Non-strange quark stars from NJL model with proper-time regularisation. (arXiv:1908.06558v1 [hep-ph])
<a href="http://arxiv.org/find/hep-ph/1/au:+Wang_Q/0/1/0/all/0/1">Qingwu Wang</a>, <a href="http://arxiv.org/find/hep-ph/1/au:+Shi_C/0/1/0/all/0/1">Chao Shi</a>, <a href="http://arxiv.org/find/hep-ph/1/au:+Zong_H/0/1/0/all/0/1">Hong-Shi Zong</a>

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 cite{xu2018}, 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 ($> 2.80times10^{14}$g/cm$^3 $)
cite{libl2019}. Besides, for a 1.4 solar mass star, the tidal Love number
$k_2$ and deformability $Lambda$ are calculated which satisfies the constrain
$200 < Lambda < 800$ cite{Bauswein2019,Margali,Abbott}.

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 cite{xu2018}, 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 ($> 2.80times10^{14}$g/cm$^3 $)
cite{libl2019}. Besides, for a 1.4 solar mass star, the tidal Love number
$k_2$ and deformability $Lambda$ are calculated which satisfies the constrain
$200 < Lambda < 800$ cite{Bauswein2019,Margali,Abbott}.

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