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Initial state fluctuations from SPS to LHC J. Milo evi University - - PowerPoint PPT Presentation

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Initial state fluctuations from SPS to LHC J. Milo evi University of Belgrade and Vin a Institute of Nuclear Sciences, Belgrade, Serbia 08.08.2016 Reimei 2016, Tokai, Japan 1 Outline v Azimuthal anisotropy conventional

slide-1
SLIDE 1
  • J. Milošević

University of Belgrade and Vinča Institute of Nuclear Sciences, Belgrade, Serbia

08.08.2016 Reimei 2016, Tokai, Japan 1

Initial state fluctuations from SPS to LHC

slide-2
SLIDE 2

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 2 ¡

Outline

v Azimuthal anisotropy

² conventional methods ² Initial-state fluctuations (ISF) and higher order Fourier harmonics

v Triangular flow at SPS, RHIC and LHC energies v Collectivity over a wide pT range in PbPb collisions v Collectivity in small pPb and smallest pp collision systems

² ISF on sub-nucleonic level

v Factorization breaking – mechanism – pT dependent event plane – η dependent event plane v Principal Component Analysis (PCA) – method v PCA method in flow physics – leading and sub-leading flow modes v The PCA analysis in pPb and PbPb collisions at the LHC energy v Conclusions

slide-3
SLIDE 3

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 3 ¡

px p

y

x y z

  • Anisotropy harmonics vn – conventional methods

vn = cosn(φ−Ψn)

event plane x-z

Ideal circle-like geometry – v2

Event Plane (EP) method two-particle correlation method

η Δ

  • 4
  • 2

2 4 φ Δ 2 4

φ Δ d η Δ d

pair

N

2

d

trig

N 1

1.6 1.7 1.8

110 ≥

trk

  • ffline

= 5.02 TeV, N

NN

s CMS pPb < 3 GeV/c

T

1 < p (b)

1<pT<3 GeV/c pPb 5.02 TeV

0-3% centrality N>110

PLB 718 (2013) 795

ridge Collective behavior?

cos(nΔφ)

four-particle cumulant method

Advantage wrt 2-part.corr.: removes two- and three- particle non- flow correlation

u vn from even higher order cumulants: vn{6}, vn{8}, ….

Lee-Yang zero method

correlates all particles of interest

Scalar Product (SP) method

|Δη| > 3

slide-4
SLIDE 4

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 4 ¡

Role of initial state fluctuations (ISF) on anisotropy

p

Pb Ψ6 Ψ4 Ψ5 Ψ3 Ψ2 Anisotropy harmonics with order higher than 2 v2, v3, v4, v5 and v6 using multiple methods Ultra-central collisions Asymmetric (pPb) high-

  • multiplicity collisions

Phys.Rev. ¡C89 ¡(2014) ¡044906 (arXiv:1310.8651) JHEP ¡1402 ¡(2014) ¡088 (arXiv:1312.1845) Phys.Le8. ¡B724 ¡(2013) ¡213 (arXiv:1305.0609)

Simple, circle-like geometry does not describe the formed system precisely enough

geometry – v2 ISF – v3

slide-5
SLIDE 5

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 5 ¡

Triangular flow – one of higher order Fourier harmonics

  • B. ¡Alver ¡and ¡G. ¡Roland ¡

PRC ¡81(2010) ¡054905 The triangular initial shape è triangular hydrodynamic flow

slide-6
SLIDE 6

track

N

80 100 120 140 160 180 200 220 240

〉 )]

3 (b)

Ψ

  • 3

(a)

Ψ cos[3( 〈 2 1/

2 4 6 8 10 12

=17.3 A GeV

≈30M PbAu collisions collected during 2000 data taking period

σ/σgeo=<5.5%>

Reimei ¡2016, ¡Tokai, ¡Japan ¡ 6 ¡

Triangular flow in PbAu at the top SPS energy

(GeV/c)

T

p

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

)

T

(p

3

v

0.01 0.02 0.03 0.04 0.05

= 5.5% 〉

geo

σ / σ 〈

not corrected for HBT correlations

  • π

corrected for HBT correlations

  • π

0.21 < η < 0.86 in center-of-mass system

accepted ¡to ¡Nucl.Phys.A

beam UV detector 2 UV detector 1 W-shield target SDD1/SDD2 RICH 1 mirror 1 RICH 2 mirror 2 8

  • 15
  • TPC drift volume

TPC read-out chamber TPC coils

  • 1

1 2 3 4 5m 1/r E-field HV cathode voltage divider

Ψ3 = 1 3arctan wi(pTi)sin(3φi)

i=1 Ntrack

∑

wi(pTi)cos(3φi)

i=1 Ntrack

∑

08.08.2016 ¡

sNN

EP ¡method ¡is ¡used

a ¡huge ¡HBT ¡effect ¡at ¡ ¡low-­‑pT

slide-7
SLIDE 7

(GeV/c)

T

p

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

)

T

(p

3

v

0.01 0.02 0.03 0.04 0.05 0.06 0.07

< 10.0%

geo

σ / σ ALICE 0 < < 10.0%

geo

σ / σ PHENIX 0 < = 5.5% 〉

geo

σ / σ 〈 CERES

±

= 2.76 TeV, h

NN

s ALICE PbPb

±

= 200 GeV, h

NN

s PHENIX AuAu

  • π

= 17.3 GeV,

NN

s CERES PbAu 08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 7 ¡

v3 vs pT – comparison to other experiments

v First pT dependent measurement of the triangular flow at the top SPS energy v Top RHIC and LHC energy gives very similar v3 magnitudes v The v3 at the top SPS energy is about half of those at top RHIC and LHC v Linear increase but with different slopes accepted ¡to ¡Nucl.Phys.A

² Note limited pT range restricted to the CERES acceptance ² ALICE uses large |Δη| gaps ² Jet yield is for more than one

  • rder of

magnitude smaller at SPS ² No option to include |Δη| gap at CERES

PHENIX

PRL 107 (2011) 252301

ALICE

PLB 719 (2013) 18

slide-8
SLIDE 8

(GeV)

NN

s

10

2

10

3

10

(200 GeV)

3

/v

3

v

0.6 0.7 0.8 0.9 1

±

= 2.76 TeV, h

NN

s ALICE PbPb

±

= 200 GeV, h

NN

s PHENIX AuAu

±

= 19.6 GeV, h

NN

s STAR AuAu

  • π

= 17.3 GeV,

NN

s CERES PbAu

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 8 ¡

Energy dependence

v RHIC 19.6 GeV is quite close to the top SPS energy of 17.3 GeV v Comparison is done at very similar centralities (<σ/σgeo> ≈ 5%) v A rather good agreement with an AMPT prediction for the ratio of about 0.6 at 19.6 GeV RHIC energy Accepted ¡to ¡Nucl.Phys.A

