Deuteron yields near the QCD phase transition

TL;DR

The paper investigates how the QCD phase transition and critical fluctuations at the CEP influence light-nucleus production, focusing on deuteron yields. It couples a two-flavor quark–meson low-energy effective theory to a nucleon coalescence model within the functional renormalization group framework to compute the equal-time two-point baryon density correlator $C_2$ and its imprint on $N_d$. The results show an enhanced $C_2$ band emanating from the CEP along the phase boundary, but the deuteron yield contribution from this density fluctuation, $N_d^{(C_2)}$, is small compared to the leading term $N_d^{(0)}$, especially on freeze-out curves that deviate from the critical region. Consequently, while CEP fluctuations leave a detectable signature in density correlators, their impact on deuteron production is mild under the studied conditions, highlighting the need for careful treatment of freeze-out dynamics when using light-nucleus yields as CEP probes.

Abstract

We investigate the influence of QCD phase transition and critical fluctuations of the critical end point (CEP) on the deuteron yield within the functional renormalization group (fRG) approach, by using the nucleon coalescence model and a low energy effective field theory of quarks and mesons. It is found that the two-point baryon density correlation function is enhanced in a narrow region radiated from the CEP along the phase boundary. The deuteron yield arising from the two-point baryon correlation is small compared to the leading-order contribution, which is attributed to the fact that in the regime of low collision energy, i.e., the region of large baryon chemical potential, the freeze-out curves deviate from the critical region, resulting in that the enhancement of the deuteron yield stemming from the critical fluctuations near the CEP is mild.

Figures (9)

• Figure 1: Diagrammatic representation of the two-baryon density correlation. Black dots denote vertices; the solid and dashed lines represent the quark and sigma propagators, respectively.
• Figure 2: Flow equations for the two-point functions $\Gamma^{(2)}_{k,\mu'\mu'}$ and $\Gamma^{(2)}_{k,\mu'\sigma}$ in \ref{['eq:d2Gamd2mu', 'eq:d2Gamdmudsigma']}. The black dots denote vertices, and the crossed circle represents the IR regulator in the fRG. The solid lines represent the quark fields. The dashed lines denote the external field $\mu'$ or the $\sigma$ field.
• Figure 3: Heatmap of the two-point baryon density correlation $C_2(\tau=0,\bm{p}=0)$ (left panel) and $C_2(\tau=0,|\bm{p}|=\sqrt{2}/\sigma_d)$ (right panel) in the QCD phase diagram. The red dot denotes the critical end point. The black solid line represents the phase boundary of chiral crossover, and other lines represent three different freeze-out curves Fu:2021oaw. The gray area depicts the region where the computation is inaccessible yet.
• Figure 4: Two-point baryon density correlation as a function of the baryon chemical potential on the phase boundary line and the three freeze-out curves. The solid and dashed lines correspond to $\bm{p}=0$ and $|\bm{p}|=\sqrt{2}/\sigma_d$, respectively.
• Figure 5: Quadratic baryon number fluctuation as a function of temperature $T$ at vanishing baryon chemical potential. The result from this work is compared to those from Ref. Fu:2015naa obtained within the $\mathrm{LPA}$ and $\mathrm{LPA}'$ approximations of the fRG approach.