Lambda-Lambda correlation from an integrated dynamical model

Transcription

1 ExHIC, March 28, 2016 Lambda-Lambda correlation from an integrated dynamical model Tetsufumi Hirano (Sophia Univ.) Collaborators: Asumi Taniguchi Hiromi Hinohara Koichi Murase References for the model: TH, K.Murase, P.Huovinen, Y.Nara, Prog. Part. Nucl. Phys. 70 (2013) 108. S.Takeuchi, K. Murase, TH, P.Huovinen, Y.Nara, Phys. Rev. C 92 (2015)

2 Contents 1. Introduction 2. High-energy nuclear collisions 3. Integrated dynamical model 4. Lambda- Lambda correlations 5. Summary

3 Interaction between hyperons H dibaryon Nagara event Neutron star core wiki/hexaquark neutrons.html Topics/NAGARA-j.htm

4 Motivation Investigation from a viewpoint of highenergy nuclear collisions Lots of hyperons produced in collisions Correlation functions Source function Parametrization for source function (talks by Morita, Shah and Ohnishi) Dynamical model to estimate source function (talk by Fabbietti) Utilize an integrated dynamical model to analyze correlation functions of hyperons

5 Contents 1. Introduction 2. High-energy nuclear collisions 3. Integrated dynamical model 4. Lambda- Lambda correlations 5. Summary

6 High-energy nuclear collisions 197 Au Au s NN = 200GeV 208 Pb Pb s NN = TeV Collisional energy Thermal energy Multi-particle production

7 Multi-particle production PHOBOS white paper (2005) # of charged hadrons ~ 700 at midrapidty in central collisions A.Andronic et al. (2005) Expected # of Lambda ~1-10 per event # of events >~10^8 High-energy nuclear experiment as hyperon factory

8 Contents 1. Introduction 2. High-energy nuclear collisions 3. Integrated dynamical model 4. Lambda- Lambda correlations 5. Summary

9 time Integrated dynamical model collision axis 0 Hadronic cascade model Microscopic description of Hadron gases Relativistic hydrodynamics Space-time evolution of QGP+hadronic fluids Monte-Carlo Glauber model Initial profile of matter

10 Monte-Carlo Glauber model Collision energy s NN pp inelastic cross section σ in b d Nuclear species Woods-Saxon distribution σ in π ρ part x, ρ coll (x )

11 MC-Glauber to hydro Initial time: τ 0 = 0.6 fm Soft/hard fraction: α = overall normalization + rapidity shape in pp Entropy density One example of initial condition The other thermodynamic variables through equation of state

12 time Integrated dynamical model collision axis 0 Hadronic cascade model Microscopic description of Hadron gases Relativistic hydrodynamics Space-time evolution of QGP+hadronic fluids Monte-Carlo Glauber model Initial profile of matter

13 Relativistic hydrodynamics Hydrodynamic equations Equation of state μ T μν = 0 T μν = e + p u μ u ν pg μν e: energy density p: pressure u μ : four flow velocity *No dissipation in this study High T Lattice result (hot QCD) Low T Hadron resonance gas See also, P.Huovinen and P.Petreczky, NPA837, 26 (2010)

14 Hydro to cascade One-particle distribution from a fluid element F.Cooper, G.Frye (1974) E d3 ΔN d 3 k = g 2π 3 T sw = 155 MeV k Δσ exp k u/t sw ± 1 Σ: T x = T sw Δσμ Nμ Thermal dist. in switching hypersurface Σ boosted by fluid velocity u μ Output from hydro as initial condition for cascade

15 time Integrated dynamical model collision axis 0 Hadronic cascade model Microscopic description of Hadron gases Relativistic hydrodynamics Space-time evolution of QGP+hadronic fluids Monte-Carlo Glauber model Initial profile of matter

16 Hadronic cascade model (JAM) Incoherent convolution of hadron-hadron scattering and resonance decays Some remarks on strangeness sector KN and KN incoming channel KN πy, KN Y, KN K N *Inverse process through detailed balance Other processes Additive quark model σ tot = σ NN n 1 3 n n s1 n n s2 n 2 See also, Y.Nara et al., PRC61, (2000), TH and Y.Nara, PTEP 01A203 (2012).

17 Emission rate Particle emission rate with momentum k at the last interaction point x S x, k = E d7 N d 3 kd 4 x One-particle momentum distribution W k = E d3 N d 3 k = d4 xs(x, k)

18 Transverse momentum spectra of pion and kaon From top to bottom: Central to peripheral Multiplied by 10^x for each result

19 Transverse momentum spectra of proton and phi

20 Transverse momentum spectra of hyperon Σ 0 Λ + γ included

21 Elliptic flow parameter of pion, kaon and proton

22 Elliptic flow parameter of phi and Lambda

23 Elliptic flow parameter of Xi and Omega

24 Short summary so far Reasonable reproduction of transverse momentum spectra and elliptic flow parameters including strange particles by using an integrated dynamical model

25 Contents 1. Introduction 2. High-energy nuclear collisions 3. Integrated dynamical model 4. Lambda- Lambda correlations 5. Summary

26 Full use of emission rate S x, k = E d7 N d 3 kd 4 x Utilize information about space-time distribution Femtoscopy HBT radii Source imaging Information about interaction between two particles

27 Distribution of the last interaction time Au+Au 200 GeV, min. bias, y < 1 Early decouple of multi-strange hadrons Sensitive to interaction with other particles

