Effective field theory of integrating out sfermions in the MSSM: Complete one-loop analysis

We apply the covariant derivative expansion of the Coleman-Weinberg potential to the sfermion sector in the minimal supersymmetric standard model, matching it to the relevant dimension-6 operators in the standard model effective field theory at one-loop level. Emphasis is paid to nondegenerate large soft supersymmetry breaking mass squares, and the most general analytical Wilson coefficients are obtained for all pure bosonic dimension-6 operators. In addition to the non-logarithmic contributions, they generally have another logarithmic contributions. Various numerical results are shown, in particular the constraints in the large $X_t$ branch reproducing the 125 GeV Higgs mass can be pushed to high values to almost completely probe the low stop mass region at the future FCC-ee experiment, even given the Higgs mass calculation uncertainty.

Figure 1

The $2\sigma T$ parameter (blue curves), $S$ parameter (cyan curves), and $hgg$ coupling (red curves) constraints, shown for the left $X_t=1\mathrm{TeV}$, middle $X_t=3\mathrm{TeV}$, and right $X_t=\sqrt{6M_{{\tilde{t}}_1}{M}_{{\tilde{t}}_2}}$ panels. For each group of the $T$, $S$, and $hgg$ curves the current constraints, ILC expected constraints, CEPC expected constraints, and FCC-ee expected constraints are denoted by solid curves, dashed curves, dot-dashed curves, and dotted curves respectively, if the constraint is strong enough to be shown on the plot. The shaded region is theoretically inaccessible for the $X_t$ choice with mixing indicated by Eq. (10). Here we choose $\tan \beta =20$ but the $\tan \beta$ dependence is weak.

Figure 2

The expected constraints from future ILC (the left column), CEPC (the middle column), and FCC-ee (the right column) experiments (see Table 3) for fixed SM like Higgs mass value of $M_h=122\mathrm{GeV}$ (the first row), $M_h=125\mathrm{GeV}$ (the second row), and $M_h=128\mathrm{GeV}$ (the third row). The $1\sigma$ and $2\sigma$ allowed region are green and yellow hatched. The individual $2\sigma$ constraint from $T$, $S$ parameters and $hgg$, $h\gamma \gamma$ couplings are shown for each experiment again as blue, cyan, red, and magenta curves respectively, if strong enough to be shown. There are still theoretically inaccessible region as hatched in gray. Here we choose $\tan \beta =20$, and the small $X_t$ solution to reproduce the required SM like Higgs mass.

Figure 3

Same as Fig. 2, but for large $X_t$ solution to reproduce the required SM like Higgs mass. The brown curves are the charge and color breaking vacuum constraint of $X_t/\sqrt{M_{{\tilde{t}}_1}^2+M_{{\tilde{t}}_2}^2}\lesssim \sqrt{3}$, and the region below and on the left are allowed.

Figure 4

The expected constraints from future ILC (the left column), CEPC (the middle column), and FCC-ee (the right column) experiments (see Table 3) for fixed SM like Higgs mass value of $M_h=125\mathrm{GeV}$, with small $X_t$ solution (the first row) and large $X_t$ solution (the second row). Other notations are the same with Fig. 2. In the large $X_t$ branch all the theoretically accessible region are consistent with the charge and color breaking vacuum constraint of $X_t/\sqrt{M_{{\tilde{t}}_1}^2+M_{{\tilde{t}}_2}^2}\lesssim \sqrt{3}$.