In this work, the production processes of heavy neutral scalar and pseudo scalar associated with standard model gauge boson $Z_L$ at future $e^{+}e^{-}$ colliders (ILC and CLIC) are examined. The total and differential cross sections are calculated f
or the processes in the context of the littlest Higgs model. Also dependence of production processes to littlest Higgs model parameters in the range of compatibility with electroweak precision measurements and decays to lepton flavor violating final states are analyzed. We have found that both heavy scalar and pseudoscalar will be produced in $e^+e^-$ colliders. Also the depending on the model parameters, the neutral heavy scalar can be reconstructed or lepton flavor violating signals can be observed.
We analyze the semileptonic rare decays of $B$ meson to $K_{1} (1270)$ and $K_{1} (1400)$ axial vector mesons. The $Bto K_{1} (1270,1400) ell^+ ell^-$ decays are significant flavor changing neutral current decays of the $B$ meson. These decays are se
nsitive to the new physics beyond SM, since these processes are forbidden at tree level at SM. These decays occurring at the quark level via $bto s ell^+ ell^- $ transition, also provide new opportunities for calculating the CKM matrix elements $V_{bt}$ and $V_{ts}$. In this study, the transition form factors of the $Bto K_{1} (1270,1400) ell^+ ell^-$ decays are calculated using three-point QCD sum rules approach. The resulting form factors are used to estimate the branching fractions of these decays.
The loop level flavor changing neutral currents transitions of the $Sigma_{b}to n l^+l^-$ and $Sigma_{c}to p l^+l^-$ are investigated in full QCD and heavy quark effective theory in the light cone QCD sum rules approach. Using the most general form o
f the interpolating current for $Sigma_{Q}$, $Q=b$ or $c$, as members of the recently discovered sextet heavy baryons with spin 1/2 and containing one heavy quark, the transition form factors are calculated using two sets of input parameters entering the nucleon distribution amplitudes, namely, QCD sum rules and lattice QCD inputs. The obtained results are used to estimate the decay rates of the corresponding transitions. Since such type transitions occurred at loop level in the standard model, they can be considered as good candidates to search for the new physics effects beyond the SM.
