Jet Substructure Analysis for Distinguishing Left- and Right-Handed Couplings of Heavy Neutrino in $W'$ Decay at the HL-LHC

The search for heavy $W'$ bosons in their decay modes to a lepton and a heavy neutrino offers a promising avenue for probing new physics beyond the Standard Model. This work focuses on such a signature with an energetic lepton plus a fat jet, originating from the heavy neutrino and containing a lepton. We have employed the jet substructure techniques to isolate the embedded lepton as a subjet of the fat jet. The Lepton Subjet Fraction ($LSF$) and Lepton Mass Drop ($LMD$) variables constructed from the lepton subjet help in separating the signal region from the background. We further study the polarization properties of the $W'$ coupling to the lepton and heavy neutrino through the decay products of the neutrino. Instead of relying on a specific model, we employ generic couplings and explore the discrimination power. Jet substructure-based angular variables $z_\ell$, $z_\theta$, and $z_k$ are combined to form BDT scores to obtain better separation power between left-chiral ($V-A$) and right-chiral ($V+A$) coupling configurations. By using $CL_s$ type profile likelihood estimator, we could achieve $\sim$ 2$\sigma$ $-$ 3$\sigma$ significance of excluding one coupling configuration in favour of the other.