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The Standard Model and Its Supersymmetric Extensions

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Constraining Supersymmetric Models

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

This chapter starts with a theoretical introduction to the Standard Model (SM) of particle physics. We outline some shortcomings of the SM, before we turn to the discussion of supersymmetric (SUSY) models. Supersymmetry is motivated and introduced, followed by a detailed description of the particle sectors of the Minimal Supersymmetric Standard Model (MSSM). Then we go to Next-to-minimal Supersymmetric Standard Model (NMSSM) and show how the Higgs and neutralino sectors are modified compared to the MSSM.

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Notes

  1. 1.

    The subscripts refer to colour, left chirality and weak hypercharge.

  2. 2.

    We adopt the sign conventions for the \(SU(2)_L\) covariant derivative used in the code FeynArts [4–9], where (for historical reasons) the \(SU(2)_L\) covariant derivative in the SM is defined by \(\partial _{\mu } - i g_2 I^a W^a_{\mu }\) (as in Eq. (2.3)), while it is defined by \(\partial _{\mu } + i g_2 I^a W^a_{\mu }\) in the (N)MSSM, as we will discuss later.

  3. 3.

    In the strong sector the gluons of \(SU(3)_C\) are also massless.

  4. 4.

    The concept of renormalization is explained in Sect. 3.2.

  5. 5.

    Note that the vev v of the SM Higgs field differs from the value v which we will define in the MSSM (in Eq. (2.58)) using a different convention. The numerical value here is \(v \sim 246\) GeV.

  6. 6.

    The evidence of neutrino oscillation (see e.g. [10]) implies that neutrinos are (against the original assumption) massive. Introducing right handed neutrinos, Dirac mass terms can easily be added. Another possibility is to write down Majorana mass terms. In this thesis neutrinos can be assumed to be massless.

  7. 7.

    In Sect. 2.1 we used Dirac notation to describe the SM fermions. However it turns out to be more convenient to use the two-component Weyl spinor notation for the fermions in the supermultiplets. For the definition of Weyl fermions see  Ref. [15].

  8. 8.

    As mentioned earlier, we define the \(SU(2)_L\) covariant derivative in the SUSY models with opposite sign than in the SM, following the FeynArts [4–9] conventions.

  9. 9.

    In literature the two Higgs doublets are often called \(H_u \equiv H_2\) and \(H_d \equiv H_1\). For the Higgs doublets we use the same notation for the chiral supermultiplets and for its scalar entry.

  10. 10.

    This scenario is challenged by the recent ATLAS bound on light charged Higgs bosons [27].

  11. 11.

    We consider the \(Z_3\)-symmetric version of the NMSSM, in which no linear or quartic terms in S appear.

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Authors and Affiliations

  1. University of Amsterdam, Amsterdam, The Netherlands

    Lisa Zeune

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  1. Lisa Zeune
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Zeune, L. (2016). The Standard Model and Its Supersymmetric Extensions. In: Constraining Supersymmetric Models . Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-22228-8_2

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