# Vector-Interaction-Enhanced Bag Model

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## Abstract

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## 1. Introduction

## 2. vBag, an Extended Bag Model

## 3. Neutron Star Mass–Radius Relation

## 4. Momentum Dependence

## 5. Conclusions

## Supplementary Materials

Supplementary File 1## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

QCD | Quantum Chromodynamics |

$D\chi SB$ | Dynamic Chiral Symmetry Breaking |

EoS | Equation of State |

MeV | Megaelectronovolt |

GeV | Gigaelectronovolt |

${M}_{\odot}$ | Solar mass |

DSE | Dyson–Schwinger equation |

NJL | Nambu–Jona-Lasinio |

MN | Munczek–Nemirovsky |

tdBag | thermodynamic bag |

UV | ultra-violet |

IR | infra-red |

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**Figure 1.**(color online) Single flavor dynamical masses (black) and corresponding pressure (red) computed within the NJL model. The latter is well fitted by the pressure of an ideal Fermi gas (with bare quark mass ${m}_{f}$) shifted by a chiral bag constant ${B}_{\chi}$ (blue). Figure from [18].

**Figure 3.**vBag EoS pressure vs. energy density for neutron star matter

**(left)**; and corresponding mass-radius relations

**(right)**. The grey band represents the possible masses of the PSR J0348+0432 pulsar [21].

**Figure 4.**The solution of MN gap equations as a function of momentum. Blue color represents real solutions and red complex for $\eta =1$ GeV:

**(top left)**chiral quark ($m=0$);

**(top right)**up quark ($m=3$ MeV);

**(bottom left)**down quark ($m=5$ MeV); and

**(bottom right)**strange quark ($m=100$ MeV). All quantities are displayed in units of $\eta $. Figure from [35].

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**MDPI and ACS Style**

Cierniak, M.; Klähn, T.; Fischer, T.; Bastian, N.-U.F.
Vector-Interaction-Enhanced Bag Model. *Universe* **2018**, *4*, 30.
https://doi.org/10.3390/universe4020030

**AMA Style**

Cierniak M, Klähn T, Fischer T, Bastian N-UF.
Vector-Interaction-Enhanced Bag Model. *Universe*. 2018; 4(2):30.
https://doi.org/10.3390/universe4020030

**Chicago/Turabian Style**

Cierniak, Mateusz, Thomas Klähn, Tobias Fischer, and Niels-Uwe F. Bastian.
2018. "Vector-Interaction-Enhanced Bag Model" *Universe* 4, no. 2: 30.
https://doi.org/10.3390/universe4020030