Primordial Nucleosynthesis Constraints on Z' Properties

TL;DR

This work addresses how TeV-scale Z' gauge bosons in $E_6$-motivated models, which imply three light right-handed neutrinos $ u_R$, affect Big Bang Nucleosynthesis. By computing the decoupling temperature $T_d( u_R)$ and the effective $ riangle N_ u$ across the parameter space spanned by $M_{Z'}$, $ heta_{E6}$, and the Z–Z' mixing $ ext{δ}$ (and incorporating uncertainties in the quark-hadron transition temperature $T_c$), the authors quantify stringent nucleosynthesis bounds that often surpass existing laboratory limits. The analysis shows that for $T_c=150$ MeV the $ riangle N_ u<0.3$ constraint typically requires $M_{Z_2} o$ a few TeV, while for $T_c=400$ MeV the bounds push to several TeV; near certain decoupling angles the constraints weaken as $ u_R$ effectively decouples from the $Z'$. The results highlight the critical role of early-universe cosmology in constraining new gauge sectors and guide prospects for future collider tests and model-building strategies that avoid overly rapid right-handed neutrino equilibration.

Abstract

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.

Figures (5)

• Figure 1: The effective number of degrees of freedom as a function of temperature for the quark-hadron transition temperature $T_c= 150$ MeV and $400$ MeV, from srednicki. $g(T)$ does not include contributions from the three right-handed neutrinos, which are added separately in the expansion rate formula.
• Figure 2: The decoupling temperature $T_d$ (top) and the equivalent number of extra neutrinos $\Delta N_\nu$ (bottom) for the $\eta$ model as a function of the $Z_2$ mass $M_{Z_2}$ for constituent quark masses, for a quark-hadron transition temperature $T_c=$ 150 MeV (circles) and 400 MeV (crosses). The left two figures are for the cases A0 and A3 defined in (\ref{['cases']}), i.e., the solid, dashed and dotted lines represent zero-mixing ($\delta = 0$), and positive and negative maximal-mixing ($\delta = \pm 0.002$), respectively. The $T_c$ = 150 MeV case has higher $T_d$ and lower $\Delta N_\nu$ for the same $M_{Z_2}$ than $T_c$ = 400 MeV. The right figures are for the intermediate mixing assumptions A1 and A2. The solid and dash-dot curves are for the mass-mixing relations $\delta= \pm 0.0051/M_{Z_2}^2$, while the dashed and dotted curves are for the $\rho_0$ constraints $\delta =\pm 0.0029/M_{Z_2}$.
• Figure 3: Same as Figure \ref{['decoupling1']} except that current quark masses are used. The upper graphs share most features with the constituent mass case except that $T_d$ can be slightly lower when $T_d > T_c$. The only significant change in $\Delta N_\nu$ is for the $T_c$ = 150 MeV maximal mixing case (see text).
• Figure 4: $T_d$ (top) and $\Delta N_\nu$ (middle) for $M_{Z_2} =$ 500, 1000, 1500, 2000, 2500, 3500, 4000, and 5000 GeV, for $T_c = 150$ MeV and constituent masses. Larger $M_{Z_2}$ corresponds to higher $T_d$ and smaller $\Delta N_\nu$. The graphs on the left are for no mixing (case A0 in (\ref{['cases']})), while the right-hand graphs are for the mass-mixing relation $|\delta | < 0.0051/M_{Z_2}^2$ (case A1). The bottom graphs are $M_{Z_2}$ corresponding to $\Delta N_\nu = 0.3$, $0.5$, $1.0$ and $1.2$, with larger $\Delta N_\nu$ corresponding to smaller $M_{Z_2}$.
• Figure 5: Same as Figure \ref{['A1-150']}, except $T_c=400$ MeV. $T_d$ is slightly smaller (for $T_d>$ 150 MeV) for fixed $M_{Z_2}$ and $\theta_{E6}$, while $\Delta N_\nu$ and the bound on $M_{Z_2}$ for fixed $\Delta N_\nu$ are increased.