Research on u-d quark stars and their tidal deformaions under new mass scaling

Strange quark matter (SQM) is considered to be the true ground state of the strong interactions, but recent studies have shown that ordinary quark matter (u-d quark matter, u-d QM) may also be the ground state of the strong interactions. By inserting an attenuation factor of Woods-Saxon potential type into the quark mass scaling, the resulting calculations of equation of state of u-d QM based on equiv-particle model show that the stability window of model parameters for stable u-d QM can be significantly enlarged with proper model parameters, which can be seen in the following figure. In this figure, the red solid and dashed lines represent the curves of <inline-formula><tex-math id="M2">\begin{document}$ \sqrt{D} $\end{document}</tex-math></inline-formula> versus <i>C</i> with and without attenuation factor, respectively, when the minimum value of the average energy per baryon is set to 930 MeV; the blue solid and dashed lines represent the curves of <inline-formula><tex-math id="M4">\begin{document}$ \sqrt{D} $\end{document}</tex-math></inline-formula> versus <i>C</i> with and without attenuation factor, respectively, when <inline-formula><tex-math id="M6">\begin{document}$ m_\mathrm{u}=0 $\end{document}</tex-math></inline-formula>. Thereby, the red and blue shaded areas are the absolute stable regions of u-d QM without and with attenuation factor in mass scaling. It is obvious that with the attenuation factor and proper model parameters, the absolute stable region (blue shaded area) for u-d QM can be much larger than that without the attenuation factor (red shaded area). The introduction of the attenuation factor allows the maximum mass of ordinary quark star (u-d quark star, u-d QS) to be larger than twice the solar mass, while the tidal deformability satisfies <inline-formula><tex-math id="M7">\begin{document}$ \varLambda_{1.4} \in [70,580] $\end{document}</tex-math></inline-formula>, which is consistent with the current astronomical observations. Therefore, the pulsars may be essentially the u-d QSs. This result provides a possibility for understanding the nature of pulsars, and it also further deepens the understanding of the strong interactions.