Implication of the Fourth Generation Standard Model to the Lepton Polarization asymmetries in the $B\to K^{\ast }{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ Decay

In this work we study the implication of the fourth generation standard model (SM4) to the single and double lepton polarization asymmetries in the $B\to K^{\ast }{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$, $(l=\mu ,\tau )$ decay. To see the variation in the values of lepton polarization asymmetries from the standard model values, we have taken lower bound values of CMS and ATLAS for $m_{t^{\mathrm{\prime }}}=404$GeV and 552GeV respectively whereas ${\varphi }_{sb}$ is vary in two allowed regions ${75}^{\circ }-{115}^{\circ }$ and ${240}^{\circ }-{290}^{\circ }$ while for the numerical values of these asymmetries $\mathrm{\mid }{\lambda }_{t^{\mathrm{\prime }}}\mathrm{\mid }$ is set to be $6\times {10}^{-3}$. It is found that both single and double lepton polarization asymmetries are sensitive to the SM4 parameters. Therefore, the measurements of the lepton polarization asymmetries for the above mentioned decay at current colliders can be helpful to clear the smog on the status of the existence of the fourth generation.