Unparticle effect on $B_s-{\overline{B}}_s$ mixing and its implications for $B_s\to J/\psi \varphi$, $\varphi \varphi$ decays

We study the effect of unparticle stuff on $B_s-{\overline{B}}_s$ mixing and consider possible implications of it for the decay modes $B_s\to J/\psi \varphi$ and $\varphi \varphi$. We find that due to the new contributions from the unparticles the $B_s-{\overline{B}}_s$ mixing phase could be observable at the CERN LHC along with the possible sizable $CP$ asymmetry parameters $S_{\psi \varphi (\varphi \varphi )}$ in $B_s\to J/\psi \varphi (\varphi \varphi )$ decay modes.

Figure 1

Correlation plot between $\Delta M_{B_s}$ in ${\mathrm{ps}}^{-1}$ and $2{\theta }_s$ in degree for a representative set of values of $|c_S^{sb}|$ as labeled in the plots.

Figure 2

Same as Fig. 1, with vectorlike unparticle contributions where the constants $|c_V^{sb}|$ are in units of ${10}^{-4}$.

Figure 3

The variation of $S_{J/\psi \varphi }^{\prime }$ versus the mixing angle ${\theta }_s$ in degrees.

Figure 4

The variation of $S_{\varphi \varphi }$ versus ${\varphi }_n$ in degrees where the thick (dashed) curve is for ${\theta }_s=20°(0°)$.