Eﬀects of QCD cri/cal point on electromagne/c probes

Eﬀects of QCD cri/cal point on electromagne/c probes Akihiko Monnai (IPhT, CNRS/CEA Saclay) with Swagato Mukherjee (BNL), Yi Yin (MIT) + Björn Schenke (BNL) + Jean-Yves Ollitrault (IPhT) Phase diagram of strongly interac/ng mater: From LaWce QCD to Heavy-Ion Collision Experiments December 1, 2017, ECT*, Italy

Probing the QCD equa/on of state at ﬁnite density (including eﬀects of QCD cri/cal point on electromagne/c probes) Akihiko Monnai (IPhT, CNRS/CEA Saclay) with Swagato Mukherjee (BNL), Yi Yin (MIT) + Björn Schenke (BNL) + Jean-Yves Ollitrault (IPhT) Phase diagram of strongly interac/ng mater: From LaWce QCD to Heavy-Ion Collision Experiments December 1, 2017, ECT*, Italy

Introduc/on n The QCD phase diagram is not well known at finite μ B 3 / 27

Introduc/on n The QCD phase diagram is not well known at finite μ B Our mo/va/on 3 / 27

Introduc/on n The QCD phase diagram is not well known at finite μ B Our mo/va/on Determine the proper/es of QCD mater at finite T, μ B Verify the existence of a QCD cri/cal point (QCP) 3 / 27

Introduc/on n Beam energy scan: an experimental explora/on of QCD phases Performed and planned at RHIC (BNL) Phase I (2009-11): 7.7-62.4 GeV Phase II (2017-20?): 3.0 GeV? HADES, FAIR (GSI) NICA (JINR) SPS (CERN) J-PARC-HI (J-PARC) etc. 4 / 27

Method n Possible approaches LaWce QCD Model calcula/ons (pnjl, etc.) Extrac/on from experimental data Pros First principle Works at finite density (restricted) Actual data Cons Sign problem at finite density Model dependent Needs a reliable model for exps 5 / 27

Viscous hydrodynamic model n for connec/ng the EoS and observables Graphics by AM Colliding nuclei Hadrons Freeze-out Hadronic fluid QGP fluid z Hadronic transport (> 10 fm/c) Freeze-out Hydrodynamic stage (~1-10 fm/c) Equilibra/on Glasma (~0-1 fm/c) LiTle bang Color glass condensate (< 0 fm/c) Hydrodynamic equa/ons are closed with the EoS that characterize thermodynamics of the system 6 / 27

At vanishing density (μ B =0) AM and J.-Y. Ollitrault, Phys. Rev. C 96, 044902 (2017) 7 / 27

Equa/on of state (EoS) n At vanishing densi/es Wuppertal-Budapest, PLB 730, 99 (2013) HotQCD, PRD 90, 094503 (2014) We have good lawce calcula/ons of the QCD EoS Is it what we see in heavy-ions collisions? 8 / 27

Equa/on of state (EoS) n We systema/cally generate varia/ons of EoS: P/T 7 6 5 4 3 2 EOS A EOS B EOS L EOS C (a) Varying DOF P/T 4 4 6 5 4 3 2 EOS D EOS E EOS L EOS F (b) Varying Tc 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 T (GeV) 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 T (GeV) Low temperature side (T < 140 GeV) is constrained by hadron resonance gas for the Cooper-Frye freeze-out 9 / 27

Mean m T and dn/dy n Observables sensi/ve to the EoS Entropy density (1/R 03 )dn/dy Number/entropy per volume Energy density over entropy density mean m T Energy per number/entropy T eff : effec/ve temperature of the medium R 0 : effec/ve radius of the medium where a, b: constant factor 10 / 27

Hydrodynamic results n (2+1)D ideal hydro, Au-Au, 0-5%, Glauber ini/al condi/ons 0.35 0.3 (a) 0.35 0.3 (b) 0.25 0.25 /s (GeV) 0.2 0.15 0.1 0.05 a = 4.534, b = 0.202 EOS A EOS B EOS L EOS C ideal (w/o dec.) (EOS A) ideal (w/o dec.) (EOS B) ideal (w/o dec.) (EOS L) ideal (w/o dec.) (EOS C) 0 0 10 20 30 40 50 60 70 80-3 s (fm ) 0 0 10 20 30 40 50 60 70 80-3 s (fm ) There is a good correspondence between the EoS and observables; a single set of (a,b) fits hydro results onto the EoS /s (GeV) 0.2 0.15 0.1 0.05 a = 4.534, b = 0.202 EOS D EOS E EOS L EOS F ideal (w/o dec.) (EOS D) ideal (w/o dec.) (EOS E) ideal (w/o dec.) (EOS L) ideal (w/o dec.) (EOS F) 11 / 27

