Primordial nucleosynthesis constraints onZ′properties

In models involving new TeV-scale $Z^{\prime }$ gauge bosons, the new ${U\left(1\right)\mathrm{}}^{\prime }$ symmetry often prevents the generation of Majorana masses needed for a conventional neutrino seesaw mechanism, leading to three superweakly interacting “right-handed” neutrinos ${\nu }_R,$ the Dirac partners of the ordinary neutrinos. These can be produced prior to big bang nucleosynthesis by the $Z^{\prime }$ interactions, leading to a faster expansion rate and too much ${}^4\mathrm{He}.$ We quantify the constraints on the $Z^{\prime }$ properties from nucleosynthesis for $Z^{\prime }$ couplings motivated by a class of $E_6$ models parametrized by an angle ${\theta }_{E6\mathrm{}}.$ The rate for the annihilation of three approximately massless right-handed neutrinos into other particle pairs through the $Z^{\prime }$ channel is calculated. The decoupling temperature, which is higher than that of ordinary left-handed neutrinos due to the large $Z^{\prime }$ mass, is evaluated, and the equivalent number of new doublet neutrinos $\Delta N_{\nu }$ is obtained numerically as a function of the $Z^{\prime }$ mass and couplings for a variety of assumptions concerning the $Z-Z^{\prime }$ mixing angle and the quark-hadron transition temperature $T_c.$ Except near the values of ${\theta }_{E6\mathrm{}}$ for which the $Z^{\prime }$ decouples from the right-handed neutrinos, the $Z^{\prime }$ mass and mixing constraints from nucleosynthesis are much more stringent than the existing laboratory limits from searches for direct production or from precision electroweak data, and are comparable to the ranges that may ultimately be probed at proposed colliders. For the case $T_c=150\mathrm{}\mathrm{MeV}$ with the theoretically favored range of $Z-Z^{\prime }$ mixings, $\Delta N_{\nu }\lesssim 0.3$ for $M_{Z^{\prime }}\gtrsim 4.3\mathrm{TeV}$ for any value of ${\theta }_{E6\mathrm{}}.$ Larger mixing or larger $T_c$ often lead to unacceptably large $\Delta N_{\nu }$ except near the ${\nu }_R$ decoupling limit.