An improved analysis of $b\to s\gamma$ in supersymmetry

An improved analysis of the $b\to s+\gamma$ decay in the minimal flavor violating case is given taking into account additional contributions in the supersymmetric sector which enter in the next-to-leading-order (NLO) and are enhanced by $\tan \beta$ factors. Specifically, we compute a set of 20 one-loop diagrams to give the most complete analysis to date of the NLO supersymmetric corrections. These modifications are computed from the effective charged Higgs and neutral Higgs couplings involving 12 loop diagrams for the charged Higgs sector and eight loop diagrams for the neutral Higgs sector. While the computations of these corrections are available in the literature, their full forms including the complex phase dependence has not be considered. Our analysis takes account of the full allowed set of 20 one-loop diagrams and is more general since it also includes the full dependence on $CP$ phases in non universal SUGRA and MSSM models. A numerical analysis is carried out to estimate the size of the corrections to $b\to s+\gamma$. We also briefly discuss the implications of these results for the search for supersymmetry.

Figure 1

Set of diagrams contributing to ${ϵ}_b^{\prime }(t)$.

Figure 2

Set of diagrams contributing to ${ϵ}_t^{\prime }(s)$.

Figure 3

Set of diagrams contributing to ${ϵ}_{bb}$.

Figure 4

Additional diagrams contributing to ${ϵ}_{bb}$.

Figure 5

Variation of the $ϵ$’s and $\mathrm{BR}(b\to s\gamma )$ with $\tan \beta$ for the parameters $m_0=400\mathrm{GeV}$, $m_{1/2}=200\mathrm{GeV}$, $A_0=700\mathrm{GeV}$ and all the phases set to zero (solid lines) and with the phases (in radiants) set to ${\xi }_1=0$, ${\xi }_2=0.8$, ${\xi }_3=0.9$, ${\theta }_{\mu }=0.6$, ${\alpha }_0=\pi$ (dash lines) or ${\xi }_1=1$, ${\xi }_2=0$, ${\xi }_3=0.3$, ${\theta }_{\mu }=1.2$, ${\alpha }_0=\pi /2$ (dot-dash lines). The thick lines represent real values while the thin lines correspond to imaginary parts.

Figure 6

The percentage difference between the approximate formulas of $S_1$ and $S_2$ and our full calculation in the SUGRA scenario. The left graph is the case with no phases, and the right graph is the case with phases. Each group contains about 1800 models where each point in the parameter space defines a model.

Figure 7

The percentage difference between the noncorrected approximate formulas as they appear in Refs. 10, 32 and our full calculation in the real mSUGRA case which has no phases (left) and in the complex SUGRA case which has phases (right).

Figure 8

Variation of the $ϵ$’s with $\tan \beta$ for the parameters of Eq. (69) and the corresponding prediction of $\mathrm{BR}(b\to s\gamma )$ using $S_1$, $S_2$ and the complete calculation ($F$).

Figure 9

The percentage difference between the approximate formulas of $S_1$ and $S_2$ and our full calculation in the MSSM scenario. The data sets contain about 1000 models. We only plot points that are experimentally acceptable. Left graph is the case with no phases, and right graph is the case with phases.

Figure 10

The values of the $ϵ$’s and the rate for $b\to s\gamma$ for the three different methods at point point (i).

Figure 11

The values of the $ϵ$’s and the rate for $b\to s\gamma$ for the three different methods at point point (ii).