Separating the transverse and longitudinal modes of $\phi$, $\rho$, $K^*$ and $K_1$ mesons through their angular-dependent two-body decay modes

TL;DR

This paper proposes methods to isolate polarization modes of spin-1 mesons via angular-dependent decay modes, enabling study of medium-induced mass shifts and insights into chiral symmetry breaking.

Contribution

It introduces a technique to separate polarization modes of various spin-1 mesons through their decay angular distributions, including the complex case of $K_1$ mesons.

Findings

Polarization modes can be isolated via angular dependencies in decay modes.

Measuring both $K_1$ and $K^*$ mesons can reveal chiral partner mass shifts.

Small vacuum widths of $K^*$ and $K_1$ make them suitable for experimental studies.

Abstract

The mass shift a spin-1 particle moving in the nuclear medium will depend on its polarization direction. To study polarization-independent mass shifts in the medium, we explore methods to isolate each polarization direction of spin-1 mesons through the angular-dependent two-body decay modes. Specifically, we study $\phi\to K^{+}K^{-}$, $\rho\to\pi\pi$, $K^{*}\to K\pi$, $\phi\to e^{+}e^{-}$ and $K_{1}\to\rho K(K^{*}\pi)$ decays. While each polarization mode can be isolated through angular dependencies, accomplishing the decomposition for the $K_1$ meson further requires measuring the polarization of the $\rho(K^*)$ meson. Concerning $K^{*}$ and $K_1$ mesons, since both particles have vacuum widths smaller than 100 MeV, they are ideal candidates for experimentally measuring chiral partners. The simultaneous observation of mass shifts of these chiral partners would provide valuable insights into the contribution of chiral symmetry breaking to the generation of hadron masses.