MSSM with Dimension-five Operators (MSSM_5)

We perform a general analysis of the R-parity conserving dimension-five operators that can be present beyond the Minimal Supersymmetric Standard Model. Not all these operators are actually independent. We present a method which employs spurion-dependent field redefinitions that removes this redundancy and establishes the minimal, irreducible set of these dimension-five operators. Their potential effects on the MSSM Higgs sector are discussed to show that the tree level bound $m_hleq m_Z$ cannot be easily lifted within the approximations used, and quantum corrections are still needed to satisfy the LEPII bound. An ansatz is provided for the structure of the remaining couplings in the irreducible set of D=5 operators, which avoids phenomenological constraints from flavor changing neutral currents. The minimal set of operators brings new couplings in the effective Lagrangian, notably wrong-Higgs Yukawa couplings and contact fermion-fermion-scalar-scalar interactions, whose effects are expected to be larger than those generated in the MSSM at loop or even tree level. This has implications in particular for LHC searches for supersymmetry by direct squark production.

Higher Dimensional Operators in the MSSM

The origin and the implications of higher dimensional effective operators in 4-dimensional theories are discussed in non-supersymmetric and supersymmetric cases. Particular attention is paid to the role of general, derivative-dependent field redefinitions which one can employ to obtain a simpler form of the effective Lagrangian. An application is provided for the Minimal Supersymmetric Standard Model extended with dimension-five R-parity conserving operators, to identify the minimal irreducible set of such operators after supersymmetry breaking. Among the physical consequences of this set of operators are the presence of corrections to the MSSM Higgs sector and the generation of wrong-Higgs Yukawa couplings and fermion-fermion-scalar-scalar interactions. These couplings have implications for supersymmetry searches at the LHC.

Supersymmetric Models with Higher Dimensional Operators

In 4D renormalisable theories, integrating out massive states generates in the low energy effective action higher dimensional operators (derivative or otherwise). Using a superfield language it is shown that a 4D N=1 supersymmetric theory with higher derivative operators in either the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, is equivalent to a 4D N=1 theory of second order (i.e. without higher derivatives) with additional superfields and renormalised interactions. We provide examples where a free theory with trivial supersymmetry breaking provided by a linear superpotential becomes, in the presence of higher derivatives terms and in the second order version, a non-trivial interactive one with spontaneous supersymmetry breaking. The couplings of the equivalent theory acquire a threshold correction through their dependence on the scale of the higher dimensional operator(s). The scalar potential in the second order theory is not necessarily positive definite, and one can in principle have a vanishing potential with broken supersymmetry. We provide an application to MSSM and argue that at tree-level and for a mass scale associated to a higher derivative term in the TeV range, the Higgs mass can be lifted above the current experimental limits.