Primordial Nucleosynthesis Constraints on Z' Properties

In models involving new TeV-scale Z' gauge bosons, the new U(1)' symmetry often prevents the generation of Majorana masses needed for a conventional neutrino seesaw, 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' interactions, leading to a faster expansion rate and too much ^4He. We quantify the constraints on the Z' properties from nucleosynthesis for Z' couplings motivated by a class of E_6 models parametrized by an angle theta_E6. The rate for the annihilation of three approximately massless right-handed neutrinos into other particle pairs through the Z' channel is calculated. The decoupling temperature, which is higher than that of ordinary left-handed neutrinos due to the large Z' mass, is evaluated, and the equivalent number of new doublet neutrinos Delta N_nu is obtained numerically as a function of the Z' mass and couplings for a variety of assumptions concerning the Z-Z' mixing angle and the quark-hadron transition temperature T_c. Except near the values of theta_E6 for which the Z' decouples from the right-handed neutrinos, the Z' 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 MeV with the theoretically favored range of Z-Z' mixings, Delta N_nu < 0.3 for M_Z' > 4.3 TeV for any value of theta_E6. Larger mixing or larger T_c often lead to unacceptably large Delta N_nu except near the nu_R decoupling limit.