² As a referent level is taken v3 value at the top RHIC energy ² v3 values integrated over 0.3 < pT < 2.1 GeV/c !

a good agreement same v3 at the top RHIC and LHC

PHENIX

PRL 107 (2011) 252301

ALICE

PLB 719 (2013) 18

STAR

PRL 116 (2016) 112302

slide-9
SLIDE 9

(GeV/c)

T

p

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

)

T

(p

3

v

0.01 0.02 0.03 0.04 0.05

= 2.4% 〉

geo

σ / σ 〈 = 9.8% 〉

geo

σ / σ 〈

08.08.2016 ¡

(GeV/c)

T

p

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

)

T

(p

n

v

0.01 0.02 0.03 0.04 0.05

= 2.4% 〉

geo

σ / σ 〈

  • π

n = 2 n = 3

(GeV/c)

T

p

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.01 0.02 0.03 0.04 0.05

= 9.8% 〉

geo

σ / σ 〈

  • π

n = 2 n = 3

Reimei ¡2016, ¡Tokai, ¡Japan ¡ 9 ¡

v3 in comparison with v2

v Elliptic flow reflects the initial anisotropy and thus depends strongly on centrality v Triangular flow comes from the ISF and weakly depends on centrality v The different centrality behavior between v2 and v3 v For very central collisions (<σ/σgeo> = 2.4%), v3 becomes close to the v2 accepted ¡to ¡Nucl.Phys.A

² Triangular flow is dominant anisotropy for ultra-central collisions at the LHC energies

CMS

JHEP 1402 (2014) 088

slide-10
SLIDE 10

(GeV/c)

T

p

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

)

T

(p

3

v

0.01 0.02 0.03 0.04 0.05

= 5.5% 〉

geo

σ / σ 〈 ,

  • π

CERES < 7% σ , 0 <

  • π

hydro+UrQMD 08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 10 ¡

Comparision with hydro+UrQMD predictions

v Relativistic hydrodynamics + transport models (hybrid models)

² vHLLE viscous hydrosolver + UrQMD hadron cascade (I. Karpenko, P. Huovinen, H. Petersen

and M. Bleicher PRC 91 (2015) 064901)

v The model predictions for hadrons within 0.2 < pT <2.0 GeV/c and -1 < η < 1 v Cerentrality samples roughly correspond to the experimental ones accepted ¡to ¡Nucl.Phys.A

² Particlization at constant energy density 0.5 GeV fm3 ² Kinetic and chemical freeze-out are dynamical ² Model predictions in a very good agreement with the CERES results ² A small disagreement appears at low-pT

slide-11
SLIDE 11

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 11 ¡

Collectivity over a wide pT range in PbPb

slide-12
SLIDE 12

20 40 60 80

n

v

0.0 0.1 0.2

0 - 5% (GeV/c)

T

p

20 40 60 80

n

v

0.0 0.1 0.2

30 - 40%

20 40 60 80

0.0 0.1 0.2

5 - 10% (GeV/c)

T

p

20 40 60 80

0.0 0.1 0.2

40 - 50%

20 40 60 80

0.0 0.1 0.2

10 - 20% (GeV/c)

T

p

20 40 60 80

0.0 0.1 0.2

50 - 60%

20 40 60 80

0.0 0.1 0.2

20 - 30% (GeV/c)

T

p

20 40 60 80

0.0 0.1 0.2

= 5.02 TeV

NN

s PbPb CMS Preliminary

{SP}

2

v {SP}

3

v

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 12 ¡

vn{SP} over a wide pT range

v low-pT - hydrodynamic flow (v2 – geometry, v3 – ISF on nucleonic level) v v2 non-zero up to very high pT v high-pT - may reflect the path-length dependence of parton energy loss v v2 is complementary to RAA measurements v v3 mainly consistent with zero at high-pT

up to 100 GeV/c

CMS ¡PAS ¡HIN-­‑15-­‑014

slide-13
SLIDE 13

20 40 60 80

n

v

0.0 0.1 0.2

5 - 10%

= 5.02 TeV

NN

s PbPb CMS Preliminary

(GeV/c)

T

p

20 40 60 80

n

v

0.0 0.1 0.2

30 - 40%

20 40 60 80

0.0 0.1 0.2

10 - 20% (GeV/c)

T

p

20 40 60 80

0.0 0.1 0.2

40 - 50%

20 40 60 80

0.0 0.1 0.2

20 - 30% (GeV/c)

T

p

20 40 60 80

0.0 0.1 0.2

50 - 60% {SP}

2

v {4}

2

v {6}

2

v {8}

2

v

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 13 ¡

Collectivity over a wide pT range

v low-pT – ratio v2{2k}/v2{SP} ≈ 0.8 and v2{4} ≈ v2{6} ≈ v2{8} ç hydrodynamics v high-pT – SP and multi-particle correlation tend to converge to the same value v v2{4} ≈ v2{6} ≈ v2{8} ≠ 0 ç collectivity (likely to be related to jet quenching) CMS ¡PAS ¡HIN-­‑15-­‑014

slide-14
SLIDE 14

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 14 ¡

Comparison with lower energy and CUJET3

v A slight increase of v2 wrt results (EP method) from 2.76 TeV collision energy v CUJET3 predictions roughly compatible with the data at high-pT (over 40 GeV/c) v At lower pT, CUJET3 overpredicts the experimental v2 CMS ¡PAS ¡HIN-­‑15-­‑014

20 40 60 80

2

v

0.0 0.1 0.2

0 - 5% (GeV/c)

T

p

20 40 60 80

2

v

0.0 0.1 0.2

30 - 40%

20 40 60 80

0.0 0.1 0.2

5 - 10% (GeV/c)

T

p

20 40 60 80

0.0 0.1 0.2

40 - 50%

20 40 60 80

0.0 0.1 0.2

10 - 20% (GeV/c)

T

p

20 40 60 80

0.0 0.1 0.2

50 - 60%

20 40 60 80

0.0 0.1 0.2

20 - 30% (GeV/c)

T

p

20 40 60 80

0.0 0.1 0.2

= 5.02 TeV

NN

s PbPb CMS Preliminary 2.76 TeV {EP}

2

v {SP}

2

v CUJET3 5.02 TeV

slide-15
SLIDE 15

low 2

v

0.05 0.10 0.15

high 2

v

0.05 0.10

< 20 GeV/c

T

14 < p CMS Preliminary = 5.02 TeV

NN

s PbPb

low 2

v

0.05 0.10 0.15 0.05 0.10

< 26 GeV/c

T

20 < p

{SP}

2

v {4}

2

v

low 2

v

0.05 0.10 0.15 0.05 0.10

< 35 GeV/c

T

26 < p < 1.25 GeV/c

T

1.0 < p

low 2

v 08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 15 ¡

Collectivity over a wide pT and centrality range

v Correlation between low-pT v2 and high-pT v2 over a wide centrality range v Each point represents one centrality bin v Strong correlation may indicate that low-pT v2 and high-pT v2 may have the same

