Deciphering core, valence and double-core-polarization contributions to parity violating amplitudes in 133Cs using different methods

As a prerequisite of probing physics beyond the Standard Model (BSM) of particle physics, it is imperative to perform calculation of parity violating electric dipole (E1PV) amplitudes within 0.5\% accuracy in atomic systems. Latest high precision calculations of E1PV of the 6s 2S→7s 2S transition in 133Cs by three different groups claim achieving its accuracy below 0.5\%, but such claims contradict on the view that their final values differ by 1\%. One of the major issues in these calculations is the opposite signs among the core correlation contribution from different works leading to 200\% difference in its value. In a review [Rev. Mod. Phys. 90, 025008 (2018)], a Letter [Phys. Rev. D 103, L111303 (2021)] and a Comment [Phys. Rev. D 105, 018301 (2022)], reliability of all these calculations are strongly contended. We unearthed here the underlying reason for getting sign discrepancies in various works by investigating how different electron correlation effects are encapsulated through the undertaken methods in the above works to determine E1PV. Detailed discussions presented in this work would help in guiding theoretical studies to improve accuracy of E1PV in atomic systems to probe BSM physics.