Fine-tuning in gauge mediated supersymmetry breaking models and induced top Yukawa coupling

It is shown that fine-tuning of the Higgs parameters stronger than a few percent is required at best in the models with gauge mediated supersymmetry breaking. With the aim of solving this problem, we consider a new type of models in which the top Yukawa coupling is induced at TeV scale through mass mixing with unknown matter fields. Then it is found that the fine-tuning problem can be eliminated essentially. We discuss some phenomenological features of this model and also consider the extension to the next-to-minimal models.

Figure 1

The minimum degrees of fine-tuning required in the MSSM with $\tan \beta =10$ are shown with respect to various messenger scales ${\Lambda }_{\mathrm{mess}}$ of the GMSB. The upper line is given by the Higgs mass bound, while the lower line is given by the selectron mass bound.

Figure 2

The minimum degrees of fine-tuning required in the MSSM with $\tan \beta =5$ are shown with respect to various messenger scales ${\Lambda }_{\mathrm{mess}}$ of the GMSB. The conditions for the lines are the same as in Fig. 1.

Figure 3

The minimum degrees of fine-tuning required in the MSSM with the messenger scale ${\Lambda }_{\mathrm{mess}}={10}^{16}\mathrm{GeV}$ are shown for various values of $\tan \beta$. The conditions for the lines are the same as in Fig. 1.

Figure 4

The supersymmetry breaking masses [$M_a(a=1,2,3)$: the gaugino masses, $m_{{\tilde{Q}}_3}$, $m_{{\tilde{\overline{u}}}_3}$: the third generation squark masses, $m_{\tilde{e}}$: the right-handed selectron mass] obtained at low energy for various messenger scales ${\Lambda }_{\mathrm{mess}}$ are shown. Here we take $B_S=⟨F_S⟩/⟨S⟩=1$ as the unit.

Figure 5

The RG flows of the soft scalar masses, $m_{\Phi }^2/|m_{\Phi }|$, $m_{\varphi }^2/|m_{\varphi }|$ and $m_{H_u}^2/|m_{H_u}|$, obtained by solving the one-loop RG equations for the extra $SU(3)$ model are shown in the case of a high messenger scale.

Figure 6

The RG flows of the gauge couplings $g_{\mathrm{ex}}$ and the Yukawa coupling $y_{\Phi }$ in the extra sector are shown in the case of ${\alpha }_{\mathrm{ex}}\sim {\alpha }_{\mathrm{ex}}^{*}$ and ${\alpha }_{y_{\Phi }}=1/\pi$ ($y_{\Phi }=2$) at the decoupling scale 5 TeV.

Figure 7

The RG flows of the soft scalar masses $m_{\Phi }$, $m_{\varphi }$, $m_{H_u}^2/|m_{H_u}|$ realized in the Case (2) are shown. The figure shows also the RG flow of $A_{\Phi }$ which is connected with the flow of $A_t$ of the MSSM at the decoupling scale.

Figure 8

The minimum degrees of fine-tuning required in the extra $SU(3)$ models with various messenger scales are shown in the case of $\tan \beta =10$. The conditions for the lines are the same as in Fig. 1. The data points for ${\Lambda }_{\mathrm{mess}}={10}^{16}\mathrm{GeV}$ are not given, since the EWSB solution is not realized.

Figure 9

The minimum degrees of fine-tuning in the case of $\tan \beta =5$ are shown in the same way as Fig. 8.