Multiparticle methods for measuring anisotropic flow!

Transcription

1 Multiparticle methods for measuring anisotropic flow From large to small systems Nicolas BORGHINI Universität Bielefeld

2 Preamble: Anisotropic (collective) flow Classical picture (before ca.2010) in collisions of large systems: Initially asymmetric collision zone (in the transverse plane) t < 0 t = 0 t = 0 + anisotropic emission of particles E dn d 3 p dn p T dp T dy [1 + 2v 1 cos( R) + 2v 2 cos 2( R) + ] pictures shamelessly stolen from Matt Luzum N.Borghini 1/32

3 Preamble: Anisotropic (collective) flow Newer picture (since 2010) in collisions of large systems: Initially asymmetric collision zone (in the transverse plane) anisotropic emission of particles = = dn d 3 / dn E N N p p T dpp T dyy 1 apple 1+2 1X n=1 2 v n cos n(' ' n) v n n 3 pictures shamelessly stolen from Matt Luzum N.Borghini 2/32

4 Preamble: Anisotropic (collective) flow dn d 3 / dn E N N p p T dpp T dyy apple 1+2 1X n=1 v n cos n(' ' n) v n n v n : Fourier coefficients of the single-particle distribution; Ψ n : n-th harmonic event plane even at (mathematically) fixed impact parameter, v n & Ψ n vary from event to event initial conditions & system evolution v n hcos n(' ' n)i v n n Goal: measure the v n coefficients (in a second step: as a function of p T, y) N.Borghini 3/32

5 Multiparticle methods for measuring anisotropic flow From large to small systems Cumulants, Lee Yang zeroes: a reminder old motivations & applications newer uses Application to smaller(?) systems overview of results caveats from the theory side N.Borghini 4/32

6 Multiparticle methods for measuring anisotropic flow From large to small systems Cumulants, Lee Yang zeroes: a reminder old motivations & applications newer uses Application to smaller(?) systems overview of results caveats from the theory side N.Borghini 4/32

7 Measuring anisotropic flow with (multiparticle) cumulants Principle: 1 Using the measured azimuths of the emitted particles, build appropriate correlators For instance, e in(' +' ) e in(' ' ) j ' k ' i ' j ' k ' l brackets? to be discussed later 2 Equate with the (theoretical) value of these correlators for events with anisotropic flow only yields flow estimate(s) e in(' ' j ' k ' k ) For instance = (v n ) 2 if only flow in the system v n {2} N.Borghini 5/32

8 Measuring anisotropic flow with (multiparticle) cumulants Principle: 1 Using the measured azimuths of the emitted particles, build appropriate correlators For instance, e in(' +' ' ) e in(' ' ) j ' k ' i j ' k ' l If only flow was present, all correlators would be equal. Due to the presence of additional sources of interparticle correlations ( nonflow ) in the system, some correlators are more equal than the others. Cumulants, in which the impact of the other sources is minimized e.g. e in(' ' i+' ' ) e in(' ) e in(' ) e in(' ) e in(' ) i j ' k ' l ' i ' k ' j ' ' i ' j ' c l ' l k n {4} N.Borghini 6/32

9 Measuring anisotropic flow with (multiparticle) cumulants Principle: 1 Using the measured azimuths of the emitted particles, build appropriate correlators For instance, e in(' +' ' ) e in(' ' ) j ' k ' i j ' k ' l If only flow was present, all correlators would be equal. Due to the presence of additional sources of interparticle correlations ( nonflow ) in the system, some correlators are more equal than the others. Cumulants, in which the impact of the other sources is minimized e.g. e in(' ' i+' ' ) e in(' ) e in(' ) e in(' ) e in(' ) i j ' k ' l ' i ' k ' j ' ' i ' j ' c l ' l k n {4} N.Borghini 6/32

10 Measuring anisotropic flow with (multiparticle) cumulants Principle: 1 Using the measured azimuths of the emitted particles, build appropriate correlators multiplicity M Old motivation of cumulants: minimize the bias from nonflow. N.B., P.M.Dinh, J.-Y.Ollitrault, PRC 63 (2001) , 64 (2001) N.Borghini 7/32

