Unparticle physics effects in $B_s$-${\overline{B}}_s$ mixing

We investigate unparticle effects in $B_s$-${\overline{B}}_s$ mixing. In particular we discuss the possibility of reproducing the experimental result of $\Delta M_s$, while having large effects on the mixing phase ${\varphi }_s$, which might be visible in current experiments.

Figure 1

Error budget for the theoretical determination of $\Delta {\Gamma }_s/\Delta M_s$. Compared to previous approaches (left) the new strategy leads to a reduction of the theoretical error by almost a factor of 3.

Figure 2

Current experimental bounds in the complex ${\Delta }_s$-plane. The bound from $\Delta M_s$ is given by the dark gray (red) ring around the origin. The bound from $\Delta {\Gamma }_s/\Delta M_s$ is given by the light gray (yellow) region and the bound from $a_{\mathrm{fs}}^s$ is given by the gray (light blue) region. The angle ${\varphi }_s^{\Delta }$ can be extracted from $\Delta {\Gamma }_s$ (solid lines) with a fourfold ambiguity—one bound coincides with the x-axis—or from the angular analysis in $B_s\to J/\Psi \varphi$ (dashed line). If the standard model is valid all bounds should coincide in the point (1, 0). The current experimental situation shows a small deviation, which might become significant, if the experimental uncertainties in $\Delta {\Gamma }_s$, $a_{\mathrm{fs}}^s$, and ${\varphi }_s$ will go down in near future.

Figure 3

Illustration of the bounds in the complex ${\Delta }_s$-plane for $|{\Delta }_s|=1$ and ${\varphi }_s^{\Delta }=-\pi /4$. We assume the following overall uncertainties: $\Delta M_s$ (dark gray or red): $\pm 15\%$, $\Delta {\Gamma }_s/\Delta M_s$ (light gray or yellow): $\pm 15\%$, $a_{\mathrm{fs}}^s$ (gray or light blue): $\pm 20\%$, and ${\varphi }_s^{\Delta }$ (solid lines): $\pm 20\%$.