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We study the anomalous triple gauge boson couplings (aTGC) in $ZW^\pm$production in $3l$ + missing $E_T$ channel at the LHC for $\sqrt{s}=13$ TeV. Weuse cross sections, azimuthal asymmetry, forward-backward asymmetry, andpolarization asymmetries of $Z$ and reconstructed $W$ to estimate simultaneouslimits on the anomalous couplings for both the effective vertex formalism aswell as the effective operator approach using the Markov-chain--Monte-Carlo(MCMC) method for luminosities $35.9$ fb$^{-1}$, $100$ fb$^{-1}$, $300$fb$^{-1}$, $1000$ fb$^{-1}$, and $3000$ fb$^{-1}$. The trilepton invariant mass($m_{3l}$)and the transverse momentum of $Z$ ($p_T(Z)$) are found to besensitive to the aTGC for the cross sections as well as for the asymmetries. Weobserved that the asymmetries significantly improve the measurement ofanomalous couplings at the high-luminosity large hadron collider (LHC) if adeviation from the Standard Model (SM) is observed.

Unravelling the anomalous gauge boson couplings in $ZW^\pm$ production at the LHC and the role of spin-$1$ polarizations