11 Measuring anisotropic flow with (multiparticle) cumulants Principle: Nonflow effects? 1 Using Quantum-statistics the measured azimuths effects of the emitted particles, build appropriate Resonance correlators decays multiplicity M k-particle correlator Old motivation Momentum of conservation cumulants: minimize the generally bias from scales nonflow. as (Mini)jets 1 N.B., P.M.Dinh, J.-Y.Ollitrault, PRC 63 (2001) , O 64 (2001) Strong & Coulomb interaction... M k 1 N.Borghini 7/32

12 Measuring anisotropic flow with (multiparticle) cumulants Principle: 1 Using the measured azimuths of the emitted particles, build appropriate correlators multiplicity M Old motivation of cumulants: minimize the bias from nonflow. N.B., P.M.Dinh, J.-Y.Ollitrault, PRC 63 (2001) , 64 (2001) Equate with the theoretical value of the cumulants for events with anisotropic flow only: c n {2} = (v n ) 2, c n {4} = -(v n ) 4, c n {6} = 4(v n ) 6, c n {8} = -33(v n ) 8 yields flow estimate v n {k} if c n {k} O 1 M k 1 N.Borghini 7/32

13 Measuring anisotropic flow with (multiparticle) cumulants Principle: 1 Using the measured azimuths of the emitted particles, build appropriate correlators multiplicity M Old motivation of cumulants: minimize the bias from nonflow. N.B., P.M.Dinh, J.-Y.Ollitrault, PRC 63 (2001) , 64 (2001) Equate with the theoretical value of the cumulants for events with anisotropic flow only: c n {2} = (v n ) 2, c n {4} = -(v n ) 4, c n {6} = 4(v n ) 6, c n {8} = -33(v n ) 8 yields flow estimate v n {k} if v n 1 O M 1 1/k N.Borghini 7/32

14 Measuring anisotropic flow with (multiparticle) cumulants Old motivation of cumulants: minimize the bias from nonflow. N.B., P.M.Dinh, J.-Y.Ollitrault, PRC 63 (2001) , 64 (2001) yields flow estimate v n {k} if v n (AGS), SPS, early-rhic era 1 O M 1 1/k and concern N.Borghini 8/32

15 Measuring anisotropic flow with Lee Yang zeroes Principle of the method: 1 Using the measured azimuths of the emitted particles, build a generating function G n (z) (which generates multiparticle averages) 2 Look for the position of the first zero of G n (z) (in practice, the first minimum of its modulus) z 0 3 Under the assumption of events with anisotropic flow only, deduce from z 0 an estimate of v n : v n { } j 01 Mz 0 j 01 = R.S.Bhalerao, N.B., J.-Y.Ollitrault, NPA 727 (2003) 373 Collectivity in Small Colliding Systems, BNL, March 4-6, 2015 N.Borghini 9/32 z 0

16 Measuring anisotropic flow with Lee Yang zeroes Lee Yang zeroes shared the same original motivation as cumulants: minimize the bias from nonflow. yields flow estimate v n { } if v n 1 O M From a theorist s point of view, LYZ-method is more aesthetic, since it directly measures many-body collectivity in the system under study. (The position of the first zero controls the asymptotic behavior of cumulants) N.Borghini 10/32

17 Measuring anisotropic flow with multiparticle methods Let us discuss a few assumptions & points which I left aside till now. The meaning of angular brackets? represent an average On the experimental side, over many (all) detected particles in an event (M), then over many events (N ev ) Both M and N ev are finite, there will be statistical fluctuations nightmarish appendices / sections in PRC 63 (2001) , PRC 64 (2001) , & NPA 727 (2003) 373 were much talked about in ( limitation of the methods ) yet have gone missing since then thanks to large M and N ev. N.Borghini 11/32

18 Measuring anisotropic flow with multiparticle methods Average over M detected particles in N ev events define the resolution parameter p v n M for large χ 1, life is easy, the statistical fluctuations decrease like 1/ p MNM N ev both on the v n {k} and on v n { } corresponds to the regime at LHC & high RHIC energies in collisions of large systems (measured with reasonable detectors ) when χ < 1, things become more involved N.Borghini 12/32

19 Measuring anisotropic flow with multiparticle methods Average over M detected particles in N ev events define the resolution parameter p v n M for large χ 1, life is easy, the statistical fluctuations decrease like 1/ p MNM N ev both on the v n {k} and on v n { } corresponds to the regime at LHC & high RHIC energies in collisions of large systems (measured with reasonable detectors ) when χ < 1, things become more involved N.Borghini 12/32