Hadronic decay and viscosity n <m T > vs. (1/R 03 )dn/dy plot for EoS L 1.4 1.2 1 <m T > (GeV) 0.8 0.6 0.4 0.2 ideal (w/o dec) a=4.534, b=0.202 ideal (w/ decay) a=3.310, b=0.292 viscous (w/ decay) a=3.387, b=0.301 viscous+ f (w/ decay) a=3.460, b=0.313 0 0 2 4 6 8 10 12 14 16 18 20 22 3-3 (1/R )dn/dy (fm ) 0 (a,b) can be determined so that all the EoS are sa/sfied 12 / 27

Comparisons to experimental data n Viscous hydro results w/ decays <m T > (GeV) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ALICE 2.76 TeV PHENIX 200 GeV STAR 200 GeV STAR 130 GeV STAR 62.4 GeV 0 0 2 4 6 8 10 12 14 16 3-3 (1/R )dn/dy (fm ) 0 EOS A EOS B EOS L EOS C Compa/ble with the lawce QCD equa/on of state within errors 4 P/T 7 6 5 4 3 2 1 EOS A EOS B EOS L EOS C (a) 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 T (GeV) 13 / 27

Comparisons to experimental data n Viscous hydro results w/ decays <m T > (GeV) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ALICE 2.76 TeV PHENIX 200 GeV STAR 200 GeV STAR 130 GeV STAR 62.4 GeV 0 0 2 4 6 8 10 12 14 16 3-3 (1/R )dn/dy (fm ) 0 EOS A EOS B EOS L EOS C 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 T (GeV) Compa/ble with the lawce QCD equa/on of state within errors Larger effec/ve # of degrees of freedom allowed by the data 4 P/T 7 6 5 4 3 2 1 EOS A EOS B EOS L EOS C (a) 13 / 27

At finite density (μ B 0) AM and B. Schenke, Phys. LeT. B 752, 317 (2016) AM, S. Mukherjee and Y. Yin, Phys. Rev. C 95, 034902 (2017) AM, S. Mukherjee and Y. Yin, in prepara/on 14 / 27

Equa/on of state (μ B 0) n LaWce QCD EoS: Taylor expansion Akihiko Monnai (IPhT), Probing the QCD equa/on of state at finite density 15 / 27

Equa/on of state (μ B 0) n LaWce QCD EoS: Taylor expansion n Match to hadron resonance gas EoS at low T 15 / 27

Equa/on of state (μ B 0) n LaWce QCD EoS: Taylor expansion n Match to hadron resonance gas EoS at low T Taylor expansion is not reliable when μ B /T is large 15 / 27

Equa/on of state (μ B 0) n LaWce QCD EoS: Taylor expansion n Match to hadron resonance gas EoS at low T Taylor expansion is not reliable when μ B /T is large The EoS of kine/c theory must match the EoS of hydrodynamics at freeze-out for energy-momentum/net baryon conserva/on Par/cle spectrum Hydrodynamics 15 / 27

Equa/on of state (μ B 0) n LaWce QCD EoS: Taylor expansion n Match to hadron resonance gas EoS at low T Taylor expansion is not reliable when μ B /T is large We have two versions available: Wuppertal-Budapest PLB 730, 99 (2013), JHEP 01, 138 (2012), PRD 92, 114505 (2015) HotQCD PRD 90, 094503 (2014), PRD 86, 034509 (2012), PRD 92, 074043 (2015) The EoS of kine/c theory must match the EoS of hydrodynamics at freeze-out for energy-momentum/net baryon conserva/on Par/cle spectrum Hydrodynamics 15 / 27

Equa/on of state (μ B 0) n We connect the equa/ons of state as 16 / 27

Equa/on of state (μ B 0) n We connect the equa/ons of state as Condi/ons of monotonous increase of thermodynamic variables,, 16 / 27

Equa/on of state (μ B 0) n We connect the equa/ons of state as Condi/ons of monotonous increase of thermodynamic variables,, - It is not a priori clear if this is sa/sfied because is nega/ve above T c 16 / 27

Equa/on of state (μ B 0) n The result where Hydro model needs Tc > 0.16 GeV for switching to UrQMD; LaWce agreement is at Tc < 0.14 GeV 17 / 27