  • rigin

v Within uncertainties, slopes between v2{SP} and v2{2k} are compatible v Extrapolations compatible to 0 within uncertainties CMS ¡PAS ¡HIN-­‑15-­‑014

Soft and hard correlation

slide-16
SLIDE 16

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 16 ¡

Collectivity in small pPb and smallest pp systems?

p

Pb

slide-17
SLIDE 17

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ η Δ

  • 4
  • 2

2 4

φ Δ

2 4

φ Δ d η Δ d

pair

N

2

d

trig

N 1

3.1 3.2 3.3 3.4 N < 260 ≤ = 5.02 TeV, 220

NN

s CMS pPb < 3 GeV/c

trig T

1 < p < 3 GeV/c

assoc T

1 < p

17 ¡ η Δ

  • 4
  • 2

2 4

φ Δ

2 4

φ Δ d η Δ d

pair

N

2

d

trig

N 1

2.4 2.6 2.8 N < 260 ≤ = 2.76 TeV, 220

NN

s CMS PbPb < 3 GeV/c

trig T

1 < p < 3 GeV/c

assoc T

1 < p

The ridge seen in all colliding systems at LHC

v Does the ridge in pp and pPb collisions originate from hydrodynamics flow like in PbPb collisions or it is connected with color-glass condensate (CGC)

JHEP 09 (2010) 091 PLB 718 (2013) 795 PLB 724 (2013) 213

high-multiplicity high-multiplicity

slide-18
SLIDE 18

100 200 300

{2}

sub 2

v

0.05 0.10

= 5 TeV

NN

s pPb = 2.76 TeV

NN

s PbPb = 13 TeV s pp = 7 TeV s pp = 5 TeV s pp

Preliminary CMS < 3 GeV/c

T

0.3 < p | > 2 η Δ |

  • ffline

trk

N

100 200 300

{2}

sub 3

v

0.01 0.02 0.03

< 3 GeV/c

T

0.3 < p | > 2 η Δ |

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 18 ¡

v2{2} and v3{2} in pp at different collision energies

v There is no or a very weak energy dependence of v2 in pp collisions v v2{2} in pp collisions shows a similar pattern as the one seen in pPb collisions (gets flat at the highest multiplicities) v The v2{2} magnitude is ordered: it is highest in PbPb, gets smaller in pPb and become smallest in pp collisions v In difference of the v2, the v3 magnitude is comparable to those in pPb and PbPb collisions v At low multiplicities, the systematic uncertainties are large for all the three systems v At high multiplicities, v3 in pp increases at a slower rate than in pPb and PbPb systems CMS ¡PAS ¡HIN-­‑16-­‑010

slide-19
SLIDE 19

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 19 ¡

c2{4} and c2{6} in pp at different collision energies

v Multi-particle correlations are used to reduce jet correlations from the away side and to explore collective nature of the long-range correlations in pp. v2{4} and v2{6} are extracted v Clear negative c2{4} at high multiplicities in pp at 13 TeV is seen v and positive c2{6} v Statistical limitations CMS ¡PAS ¡HIN-­‑16-­‑010

  • ffline

trk

N

50 100 150 200

{4}

2

c

0.00 0.01 0.02 0.03

3 −

10 × = 13 TeV s = 7 TeV s = 5 TeV s = 5 TeV

NN

s Preliminary CMS pp pPb < 3 GeV/c

T

0.3 < p | < 2.4 η |

  • ffline

trk

N

50 100 150 200

{6}

2

c

0.00 0.05 0.10

6 −

10 × = 13 TeV s pp = 5 TeV

NN

s pPb Preliminary CMS < 3 GeV/c

T

0.3 < p | < 2.4 η |

vn 4

{ }=

−cn 4

{ }

4

vn{6} =

1 4 cn{6} 6

slide-20
SLIDE 20

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 20 ¡

v2 in pp compared to pPb and PbPb results

v Elliptic flow in pp measured using 2- and multi-particle correlations – compared to pPb and PbPb results v v2{2}/v2{4}(pp) ≤ v2{2}/v2{4}(pPb) ç related to initial-state (IS) fluctuations v smaller v2{2}/v2{4} ç less IS fluctuating sources (PRL 112 (2014) 082301) v2{2} ≥ v2{4} ≈ v2{6} collectivity! CMS ¡PAS ¡HIN-­‑16-­‑010

  • ffline

trk

N

50 100 150

2

v

0.05 0.10

= 13 TeV s pp < 3.0 GeV/c

T

0.3 < p | < 2.4 η | Preliminary CMS

|>2} η Δ {2, |

sub 2

v {4}

2

v {6}

2

v {8}

2

v {LYZ}

2

v

  • ffline

trk

N

100 200 300 0.05 0.10

= 2.76 TeV

NN

s PbPb < 3.0 GeV/c

T

0.3 < p | < 2.4 η |

  • ffline

trk

N

100 200 300 0.05 0.10

= 5 TeV

NN

s pPb < 3.0 GeV/c

T

0.3 < p | < 2.4 η |

slide-21
SLIDE 21

η Δ

4 2 − 2 4

( r a d i a n s ) φ Δ

2 4 φ Δ d η Δ d

pair

N

2

d

trig

N 1 0.10 0.12

Preliminary = 13 TeV s CMS pp < 20

  • ffline

trk

N ≤ 10 < 3 GeV/c

assoc T

, p

trig T

1 < p

±

  • h

±

h η Δ

4 2 − 2 4

( r a d i a n s ) φ Δ

2 4 φ Δ d η Δ d

pair

N

2

d

trig

N 1 0.12 0.14 0.16 ±

  • h

S

K η Δ

4 2 − 2 4

( r a d i a n s ) φ Δ

2 4 φ Δ d η Δ d

pair

N

2

d

trig

N 1 0.12 0.14 0.16 ±

  • h

Λ / Λ η Δ

4 2 − 2 4

( r a d i a n s ) φ Δ

2 4 φ Δ d η Δ d

pair

N

2

d

trig

N 1 1.65 1.70 1.75

Preliminary = 13 TeV s CMS pp < 150

  • ffline

trk

N ≤ 105 < 3 GeV/c

assoc T

, p

trig T

1 < p

±

  • h

±

h η Δ

4 2 − 2 4

( r a d i a n s ) φ Δ

2 4 φ Δ d η Δ d

pair

N

2

d

trig

N 1 1.70 1.75 1.80 ±

  • h

S

K η Δ

4 2 − 2 4

( r a d i a n s ) φ Δ

2 4 φ Δ d η Δ d

pair

N

2

d

trig

N 1 1.60 1.65 ±

  • h

Λ / Λ

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 21 ¡

2D 2-particle corr. function in low- and high-multiplicity pp

v charged-charged or charged- strange (KS

0 and / )

particles v particles are correlated within given multiplicity bin v The ridge, at Δϕ ≈ 0 and elongated at Δη, is seen only in high-multiplicity pp events v The ridge is present not only for charged, but also for strange particles v What is the origin of the ridge in the smallest pp system? CMS ¡PAS ¡HIN-­‑16-­‑010

