# Constraining the Hadron-Quark Phase Transition Chemical Potential via Astronomical Observation

## TL;DR

This paper constrains the chemical potential of the hadron-quark phase transition in neutron stars using observational data, combining relativistic mean field theory and Dyson-Schwinger equations to model matter phases.

## Contribution

It introduces a sound speed interpolation scheme to model the phase transition region and constrains the transition chemical potential with astrophysical observations.

## Key findings

- Most probable phase transition chemical potential identified.
- Constraints derived from maximum neutron star mass and tidal deformability.
- Method bridges theoretical models with observational data.

## Abstract

We investigate the chemical potential and baryon number density of the hadron-quark phase transition in neutron star matter. The hadron matter is described with relativistic mean field theory, and the quark matter is described with the Dyson-Schwinger equation approach of QCD. In order to study the first-order phase transition, we develop the sound speed interpolation scheme to construct the equation of state in the middle density region where the hadron phase and quark phase coexist. The phase transition chemical potential is constrained with the maximum mass, the tidal deformability and the radius of neutrons stars. And the most probable value of the phase transition chemical potential is found.