Equa/on of state (μ B 0) n The result where Hydro model needs Tc > 0.16 GeV for switching to UrQMD; LaWce agreement is at Tc < 0.14 GeV We can also introduce a test cri/cal point 17 / 27

QCD cri/cal point (QCP) n A landmark in the QCD-land (which may or may not exist) 18 / 27

QCD cri/cal point (QCP) n What observables are sensi/ve to a QCP? Proposed so far: - Event-by-event fluctua/on of mul/plici/es - Rapidity slope of directed flow v 1 etc. STAR, PRL 112, 032302 STAR, PRL 108, 202301 We consider the effects of viscosity evolu/on on the QCP by looking at dileptons 19 / 27

Electromagne/c probes n For probing the cri/cal point Dileptons t Photons Cri/cal point The QGP is EM transparent Photons and dileptons know the history of the /me evolu/on Graphics by AM z The QCP can leave imprint via cri/cal behavior of viscosity in two ways: 1. Modifica/on of bulk evolu/on 2. δf correc/on in the emission rate 20 / 27

Near the cri/cal point n Bulk viscosity becomes dominant Shear viscosity: Bulk viscosity: Baryon diffusion: : correla/on length We focus on bulk viscosity in this study 21 / 27

Near the cri/cal point n Bulk viscosity becomes dominant Shear viscosity: Bulk viscosity: Baryon diffusion: : correla/on length We focus on bulk viscosity in this study Parameteriza/on for bulk viscosity where A. Buchel, PLB 663, 276 (2008) is parameterized based on Ising model 21 / 27

Near the cri/cal point n Bulk viscosity becomes dominant Relaxa/on /me is mo/vated by -Pêp 1.2 1.0 0.8 0.6 C P =0.25, CP C P =1, CP C P =4, CP C P =1, No-CP 0.4 0.2 0.0-2.5-2.0-1.5-1.0-0.5 0.0 0.5 HT c -TLêDT - Causal hydro is applicable when is frozen at large - The relaxa/on /me from an AdS/CFT approach ( ) is free of cavita/on ( ) 22 / 27

Dileptons n How is the emission rate affected δf correc/on in the emission rate QGP Hadron (1) (2) 23 / 27

Dileptons n How is the emission rate affected δf correc/on in the emission rate QGP Hadron (1) (2) (1) Equilibrium emission rate K. Kajan/e, J. Kapusta, L. McLerran, A. Mekjian, PRD 34, 2746 0.006 sigma q sigma pi 0.005 0.004 cross section 0.003 0.002 0.001 0 0 0.5 1 1.5 2 2.5 M(GeV) 23 / 27

Dileptons n Bulk viscous correc/ons Grad moment method (Israel-Stewart) in Boltzmann approx. The off-equilibrium rate is and can be calculated in kine/c theory as func/ons of T and μ B 24 / 27

Dileptons n Invariant mass spectra: w/ 1+1 D non-boost invariant hydro ) -1 dn/dmdy (GeV -1 10-2 10-3 10 1 1 Preliminary ideal Preliminary ideal Y = 0 bulk (w/ f) Y = 2 bulk (w/ f) -1 10 QCP (w/ f) QCP (w/ f) ) -1 dn/dmdy (GeV -2 10-3 10-4 10 0.4 0.6 0.8 1 1.2 1.4 M (GeV) -4 10 0.4 0.6 0.8 1 1.2 1.4 M (GeV) Bulk viscosity enhances low M spectra; the QCP can be visible QGP: parton gas w/ m th Hadron: pion gas *Results are sensi/ve to the form of δf, m th, # of hadronic components, etc. 25 / 27

Summary n Equa/on of state can be probed in heavy-ion collisions μ B = 0 - There is a mapping between ε/s vs. s and <m T > vs. dn/r 3 dy - The data is compa/ble with lawce QCD EoS, more # of DOF may also work μ B 0 - EoS is constructed using lawce QCD and resonance resonance gas - If there is a cri/cal point, its signal may appear in invariant mass spectra of dileptons n Future prospects Systema/c probing of the EoS at finite density - Changing the loca/on of test QCP, comparing to the BES data, etc. 26 / 27

Fine n Grazie per l'atenzione! Akihiko Monnai IPhT, Probing the QCD equa/on of state at ﬁnite density 27 / 27

Where do the QCD mater go through? n in heavy-ion collisions Chun Shen, QM17 talk J. Gunther et al., EPJ Web Conf. 137 (2017) 07008 Much more broadly spread in event-by-event hydrodynamics (up to μ B around 0.7 GeV) 28 / 27