Throwing triangles against a wall

Transcription

1 Throwing triangles against a wall Wojciech Broniowski Institute of Nuclear Physics PAN, Cracow, and Jan Kochanowski U., Kielce Rencontres QGP-France 2014, September 2014, Etrétat 12 C He [research with Enrique Ruiz Arriola, Piotr Bo»ek, Maciej Rybczy«ski] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

2 Instead of outline Two phenomena are related: α clustering in light nuclei harmonic ow in ultra-relativistic nuclear collisions Surprising link: lowest-energy ground-state structure highest energy reactions New method of investigating many-particle nuclear correlations Another test of collective dynamics/harmonic ow WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

3 α clusters WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP 2014 / 40

4 Some history David Brink: After Gamow's theory of α-decay it was natural to investigate a model in which nuclei are composed of α-particles. Gamow developed a rather detailed theory of properties in his book "Constitution of Nuclei" published in 191 before the discovery of the neutron in 192. He supposed that 4n-nuclei like 8 Be, 12 C, 16 O... were composed of α-particles Generated by CamScanner from intsig.com Generated by CamScanner from intsig.com WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

5 α clusters in light nuclei ground Hoyle 0 + other excited, Be 12 C How can we detect the α clusters in the ground state? What is their spatial arrangement? Assessment of n-body correlations (one-body not enough) [Recent status: SOTANCP Conference, Yokohama, May 2014] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

6 Flow WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

7 Ultra-relativistic A+A collisions (LHC, RHIC, SPS) Lorentz contraction Collision: essentially instantaneous passage, frozen conguration Reduction of the ground-state wave function of the nucleus (like measurement) Development: detection of particles in the transverse direction WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

8 Phenomenon of ow Quark-gluon plasma is formed! Initial shape nal ow transmutation detectable in the asymmetry of the momentum distribution of detected particles follows from collectivity WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

9 Merge the two ideas (α's and ow) [WB & ERA, PRL 112 (2014) ] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

10 From α clusters to ow in relativistic collisions α clusters asymmetry of shape asymmetry of initial reball hydro or transport collective harmonic ow nuclear triangular geometry reball triangular geometry triangular ow Generated by CamScanner from intsig.com What are the signatures, chances of detection? (some blurring by uctuations) Easy snap-shot but dicult development Described later: HeAu at RHIC [PHENIX proposal, 201] The case of 12 C is more promising, as it leads to more abundant reballs WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

11 Our making 12 C Three α's in a triangular arrangement, generate nucleon positions with Monte Carlo, parameters (size of the cluster, distance between clusters) properly adjusted (t one-body radial distributions from other calculations, t EM form factor) WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

12 12 C- 208 Pb single event Why ultra-relativistic? Reaction time is much shorter than time scales of the structure a frozen snapshot of the nuclear conguration 5 4 y [fm] x [fm] wounding range determined by σ inel NN Here N w > 70 - at-on orientation (for the moment) Imprints of the three α clusters clearly visible Simulations with GLISSANDO 2 WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

13 ... more events 5 4 y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

14 ... more events 5 4 y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

15 ... more events 5 4 y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

16 ... more events 5 4 y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

17 ... more events 5 4 y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

18 ... more events 5 4 y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

19 ... more events 5 4 y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

20 ... more events 5 4 y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

21 Geometry of nucleus geometry of reball Triangular nucleus causes triangular damage! 4 2 y [fm] x [fm] y [fm] x [fm] intrinsic density of 12 C geometry of the reball (at-on collision) WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

22 Eccentricity parameters (event-by-event) (yesterday's talk by J.-Y. Ollitrault) We need quantitative measures of deformation Eccentricity parameters ɛ n (Fourier analysis) j ρn j einφ j ɛ n = j ρn j describe the shape of each event (j labels the sources in the event, n=rank) n = 2 ellipticity, n = triangularity,... Two components: intrinsic (from existent mean deformation of the reball) from uctuations (Gaussian smearing of sources, σ = 0.4 fm) WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

23 Geometry vs multiplicity correlations in 12 C-Pb Two extreme cases of angular orientation cluster plane parallel or perpendicular to the transverse plane: at-on higher multiplicity higher triangularity lower ellipticity sidewise lower multiplicity lower triangularity higher ellipticity WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

24 Ellipticity and triangularity vs multiplicity σ( )/< 2 > 2 σ( ))/< > < 2 > < > N w N w clustered unclustered Clusters: (qualitative signal!) When N w then ɛ and ɛ 2 and σ(ɛ )/ɛ, σ(ɛ 2 )/ɛ 2 No clusters: similar behavior for n = 2 and n = WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

25 Shape-ow transmutation The eccentricity parameters are transformed (in all models based on collective dynamics) into asymmetry of the transverse-momentum ow. Linear response: v n ɛ n, response grows with multiplicity v n Ε n v 2 Ε 2 v Ε 0.05 clustered unclustered [wounded nucleon model + Bo»ek's +1 viscous hydro (η/s = 0.08, τ 0 = 0.6 fm) + THERMINATOR (T f = 150 MeV)] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

26 Hydro without hydro (recall yesterday's talk by J.-Y. Ollitrault) We have to a very good approximation v n = κ n ɛ n, n = 2,,... (κ n depends on mutiplicity and hydro details) Cumulant moments: ɛ n {2} 2 = ɛ 2 n, ɛ n {4} 4 = 2 ɛ 2 n ɛ 4 n Ratio's insensitive to response: v n {m} v n {2} = ɛ n{m}, m = 4, 6,... ɛ n {2} (infer info on ow from just the eccentricities, no hydro!) Fluctuations only: ratio drops with N w ( N 1/m 1/2 w ) Geometry: ratio tends to 1 from below as N w WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

