# Non-strange quark stars from NJL model with proper-time regularisation

## TL;DR

This paper models light quark stars using an improved NJL model with proper-time regularisation, successfully predicting two-solar-mass stars and matching observational constraints on surface energy density and tidal deformability.

## Contribution

It introduces a proper-time regularisation in the NJL model and constrains model parameters using pulsar observations, enabling realistic quark star predictions.

## Key findings

- Achieves two-solar-mass pure quark stars.
- Surface energy density exceeds $2.80\times10^{14}$ g/cm$^3$.
- Tidal deformability for 1.4 solar mass star within observational bounds.

## Abstract

The structure of light quark star is studied within a new two-flavor NJL model. By retaining the contribution from the vector term in the Fierz-transformed Lagrangian, a two-solar-mass pure quark star is achieved. To overcome the disadvantage of three-momentum truncation in the regularisation procedure, we introduce the proper-time regularisation. We also employ the newly proposed definition of vacuum pressure, in which the quasi-Wigner vacuum (corresponding to the quasi-Winger solution of the gap equation) is used as the reference ground state. Free parameter includes only a mixing constant $\alpha$ which weighs contribution from Fierz-transformed Lagrangian. We constrain $\alpha$ to be around $0.9$ by the observed mass of pulsars $PSR J0348+0432$ and $PSR J1614-2230$. We find the calculated surface energy density meets the requirement ($> 2.80\times10^{14}$g/cm$^3 $). Besides, for a 1.4 solar mass star, the tidal Love number $k_2$ and deformability $\Lambda$ are calculated which satisfies the constrain $200 < \Lambda < 800$.