Jet Substructure and Multivariate Analysis Aid in Polarization Study of Boosted, Hadronic $W$ Fatjet at the LHC

Study of polarization of heavy particles is an important branch of research in today's collider studies. The massive $W$ boson has two types of polarization states, which usually are studied via the angular distribution of its decay products. We have studied polarization of hadronic and boosted $W$ boson using jet substructure technique at 14 TeV LHC. Two different methods, viz. N-subjettiness and Soft Drop, were used to find the subjets, which are approximately considered to be the two hadronic decay products of $W$, inside boosted $W$ jets. These subjets were then used to find the distribution of $p_\theta$ and $z_j$ to prepare the templates of longitudinally and transversely polarized $W$. We then used these templates to find the fractions of different $W$ polarization in a mixed sample to a relatively good accuracy.