QCD phase diagram for small densities from simulations at imaginary mu

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1QCD phase diagram for small densities from simulations at imaginary μP.de Forcrand a and O.Philipsen b ?a ETH,CH-8093Z¨u rich,Switzerland and CERN Theory Division,CH-1211Geneva 23,Switzerland b Center for Theoretical Physics,MIT,Cambridge,MA 02139-4307,USA We present results on the QCD phase diagram for small densities without reweighting.Our simulations are performed with an imaginary chemical potential μI for which the fermion determinant is positive.On an 83×4lattice with 2?avors of staggered quarks,we map out the pseudo-critical temperature T c (μI ).For μI /T ≤π/3,this is an analytic function whose Taylor expansion converges rapidly,with truncation errors smaller than statistical ones.The result is analytically continued to give the location of the pseudo-critical line for real μB <～500MeV.1.INTRODUCTION In view of heavy ion collision experiments a pressing task for lattice QCD is to map out the decon?nement transition in the (μ,T )-plane.The complexity of the fermion determinant at ?nite baryon density renders standard Monte Carlo techniques impossible [1].One way of circum-venting this ‘sign problem’are multi-dimensional reweighting techniques,and a phase diagram has been presented last year [2].Reweighting gener-ally breaks down for large volumes and/or densi-ties,and one di?culty of the approach is to know when that happens.In [3]both reweighting fac-tor and observables were expanded in a Taylor series in μ/T ,and the ?rst coe?cients were mea-sured [3].This method allows to simulate larger

volumes,but a priori nothing is known about the error introduced by truncating the series.Here we present an alternative method avoiding reweighting altogether.We simulate at imaginary μfor which there is no sign problem and arbitrar-ily large volumes are feasible.Observables are ?tted by truncated Taylor series in μ/T ,keeping full control over the associated systematic error.The series may then be continued to real μ,pro-vided the observable is analytic [4].This strategy has been successfully tested for screening masses

[5],here we extend it to the critical line itself.A detailed account of this work is given in [6].

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