Throwing triangles against the wall:

Transcription

1 Throwing triangles against the wall: ultrarelativistic heavy-ion collisions detecting shape of light nuclei Wojciech Broniowski Institute of Nuclear Physics PAN, Cracow, and Jan Kochanowski U., Kielce University of Warsaw, 16 October C 3 He [research with Enrique Ruiz Arriola, Piotr Bo»ek, & Maciej Rybczy«ski] WB (IFJ PAN & UJK) Throwing triangles UW / 44

2 Instead of outline Details may be found in: 12 C: WB & E.Ruiz Arriola, PRL 112 (2014) (News and Commentary in Physics, An Untested Window into Nuclear Structure, 3 He: Piotr Bo»ek & WB, arxiv: 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 UW / 44

3 α clusters WB (IFJ PAN & UJK) Throwing triangles UW / 44

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 1931 before the discovery of the neutron in 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 UW / 44

5 Binding α very tightly bound WB (IFJ PAN & UJK) Throwing triangles UW / 44

6 Fragmentation Evidence from dissociation in nuclear track emulsions [Zarubin 2013 (BECQUEREL)] Example: dissociation of 7 Be (energy of a few A GeV) (neutrons not specied) channel 4 He+ 3 He 3 He+ 3 He 4 He+2p 4 He+d+p 3 He+2p 3 He+d+p 3 He+2d 3 He+t+p 3p+d 6 Li+p N % Numerous ongoing experiments (GANIL, Osaka,...) Was the cluster there or is it created at break-up? These studies cannot reveal the geometry (cluster arrangement) WB (IFJ PAN & UJK) Throwing triangles UW / 44

7 α clusters in light nuclei theoretical calculations ground Hoyle 0 + other excited, Be 12 C [Fynbo+Freer: Physics 4 (2011) 94] 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: SOTANCP3 Conference, Yokohama, May 2014] WB (IFJ PAN & UJK) Throwing triangles UW / 44

8 16 O Ab initio calculations of 16 O with chiral NN force strong α clusterization [Bochum-Jülich, PRL 112 (2014) ] ground state excited WB (IFJ PAN & UJK) Throwing triangles UW / 44

9 Computational techniques Funaki et al.: certain states in self-conjugated nuclei... can be described as product states of α particles, all in the lowest 0S state. We dene a state of condensed α particles in nuclei as a bosonic product state in good approximation, in which all bosons occupy the lowest quantum state of the corresponding bosonic mean-eld potential (αbec) Another approach: Fermionic Molecular Dynamics (FMD) Quantum Variational Monte Carlo (with 2- and 3-body forces) for A=2-12 [R. Wiringa et al., ] All approaches light nuclei have clusters Goal (not yet accurately reached): reproduce ground-state energy, excitation spectrum, EM form factor,... WB (IFJ PAN & UJK) Throwing triangles UW / 44

10 Flow WB (IFJ PAN & UJK) Throwing triangles UW / 44

11 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 UW / 44

12 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 UW / 44

13 Elliptic ow dn/dφ = A ( n v n cos[n(φ Ψ n )] ) [ALICE] WB (IFJ PAN & UJK) Throwing triangles UW / 44

14 Major observation in HIC signature of QGP [ALICE] WB (IFJ PAN & UJK) Throwing triangles UW / 44

15 Harmonic ow Wounded nucleons experienced at least one inelastic collision [Biaªas, Bªeszy«ski & Czy»] y x Initial reball is asymmetric in the transverse plane from 1) geometry 2) uctuations collectivity! ow generated Strong elliptic ow, triangular ow (in Au+Au entirely from uctuations), higher-order harmonic ow WB (IFJ PAN & UJK) Throwing triangles UW / 44

16 Merge the two ideas (α's and ow) WB (IFJ PAN & UJK) Throwing triangles UW / 44

17 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: 3 HeAu at RHIC [PHENIX proposal, 2013] The case of 12 C is more promising, as it leads to more abundant reballs WB (IFJ PAN & UJK) Throwing triangles UW / 44

18 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 UW / 44

19 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 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 UW / 44

20 ... more events y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles UW / 44

21 ... more events y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles UW / 44

22 ... more events y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles UW / 44

23 ... more events y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles UW / 44

24 ... more events y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles UW / 44

25 ... more events y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles UW / 44

26 ... more events y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles UW / 44

27 ... more events y [fm] x [fm] WB (IFJ PAN & UJK) Throwing triangles UW / 44

28 Eccentricity parameters (event-by-event) We need quantitative measures of deformation (heavily used in heavy-ion analyses) Eccentricity parameters ɛ n (Fourier analysis) ɛ n e inφn = dxdy ρ(x, y)ρ n e inφ dxdy ρ(x, y)ρ n n = 2 ellipticity, n = 3 triangularity,... Φ n angle of the principal axes ρ = x 2 + y 2, tanφ = y/x ρ(x, y) reball density Two components: intrinsic (from existent mean deformation of the reball) from uctuations WB (IFJ PAN & UJK) Throwing triangles UW / 44

