^{1}

^{1,2,3,4}

^{1,5}

^{1}

^{2}

^{1}

^{2}

^{6}

^{1,3}

^{3}.

We provide the most accurate results for the QCD transition line so far. We optimize the definition of the crossover temperature

One of the most important open problems in the study of quantum chromodynamics (QCD) at finite temperature and density is the determination of the phase diagram of the theory in the temperature (

Extending our knowledge to the

In this Letter, we address the problem of calculating the Taylor coefficients of the crossover temperature around

We also study the strength of the crossover by extrapolating the width of the transition and the value of the chiral susceptibility at the transition to real

For the lattice simulations, we use 4-stout improved staggered fermions with an aspect ratio of

The main observables in this study are the renormalized dimensionless chiral condensate and susceptibility, respectively defined as

Our normalization choice in Eq.

Renormalized chiral condensate

Keeping the previous observations in mind, one can perform a precise determination of

There are ambiguities in steps i)–iv). We estimate their systematics by carrying out many versions of these steps. For all these variations and the estimation of the errors, see the Supplemental Material

Compilation of

Top: Transition line extrapolated from lattice simulations at imaginary chemical potential using an analytical continuation with the ansatz used in step iv) of our analysis (green band) compared with an extrapolation using the formula in Eq.

Since Ref.

In Fig.

In Ref.

A natural definition of the width of the susceptibility peak is given by its second derivative at

We conclude that the half-width of the transition—shown in the upper panel of Fig.

Top: Half-width

Finally, as a proxy for the strength of the crossover, we study the value of the chiral susceptibility at the crossover temperature. We get this for each

The main result of this work is a precise determination of the parameters

We also studied the strength of the phase transition as a function of

This project was funded by the DFG Grant No. SFB/TR55. The project also received support from the BMBF Grant No. 05P18PXFCA. This work was also supported by the Hungarian National Research, Development, and Innovation Office, NKFIH Grant Nos. KKP126769 and K113034. A. P. is supported by the J. Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the ÚNKP-19-4 New National Excellence Program of the Ministry for Innovation and Technology. This material is based upon work supported by the National Science Foundation under Grant No. PHY-1654219 and by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics within the framework of the Beam Energy Scan Topical (BEST) Collaboration. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer JURECA/Booster at Jülich Supercomputing Centre (JSC), on HAZELHEN at HLRS, Stuttgart as well as on SUPERMUC-NG at LRZ, Munich. We acknowledge PRACE for awarding us access to Piz Daint hosted at CSCS, Switzerland. C. R. also acknowledges the support from the Center of Advanced Computing and Data Systems at the University of Houston.