Survival of New Physics: An Anomaly-free Neutral Gauge Boson at the LHC

An anomaly-free $U(1)'$ effective Lagrangian as the most common new physics beyond the standard model is proposed to survey the maximal parameter space constrained by electroweak precise measurements at the LEP and direct detection in dilepton decay channel at the LHC at $\sqrt{s}=7$ TeV. By the global fit of effective couplings of $Z$ boson to the SM fermions, $\Delta_{11},\Delta_{21},g_2\Delta_{31}$ related to mixings and $r$ related to $U(1)'$ charge assignment are bounded. The allowed areas are plotted in the not only $r$-$g_2$ but also $m_{Z'}$-$g_2$ planes, which show that a sub-TeV $Z'$ is still permissible as long as the coupling $g_2\sim 0.01$. The results provides a prime requirement to an extra $U(1)'$ gauge boson and hinds the direction of possible new physics beyond the standard model. The possible signal in dilepton decay channel at LHC at $\sqrt{s}=14$ TeV is also provided.