Λ

Λ Λ

collective behavior in pp?

slide-22
SLIDE 22

(GeV/c)

T

p

2 4

{2}

sub 2

v

0.00 0.05 0.10 0.15

Preliminary = 13 TeV s CMS pp | > 2 η Δ | < 20)

  • ffline

trk

N ≤ < 150) - (10

  • ffline

trk

N ≤ (105

S

K Λ / Λ

±

h

0.0 0.5 1.0 1.5 q

/n {2}

sub 2

v

0.00 0.02 0.04

S

Polynomial fits to K

(GeV)

q

/n

T

KE

0.0 0.5 1.0 1.5

Data/Fit

0.5 1.0 1.5

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 22 ¡

NCQ scaled v2 in pp collisions compared to pPb and PbPb

0.0 0.1 0.2 0.3

(GeV)

T

p

2 4

2

v

0.0 0.1 0.2 0.3 = 5.02 TeV

NN

s CMS pPb

1 −

= 35 nb

int

L < 150

trk

  • ffline

N ≤ 120 (0.5-2.5%)

S

K Λ / Λ

±

h

0.0 0.00 0.05 0.10 0.0 0.5 1.0 1.5 2.0

q

/n

2

v

0.00 0.05 0.10

S

Polynomial fits to K

0.0 0.6 0.8 1.0 1.2 1.4

(GeV)

q

/n

T

KE

0.0 0.5 1.0 1.5 2.0

Data/Fit

0.6 0.8 1.0 1.2 1.4 0.0 0.1 0.2 0.3

(GeV)

T

p

2 4

2

v

0.0 0.1 0.2 0.3 = 2.76 TeV

NN

s CMS PbPb

1 −

b µ = 2.3

int

L < 150

trk

  • ffline

N ≤ 120 3%) ± (67

S

K Λ / Λ

±

h 0.0 0.00 0.05 0.10 0.0 0.5 1.0 1.5 2.0

q

/n

2

v

0.00 0.05 0.10

S

Polynomial fits to K

0.0 0.6 0.8 1.0 1.2 1.4

(GeV)

q

/n

T

KE

0.0 0.5 1.0 1.5 2.0

Data/Fit

0.6 0.8 1.0 1.2 1.4

v Significant magnitude of the NCQ scaled v2 in pp, comparable to the ones seen in pPb and PbPb collisions

CMS ¡PAS ¡HIN-­‑16-­‑010 Phys.Le8.B ¡742 ¡(2015) ¡200 Phys.Le8.B ¡742 ¡(2015) ¡200

collectivity!

slide-23
SLIDE 23

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 23 ¡

Factorization breaking – pT dependent event plane fluctuations

slide-24
SLIDE 24

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 24 ¡

Initial-state inhomogeneity

Not a smooth but a lumpy structure ² The goal is to map initial-state and its fluctuations in 3D ² Local hotspots perturb the EP of a smooth medium, so Ψn(pT) contains information about initial-state fluctuations Phys.Rev.C 92 (2015) 034911 ² Within hydrodynamics, initial-state fluctuations could appear as (sub-leading) flows fluctuations Δε(r,ϕ,η)

v3

(2)

  • nly for high-pT particles

a very tiny effect Example: sub-leading triangular flow

slide-25
SLIDE 25

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 25 ¡

Factorization breaking

v How to connect vn(pT) and VnΔ(pT)? v Usual assumption that EP angle Ψn does not depend on pT leads to factorization v then: VnΔ(pT1, pT2) = VnΔ(pT1, pT1) × VnΔ(pT2, pT2) = vn(pT1)× vn(pT2) v Gardim et al., PRC 87 (2013) 031901 and Heinz et al., PRC 87 (2013) 034913 proposed that not only vn depends on pT, but also Ψn could depends on pT due to event-by-event (EbE) fluctuating initial state

initial state fluctuations Ψn(pT) factorization breaking

→ →

even if hydro flow is the only source of the correlation

VnΔ(pT1, pT2) = vn(pT1)vn(pT2)cos n(Ψn(pT1) − Ψn(pT2))

[ ]

≠ VnΔ(pT1, pT1) × VnΔ(pT2, pT2)

slide-26
SLIDE 26

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 26 ¡

Factorization breaking

v new observable: rn =

VnΔ(pT trig, pT assoc) VnΔ(pT trig, pT trig) VnΔ(pT assoc, pT assoc) =

v Large effect is expected and confirmed in ultra central PbPb collisions CMS collaboration: Studies of azimuthal dihadron correlations in ultra-central PbPb collisions at √sNN = 2.76 TeV , JHEP 1402 (2014) 088 ¡

vn(pT trig)vn(pT assoc)cos n(Ψn(pT trig) − Ψn(pT assoc))

# $ % &

vn 2(pT trig)vn 2(pT assoc) = 1 <1 >1

' ( ) ) * ) ) + , ) )

  • )

)

  • fact. holds
  • fact. breaks

non-flow v As in pPb collisions initial-state fluctuations play a dominant role could we expect a similar (in size) effect? v Two hydro models with different initial conditions and η/s were developed:

² Heinz-Shen VISH2+1: PRC 87 (2013) 034913 ² Kozlov et. al.: ¡arXiv:1405.3976

v Constraining of initial conditions and η/s by comparing to the exp. data?

slide-27
SLIDE 27

08.08.2016 ¡

0.5 1 1.5 2

)

T b

,p

T a

(p

2

r

0.8 1 = 2.76 TeV

NN

s CMS PbPb

0-0.2% centrality

< 1.5 GeV/c

T a

1.0 < p

0.5 1 1.5 2

)

T b

,p

T a

(p

2

r

0.8 1

0-5%

0.5 1 1.5 2

)

T b

,p

T a

(p

2

r

0.8 1

5-10%

0.5 1 1.5 2

)

T b

,p

T a

(p

2

r

0.8 1

10-20%

0.5 1 1.5 2

)

T b

,p

T a

(p

2

r

0.8 1

20-30%

0.5 1 1.5 2

)

T b

,p

T a

(p

2

r

0.8 1

30-40%

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2

)

T b

,p

T a

(p

2

r

0.8 1

40-50%

0.5 1 1.5 2

< 2.0 GeV/c

T a

1.5 < p Data

VISH2+1 Hydro /s = 0.12 η MC-Glauber, /s = 0.12 η MC-KLN,

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2 0.8 1 0.5 1 1.5 2

< 2.5 GeV/c

T a

2.0 < p

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2 0.8 1 0.5 1 1.5 2

< 3.0 GeV/c

T a

2.5 < p

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2 2.5

Reimei ¡2016, ¡Tokai, ¡Japan ¡ 27 ¡

pT

trig

0-0.2% 40-50% v The effect increases with rise of pT

trig and

pT

trig-pT assoc

v Approaching the central collisions, the effect dramatically increases achieving value over 20% v For semi-central collisions, the effect achieves only a size of 2−3% arXiv: ¡1503.01692 ¡ ¡ PRC 92 (2015) 034911

