Constraining the Symmetry Energy Around Twice Saturation Density Using Elliptic Flow

Transcription

1 Constraining the Symmetry Energy Around Twice Saturation Density Using Elliptic Flow Dan Cozma IFIN-HH Magurele (Bucharest), Romania NUSYM16 Beijing, China June 016

2 Motivation & Content The Model Recent Upgrades Coalescence Model Interaction Potential AsyEoS Constraints Observables Constraints for L & Ksym Model Dependence DEFR ( n, Y) (ρ)= V sym (x, ρ )= n Y v v { (x= 1,ρ) Gogny n Y v v V sym (x, ρ ), V Gogny ρ), sym (0, (x=1,ρ) ρ ρ ρ >ρ Gogny interaction (MDI): x L [MeV] Future Prospects Summary & Conclusions Das, Gupta, Gale, Li, PRC 67, (003)

3 Transport Model Quantum Molecular Dynamics (TuQMD): previously applied to study: - dilepton - EoS emission in HIC: K.Shekter, PRC 68, (003); D. Cozma, PLB640,170 (006); E.Santini PRC78,03410 (008) of symmetric nuclear matter: C. Fuchs, PRL 86, 1974 (001); Z.Wang NPA 645, 177 (1999) - In-medium effects and HIC dynamics: C. Fuchs, NPA 66,987 (1997); U. Maheswari NPA 68,669 (1998) upgrades implemented in Bucharest: - various parametrizations for the EoS: optical potential, symmetry energy PRC 88, (013) - various parametrizations for elastic cross-sections (also in medium ones) PLB 700, 139 (011) - threshold effects for baryon resonance & π meson emission/absorption PLB 753, 166 (016) - pion optical potential arxiv: planned: threshold effects for reactions involving strangeness degrees of freedom some recent upgrades (of interest for the current study): - improved density profiles - reduced Coulomb strength (factor 0.9) - MST coalescence algorithm - new Gogny type EoS parametrization

4 Density Profiles; Coulomb Strength Stability of nuclei: L=4.33 fm light nuclei L=8.66 fm heavy nuclei Static properties: rms, skin lower values for L Compromise needs to be made: cannot satisfy both Coulomb strength: 1 exp[ ( r t ) /(0.5 L )]f ( t, L ) 3 / ( 0.5 π L ) h (r ) rf (r ) g (r ) r ρ(r) ( 1)n n (n) h (r, L)=g (r )+ ( L ) g (r ) n n=1 n! 8 ρ( r )= d 3 t - enforce agreement with Coulomb contribution to the empirical mass formula: scale strength by a factor of 0.9 Liu, Wang, Deng, Wu, PRC 84, (011). - needed for a closer reproduction of experimental ratio of average pt of charged Cozma, arxiv: pions

5 Coalescence Algorithm Minimum spanning tree (MST) phase space algorithm 3 different variants Coales0 nucleons in unphysical cluster ignored Coales1 - unphysical clusters decayed into possible stable daughters or broken into free nucleons Ex: 4Li p+ 3Li 3p p+p+p Coales - motivated by overestimation of proton multiplicities and underestimation of deuterons in Coales1 - clusters with excess protons: pp H (weak process) All clusters with A <= 8 included; heavier clusters discarded Multiplicities of p,n,h, 3H, 3He, 4He fitted to FOPI data δpn=δpp=0.3 GeV/c fixed δrpp, δrpn,δrnn adjusted W. Reisdorf et al, NPA 848, 366 (010) AsyEoS dependent fit ( eosdep ) and its average over x ( eosave )

6 Coalescence Algorithm Fit quality: stiffness dependent parameters coalescence time stiffness averaged parameters stiffness

7 Coalescence Algorithm FOPI-LAND PRC 88, (013) elliptic flow scale 1.15 δpn=0.3 GeV/c δpp=0.3 GeV/c δrpp=5.39 fm Δrpn=5.57 fm Δrnn=3.38 fm coales1 ASYEOS P. Russotto et al. (ASYEOS Coll) NuSYM15

