Relativistic corrections to hadron-hadron correlation function

Abstract

Femtoscopy offers a sensitive probe of hadron emission sources and hadronic interactions. In this study, we examine relativistic corrections to scattering phase shifts and correlation functions using the two-body Dirac equation framework. We analyze the impact of the Darwin term and spin-dependent potentials, showing that these relativistic effects, especially spin-related interactions, significantly enhance the proton-proton correlation function. Our findings emphasize the necessity of including relativistic corrections for precise femtoscopic analyses.

Figures (5)

• Figure 1: The non-relativistic potential (red line) and relativistic potentials without spin-dependent interactions (black dashed line). For the relativistic potential, we take $\omega=2~\rm GeV$ and $m=0.938~\rm GeV$, which corresponds to $b=0~\rm GeV$.
• Figure 2: (Top panel) Scattering phase as a function of $k$. (Bottom panel) The correlation function. The black dashed lines are the non-relativistic case, while the red solid lines correspond to the relativistic case without spin-dependent potentials.
• Figure 3: Spin-singlet state: (top panel) Scattering phase as a function of $k$. (Bottom panel) The correlation function.
• Figure 4: Spin-triplet state: (top panel) scattering phase as a function of $b$. The red line and black-dashed lines correspond to the $S-$wave ($\delta_S$) and $D-$wave ($\delta_D$) components, respectively. (Bottom panel) The correlation functions of $S-$wave ($C_S$) and $D-$wave ($C_D$) components.
• Figure 5: The correlation function of spin-singlet (red-dotted line), triplet (blue-dashed line), spin-averaged case (thick-black line), and the non-relativistic case (thin-green line).