Event-by-event hydrodynamical description of QCD matter

Transcription

1 Event-by-event hydrodynamical description of QCD matter Máté Csanád, Sándor Lökös Eötvös University, Budapest 53rd International School of Subnuclear Physics, Erice, Sicily, / 15

2 Outline 1 sqgp and the hydrodynamical approach 2 N-pole asymmetries in the description 3 The elliptical Buda-Lund model and its properties 4 General asymmetries in the model 5 Observables from the generalized model 2 / 15

3 sqgp sqgp discovered at RHIC and also created at LHC Almost perfect uid, expanding hydrodynamical system Hadrons created at the freeze-out, leptons, photons created previous the freeze-out too 3 / 15

4 Perfect uid hydrodynamics Hydro solutions or models Relativistic, exact, analytic solution: Famous solution: Landau-Khalatnikov, Hwa-Bjorken There is many new solutions Geometry? The most basic concept: spherical symmetry Non-central collisions assuming elliptical asymmetry More precise description: higher order asymmetries including! Generalize the space-time and the velocity eld distribution too! 4 / 15

5 The elliptical Buda-Lund model Csanád, Csörg, Lorstad Nucl.Phys.A742, (2004) Final state parametrization with source function: S(x, p) = g p µ d 4 Σ µ (x) (2π) 3 B(x, p) + s q p µ d 4 Σ µ (x) = p µ u µ δ(τ τ 0 )d 4 x the Cooper-Frye factor, assuming instant freeze-out. B(x, p) is the Boltzmann-factor. Scaling variable: s = r 2 x 2X 2 + r 2 y 2 z + r 2Y 2 2Z 2 Thermodynamical quantities depend only on s not on the coordinates Derived the velocity eld from a potential: u µ = γ (1, x Φ, y Φ, z Φ) ( ) Φ = r 2 Ẋ + x 2X r 2 Ẏ + y 2Y r 2 Ż z 2Z 5 / 15

6 Generalization Spatial distribution (with ɛ n asymmetry parameter): Elliptical symmetry: s = r 2 R 2 (1 + ɛ 2 cos(2ϕ)) + r Triangular symmetry: s = r 2 Generally: s = r 2 R 2 ( 2 z Z 2 R 2 (1 + ɛ 3 cos(3ϕ)) + r 1 + ) N ɛ n cos(nϕ) n=2 2 z Z 2 + r 2 z Z 2 This s can be use in a hydro solution: Csanád, Szabó PhysRevC The generalized potential of velocity eld (with χ n asymmetry parameter): Elliptical symmetry: Φ = r 2 (1 + χ 2H 2 cos(2ϕ)) + r 2 z 2H z Triangular symmetry: Φ = r 2 (1 + χ 2H 3 cos(3ϕ)) + r 2 z 2H z Generally: ( ) N Φ = r χ n cos(nϕ) 2H n=2 + r 2 z 2H z 6 / 15

7 Observables from the new model Invariant momentum distribution: N 1 (p) = S(x, p)d 4 x Flows: N 1 (p) = N 1 (p t ) (1 + 2 n=1 v n cos(nα)) where the ow v n (p t ) = cos(nα) Bose-Einstein correlations: The correlation function is the Fourier transformation of the source function: C(q) = 1 + S(r) exp(iqr)dr 2 The asymmetries is measured in the corresponding event plane Elliptical asymmetry 2 nd order event plane Triangular asymmetry 3 rd order event plane No interplay among the asymmetries! 7 / 15

8 Flows from the model Elliptic (v 2 ) and triangular (v 3 ) ows can be derived from the model Mixing of the parameters: the spatial distribution asymmetry (ɛ 2,3) and the velocity eld asymmetry (χ 2,3) form the ows together 8 / 15

9 Azimuthally sensitive HBT radii Useful to describe the geometry of the source The correlation function is the Fourier transformation of the source Elliptical case: both of it is Gaussian but with inverse width S(r) e r 2 x 2R 2 r2 y x 2R 2 r2 z y 2R 2 z C(k) = 1 + e k2 x R2 x k2 y R2 y k2 z R2 z Size and geometry of the source can be measured! Experimentally it is measured in the out side long pair coordinates: R x,y,z R o,s,l The dierence between out and side radii is indicate the kind of phase transition 9 / 15

10 Azimuthally sensitive HBT radii The transverse angle which is appear in momentum space: (p t, α, p z ). R 2 o = x 2 o x o 2, R 2 s = x 2 s x s 2 where: x o = r cos(ϕ α), x s = r sin(ϕ α) The average is an integrating over the source function with weight x o respect the spatial coordinates (r, ϕ, r z ) Parametrization: Elliptical case: R 2 = R 2 + R 2 cos(2α) o/s o/s,0 o/s,2 Parametrization: Triangular case: R 2 o/s = R 2 o/s,0 + R 2 o/s,3 cos(3α) or x s 10 / 15

11 Azimuthally sensitive HBT radii Mixing of the parameters: spatial distribution and velocity eld form the azimuthally sensitive HBT radii together. Elliptical case: in the second order reaction plane ɛ 2 : asymmetry in space-time, χ 2 : asymmetry in velocity eld Parametrization: Elliptical case: R 2 o/s = R 2 o/s,0 + R 2 o/s,2 cos(2α) 11 / 15

12 Azimuthally sensitive HBT radii Mixing of the parameters: spatial distribution and velocity eld form the azimuthally sensitive HBT radii together. Triangular case: in the third order reaction plane ɛ 3 : asymmetry in space-time, χ 3 : asymmetry in velocity eld Parametrization: Triangular case: R 2 o/s = R 2 o/s,0 + R 2 o/s,3 cos(3α) 12 / 15

13 Conclusion and outlook Hydrodynamical approach can be used as a phenomenological tool to describe QCD matter The geometry of the source can be investigated General asymmetries can be built into a model Observables can be derived from the generalized model No mixing between 2 nd and 3 rd order asymmetries There is mixing between the spatial and velocity eld asymmetries It is important to explore these mixing based on a realistic model THANK YOU FOR YOUR ATTENTION! 13 / 15

14 Values of the parameters Name Value m 140 T a b -0.1 R 10 Z 15 H 10 H z 16 ɛ χ ɛ χ / 15

15 Eect of the parameter on the source 15 / 15