8 AsyEoS Constraints (Update) flow difference: +46 Lsym =19 80 MeV +91 K sym =7 508 MeV +3 L sym= MeV +107 K sym = MeV flow ratio: + 45 Lsym = MeV +91 K sym = MeV F O P I L A N D Y.Leifels et al., PRL 71, 963 (1993) +1 L sym = 6 1 MeV +100 K sym = MeV Lsym =89±45 MeV Additionally: Cugnon Li-Machleidt cs: -15 MeV Momentum dependent part EoS: + 5 MeV M.D. Cozma et al. PRC 88, (013) Y. Wang et al. PRC 89, (014)

9 Isospin dependence of EoS momentum dependent generalization of the Gogny interaction: Das, Das Gupta, Gale, Li PRC67, (003) MDI potential f τ ( p, p ') f τ ' ( p, p ' ) E 1 1 B (ρ,β, x)= A 1 u+ A ( x)u β + (1 x β )+ C d p d p ' τ τ ' τ,τ' N σ +1 u ρ0 1+( p p ' ) / Λ ρ x B σ 1 A ( x)= A 0 + u u= ρ 0 σ +1 L ρ ρ0 3 ρ0 (ρ ρ0 ) S(ρ)=J + + K sym 18 E (ρ,β)= E s (ρ/ ρ )γ N momentum independent power law 800 E s 49 J 17 E s 791 L= (J )+ (J ) E s 17 E s 49 J 9J K sym= (J ) 14 4 E s D. Blaschke et al. ArXiv: ρ0 K A K vol (1+cA 1/3 )+ K τ (( N Z )/ A) + K Coul Z A 4/3 J K τ = K sym 6 L 0 L K0 results from experiment/theory GMR: Kτ=-550±100 MeV T.Li et al. PRL 99, (007) -590±0 MeV J.Stone et al. PRC 89, (014) Higher Order Effects: -370±10 MeV L.W. Chen PRC 80, 0143 (009)

10 New potential S(0.10 fm 3 )=5.7 MeV momentum dependent potential MDI σ E 1 1 Bu Du (ρ,β, x, y)= A 1 u+ A ( x, y)u β + (1 x β )+ (1 y β ) N σ+1 3 f τ ( p, p ' ) f τ '( p, p ' ) C τ τ ' d p d p ' τ, τ ' u ρ0 1+( p p ' ) / Λ ρ x B σ 1 y D A ( x, y )= A 0 + u + u u= ρ 0 σ +1 3 B.A. Brown, PRL111, 350 (013) Fit: U,K,J0,m* -isoscalar S(ũ),L,Ksym,δmisv -isovector 0 Al, x, y C l C u Δmisv=0. mn momentum dependent part: similar with that of J. Xu et al. PRC 91, (015) (see also C. Hartnack, J. Aichelin PRC 49, 801 (1994) ) used previously to test model dependence: flow ratio PRC 88, 4491 (013) pion multiplicity ratio PLB 753, 166 (016) independent part: extra term (vary L vs. Ksym and also J0 vs. K independently) from J. Xu et al. PRC 91, (015) from B.-J. Cai, arxiv: (014)

11 Sensitivity to Ksym (and J) 3 dimensional parameter space: heavy-ion observables 1 dim constraint +nuclear structure determine values FOPI-LAND mmdi potential, vacuum Cugnon elastic cross-sections 3 S(0.10 fm )=5.7 MeV B.A. Brown, PRL111, 350 (013)

12 Constraints for L and Ksym MDI mmdi L = 57 ±15 MeV Ksym= -100 ± 7 MeV J = 33.6 ±.7 MeV full MDI freedom L and Ksym constrained as for MDI vacuum Li-Machleidt elastic cs L = 65 ±15 MeV Ksym= 00 ± 50 MeV J = 3.3 ± 3.9 MeV

