MSSM Higgs with dimension-six operators

TL;DR

This paper explores how adding dimension-five and dimension-six operators to the MSSM Higgs sector can significantly increase the Higgs mass, potentially reducing fine-tuning issues and aligning with experimental bounds.

Contribution

It provides a comprehensive analysis of the effects of higher-dimensional operators on the MSSM Higgs mass, including the impact of their generation, corrections, and treatment of higher derivatives.

Findings

Dimension-six operators can contribute comparably to dimension-five operators due to tanβ enhancement.

Effective operators can increase the lightest Higgs mass by 10-30 GeV, easing MSSM fine-tuning.

Proper treatment of higher derivatives ensures the validity of the effective theory at scales below M.

Abstract

We investigate an extension of the MSSM Higgs sector by including the effects of all dimension-five and dimension-six effective operators and their associated supersymmetry breaking terms. The corrections to the masses of the neutral CP-even and CP-odd Higgs bosons due to the d=5 and d=6 operators are computed. When the d=5 and d=6 operators are generated by the same physics (i.e. when suppressed by powers of the same scale M), due to the relative $\tan\beta$ enhancement of the latter, which compensates their extra scale suppression (1/M), the mass corrections from d=6 operators can be comparable to those of d=5 operators, even for conservative values of the scale M. We identify the effective operators with the largest individual corrections to the lightest Higgs mass and discuss whether at the microscopic level and in the simplest cases, these operators are generated by "new physics" with a sign consistent with an increase of m_h. Simple numerical estimates easily allow an increase of m_h due to d=6 operators alone in the region of 10-30 GeV, while for a much larger increase light new states beyond MSSM may be needed, in which case the effective description is unreliable. Special attention is paid to the treatment of the effective operators with higher derivatives. These can be removed by non-linear field redefinitions or by an "unfolding" technique, which effectively ensure that any ghost degrees of freedom (of mass $\geqsim M$) are integrated out and absent in the effective theory at scales much smaller than M. Considering general coefficients of the susy operators with a scale of new physics above the LHC reach, it is possible to increase the tree-level prediction for the Higgs mass to the LEPII bound, thus alleviating the MSSM fine-tuning.