Exploring the QCD Phase diagram with imaginary chemical potential - PowerPoint PPT Presentation

Universität Bielefeld Exploring the QCD Phase diagram with imaginary chemical potential with HISQ action Jishnu Goswami Collaborators: Frithjof Karsch, Christian Schmidt, and Anirban Lahiri � 1

Plan of the talk • Introduction • Status on chiral phase transition with HISQ at 𝜈 =0 • Status on chiral phase transition in the RW plane. • Results and discussions. � 2

Introduction Central Question: Nature of the chiral symmetry restoring transition at 𝜈 =0 at the chiral limit?? Does a 1st order chiral symmetry restoring transition exist at 𝜈 =0 below ◆ 2 ✓ µ T a certain critical quark mass (m cri ) ?? N f = phys. point 2 The 1st order region is N f = 3 crossover 1 st 0 ∞ 1 st = 1 Z (2) Z (2) expected to be largest in the N f RW plane( 𝜈 /T=(2k+1) 𝜌 /3 ). Thus critical mass in the RW tric 1 st tr. ◆ 2 ✓ π plane puts a bound on the 2 nd 3d Ising ∞ − 1 st tr. tric 3 critical mass at 𝜈 =0. m u,d m s Possible scenario of extended 3d Columbia plot O. Philipsen and C. Pinke. Phys. Rev. D93, 114507, 2016. � 3

Chiral transition for zero chemical potential with HISQ • HotQCD results on chiral phase transition, [ ] μ = 0 N f =3 : 1st order phase N f =2+1 : No hint of 1st order transition ruled out for phase transition for m 𝜌 >55 MeV. 230 MeV > m 𝜌 > 80 MeV. chiral transition is most likely Bound on critical pion 2nd order O(N) rather than Z(2). mass is given as, A. Lahiri et. al. , QM 2018, arXiv:1807.05727 m 𝜌 cr ≲ 50 MeV from the Pure chiral limit N f = 2 N f = 2 scaling analysis. Gauge 1 st U (2) L ⊗ U (2) R / U (2) V ? Bazavov et. al. PRD 95, 074505 (2017) O (4) ? N f = 3 Z(2) phys. point m tric s crossover N f = 1 m s Z ( 2 ) 1 st m ud � 4

Studies in the RW plane Possible scenario of RW end point Mostly with unimproved actions —plenary by S. Mukherjee m 𝜌 ﹥ 1 GeV, for the ‘heavy quark mass RW transition’ ‘small quark mass RW transition’ ( N f = 2) Standard staggered action: m 𝜌 ～ 400 MeV (N 𝝊 =4) Standard Wilson action : m 𝜌 ～ 930 MeV( N 𝝊 =4) m 𝜌 ～ 680 MeV (N 𝝊 =6) 1st order end point (of the line of 1st order RW transitions) exist already for 𝜈 /T= 𝜌 /3 and m cri >m phy. The results are strongly fermion discretization scheme and cut-o ff (N 𝝊 ) dependent. P . de Forcrand et. al, PRL 105, 152001(2010), Owe Philipsen et. al, PRD 89, 094504(2014), Christopher Czaban et al, PRD 93, 054507 (2016) � 5

Studies in the RW plane Very recent studies with improved actions , • Stout improved staggered fermions( N f =2+1): At the physical quark mass point( m 𝜌 ～ 135 MeV) a 2nd order transition in the 3d-Ising universality class happens instead of a 1st order at the RW endpoint. C. Bonati et. al,PRD 93, 074504 (2016) No 1st order end point (of the line of 1st order RW transitions) for m 𝜌 >50 MeV . C. Bonati et. al,arXiv:1807.02106 [hep-lat] • HISQ( N f =2): Order of the phase transition at physical point is not clear(large cut-o ff e ff ects) . L.K.Wu, et al. PRD 97,114514(2018) � 6

Studies with HISQ in the RW plane Z ( T , μ ) = ∫ [ 𝒠 U ] det [ M ud ( μ f )] 1/2 det [ M s ( μ f )] 1/4 exp[ − S G ] Action, M q = D HISQ ( μ f ) + m q Simulation details, N f = 2 + 1, μ T = π m π m l 3 N σ N τ We vary 𝛾 in the range [5.850-6.038], m s (MeV) corresponds to, ∼ T c ± 0.1 T c 8 4 1/27 135 Generally we generated 20k trajectory per 𝛾 value away 12 4 1/27 135 from 𝛾 c and 80k trajectory near 𝛾 c 1/27,1/40, 135, 110, 16 4 1/60 90 We work on the 2nd RW plane 135, 24 4 1/27,1/40 110 � 7

<latexit sha1_base64="gRtvq7rDWgrqzr8hjBTQJw8TnZQ=">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</latexit> <latexit sha1_base64="gRtvq7rDWgrqzr8hjBTQJw8TnZQ=">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</latexit> <latexit sha1_base64="gRtvq7rDWgrqzr8hjBTQJw8TnZQ=">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</latexit> <latexit sha1_base64="gRtvq7rDWgrqzr8hjBTQJw8TnZQ=">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</latexit> Ising endpoint of a first order line E ff ective Ising Hamiltonian which H eff ( t , ξ ) = t ℰ + h ℳ defines the universal critical behaviour of the system temperature like under Z(2) transformation, magnetization field like operator ℰ → ℰ energy like (order parameter) operator ℳ → − ℳ magnetic field like Corresponding critical behaviour of QCD in 2nd RW plane [Z(2) transformation], order parameter Im L → − Im L Re L → Re L energy like μ = μ RW i.e. at ( 0 , if β < β c V →∞ h Im L i ⌘ lim V →∞ h | Im L | i = h → 0 lim lim non-zero , if β > β c � 8