13 Constraints for L and Ksym ASYEOS+FOPI-LAND Only ASYEOS data precise enough! FOPI-LAND J.M.Lattimer & A.W. Steiner, EPJA 50, 40 (014) mmdi mmdi L=57 MeV

14 Model dependence mmdi+cugnon mmdi compatibility with Kτ in-medium cross-sections standard choice: MDI + vacuum Li-Machleidt cross-sections Cugnon parametrization of NN cs: Cugnon, Mizutani, Vandermuelen, NPA 35, 505 (1981) Li-Machleidt PRC 48, 170 (1993); PRC 49, 566 (1994) relevance of in-medium effect on cross-sections rapidity/pt dependent flows: Y.Wang et al., PRC89, , (014) nuclear stopping: Z.Basrak et al., arxiv:

15 Isovector mass splitting Existing constraints: N-A scattering ρ0! higher densities?? Δm*=(0.3±0.15)β C.Xu et al. PRC 8, (015) Δm*=(0.41±0.15)β X.H. Li et al. PRB 743, 408 (015) Empirical Constraints on Esym Δm*=0.7β B.A. Li et al., PLB 77, 76 ρ0 & β=0.5 IVGDR,EDP, ISGQR Δm*=(0.33±0.16)β Z.Zhang et al. PRC 93, (016) Δm*=0.0 HICs: DR of n/p in Sn+Sn MDI Δm*>0.0 D.D.S.Coupland et al., arxiv (014)

16 EFT Models & Astrophysics χeft Hebeler et al., PRL 105, (010) Hebeler et al., ApJ 773, 11 (013) QMC Gandolfi et al, PRC 85, 03801R (01) Steiner et al, PRL 108, (01) - N+3N model constrain neutron matter up to ρ0 - extrapolation to high density (ρ0) uncertain - high density polytopes - rule out many EoSs using measured NS masses MNS=1.97±0.04 Mʘ Demorest et al., Nature 467, 1081 (010) MPSR=.40±0.1 Mʘ MPSR>1.66 Mʘ vankerkwijk et al, ApJ 78, 95 (011)

17 Future Prospects (HICs) Elliptic Flow Ratio Experimental Side: Elliptic Flow: mandatory to distinguish p vs ch ASYEOS GSI Pions: upcoming data SAMURAI TPC Coll multiplicity & average pt ratios needed optimization of cuts Strangeness: available/upcoming HADES deep subthreshold data M. Lorentz et al., J. Phys. Conf. Ser. 668, 010 (016) Pion Multiplicity Ratio Theoretical Side: Elliptic Flow: coalescence model in-medium effects on cross-sections Pions: pion optical potential ArXiv: Strangeness: include into GEC transport model Theory: Ferini et al., PRL 97, 0301 (006) M.D. Cozma arxiv:

18 Summary / Conclusions Improved Transport Model: improved density profiles of nuclei MST coalescence model- not yet a satisfactory description of FOPI cluster multiplicities -good description of elliptic flow parameters - to do: rapidity/pt dependent FOPI flows MDI potential momentum dependent part in agreement with the empirical one (pa reactions) - extra term to vary L and Ksym independently (also independent of isovector mass difference) Constraints for AsyEoS: MDI lower value for L than previously L = 65 ±15 MeV Ksym= 00 ± 50 MeV J = 3.3 ± 3.9 MeV MDI EFRnh/nch sensitive to L - EFRnp sensitive to L & Ksym - sensitivity to J suppressed (determined from nuclear structure constraint for S) - ASYEOS data precise enough useful constraint for Ksym -extracted values depend on data set (?multiplicity spectra) -moderate model dependence (largest due to in-medium cs) - EoS compatible with NS masses and (at the lower limit) with compressibility of nuclei Perspectives: higher accuracy EFRnp needed (ASYEOS Coll) use future pion and (possibly) strangeness production data in HICs to extend the study to higher densities