20 Measuring anisotropic flow with multiparticle methods Let us discuss a few assumptions & points which I left aside till now. The meaning of angular brackets? represent an average On the experimental side, over many (all) detected particles in an event, then over many events On the theoretical side as hidden in the relations between flow and the cumulants or the position of the first zero: first over the particles in an event, with an azimuthal distribution modulated by v n (); then over events, assuming an isotropic distribution of Ψ n and a constant v n. N.Borghini 13/32

21 Measuring anisotropic flow with multiparticle methods Let us discuss a few assumptions & points which I left aside till now. The meaning of angular brackets? represent an average On the experimental side, over many (all) detected particles in an event, then over many events On the theoretical side as hidden in the relations between flow and the cumulants or the position of the first zero: first over the particles in an event, with an azimuthal distribution modulated by v n (); then over events, assuming an isotropic distribution of Ψ n and a constant v n. can be corrected for if it only reflects the detector properties N.Borghini 13/32

22 Measuring anisotropic flow with multiparticle methods Let us discuss a few assumptions & points which I left aside till now. The meaning of angular brackets? represent an average On the experimental side, over many (all) detected particles in an event, then over many events On the theoretical side as hidden in the relations between flow and the cumulants or the position of the first zero: first over the particles in an event, with an azimuthal distribution modulated by v n (); then over events, assuming an isotropic distribution of Ψ n and a constant v n. is it so obvious when there is physics at play? ( engineered events) N.Borghini 13/32

23 Measuring anisotropic flow with multiparticle methods Let us discuss a few assumptions & points which I left aside till now. The meaning of angular brackets? represent an average On the experimental side, over many (all) detected particles in an event, then over many events On the theoretical side as hidden in the relations between flow and the cumulants or the position of the first zero: first over the particles in an event, with an azimuthal distribution modulated by v n (); then over events, assuming an isotropic distribution of Ψ n and a constant v n. too idealistic N.Borghini 13/32

24 Multiparticle methods for measuring anisotropic flow From large to small systems Cumulants, Lee Yang zeroes: a reminder old motivations & applications newer uses Application to smaller(?) systems overview of results caveats from the theory side N.Borghini 14/32

25 Anisotropic flow fluctuations in an experimental centrality bin are unavoidable; and physical Introduce a probability distribution p(v n ) at fixed Ψ n. to first approximation, mean value v n and standard deviation δv n. if δv n v n then v n {2} = v n + δv n, v n {4} = v n {6} = v n {8} = v n - δv n use cumulants to estimate v n and δv n. if δv n v n then the above identities no longer hold argue that differences between higher-order cumulant estimates v n {4}, v n {6}, v n {8} reflect non-gaussianities of p(v n ). more in Jiangyong s talk N.Borghini 15/32

26 Multiparticle methods for measuring anisotropic flow From large to small systems Cumulants, Lee Yang zeroes: a reminder old motivations & applications newer uses minimize nonflow statistics not an issue (2002-1?) reconstruct flow fluctuations Application to smaller(?) systems overview of results caveats from the theory side N.Borghini 16/32

27 Multiparticle methods for measuring anisotropic flow From large to small systems Cumulants, Lee Yang zeroes: a reminder old motivations & applications newer uses Application to smaller(?) systems overview of results caveats from the theory side N.Borghini 17/32

28 Multiparticle measurements of anisotropic flow in small systems ATLAS Coll., Phys. Lett. B 725 (2013) 60 N.Borghini 18/32

29 Multiparticle measurements of anisotropic flow in small systems ALICE Coll., Phys. Rev. C 90 (2014) N.Borghini 19/32

30 Multiparticle measurements of anisotropic flow in small systems ALICE Coll., Phys. Rev. C 90 (2014) N.Borghini 20/32

31 Multiparticle measurements of anisotropic flow in small systems CMS Coll., arxiv:1502:05382 N.Borghini 21/32

32 Multiparticle measurements of anisotropic flow in small systems CMS Coll., arxiv:1502:05382 N.Borghini 22/32

33 Multiparticle measurements of anisotropic flow in small systems CMS, arxiv:1502:05382 N.Borghini 23/32

34 Multiparticle methods for measuring anisotropic flow From large to small systems Cumulants, Lee Yang zeroes: a reminder old motivations & applications newer uses Application to smaller(?) systems overview of results caveats from the theory side N.Borghini 24/32

