Towards a Unified Effective Field Framework for Gravity and Weak Interaction: A Lagrangian- and Symmetry-Based Reconstruction

We present a single, symmetry– and Lagrangian–based master portal EFT that organizes gravity–gauge interactions for U(1)Y , SU(2)L (with Higgs), and SU(3)c into an aligned dimension–six basis and a common phenomenology pipeline. The integrative novelty is three–fold: (i) a unified curvature–gauge/Higgs operator grammar across the three gauge sectors, (ii) an explicit post–EWSB projection that maps weak–sector portal coefficients into neutral (A,Z) combinations (emergence of electromagnetism at the coefficient level via Eq. (5.2)), and (iii) a gravity–aware forward–limit prescription (pole–subtracted positivity [3, 4] ) together with “plug–and–play” bounds that translate experimental or astrophysical inputs directly into constraints on (βi,γ2)/Λ2. We also provide an illustrative one–loop UV matching (heavy SU(2)L doublet) that sets the parametric size and sign priors for the portal coefficients, and a practical dictionary to (geo)SMEFT [2]. Parity non–conservation in the weak sector is shown to remain entirely Standard–Model in origin (left–handed fermion couplings), with the portal operators taken P– and CP–even by default. The framework is designed to be ready–to–use: all three sectors can be constrained in parallel, within linearized gravity and low curvature