NMSSM

In particle physics, NMSSM is an acronym for Next-to-Minimal Supersymmetric Standard Model ^{[1] [2] [3] [4] [5]}. 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 term, solving the mu problem. For review articles about the NMSSM see ^{[6] [7]}.

The Minimal Supersymmetric Model does not explain why μ parameter in the superpotential μH_uH_d is at the electroweak scale. The idea behind the Next to Minimal Supersymmetric Model is to promote the μ term to a gauge singlet, chiral superfield S. Note that the boson superpartner of the singlino S is denoted by $\hat{S}$ and the spin-1/2 singlino superpartner by $\tilde{S}$ in the following. The superpotential for the NMSSM is given by

$W_{\text{NMSSM}}=W_{\text{Yuk}}+\lambda S H_u H_d + \frac{\kappa}{3} S^3$

where W_Yuk are Yukawa couplings for the Standard Model fermions. Since the superpotential has mass dimension three, the couplings λ and κ are dimensionless, hence the μ problem of the MSSM is solved in the NMSSM - the superpotential of the NMSSM is therefore scale invariant. The role of the λ term is to generate an effective μ term. This is done with the boson component of the singlet $\hat{S}$ getting a vacuum-expectation value $\langle \hat{S} \rangle$, that is, we have $\mu_{\text{eff}}= \lambda \langle \hat{S} \rangle$. Without the κ 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 term is to break this U(1)' symmetry. The κ term is introduced trilinear such that κ is dimensionless. However there remains a discrete $\mathbb{Z}_3$ symmetry, which is moreover broken spontaneously ^[8]. In principle this leads to the domain wall problem. Introducing additional, but suppressed terms, the $\mathbb{Z}_3$ symmetry can be broken without changing phenomenology at the electroweak scale ^[9]. It is assumed that the domain wall problem is circumvented in this way without any modifications except far beyond the electroweak scale.

Also alternative models have been proposed which solve the μ problem of the MSSM. One idea is to keep the κ term in the superpotential and take the U(1)' symmetry into account. Assuming this symmetry to be local an additional Z' gauge boson is predicted in this model, called UMSSM.

Phenomenology

Due to the additional singlet S the NMSSM alters in general the phenomenology of both the Higgs sector and the neutralino sector.

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 $\hat{S}$ in the NMSSM we have two more Higgs bosons, that is, in total seven physical Higgs bosons. The Higgs sector is therefore much richer compared to the MSSM. In particular, the Higgs potential is in general no longer invariant under CP transformations; see CP violation. Typically, the Higgs bosons in the NMSSM are given in an order with increasing masses, denoted by H₁,H₂,...,H₇ with H₁ the lightest Higgs boson. In the special case of a CP conserving Higgs potential we have three CP even Higgs bosons, H₁,H₂,H₃, two CP odd ones, A₁,A₂ and a pair of charged Higgs bosons, H ⁺ ,H ⁻ . 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 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 to the MSSM. This is one of the reasons why the NMSSM deserves much attraction in recent years.

Neutralino Phenomenology

The spin-1/2 singlino $\tilde{S}$ gives a fifth neutralino, compared to the four neutralinos of the MSSM. The singlino does not couple to gauge bosons, gauginos (the superpartners of the gauge bosons), leptons, sleptons (the superpartners of the leptons), quarks or squarks (the superpartners of the quarks). Supposed that a supersymmetric partner particle is produced at a collider, for instance at the LHC, the singlino is omitted in cascade decays and therefore escapes detection. However in case 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 transversal energy in the detector.

References

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3. ^ Nilles, H. P.; Srednicki, M.;Wyler, D. (1983). Phys. Lett. B120: 346. 
4. ^ Frere, J. M.; Jones, D. R. T.; Raby, S. (1983). Nucl. Phys. B222: 11. 
5. ^ Derendinger, J. P.; Savoy, C. A. (1984). Nucl. Phys. B237: 307. 
6. ^ Maniatis, M. (2010). Int. J. Mod. Phys. 25. arXiv:0906.0777. Bibcode 2010IJMPA..25.3505M. doi:10.1142/S0217751X10049827. 
7. ^ Ellwanger, U.; Hugonie, C.;Teixeira, A.M. (2010). Phys.Rept. 496. arXiv:0910.1785. Bibcode 2010PhR...496....1E. doi:10.1016/j.physrep.2010.07.001. 
8. ^ Zeldovich, Y. B.; Kobzarev, I. Y.;Okun, L. B. (1974). Zh. Eksp. Teor. Fiz. 67. 
9. ^ Panagiotakopoulos, P.; Tamvakis, K. (1999). Phys. Lett. B 446. arXiv:hep-ph/9809475. Bibcode 1999PhLB..446..224P. doi:10.1016/S0370-2693(98)01493-2.