Abstract
We discuss the phase structure of QCD for $N_f=2$ and $N_f=2+1$ dynamical quark flavours at finite temperature and baryon chemical potential. It emerges dynamically from the underlying fundamental interactions between quarks and gluons in our work. To this end, starting from the perturbative high-energy regime, we systematically integrate-out quantum fluctuations towards low energies by using the functional renormalisation group. By dynamically hadronising the dominant interaction channels responsible for the formation of light mesons and quark condensates, we are able to extract the phase diagram for $\mu_B/T \lesssim 6$. We find a critical endpoint at $(T_\text{CEP},{\mu_B}_{\text{CEP}})=(107, 635)\,\text{MeV}$. The curvature of the phase boundary at small chemical potential is $\kappa=0.0142(2)$, computed from the renormalised light chiral condensate $\Delta_{l,R}$. Furthermore, we find indications for an inhomogeneous regime in the vicinity and above the chiral transition for $\mu_B\gtrsim 417$ MeV. Where applicable, our results are in very good agreement with the most recent lattice results. We also compare to results from other functional methods and phenomenological freeze-out data. This indicates that a consistent picture of the phase structure at finite baryon chemical potential is beginning to emerge. The systematic uncertainty of our results grows large in the density regime around the critical endpoint and we discuss necessary improvements of our current approximation towards a quantitatively precise determination of QCD phase diagram.
Highlights
The detailed understanding of the QCD phase structure at finite temperature and density is essential for our understanding of the formation of matter, and for the interpretation and prediction of the wealth of data collected at running and planned heavy-ion experiments
With increasing μB, the crossover becomes sharper and we find a critical endpoint at ðTCEP; μBCEP Þ 1⁄4 ð107; 635Þ MeV: ð1Þ
The quarkmeson vertex running counterbalances the strong scale dependence of the meson wave function renormalization. This is explicitly seen in Fig. 16: On the left side we show the temperature and chemical potential dependence of the physical Yukawa coupling, hk1⁄40
Summary
The detailed understanding of the QCD phase structure at finite temperature and density is essential for our understanding of the formation of matter, and for the interpretation and prediction of the wealth of data collected at running and planned heavy-ion experiments. With the present work many significant steps toward a self-consistent quantitative description of the QCD phase structure are taken This requires the derivation of many novel and the significant extension of existing RG flow equations for correlation functions in QCD. III, IV we discuss in detail the underlying systematic truncation scheme, and specify the flows for correlation functions including the propagators, vertices, and the effective potential These flow equations are temperatureand density-dependent counter parts with significant systematic extensions of the vacuum QCD flows put forward in [28,29], as well as flows in low energy effective models of QCD. Many technical details of our calculations are deferred to the Appendixes
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