The $\gamma b\bar{b}$ production via ${\gamma }^{\ast }{\gamma }^{\ast }$ collisions at the ILC and LHC

Taking into account of the mixing of Higgs-radion in the Randall-Sundrum model and the vector anomalous couplings, we investigate the production of $b\bar{b}$ associated with the photon through ${\gamma }^{\ast }{\gamma }^{\ast }$ collisions at the International Linear Collider (ILC) and Large Hadron Collider (LHC). The total cross-section depends strongly on the vacuum expectation value (VEV) of the radion field ${\mathrm{\Lambda }}_{\phi }$, the radion mass $m_{\phi }$, the parameters of anomalous couplings. The result shows that the total cross-section in $\gamma b\bar{b}$ production at the LHC is much larger than that at the ILC. The production cross-section gives the largest value at the dominated state, $m_{\phi }=m_h=125$ GeV.