27 Cumulant moments wounded nucleon model < 2 2 > (BEC) < 2 > (BEC) < 2 2 > (uniform) < 2 > (uniform) 10% 1% 0.1% N w WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

28 Ratios of cumulant moments v n {4}/v n {2} (wounded) n=2, BEC n=, BEC n=2, VMC n=, VMC 1% 0.1% % N w WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

29 Double ratio of cumulant moments (v {4}/v {2})/(v {4}/v 2 {2}) BEC, wounded BEC, mixed+gamma VMC, wounded uniform 10% 2 1% 0.1% N w Test the wave function and the early production model WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

30 He-Au PB & WB, arxiv: WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

31 He-Au (being presently analyzed by PHENIX) [hydro: J. Nagle et al., arxiv: ] [hydro without hydro: Piotr Bo»ek and WB, arxiv: ] Sampling from ab initio MC Green's function method [Carlsson & Schiavilla 1998] {m} n % {2} {4} {2} 1% 0.1% {4} N w WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

32 He-Au (being presently analyzed by PHENIX) [hydro: J. Nagle et al., arxiv: ] [hydro without hydro: Piotr Bo»ek and WB, arxiv: ] Sampling from ab initio MC Green's function method [Carlsson & Schiavilla 1998] {m} n % {2} {4} {2} 1% 0.1% {4} N w (Not equilateral! Sidewise: ɛ 2 1, ɛ /5) WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

33 Ratio for He-Au v n {4}/v n {2} v 2 {4}/v 2 {2}, wounded v {4}/v {2}, wounded 10% 1% v 2 {4}/v 2 {2}, mixed+gamma v {4}/v {2}, mixed+gamma 0.1% N w Large-N w behavior exhibits both geometric triangularity and ellipticity! (to be conrmed by the experiment!) WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

34 p, d, He {2} n {2} He-Au {2} He-Au 2 {2} d-au {2} d-au 2 {2} p-au {2} p-au N w WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP 2014 / 40

35 Conclusions WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

36 Nuclear structure from ultra-relativistic heavy ion collisions Snapshots of the ground-state wave function Spatial correlations in the ground state geometric harmonic ow Signatures in clustered 12 C- 208 Pb collisions Increase of triangularity with multiplicity for the highest multiplicity events Anticorrelation of ellipticity and triangularity Very clear signals from ratios of cumulant moments Stronger eect at lower σ inel NN (i.e., at lower collision energies) Even stronger eect on the 12 C side in rapidity 12 C lead to larger/more collective reball than He Ratios depend on the nuclear wave function and the initial-state model, but not on hydro Extensions: 7,9 Be, 16 O Data (RHIC, NA61@SPS) would allow to place constrains on the spatial structure of the light projectiles and verify the reball formation models WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

37 Back-up WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

38 Intrinsic distributions Ground state of 12 C is a 0 + state (rotationally symmetric wave function). The meaning of deformation concerns multiparticle correlations between the nucleons Superposition over orientations: Ψ 0 +(x 1,..., x N ) = 1 4π dωψ intr (x 1,..., x N ; Ω) The intrinsic density of sources of rank n is dened as the average over events, where the distributions in each event have aligned principal axes: fn intr ( x) = f(r( Φ n ) x). Brackets indicate averaging over events and R( Φ n ) is the inverse rotation by the principal-axis angle in each event WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

39 Digression: d-a by Bo»ek The deuteron has an intrinsic dumbbell shape with very large deformation: rms 2 fm Initial entropy density in a d-pb collision with N part = 24 [Bo»ek 2012] y fm x fm WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

40 Digression: d-a by Bo»ek The deuteron has an intrinsic dumbbell shape with very large deformation: rms 2 fm Initial entropy density in a d-pb collision with N part = 24 [Bo»ek 2012] y fm x fm v PHENIX, 200 GeV, d+au, 0-5%, η [0.48,0.7] ATLAS, 5.02 TeV, p+pb, 0-2%, η [2,5] hydro., d+au s NN =200 GeV Bozek, priv. comm., 0.05 Bzdak, et al , priv comm: η/s = 0.08, IP-Glasma, N = 20 part η/s = 0.08, MC-Glauber, N = part ± p h (GeV/c) T Resulting large elliptic ow conrmed with the later RHIC analysis WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

41 Dependence on the collision energy σ( ))/< > < 2 > < > 0.25 inel σ NN =2mb, a=0.145 N w inel =42mb, a=0.145 σ NN σ( ))/< > < 2 > < > 0.25 N w inel =7mb, a=0.12 σ NN σ( ))/< > < 2 > < > 0.2 N w σnn inel =2mb (SPS) 42mb (RHIC) 72mb (LHC) Qualitative conclusions hold from SPS to the LHC WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40

42 Other systems (distributions matched to Wiringa's et al. radial densities) Be-Pb, SPS < 2 > < > < 4 > 0.25 N w Be-Pb, SPS < 2 > < > < 4 > 0.25 N w C-Au, RHIC < 2 > < > < 4 > 0.22 N w O-Pb, tet., SPS < 2 > < > < 4 > 0.22 N w O-Pb, sq., SPS < 2 > < > < 4 > 0.22 N w [work with Maciej Rybczy«ski] WB (IFJ PAN & UJK) Throwing triangles Rencontres QGP / 40