PbPb case

slide-28
SLIDE 28

08.08.2016 ¡

0.5 1 1.5 2

)

T b

,p

T a

(p

3

r

0.8 1 = 2.76 TeV

NN

s CMS PbPb

0-0.2% centrality

< 1.5 GeV/c

T a

1.0 < p

0.5 1 1.5 2

)

T b

,p

T a

(p

3

r

0.8 1

0-5%

0.5 1 1.5 2

)

T b

,p

T a

(p

3

r

0.8 1

5-10%

0.5 1 1.5 2

)

T b

,p

T a

(p

3

r

0.8 1

10-20%

0.5 1 1.5 2

)

T b

,p

T a

(p

3

r

0.8 1

20-30%

0.5 1 1.5 2

)

T b

,p

T a

(p

3

r

0.8 1

30-40%

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2

)

T b

,p

T a

(p

3

r

0.8 1

40-50%

0.5 1 1.5 2

< 2.0 GeV/c

T a

1.5 < p Data

VISH2+1 Hydro /s = 0.12 η MC-Glauber, /s = 0.12 η MC-KLN,

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2 0.8 1 0.5 1 1.5 2

< 2.5 GeV/c

T a

2.0 < p

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2 0.8 1 0.5 1 1.5 2

< 3.0 GeV/c

T a

2.5 < p

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2 2.5

Reimei ¡2016, ¡Tokai, ¡Japan ¡ 28 ¡

pT

trig

0-0.2% 40-50% arXiv: ¡1503.01692 ¡ PRC 92 (2015) 034911

PbPb case

v Factorization holds better for V3 v Breaking visible

  • nly for the highest

pT

trig-pT assoc ¡

v Very weakly depends on centrality

slide-29
SLIDE 29

)

T b

,p

T a

(p

2

r

0.7 0.8 0.9 1

= 5.02 TeV

NN

s pPb /s = 0.08 η = 0.4fm, σ Kozlov et al., = 2.76 TeV

NN

s PbPb /s = 0.12 η VISH2+1, MC-Glauber, /s = 0.12 η VISH2+1, MC-KLN, /s = 0.08 η = 0.4fm, σ Kozlov et al.,

PbPb centrality(%)

CMS

2.0 GeV/c ≈

T b

  • p

T a

p < 3.0 GeV/c

T a

2.5 < p

0.1 2.5 7.5 15.0 25.0 35.0 45.0 55.0

tracks |<2.4 η |

N

3

10

)

T b

,p

T a

(p

3

r

0.9 1 1.1 1.2 1.3

0.1 2.5 7.5 15.0 25.0 35.0 45.0 55.0

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 29 ¡

rn multiplicity dependence at the highest ΔpT

arXiv: 1503.01692 PRC 92 (2015) 034911

v Dramatic increase at ultra- central PbPb. For small centralities (>5%) ≈ few % v The r2 in pPb is a bit smaller than in PbPb v Strong r3 multiplicity dependence in pPb, but very weak in PbPb v A non-flow effect in pPb for the highest pT

trig in lower

multiplicities v VISH2+1 qualitatively describes CMS data v Kozlov et al. hydro model describes pPb. Gives stronger effect for PbPb and fails for r3 at lower multiplicity

VISH2+1: PRC 87 (2013) 034913 Kozlov et al.: ¡arXiv:1405.3976

slide-30
SLIDE 30

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 30 ¡

Factorization breaking – η dependence

Bozek et al., arXiv: 1011.3354 Global twist Dumitru et al., arXiv: 1108.4764

slide-31
SLIDE 31

08.08.2016 ¡

Tracker HF- HF+

η a a b

5.2

  • 5.2

3.0

  • 3.0

2.4

  • 2.4

)

b

η ,

a

η (

Δ n

V )

b

η ,

a

η (-

Δ n

V

)

b

η ,

a

η (

Δ n

V )

b

η ,

a

η (-

Δ n

V ≡ )

b

η ,

a

η (

n

r

Reimei ¡2016, ¡Tokai, ¡Japan ¡ 31 ¡

η-dependent rn using Hadronic Forward (HF)

r

n ηa,ηb

( ) ≈

cos n Ψn −ηa

( )− Ψn ηb ( )

( )

$ % & ' ( ) cos n Ψn ηa

( )− Ψn ηb ( )

( )

$ % & ' ( )

For symmetric collision: For asymmetric collision:

r

n ηa,ηb

( )×r

n −ηa,−ηb

( ) ≈

cos n Ψn −ηa

( )− Ψn ηb ( )

( )

% & ' ( ) * cos n Ψn ηa

( )− Ψn ηb ( )

( )

% & ' ( ) * cos n Ψn ηa

( )− Ψn −ηb ( )

( )

% & ' ( ) * cos n Ψn −ηa

( )− Ψn −ηb ( )

( )

% & ' ( ) *

slide-32
SLIDE 32

08.08.2016 ¡

0.0 0.5 1.0 1.5 2.0

)

b

η ,

a

η (

2

r × )

b

η ,-

a

η (-

2

r

0.7 0.8 0.9 1.0

< 150

  • ffline

trk

N ≤ 120 = 5.02 TeV

NN

s CMS pPb

  • 1

= 35 nb

int

L

< 5.0

b

η 4.4 < < 4.0

b

η 3.0 < Exponential fits

a

η

0.0 0.5 1.0 1.5 2.0

)

b

η ,

a

η (

2

r × )

b

η ,-

a

η (-

2

r

0.7 0.8 0.9 1.0

< 220

  • ffline

trk

N ≤ 185

0.0 0.5 1.0 1.5 2.0 0.7 0.8 0.9 1.0 < 3.0 GeV/c

a T

0.3 < p > 0 GeV/c

b T

p

< 185

  • ffline

trk

N ≤ 150

a

η

0.0 0.5 1.0 1.5 2.0 0.7 0.8 0.9 1.0

< 260

  • ffline

trk

N ≤ 220 Reimei ¡2016, ¡Tokai, ¡Japan ¡ 32 ¡

η-dependent rn in pPb

v A significant factorization breakdown in η found in pPb collisions with increase of ηa v The effect increases approximately linearly with ηa v Parameterization with Fn

η

is purely empirical introduced just to quantify behavior of the data

r

n ηa,ηb

( ) ≈ e−2Fn

ηηa

arXiv: 1503.01692 PRC 92 (2015) 034911

slide-33
SLIDE 33

08.08.2016 ¡

tracks |<2.4 η |

N

2

10

3

10

n η

F 0.00 0.02 0.04 0.06 0.08

0.1 2.5 7.5 15.0 25.0 35.0 45.0 55.0

PbPb centrality(%)

