Bounds on the mass ofWRand theWL−WRmixing angleζin generalSU(2)L×SU(2)R×U(1)models

Abstract

We consider the phenomenological constraints on the mass $M_R$ and the $W_L-W_R$ mixing angle $\zeta$ in a very general class of $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ models. In particular, almost no model-dependent assumptions are made concerning left-right symmetry or the Higgs structure of the theory, which means that $U^R$, the mixing matrix for right-handed quarks, is unrelated to the left-handed Cabibbo-Kobayashi-Maskawa matrix $U^L$. We consider a number of possibilities for the neutrinos occurring in right-handed currents, including (a) heavy Majorana neutrinos, (b) heavy Dirac neutrinos, (c) intermediate-mass (10-100 MeV) neutrinos, and (d) light neutrinos (e.g., the Dirac partners of the ordinary left-handed neutrinos). For each case we utilize relevant constraints from the $K_L-K_S$ mass difference, $B_d{\overline{B}}_d$ oscillations, the $b$ semileptonic branching ratio and decay rate, neutrinoless double-beta decay, theoretical relations between mass and mixing, universality, nonleptonic kaon decays, muon decay, and astrophysical constraints from nucleosynthesis and SN 1987A. As is to be expected the limits on $M_R$ are considerably weaker than for the special case of manifest or pseudomanifest left-right symmetry ($M_R>1.4\mathrm{}$ TeV). In fact, if extreme fine-tuning is allowed the $W_R$ could be as light as the ordinary $W_L$. However, with reasonable restrictions on fine-tuning one obtains $M_R>300\mathrm{}$ GeV for $g_R=g_L$, with more stringent limits holding for most of parameter space. If $\mathrm{CP}$-violating phases in $U^R$ are small the limit on mixing ($\left|\zeta \right|<\mathrm{}0.0025\mathrm{}$ for $g_R=g_L$) is almost as stringent as for the case of left-right symmetry. For large phases $\left|\zeta \right|$ could be as large as ∼0.013.