Naturalness in low-scale SUSY models and “non-linear” MSSM

I. Antoniadis; E. M. Babalic; D. M. Ghilencea

doi:10.1140/epjc/s10052-014-3050-9

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2014) 74: 3050
https://doi.org/10.1140/epjc/s10052-014-3050-9

Regular Article - Theoretical Physics

Naturalness in low-scale SUSY models and “non-linear” MSSM

I. Antoniadis¹, E. M. Babalic²^,3 and D. M. Ghilencea¹^,2^*

¹ CERN Theory Division, 1211, Geneva 23, Switzerland
² Theoretical Physics Department, National Institute of Physics and Nuclear Engineering (IFIN-HH), MG-6, 077125 , Bucharest, Romania
³ Department of Mathematics and Natural Sciences, University of Craiova, 13 A. I., Cuza street, 200585 , Craiova, Romania

^* e-mail: ghilencea@theory.nipne.ro

Received: 17 July 2014
Accepted: 31 August 2014
Published online: 25 September 2014

Abstract

In MSSM models with various boundary conditions for the soft breaking terms ( $m_\mathrm{soft}$ ) and for a Higgs mass of 126 GeV, there is a (minimal) electroweak fine-tuning $\Delta \approx 800$ to $$1000$$ for the constrained MSSM and $\Delta \approx 500$ for non-universal gaugino masses. These values, often regarded as unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking, rather than of SUSY itself. A minimal modification of these models is to lower the SUSY breaking scale in the hidden sector ( $\sqrt{f}$ ) to few TeV, which we show to restore naturalness to more acceptable levels $\Delta \approx 80$ for the most conservative case of low $\tan \beta$ and ultraviolet boundary conditions as in the constrained MSSM. This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce $\Delta$ . In the present case $\Delta$ is reduced due to additional (effective) quartic Higgs couplings proportional to the ratio $m_\mathrm{soft}/\sqrt{f}$ of the visible to the hidden sector SUSY breaking scales. These couplings are generated by the auxiliary component of the goldstino superfield. The model is discussed in the limit its sgoldstino component is integrated out so this superfield is realized non-linearly (hence the name of the model) while the other MSSM superfields are in their linear realization. By increasing the hidden sector scale $\sqrt{f}$ one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.