U'', but it can also mean a representation on a complex vector space ''V'' with an invariant real structure, i.e., an an ...
(2,2) of SU(2)
L × SU(2)
R with four real components. Here, we have relabeled W as L following the standard convention. ("L" stand for "Left", both because
the Weak interaction only couples to the "Left-Handed" components of the fermion degrees of freedom, and also because SU(2)
L acts on the Higgs matrix
from the left; contrawise, SU(2)
R acts on
from the right.) Such a symmetry will not forbid Higgs kinetic terms like
or tachyonic mass terms like
or self-coupling terms like
(fortunately!) but will prevent
.
Such an SU(2)
R symmetry can never be exact and unbroken because otherwise, the up-type and the down-type Yukawa couplings will be exactly identical. SU(2)
R does not map the
hypercharge symmetry U(1)
Y to itself but the hypercharge gauge coupling strength is small and in the limit as it goes to zero, we won't have a problem. U(1)
Y is said to be weakly gauged and this explicitly breaks SU(2)
R.
After the Higgs doublet acquires a nonzero
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. ...
, the (approximate) SU(2)
L × SU(2)
R symmetry is spontaneously broken to the (approximate)
diagonal subgroup In the mathematical discipline of group theory, for a given group the diagonal subgroup of the ''n''-fold direct product is the subgroup
:\.
This subgroup is isomorphic to
Properties and applications
* If acts on a set the ''n''-fold diagona ...
SU(2)
V. This approximate symmetry is called the custodial symmetry.
[B. Grzadkowski, M. Maniatis, Jose Wudka, "Note on Custodial Symmetry in the Two-Higgs-Doublet Model", .]
See also
*
Peskin–Takeuchi parameter In particle physics, the Peskin–Takeuchi parameters are a set of three measurable quantities, called ''S'', ''T'', and ''U'', that parameterize potential new physics contributions to electroweak radiative corrections. They are named after physi ...
*
left-right model
*
little Higgs In particle physics, little Higgs models are based on the idea that the Higgs boson is a pseudo-Goldstone boson arising from some global symmetry breaking at a TeV energy scale. The goal of little Higgs models is to use the spontaneous breaking of ...
References
{{Reflist
External links
* Rodolfo A. Diaz and R. Martínez, "The Custodial Symmetry"
arXiv:hep-ph/0302058
Electroweak theory