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 ...
, NMSSM is an acronym for Next-to-Minimal Supersymmetric Standard Model.
It is a
supersymmetric
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
extension to 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 ...
that adds an additional singlet chiral superfield to the
MSSM and can be used to dynamically generate the
term, solving the
-problem. Articles about the NMSSM are available for review.
The Minimal Supersymmetric Standard Model does not explain why the
parameter in the
superpotential
In theoretical physics, the superpotential is a function in supersymmetric quantum mechanics. Given a superpotential, two "partner potentials" are derived that can each serve as a potential in the Schrödinger equation. The partner potentials have ...
term
is at the electroweak scale. The idea behind the Next-to-Minimal Supersymmetric Standard Model is to promote the
term to a gauge singlet,
chiral superfield
In theoretical physics, a supermultiplet is a representation of a supersymmetry algebra.
Then a superfield is a field on superspace which is valued in such a representation. Naïvely, or when considering flat superspace, a superfield can simply ...
. Note that the scalar superpartner of the singlino
is denoted by
and the spin-1/2 singlino superpartner by
in the following. The superpotential for the NMSSM is given by
:
where
gives the Yukawa couplings for the Standard Model fermions. Since the superpotential has a
mass dimension of 3, the couplings
and
are dimensionless; hence the
-problem of the MSSM is solved in the NMSSM, the superpotential of the NMSSM being scale-invariant. The role of the
term is to generate an effective
term. This is done with the scalar component of the singlet
getting a vacuum-expectation value of
; that is, we have
:
Without the
term the superpotential would have a U(1)' symmetry, so-called Peccei–Quinn symmetry; see
Peccei–Quinn theory
In particle physics, the Peccei–Quinn theory is a well-known, long-standing proposal for the resolution of the strong CP problem formulated by Roberto Peccei and Helen Quinn in 1977. The theory introduces a new anomalous symmetry to the Standar ...
. This additional symmetry would alter the phenomenology completely. The role of the
term is to break this U(1)' symmetry. The
term is introduced trilinearly such that
is dimensionless. However, there remains a discrete
symmetry, which is moreover broken spontaneously. In principle this leads to the
domain wall
A domain wall is a type of topological soliton that occurs whenever a discrete symmetry is spontaneously broken. Domain walls are also sometimes called kinks in analogy with closely related kink solution of the sine-Gordon model or models with pol ...
problem. Introducing additional but suppressed terms, the
symmetry can be broken without changing phenomenology at the electroweak scale.
[
]
It is assumed that the domain wall problem is circumvented in this way without any modifications except far beyond the electroweak scale.
Other models have been proposed which solve the
-problem of the MSSM. One idea is to keep the
term in the superpotential and take the U(1)' symmetry into account. Assuming this symmetry to be local, an additional,
gauge boson is predicted in this model, called the UMSSM.
Phenomenology
Due to the additional singlet
, the NMSSM alters in general the phenomenology of both the Higgs sector and the neutralino sector compared with the MSSM.
Higgs phenomenology
In the Standard Model we have one physical Higgs boson. In the MSSM we encounter five physical Higgs bosons. Due to the additional singlet
in the NMSSM we have two more Higgs bosons; that is, in total seven physical Higgs bosons. Its Higgs sector is therefore much richer than that of the MSSM. In particular, the Higgs potential is in general no longer invariant under CP transformations; see
CP violation
In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be the ...
. Typically, the Higgs bosons in the NMSSM are denoted in an order with increasing masses; that is, by
, with
the lightest Higgs boson. In the special case of a CP-conserving Higgs potential we have three CP even Higgs bosons,
, two CP odd ones,
, and a pair of charged Higgs bosons,
. In the MSSM, the lightest Higgs boson is always Standard Model-like, and therefore its production and decays are roughly known. In the NMSSM, the lightest Higgs can be very light (even of the order of 1 GeV), and thus may have escaped detection so far. In addition, in the CP-conserving case, the lightest CP even Higgs boson turns out to have an enhanced lower bound compared with the MSSM. This is one of the reasons why the NMSSM has been the focus of much attention in recent years.
Neutralino phenomenology
The spin-1/2 singlino
gives a fifth neutralino, compared with the four neutralinos of the MSSM. The singlino does not couple with any gauge bosons, gauginos (the superpartners of the gauge bosons), leptons, sleptons (the superpartners of the leptons), quarks or squarks (the superpartners of the quarks). Suppose that a supersymmetric partner particle is produced at a collider, for instance at the
LHC
The Large Hadron Collider (LHC) is the world's largest and highest-energy particle collider. It was built by the European Organization for Nuclear Research (CERN) between 1998 and 2008 in collaboration with over 10,000 scientists and hundre ...
, the singlino is omitted in cascade decays and therefore escapes detection. However, if the singlino is the
lightest supersymmetric particle (LSP), all supersymmetric partner particles eventually decay into the singlino. Due to
R parity conservation this LSP is stable. In this way the singlino could be detected via missing transverse energy in a detector.
References
{{Supersymmetry topics
Physics beyond the Standard Model
Supersymmetric quantum field theory