CMS = 2.76 TeV

NN

s PbPb = 5.02 TeV

NN

s pPb

n = 2, 0-0.2% n = 2 n = 3 n = 4 n = 2 Reimei ¡2016, ¡Tokai, ¡Japan ¡ 33 ¡

η-dependent rn vs multiplicity

arXiv: 1503.01692 PRC 92 (2015) 034911

v In PbPb, higher-orders F3

η and F4 η, show much stronger

factorization breaking than for the second order v The F2

η has a minimum

around midcentral PbPb and increases for peripheral and most central collisions v At similar multiplicity, F2

η in pPb larger than

the one in PbPb v Except for the most central PbPb, there is a very weak centrality dependence of F3

η

slide-34
SLIDE 34

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 34 ¡

Principal Component Analysis as a new tool to study flow

slide-35
SLIDE 35

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 35 ¡

Principal Component Analysis (PCA) method

v Random data generated by 2D multivariate Gauss distribution

A simple 2D example  Xn = x1, x2,…, xn

( )

 Yn = y1, y2,…, yn

( )

v a matrix

Σ = var(X) cov(X,Y) cov(X,Y) var(Y) " # $ $ % & ' '

v eigenvectors ei and eigenvalues λi by diagonalization Σ

e

[ ]

T Σ e

[ ] = diag(λ1,λ2)

v First Principal Component: eigenvector e1 points to maximum variance of data

  • cloud. Its magnitude is

v Second Principal Component: eigenvector e2 points to the next maximum variance of data cloud. Its magnitude is λ1e1 λ2e2

slide-36
SLIDE 36

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 36 ¡

PCA method in hydrodynamic flow - prescription

Two very recent theoretical papers: R.S.Bhalerao, ¡J-­‑Y. ¡Ollitrault, ¡S.Pal ¡and ¡D.Teaney, ¡ ¡ Phys.Rev.LeQ. ¡114 ¡(2015) ¡152301 ¡and A.Mazeliauskas ¡and ¡D.Teaney, ¡Phys.Rev. ¡C91 ¡(2015) ¡ 044902 ¡introduced the PCA as a new method to study hydrodynamics flows

VnΔ = cos(nΔφ)

S −

cos(nΔφ)

B

cos(nΔφ)

S and

cos(nΔφ)

B

are calculated for pairs with |Δη|>2 v 7 pT bins (0.3<pT<3.0 GeV/c); the eigenvalue problem of a matrix [VnΔ(pi,pj)] where

PhysRev.C 92 (2015) 034911 arXiv:1503.01692 and other CMS analyses

v Input: two-particle Fourier coefficients measured as

v “The simplest correlations are pairs. The principal component analysis is a method which extracts all the information from pair correlations in a way which facilitates comparison between theory and experiment.” J.-Y. Ollitrault

In this analysis:

e(1) e(2) . . . . e(7) ! " # $ % & VnΔ(p1, p1) VnΔ(p2,p1) VnΔ(p3,p1) . . . . VnΔ(p1, p2) VnΔ(p2, p2) VnΔ(p3, p2) . . . . VnΔ(p1, p3) VnΔ(p2, p3) VnΔ(p3, p3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VnΔ(p7, p7) ( ) * * * * * * * * * * + ,

  • e(1)

e(2) . . . . e(7) ! " # # # # # # # # # # $ % & & & & & & & & & & = diag λ(1) λ(2) . . . . λ(7) ! " # $ % &

slide-37
SLIDE 37

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 37 ¡

PCA method in hydrodynamic flow - prescription

v experimental data è VnΔ(pi,pj) è it has its own statistical error ΔVnΔ(pi,pj) v The error propagation through Vn

(α) up to vn (α)

v The new introduced pT dependent variable, flow mode, is defined as

Vn

(α)(pi) =

λ(α)e(α) pi

( )

v corresponding single-particle flow mode vn

(α)(p) = Vn (α)(p)

M(p)

v Δλα and Δeα as RMS of the distributions like ones shown above. Matrix elements VnΔ were perturbed (10k times) within its ΔVnΔ à matrix [VnΔ] nonlinearly perturbed where α=1,…,7

λ distribution, α=2 e distribution, α=2 α=2 signal 200 times smaller wrt α=1 α=2 ¡ α=1 ¡ 2.5<pT<3.0 GeV/c

CMS Preliminary

slide-38
SLIDE 38

1 2 3

2 ) α (

v

0.1 0.2 0.3

<260

trk

  • ffline

N ≤ 220

= 5.02 TeV

NN

s pPb

(GeV/c)

T

p

1 2 3

2 ) α (

v

0.1 0.2 0.3

CMS Preliminary

<185

trk

  • ffline

N ≤ 150

(GeV/c) p

1 2 3

n

v

0.1 0.2 0.3

, PLB 724 (2013) 213 |>2} η Δ {2, |

2

v =1 α =2 α

<220

trk

  • ffline

N ≤ 185

(GeV/c)

T

p

1 2 3

n

v

0.1 0.2 0.3

<150

trk

  • ffline

N ≤ 120 08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 38 ¡

Results – elliptic flows in pPb collisions

v The leading flow mode, α=1, practically identical to the v2 measured using two-particle correlations v The sub-leading flow mode, α=2, is essentially equal to zero at small pT and increases up to 4-5% going to the high-pT v The first experimental measurement of the elliptic sub-leading flow v Systematical uncertainties small or comparable to statistical ones only at high-pT CMS ¡PAS ¡HIN-­‑15-­‑010

slide-39
SLIDE 39

1 2 3

2 ) α (

v

0.1 0.2

= 2.76 TeV

NN

s PbPb

CMS Preliminary

0-0.2%

(GeV/c)

T

p

1 2 3

2 ) α (

v

0.1 0.2

20-30%

(GeV/c) p

1 2 3

0.1 0.2

0-5%

(GeV/c)

T

p

1 2 3

0.1 0.2

30-40%

(GeV/c) p

1 2 3

0.1 0.2

0-10%

(GeV/c) p

1 2 3

0.1 0.2

PLB 708 (2012) 249 ALICE , |>0.8} η Δ {|

2

v =1 α =2 α

10-20%

(GeV/c)

T

p

1 2 3

0.1 0.2

40-50%

(GeV/c)

T

p

1 2 3

0.1 0.2

50-60%

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 39 ¡

Results – elliptic flows in PbPb collisions

v The leading flow mode, α=1, essentially equal to the v2 measured by ALICE using two-particle correlations v The sub-leading flow mode, α=2, is positive at UCC and for collisions with centralities above 20% v In the region 0-20% centrality comparable with zero v Similar behavior wrt the r2 results (10.1103/PhysRevC.92.034911, arXiv: 1503.01692) CMS ¡PAS ¡HIN-­‑15-­‑010

slide-40
SLIDE 40

1 2 3

3 ) α (

v

0.05 − 0.05 0.1

= 5.02 TeV

NN

s pPb

<260

trk

  • ffline

N ≤ 220

(GeV/c)

