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Perturbative Calculations

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Constraining Supersymmetric Models

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Abstract

In order to obtain precise theoretical predictions for observables in the SM or its extensions, which can be compared to other models and to experimental data, loop diagrams need to be calculated. This chapter introduces the basic concepts of regularization and renormalization needed for loop calculations.

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Notes

  1. 1.

    With the exception of one SM diagram, which required a specific treatment and where we use another regularization scheme called Pauli–Villars regularization [1].

  2. 2.

    In this work the calculation of diagrams beyond one-loop is not discussed.

  3. 3.

    In practise, the loop calculations are done with the programs FeynArts (Version 3.5) [4–9] and FormCalc (Version 6.2) [10]. In FormCalc the user can choose between DR and CDR.

  4. 4.

    DRED is a regularization scheme, in which the integration momenta are D-dimensional, while the Dirac algebra is kept 4-dimensional.

  5. 5.

    The sign in front of \(s_W\) depends on the choice for the SU(2) covariant derivative. Like \(\delta Z_{e}\) is given here, it assumes our SM convention. Using our the (N)MSSM convention, the renormalization constant of the electric charge is defined with a + sign between the two terms.

  6. 6.

    Irreducible means that the diagram cannot be cut into two non-trivial parts by cutting a single line carrying non-zero momentum.

  7. 7.

    A similar renormalization scheme for Dimensional Reduction, which is often used in supersymmetry (e.g. for the renormalization of the parameter \(\tan \beta \)) is the \(\overline{\mathrm {DR}}\) scheme.

  8. 8.

    This feature is not restricted to the \(\overline{\mathrm {MS}}\) renormalization scheme. In the on-shell scheme the equivalent to the scale \(\mu \) is the scale M where the renormalization condition is fixed. The variation of M plays the same role as the variation of \(\mu \) in \(\overline{\mathrm {MS}}\).

  9. 9.

    A scale dependent coupling is termed a running coupling.

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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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Correspondence to Lisa Zeune .

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Zeune, L. (2016). Perturbative Calculations. In: Constraining Supersymmetric Models . Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-22228-8_3

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