Effect of quantum fluctuations in the high-energy cold nuclear equation of state and in compact star observables

We present a functional renormalization group (FRG) calculation of the equation of state (EoS) using our novel technique to treat fluctuations at finite chemical potential. The goal of this calculation was to provide a proof of concept for this technique as well as to estimate the size of the quantum effects in the equation of state and compact star parameters. We used the simplest nontrivial model where massless fermions are coupled to scalars through Yukawa coupling. We compared our results to the one-loop and the mean-field approximations of the same model and other high-density nuclear matter equations of state. We found a $10–20\%$ difference in the EoS between these approximations. We have also calculated the mass-radius relation for a compact star using the Tolmann-Oppenheimer-Volkov equation with this EoS and observed a $\sim 5\%$ effect due to quantum fluctuations.

Figure 1

The Wetterich equation including the exact propagator and the regulator.

Figure 2

The Wetterich equation with our ansatz including a Yukawa-like coupling with one fermion and one boson field.

Figure 3

Equation of state $p\left(\mu \right)$ calculated from the functional renormalization group method (FRG-LPA, blue “$*$”), in the one-loop approximation (1-Loop, green “$\times$”), and in the mean-field approximation (MF, red “$+$”) from the bottom to the top respectively.

Figure 4

Comparison of the calculated EoS on logarithmic scales in the mean-field (red open squares) and one-loop (green full squares) approximations and via the FRG (blue open circles). Results are compared to SQM3 [16], WFF1 [17] and AP4 [18] EoS from Ref. [3].

Figure 5

Comparison of the $M\left(R\right)$ diagrams corresponding to compact stars calculated from the EoS in the mean-field, one-loop, and high order FRG approximations. The SQM3 [16], WFF1 [17] and AP4 [18] EoS from Ref. [3] are drawn jointly.