# Deciphering the $X(3872)$ via its polarization in prompt production at the CERN LHC

## TL;DR

This paper predicts the polarization states of the exotic hadron $X(3872)$ and its decay product $J/ar{J}$ at the LHC, using nonrelativistic QCD, to help determine its internal structure and nature.

## Contribution

It provides the first detailed NLO QCD calculation of $X(3872)$ polarization in prompt production, considering its mixed state hypothesis and decay polarization effects.

## Key findings

- $X(3872)$ is predicted to be largely longitudinally polarized.
- $J/ar{J}$ from $X(3872)$ decay is predicted to be largely transversely polarized.
- The polarization measurements can help identify the nature of $X(3872)$ and similar exotic states.

## Abstract

Based on the hypothesis that the $X(3872)$ exotic hadron is a mixture of $\chi_{c1}(2P)$ and other states and that its prompt hadroproduction predominately proceeds via its $\chi_{c1}(2P)$ component, we calculate the prompt-$X(3872)$ polarization at the CERN LHC through next-to-leading order in $\alpha_s$ within the factorization formalism of nonrelativistic QCD, including both the color-singlet $^3\!P_1^{[1]}$ and color-octet $^3\!S_1^{[8]}$ $c\bar c$ Fock states. We also consider the polarization of the $J/\psi$ produced by the subsequent $X(3872)$ decay. We predict that, under ATLAS, CMS, and LHCb experimental conditions, the $X(3872)$ is largely longitudinally polarized, while the $J/\psi$ is largely transversely polarized. We propose that the LHC experiments perform such polarization measurements to pin down the nature of the $X(3872)$ and other $X$, $Y$, $Z$ exotic states with non-zero spin.