LHCb: $2\beta_s$ measurement at LHCb

A measurement of $2\beta_s$, the phase of the $B_s-\bar{B_s}$ oscillation amplitude with respect to that of the ${\rm b} \rightarrow {\rm c^{+}}{\rm W^{-}}$ tree decay amplitude, is one of the key goals of the LHCb experiment with first data. In the Standard Model (SM), $2\beta_s$ is predicted to be $0.0360^{+0.0020}_{-0.0016} \rm rad$. The current constraints from the Tevatron are: $2\beta_{s}\in[0.32 ; 2.82]$ at 68$\%$CL from the CDF experiment and $2\beta_{s}=0.57^{+0.24}_{-0.30}$ from the D$\oslash$ experiment. Although the statistical uncertainties are large, these results hint at the possible contribution of New Physics in the $B_s-\bar{B_s}$ box diagram. After one year of data taking at LHCb at an average luminosity of $\mathcal{L}\sim2\cdot10^{32}\rm cm^{-2} \rm s^{-1}$ (integrated luminosity $\mathcal{L}_{\rm int}\sim 2 \rm fb^{-1}$), the expected statistical uncertainty on the measurement is $\sigma(2\beta_s)\simeq 0.03$. This uncertainty is similar to the $2\beta_s$ value predicted by the SM