28 Distribution of particle emission point Pion case S(t, x, 0.3 < k x < 0.9GeV) S(x, y, 0.3 < k x < 0.9GeV) Non-trivial shape of distribution No longer simple Gaussian

29 Koonin-Pratt equation C 2 q = W 2(k 1, k 2 ) W 1 k 1 W 2 (k 2 ) = 1 + K q, r D P r, q d 3 r D P r, q d 3 r K(Q, r): Kernel Information about two-particle wave functions D P r : Un-normalized source function Information about relative distance of emission points S.E.Koonin, Phys. Lett. 70B, 43 (1977), S.Pratt et al., Phys. Rev. C 42, 2646 (1990)

30 Kernel for spin ½ particles K q, r = Ψ = 1 4 Ψ s Ψ t 2 1 Ψ 12 : Two-particle wave function in scattering state in Pair Co-Moving System (PCMS) Ψ s : Spin-singlet (symmetric in coordinate space) Ψ t : Spin-triplet (anti-symmetric in coordinate space)

31 Schrödinger eq. Schrödinger eq. in the radial coordinate with swave approximation (E > 0) d 2 u(r) dr 2 = 2μ ħ 2 V r E u r Initial value problem u 0 = 0: Regular at r = 0 du dr μ = m Λ 2 r = 0 = 1: Later determined by normalization Normalized solution (asymptotically parametrized by phase shift) u r = r χ(r) 1 k eiδ sin kr + δ,

32 Wave function in scattering state V ΛΛ r = V 1 exp r 2 μ 2 1 +V 2 exp( r 2 μ 2 2 ) fss2 potential model V 1 = MeV V 2 = MeV μ 1 = 0.92 fm μ 2 = 0.41 [fm] k = 1 [fm 1 ] Y.Fujiwara et al. (2007) Solving Schrödinger eq. numerically Wave function for kernels

33 Wave function in kernel s-wave approximation: q r Ψ s = 2 cos 2 q r Ψ t = i 2 sin 2 + χ r j 0 qr 2 s-wave scattering state plane wave *No scattering wave in triplet state due to parity 1 l in s-wave approximation

34 Source function D P r, q = d 4 x 1 d 4 x 2 S 1 S 2 δ 3 r x 1 x 2 = dt d 4 R S x 1, k 1 S(x 2, k 2 ) S(x, k): One-particle emission rate t = t 1 t 2 : Relative emission time r = x 1 x 2 : Relative distance of emission points in PCMS R = (x 1 + x 2 ) 2: Four-dimensional center-of-mass coordinates P = (k 1 + k 2 )/2: Average momentum (vanishing in PCMS)

35 Emission rate of Lambda Lambda case S(x, y) Au+Au, s NN = 200 GeV 0-80% centrality rapidity <0.5 No contribution from long-lived resonances No longer Gaussian as is the case for pions A dip at origin Typical length ~5 fm

36 Correlation function in model calculations Two Λs from the same event (x 1, k 1 ) (x 2, k 2 ) Variable transformation (t, r, q ) (R, P ) Lorentz transformation to PCMS (r, q) C 2 q = 1 + event combination event combination K(q, r) 1 (q, r)

37 Feed-down contribution At least one in the Λ-pair from the following decay channels (B. R. ~100%) Σ 0 Λγ, Ξ Λπ or Ξ 0 Λπ 0, assume K(q, r) 0 as r 1 q # of events: 300K min. bias Analysis of 0-80% centrality 240K events

38 Effect of feed-down contribution C 2 (q) 1 q Contribution from core Width 1 r core Contribution from halo Width 1 r halo

39 Discussion on feed-down contribution C 2 q = 1 + ΛΛ K q, r + FD 0 N ΛΛ q + N FD q = 1 + λ(q) ΛΛ K q, r N ΛΛ q Feed-down correction λ q = N ΛΛ N ΛΛ + N FD Correlation of Lambda solely from core region

40 Feed-down correction factor λ MFO = 1 Np N tot 2 In our simulations, λ MFO ~ ~(0.6056) 2 λ q λ MFO *MFO: K.Morita, T.Furumoto, A.Ohnishi, PRC91, (2015).

41 Lambda-Lambda correlation function fss2 potential model Au+Au, s NN = 200 GeV 0-80% centrality rapidity <0.5 Small correlation at q > ~0.1 GeV Need to check other potential model May need to gain more statistics *# of events: ~10^5 events (this study) ~10^8 events (STAR) STAR, PRL114, (2015).

42 Contents 1. Introduction 2. High-energy nuclear collisions 3. Integrated dynamical model 4. Lambda- Lambda correlations 5. Summary

43 Summary and outlook First attempt to calculate Lambda-Lambda correlation function in high energy nuclear collisions within an integrated dynamical model Non-trivial shape of emission rate of Lambda Large contribution from long-lived resonances Deviation from the STAR data within a certain model potential ( fss2 ) Constraint of Lambda-Lambda potential from data (any other combination?)

44 Modified BGK model Formation of hadron strings Y beam rapidity Y beam Number of participants From Glauber model Parametrization of entropy density dist.

45 Some details of initial conditions in longitudinal direction s 0 τ 0, η s, x = ds τ 0 dη s d 2 x = C τ 0 f pp (η s ) 1 α 2 Y b η s Y b ρ A x + Y b + η s Y b ρ B (x ) + αρ coll (x ) f pp η s = exp θ( η s Δη) η s Δη 2 σ η 2 RHIC energy: C = 15.0, α = 0.18, τ 0 = 0.6 fm, Δη = 1.3, σ η = 2.1