29 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 UW / 44

30 Ellipticity and triangularity vs multiplicity σ( )/< 2 > 2 σ( ))/< 3 > 3 < 2 > < 3 > N w N w clustered unclustered Clusters: (qualitative signal!) When N w then ɛ 3 and ɛ 2 and σ(ɛ 3 )/ ɛ 3 = σ(v 3 )/ v 3, σ(ɛ 2 )/ ɛ 2 = σ(v 2 )/ v 2 No clusters: similar behavior for n = 2 and n = 3 WB (IFJ PAN & UJK) Throwing triangles UW / 44

31 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 3 Ε clustered unclustered [wounded nucleon model + Bo»ek's 3+1 viscous hydro (η/s = 0.08, τ 0 = 0.6 fm) + THERMINATOR (T f = 150 MeV)] WB (IFJ PAN & UJK) Throwing triangles UW / 44

32 Hydro without hydro linear response to uctuations We have to a very good approximation v n = κ n ɛ n, n = 2, 3,... (κ n depends on mutiplicity and hydro details) Equality of scale-independent ratios, e.g., σ(ɛ n )/ ɛ n = σ(v n )/ v n 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 UW / 44

33 Ratios of cumulant moments v n {4}/v n {2} (wounded) n=2, BEC n=3, BEC n=2, VMC n=3, VMC 1% 0.1% % N w WB (IFJ PAN & UJK) Throwing triangles UW / 44

34 3 He-Au WB (IFJ PAN & UJK) Throwing triangles UW / 44

35 3 He-Au (being presently analyzed by PHENIX) [hydro: J. Nagle et al., arxiv: ] [hydro without hydro: Bo»ek & WB, arxiv: ] Sampling from ab initio MC Green's function method [Carlsson & Schiavilla 1998] {m} n % {2} {4} 3 {2} 1% 0.1% 3 {4} N w WB (IFJ PAN & UJK) Throwing triangles UW / 44

36 3 He-Au (being presently analyzed by PHENIX) [hydro: J. Nagle et al., arxiv: ] [hydro without hydro: Bo»ek & WB, arxiv: ] Sampling from ab initio MC Green's function method [Carlsson & Schiavilla 1998] {m} n % {2} {4} 3 {2} 1% 0.1% 3 {4} N w (Not equilateral! Sidewise: ɛ 2 1, ɛ 3 3/5) WB (IFJ PAN & UJK) Throwing triangles UW / 44

37 Ratio for 3 He-Au v n {4}/v n {2} v 2 {4}/v 2 {2}, wounded v 3 {4}/v {2}, wounded 3 10% 1% v 2 {4}/v 2 {2}, mixed+gamma v 3 {4}/v {2}, mixed+gamma 3 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 UW / 44

38 p, d, 3 He {2} n {2} He-Au 3 {2} He-Au 2 {2} d-au 3 {2} d-au 2 {2} p-au 3 {2} p-au N w WB (IFJ PAN & UJK) Throwing triangles UW / 44

39 Conclusions WB (IFJ PAN & UJK) Throwing triangles UW / 44

40 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 event-by-event scaled standard deviation or ratios of cumulant moments Eect persists in forward and backward rapidities 12 C lead to larger/more collective reball than 3 He Extensions: 7,9 Be, 16 O Experiments needed! Data (RHIC, NA61@SPS) will allow to place constrains on the spatially deformed structure of the light projectiles and/or verify the reball formation models WB (IFJ PAN & UJK) Throwing triangles UW / 44

41 Back-up WB (IFJ PAN & UJK) Throwing triangles UW / 44

42 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 UW / 44

43 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 UW / 44

44 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 UW / 44

45 Dependence on the collision energy σ( ))/< 3 > 3 < 2 > < 3 > 0.25 inel σ NN =32mb, a=0.145 N w inel =42mb, a=0.145 σ NN σ( ))/< 3 > 3 < 2 > < 3 > 0.25 N w inel =73mb, a=0.12 σ NN σ( ))/< 3 > 3 < 2 > < 3 > 0.2 N w σnn inel =32mb (SPS) 42mb (RHIC) 72mb (LHC) Qualitative conclusions hold from SPS to the LHC WB (IFJ PAN & UJK) Throwing triangles UW / 44

46 Other systems (distributions matched to Wiringa's et al. radial densities) Be-Pb, SPS < 2 > < 3 > < 4 > 0.25 N w Be-Pb, SPS < 2 > < 3 > < 4 > 0.25 N w C-Au, RHIC < 2 > < 3 > < 4 > 0.22 N w O-Pb, tet., SPS < 2 > < 3 > < 4 > 0.22 N w O-Pb, sq., SPS < 2 > < 3 > < 4 > 0.22 N w [work with Maciej Rybczy«ski] WB (IFJ PAN & UJK) Throwing triangles UW / 44