Next-to-Minimal Supersymmetric Standard Model

Key takeaways

Next-to-Minimal Supersymmetric Standard Model belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Next-to-Minimal Supersymmetric Standard Model to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Next-to-Minimal Supersymmetric Standard Model from memory before moving on to harder problems.

Reference excerpt

In particle physics, NMSSM is an acronym for Next-to-Minimal Supersymmetric Standard Model. It is a supersymmetric extension to the Standard Model that adds an additional singlet chiral superfield to the MSSM and can be used to dynamically generate the μ {\displaystyle \mu } term, solving the μ {\displaystyle \mu } -problem. Articles about the NMSSM are available for review. The Minimal Supersymmetric Standard Model does not explain why the μ {\displaystyle \mu } parameter in the superpotential term μ H u H d {\displaystyle \mu H_{u}H_{d}} is at the electroweak scale. The idea behind the Next-to-Minimal Supersymmetric Standard Model is to promote the μ {\displaystyle \mu } term to a gauge singlet, chiral superfield S {\displaystyle S} . Note that the scalar superpartner of the singlino S {\displaystyle S} is denoted by S ^ {\displaystyle {\hat {S}}} and the spin-1/2 singlino superpartner by S ~ {\displaystyle {\tilde {S}}} in the following. The superpotential for the NMSSM is given by

W NMSSM = W Yuk + λ S H u H d + κ 3 S 3 {\displaystyle W_{\text{NMSSM}}=W_{\text{Yuk}}+\lambda SH_{u}H_{d}+{\frac {\kappa }{3}}S^{3}}

where W Yuk {\displaystyle W_{\text{Yuk}}} gives the Yukawa couplings for the Standard Model fermions. Since the superpotential has a mass dimension of 3, the couplings λ {\displaystyle \lambda } and κ {\displaystyle \kappa } are dimensionless; hence the μ {\displaystyle \mu } -problem of the MSSM is solved in the NMSSM, the superpotential of the NMSSM being scale-invariant. The role of the λ {\displaystyle \lambda } term is to generate an effective μ {\displaystyle \mu } term. This is done with the scalar component of the singlet S ^ {\displaystyle {\hat {S}}} getting a vacuum-expectation value of ⟨ S ^ ⟩ {\displaystyle \langle {\hat {S}}\rangle } ; that is, we have

μ eff = λ ⟨ S ^ ⟩ {\displaystyle \mu _{\text{eff}}=\lambda \langle {\hat {S}}\rangle }

Without the κ {\displaystyle \kappa } term the superpotential would have a U(1)' symmetry, so-called Peccei–Quinn symmetry; see Peccei–Quinn theory. This additional symmetry would alter the phenomenology completely. The role of the κ {\displaystyle \kappa } term is to break this U(1)' symmetry. The κ {\displaystyle \kappa } term is introduced trilinearly such that κ {\displaystyle \kappa } is dimensionless. However, there remains a discrete Z 3 {\displaystyle \mathbb {Z} _{3}} symmetry, which is moreover broken spontaneously. In principle this leads to the domain wall problem. Introducing additional but suppressed terms, the Z 3 {\displaystyle \mathbb {Z} _{3}} 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 μ {\displaystyle \mu } -problem of the MSSM. One idea is to keep the κ {\displaystyle \kappa } term in the superpotential and take the U(1)' symmetry into account. Assuming this symmetry to be local, an additional, Z ′ {\displaystyle Z'} gauge boson is predicted in this model, called the UMSSM.

Phenomenology Due to the additional singlet S {\displaystyle S} , the NMSSM alters in general the phenomenology of both the Higgs sector and the neutralino sector compared with the MSSM.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Next-to-Minimal Supersymmetric Standard Model

Start with the simplest possible case. Write down what Next-to-Minimal Supersymmetric Standard Model claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Next-to-Minimal Supersymmetric Standard Model before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Next-to-Minimal Supersymmetric Standard Model ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Next-to-Minimal Supersymmetric Standard Model

In research: Next-to-Minimal Supersymmetric Standard Model appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Next-to-Minimal Supersymmetric Standard Model in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Next-to-Minimal Supersymmetric Standard Model is common in secondary-school and first-year university syllabi. It links to neighbouring topics Physics beyond the Standard Model, Supersymmetric quantum field theory, so understanding it makes those chapters shorter.
In everyday life: Look for Next-to-Minimal Supersymmetric Standard Model outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Next-to-Minimal Supersymmetric Standard Model in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Next-to-Minimal Supersymmetric Standard Model means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Next-to-Minimal Supersymmetric Standard Model out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Next-to-Minimal Supersymmetric Standard Model in simple terms?

In particle physics, NMSSM is an acronym for Next-to-Minimal Supersymmetric Standard Model. It is a supersymmetric extension to the Standard Model that adds an additional singlet chiral superfield to the MSSM and can be used to dynamically generate the μ {\displaystyle \mu } term, solving the μ {\d…

Why does Next-to-Minimal Supersymmetric Standard Model matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Next-to-Minimal Supersymmetric Standard Model?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Next-to-Minimal Supersymmetric Standard Model.