35 Measuring anisotropic flow with multiparticle methods Average over M detected particles in N ev events define the resolution parameter p v n M for large χ 1, life is easy, the statistical fluctuations decrease like 1/ p MNM N ev both on the v n {k} and on v n { } corresponds to the regime at LHC & high RHIC energies in collisions of large systems (measured with reasonable detectors ) when χ < 1, things become more involved what does this mean for small systems? N.Borghini 25/32

36 Multiparticle methods for measuring anisotropic flow in small systems Average over M detected particles in N ev events define the resolution parameter when χ < 1, things become more involved from NPA 727 (2003) 373 (page 411 ) p v n M N.Borghini 26/32

37 Multiparticle methods for measuring anisotropic flow in small systems Average over M detected particles in N ev events define the resolution parameter p v n M when χ < 1, things become more involved: at small χ: - Gaussian errors on the cumulants c n {2k}, with width measurement of v n becomes more difficult; 1 p M 2k N ev may spoil the attempts to pinpoint p(v n ) (= the physical fluctuations of the measured signal). N.Borghini 27/32

38 Multiparticle methods for measuring anisotropic flow in small systems Average over M detected particles in N ev events define the resolution parameter p v n M when χ < 1, things become more involved: at small χ: - Gaussian errors on the cumulants c n {2k}, with width measurement of v n becomes more difficult; 1 p M 2k N ev may spoil the attempts to pinpoint p(v n ) (= the physical fluctuations of the measured signal). N.Borghini 27/32

39 Multiparticle methods for measuring anisotropic flow in small systems Average over M detected particles in N ev events define the resolution parameter p v n M when χ < 1, things become more involved: at small χ: - Gaussian errors on the cumulants c n {2k}, with width - error on v n { } grows exponentially 1 p M 2k N ev N.Borghini 27/32

40 Multiparticle methods for measuring anisotropic flow in small systems from NPA 727 (2003) 373 (LYZ-method page 385) statistical fluctuations (finite N ev ) of the generating function N.Borghini 28/32

41 Multiparticle methods for measuring anisotropic flow in small systems p Simulations (N ev = yet slow ln N Nev -dependence, M = 300) without flow, analyzed with Lee Yang zeroes 0.04 from NPA 727 (2003) = j 01 p 2lnNev N ev V 2 { } V 2 { } V spurious 0 0 /8 /4 3 /8 /2 N.Borghini 29/32

42 Multiparticle methods for measuring anisotropic flow in small systems p Simulations (N ev = yet slow ln N Nev -dependence, M = 300) without flow, analyzed with Lee Yang zeroes 0.04 from NPA 727 (2003) = j 01 p 2lnNev N ev V 2 { } V 2 { } jumps in the reconstructed flow estimates LY-zeroes V spurious 0 0 /8 /4 3 /8 /2 N.Borghini 29/32

43 Multiparticle methods for measuring anisotropic flow in small systems p Simulations (N ev = yet slow ln N Nev -dependence, M = 300) without flow, analyzed with Lee Yang zeroes 0.04 from NPA 727 (2003) = j 01 p 2lnNev N ev V 2 { } V 2 { } V spurious jumps in the reconstructed flow estimates LY-zeroes ugly-looking (not v n -driven) generating functions 0 0 /8 /4 3 /8 /2 N.Borghini 29/32

44 Multiparticle measurements of anisotropic flow in small Are you sure of your error bars? remember N.Borghini 30/32

45 Multiparticle measurements of anisotropic flow in small systems Do not ask cumulants / Lee Yang-zeroes to provide you with any meaningful onset of collectivity (unfortunately) remember N.Borghini 30/32

46 Multiparticle methods for measuring anisotropic flow From large to small systems Cumulants, Lee Yang zeroes: a reminder old motivations & applications newer uses minimize nonflow statistics not an issue (2002-?) reconstruct flow fluctuations Application to smaller(?) systems overview of results caveats from the theory side minimize nonflow statistics will strike back N.Borghini 31/32

47 Multiparticle methods for measuring anisotropic flow From large to small systems Event-plane method: born 1984, refinements in 1993, 1997; many successful applications criticized (nonflow) in , when applied to small v n Cumulants (resp. Lee Yang zeroes): born 2000 (resp. 2003); many successful applications now 15 (resp. 12) year old Beware of limitations in small systems N.Borghini 32/32