T

p

1 2 3

3 ) α (

v

0.05 − 0.05 0.1

<185

trk

  • ffline

N ≤ 150

CMS Preliminary

(GeV/c) p

1 2 3

n

v

0.05 0.05 0.1

, PLB 724 (2013) 213 |>2} η Δ {2, |

3

v =1 α =2 α

<220

trk

  • ffline

N ≤ 185

(GeV/c)

T

p

1 2 3

n

v

0.05 0.05 0.1

<150

trk

  • ffline

N ≤ 120 08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 40 ¡

Results – triangular flows in pPb collisions

v The leading triangular flow mode, α=1, nearly identical to the v3 measured using two- particle correlations v The sub-leading flow mode, α=2, is comparable with zero within the given uncertainties. v The first experimental measurement of the triangular sub-leading flow CMS ¡PAS ¡HIN-­‑15-­‑010

slide-41
SLIDE 41

1 2 3

3 ) α (

v

0.1 0.2 0.3

= 2.76 TeV

NN

s PbPb

CMS Preliminary

0-0.2%

(GeV/c)

T

p

1 2 3

3 ) α (

v

0.1 0.2 0.3

20-30%

(GeV/c) p

1 2 3

0.1 0.2 0.3

0-5%

(GeV/c)

T

p

1 2 3

0.1 0.2 0.3

30-40%

(GeV/c) p

1 2 3

0.1 0.2 0.3

0-10%

(GeV/c) p

1 2 3

0.1 0.2 0.3

10-20%

PLB 708 (2012) 249 ALICE , |>0.8} η Δ {|

3

v =1 α =2 α

(GeV/c)

T

p

1 2 3

0.1 0.2 0.3

40-50%

(GeV/c)

T

p

1 2 3

0.1 0.2 0.3

50-60%

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 41 ¡

Results – triangular flows in PbPb collisions

v Again, the leading flow mode, α=1, essentially equal to the v3 measured by ALICE using two-particle correlations v The sub-leading flow mode, α=2, is, within the uncertainties, equal to zero v Results have a similar centrality dependence to that observed for r3 (Phys. Rev C 92

(2015) 034911, arXiv: 1503.01692)

CMS ¡PAS ¡HIN-­‑15-­‑010

slide-42
SLIDE 42

(GeV/c)

T

p

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

)

T

(p

3

v

0.01 0.02 0.03 0.04 0.05

= 5.5% 〉

geo

σ / σ 〈 ,

  • π

CERES < 7% σ , 0 <

  • π

hydro+UrQMD

  • ffline

trk

N

50 100 150 2

v

0.05 0.10

= 13 TeV s pp < 3.0 GeV/c

T

0.3 < p | < 2.4 η | Preliminary CMS |>2} η Δ {2, |

sub 2

v {4}

2

v {6}

2

v {8}

2

v {LYZ}

2

v

0.05 0.10

20 40 60 80

0.0 0.1 0.2

20 - 30%

42 ¡ 08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡

Conclusions

v The first v3(pT) measurement at the top SPS energy with CERES using the event plane method v The v2 and v3 measured up to 100 GeV/c in PbPb at 5 TeV v The v2 and v3 in small pPb and smallest pp system formed in collisions at the LHC energies v A strong factorization breaking effect for n=2 appears approaching UCC PbPb collisions v The sub-leading flow modes are for the first time experimentally measured in both pPb and PbPb collisions at the LHC energies v The sub-leading elliptic flow modes is in a qualitative agreement with the r2 factorization-breaking results v The sub-leading triangular flow modes in both collision system is small if not zero showing that the triangular flow factorizes much better than the elliptic flow v These results could help in better understanding of the initial-state fluctuations

CMS Preliminary

up to 100 GeV/c

vn ¡

slide-43
SLIDE 43

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 43 ¡

Backup slides

slide-44
SLIDE 44

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 44 ¡

r2 in ultra-central PbPb collisions and VISH2+1

arXiv: ¡1503.01692, ¡PRC ¡92 ¡(2015) ¡034911

v The effect increases with rise of pT

trig and pT trig-pT assoc

v The biggest effect seen in ultra-central collisions while for semi-central collisions, the effect achieves only a size of 2−3% v The VISH2+1 model qualitatively gives a good description of CMS data for both MC-Glauber and MC-KLN initial conditions v Large insensitivity to η/s è an independent constraint to the initial-state

VISH2+1: ¡PRC ¡87 ¡(2013) ¡034913

r2

pT

trig-pT assoc (GeV/c)

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2

)

T b

,p

T a

(p

2

r

0.6 0.7 0.8 0.9 1

< 1.5 GeV/c

T a

1.0 < p 0-0.2% centrality

= 2.76 TeV

NN

s CMS PbPb

Data

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2

< 2.0 GeV/c

T a

1.5 < p VISH2+1 Hydro MC-Glauber /s = 0.20 η /s = 0.12 η /s = 0.08 η MC-KLN /s = 0.20 η /s = 0.12 η /s = 0.08 η

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2

< 2.5 GeV/c

T a

2.0 < p

(GeV/c)

T b

  • p

T a

p

0.5 1 1.5 2 2.5

< 3.0 GeV/c

T a

2.5 < p

slide-45
SLIDE 45

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡

0.5 1 1.5 2 0.96 0.97 0.98 0.99 1 1.01

CMS Preliminary = 5.02 TeV

NN

s pPb < 260

trk

  • ffline

N ≤ 220

< 1.5 GeV/c

T trig

1.0 GeV/c < p

0.5 1 1.5 2 0.96 0.97 0.98 0.99 1 1.01

<220

trk

  • ffline

N ≤ 185

0.5 1 1.5 2 0.96 0.97 0.98 0.99 1 1.01

<185

trk

  • ffline

N ≤ 150

0.5 1 1.5 2 0.96 0.97 0.98 0.99 1 1.01

<150

trk

  • ffline

N ≤ 120

0.5 1 1.5 2

< 2.0 GeV/c

T trig

1.5 GeV/c < p

CMS

0.5 1 1.5 2

2

r

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

< 2.5 GeV/c

T trig

2.0 GeV/c < p

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 2.5

< 3.0 GeV/c

T trig

2.5 GeV/c < p

0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5

45 ¡

r2

pT

trig

pT

trig-pT assoc (GeV/c)

