I. Jack

The Standard model effective potential at two loops

Abstract We calculate the standard model effective potential to two loops using minimal subtraction, and use the result to deduce the two-loop beta functions for the scalar m2 and quartic self-interaction.

Soft supersymmetry breaking and finiteness

We calculate the two-loop β-functions for soft supersymmetry-breaking interactions in a general supersymmetric gauge theory, emphasising the role of the evanescent couplings and masses that are generic to a non-supersymmetric theory. We also show that a simple set of conditions sufficient for one-loop finiteness renders atheory two-loop finite, and we speculate on the possible significance of finite softly broken theories.

N = 1 supersymmetry and the three-loop gauge β-function

Abstract We calculate the three-loop gauge β-function for an abelian N = 1 supersymmetric gauge theory, using DRED. We construct a coupling constant redefinition that relates the result to the corresponding term in the NSVZ β-function, and by generalising this redefinition to the non-abelian case we derive the DRED three-loop gauge β-function for the non-abelian case.

Decoupling of the epsilon -scalar mass in softly broken supersymmetry.

It has been shown recently that the introduction of an unphysical [epsilon]-scalar mass [ital [tilde m]] is necessary for the proper renormalization of softly broken supersymmetric theories by dimensional reduction (DR). In these theories, both the two-loop [beta] functions of the scalar masses and their one-loop finite corrections depend on [ital [tilde m]][sup 2]. We find, however, that the dependence on [ital [tilde m]][sup 2] can be completely removed by slightly modifying the DR renormalization scheme. We also show that previous DR calculations of one-loop corrections in supersymmetry which ignored the [ital [tilde m]][sup 2] contribution correspond to using this modified scheme.

Scheme dependence and the NSVZ β-function

Abstract We investigate the connection between the NSVZ and the DRED forms of the gauge β-function in an N = 1 supersymmetric gauge theory. We construct a coupling constant redefinition that relates the two forms up to four loops. By abelian calculations, we are able to infer the complete non-abelian form of β g (3)DRED and also β g (4)DRED except for one undetermined parameter.

The gaugino β-function

We present an elegant exact formula for the gaugino

Fayet-Iliopoulos D-terms and anomaly mediated supersymmetry breaking

\beta

N = 1 supersymmetry and the three-loop anomalous dimension for the chiral superfield

-function in a softly-broken supersymmetric gauge theory, of the form

Renormalisation invariance and the soft β-functions

\beta_M = {\cal O}(\beta_g/g)

Non-standard soft supersymmetry breaking

, where