Spin Density Matrix Elements in Exclusive $\rho ^0$ Meson Muoproduction

TL;DR

This study measures Spin Density Matrix Elements in exclusive $ ho^0$ meson muoproduction, revealing violations of s-channel helicity conservation and insights into natural and unnatural parity exchanges, aiding GPD modeling.

Contribution

It provides the first detailed measurement of SDMEs in $ ho^0$ muoproduction at COMPASS, offering new data to inform GPD models and understand helicity-flip processes.

Findings

Non-zero SDMEs indicate s-channel helicity violation.

Dominance of natural-parity-exchange transitions observed.

Unnatural-parity-exchange contributions are negligible.

Abstract

We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive $\rho ^0$ meson muoproduction at COMPASS using 160~GeV/$c$ polarised $ \mu ^{+}$ and $ \mu ^{-}$ beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0~GeV/$c^2$ $< W <$ 17.0~GeV/$c^2$, 1.0 (GeV/$c$)$^2$ $< Q^2 <$ 10.0 (GeV/$c$)$^2$ and 0.01 (GeV/$c$)$^2$ $< p_{\rm{T}}^2 <$ 0.5 (GeV/$c$)$^2$. Here, $W$ denotes the mass of the final hadronic system, $Q^2$ the virtuality of the exchanged photon, and $p_{\rm{T}}$ the transverse momentum of the $\rho ^0$ meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons ($\gamma^*_T \to V^{ }_L$) indicate a violation of $s$-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive $\rho ^0$ production.