Meson mixing bounds on Z′ mass in the alignment limit: establishing the phenomenological viability of the 331 model

We perform a systematic study of flavor-changing neutral currents (FCNCs) in the 331 model with right-handed neutrinos (331RHNs), analyzing constraints on the Z′ boson mass from K-, D-, Bd-, and Bs-meson oscillations. By explicitly incorporating scalar sector dynamics and quark rotation ambiguities VLu,d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left({V}_L^{u,d}\right) $$\end{document}, we demonstrate that Z′ mass limits depend critically on the parametrization of Cabibbo-Kobayashi-Maskawa (CKM) matrix factors. Three scenarios are explored: (i)VLu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {V}_L^u $$\end{document} = VCKM†\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {V}_{\textrm{CKM}}^{\dagger } $$\end{document} (FCNCs restricted to D-mesons), (ii)VLd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {V}_L^d $$\end{document} = VCKM (dominant Bs constraints), and (iii) a hybrid mixing pattern. Strikingly, scenario i) reduces the Z′ mass bound to MZ′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {M}_{Z^{\prime }} $$\end{document} ≳ 600 GeV — two orders of magnitude below literature values — by leveraging large experimental uncertainties in D-D¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{D} $$\end{document} oscillations. Conversely, scenario ii) requires MZ′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {M}_{Z^{\prime }} $$\end{document} ≳ 165 TeV due to stringent Bs data. We further establish the alignment limit cos(ϕ + φ) = 0 for the SM-like Higgs, showing its viability depends on VLu,d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {V}_L^{u,d} $$\end{document} configurations, with Bs systems enforcing |cos(ϕ + φ)| < 0.01 in down-sector FCNC scenarios. Our analysis reveals that strategic choices of quark mixing matrices can suppress FCNC visibility, reconciling the 331 framework with flavor data without ultra-heavy Z′ bosons. This work provides the first unified treatment of SM-like Higgs- and Z′-mediated FCNCs in 331 models, identifying viable parameter spaces for collider phenomenology.