220<Ntrk

  • ffline<260

v The effect increases with pT

trig and

pT

trig-pT assoc

v Maximum around ¡2-­‑3% ¡ v ¡Nearly ¡no ¡ ¡ dependence ¡on ¡ mulYplicity ¡

arXiv: ¡1503.01692 ¡ PRC 92 (2015) 034911

r2 from high-multiplicity pPb collisions

120<Ntrk

  • ffline<150
slide-46
SLIDE 46

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡

0.5 1 1.5 2 0.96 0.97 0.98 0.99 1 1.01

CMS Preliminary = 5.02 TeV

NN

s pPb < 260

trk

  • ffline

N ≤ 220

< 1.5 GeV/c

T trig

1.0 GeV/c < p

0.5 1 1.5 2 0.96 0.97 0.98 0.99 1 1.01

<220

trk

  • ffline

N ≤ 185

0.5 1 1.5 2 0.96 0.97 0.98 0.99 1 1.01

<185

trk

  • ffline

N ≤ 150

0.5 1 1.5 2 0.96 0.97 0.98 0.99 1 1.01

<150

trk

  • ffline

N ≤ 120

0.5 1 1.5 2

< 2.0 GeV/c

T trig

1.5 GeV/c < p

CMS /s=0.08 η Kozlov et. al.,

0.5 1 1.5 2

2

r

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

< 2.5 GeV/c

T trig

2.0 GeV/c < p

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 2.5

< 3.0 GeV/c

T trig

2.5 GeV/c < p

0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5

46 ¡

r2

pT

trig

pT

trig-pT assoc (GeV/c)

220<Ntrk

  • ffline<260

Kozlov et al. hydro model qualitatively describes data

arXiv: ¡1503.01692 ¡ PRC 92 (2015) 034911

pPb r2: comparison to Kozlov et. al hydro model

120<Ntrk

  • ffline<150

Kozlov et al.: ¡arXiv:1405.3976

slide-47
SLIDE 47

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 47 ¡

0.5 1 1.5 2 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

<260

trk

  • ffline

N ≤ 220

< 1.5 GeV/c

T trig

1.0 GeV/c < p

0.5 1 1.5 2 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

<220

trk

  • ffline

N ≤ 185 CMS Preliminary = 5.02 TeV

NN

s pPb

0.5 1 1.5 2 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

<185

trk

  • ffline

N ≤ 150

0.5 1 1.5 2 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

<150

trk

  • ffline

N ≤ 120

0.5 1 1.5 2

< 2.0 GeV/c

T trig

1.5 GeV/c < p

CMS

0.5 1 1.5 2

3

r

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

< 2.5 GeV/c

T trig

2.0 GeV/c < p

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 2.5

< 3.0 GeV/c

T trig

2.5 GeV/c < p

0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5

r3

pT

trig

pT

trig-pT assoc (GeV/c)

220<Ntrk

  • ffline<260

v V3 factorize better than V2 v A direct indication

  • f non-flow effect

seen in r3 for the highest pT

trig in lower

multiplicity bins

arXiv: ¡1503.01692 ¡ PRC 92 (2015) 034911

r3 from high-multiplicity pPb collisions

120<Ntrk

  • ffline<150
slide-48
SLIDE 48

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡

0.5 1 1.5 2 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

<260

trk

  • ffline

N ≤ 220

< 1.5 GeV/c

T trig

1.0 GeV/c < p

0.5 1 1.5 2 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

<220

trk

  • ffline

N ≤ 185 CMS Preliminary = 5.02 TeV

NN

s pPb

0.5 1 1.5 2 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

<185

trk

  • ffline

N ≤ 150

0.5 1 1.5 2 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

<150

trk

  • ffline

N ≤ 120

0.5 1 1.5 2

< 2.0 GeV/c

T trig

1.5 GeV/c < p CMS /s=0.08 η Kozlov et. al.,

0.5 1 1.5 2

3

r

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2

< 2.5 GeV/c

T trig

2.0 GeV/c < p

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 2.5

< 3.0 GeV/c

T trig

2.5 GeV/c < p

0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5

48 ¡

r3

pT

trig

pT

trig-pT assoc (GeV/c)

220<Ntrk

  • ffline<260

v Kozlov et al. hydro model qualitatively describes data except in lower multiplicity bins for the highest pT

trig

arXiv: ¡1503.01692 ¡ PRC 92 (2015) 034911 120<Ntrk

  • ffline<150

pPb r3: comparison to Kozlov et. al hydro model

Kozlov et al.: ¡arXiv:1405.3976

slide-49
SLIDE 49

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 49 ¡

η-dependent rn in PbPb

0.0 0.5 1.0 1.5 2.0

)

b

η ,

a

η (

2

r

0.85 0.90 0.95 1.00

0-0.2% centrality = 2.76 TeV

NN

s CMS PbPb

< 5.0

b

η 4.4 < < 4.0

b

η 3.0 < Exponential fits

a

η

0.0 0.5 1.0 1.5 2.0

)

b

η ,

a

η (

2

r

0.85 0.90 0.95 1.00

20-30%

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

0-5%

< 3.0 GeV/c

a T

0.3 < p > 0 GeV/c

b T

p

a

η

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00 30-40% 0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

5-10%

a

η

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

40-50%

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

10-20%

a

η

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

50-60%

0.0 0.5 1.0 1.5 2.0

)

b

η ,

a

η (

3

r

0.85 0.90 0.95 1.00

0-0.2% centrality = 2.76 TeV

NN

s CMS PbPb

< 5.0

b

η 4.4 < < 4.0

b

η 3.0 < Exponential fits

a

η

0.0 0.5 1.0 1.5 2.0

)

b

η ,

a

η (

3

r

0.85 0.90 0.95 1.00

20-30%

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

0-5%

< 3.0 GeV/c

a T

0.3 < p > 0 GeV/c

b T

p

a

η

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00 30-40% 0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

5-10%

a

η

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

40-50%

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

10-20%

a

η

0.0 0.5 1.0 1.5 2.0 0.85 0.90 0.95 1.00

50-60%

v The r2 factorization

  • breaking effect

increases with increase of ηa v Except for the most central collisions, the increase is approximately linear v The effect of factorization breaking is much stronger for higher-order harmonic r3 – opposite to the pT dependence v Almost linear increase

  • f the effect size

v Parameterization:

r

n ηa,ηb

( ) ≈ e−2Fn

ηηa

arXiv: 1503.01692 PRC 92 (2015) 034911

slide-50
SLIDE 50

)

T b

,p

T a

(p

2

r

0.7 0.8 0.9 1

= 5.02 TeV

NN

s pPb /s = 0.08 η = 0.4fm, σ Kozlov et al., = 2.76 TeV

NN

s PbPb /s = 0.12 η VISH2+1, MC-Glauber, /s = 0.12 η VISH2+1, MC-KLN, /s = 0.08 η = 0.4fm, σ Kozlov et al.,

PbPb centrality(%)

CMS

2.0 GeV/c ≈

T b

  • p

T a

p < 3.0 GeV/c

T a

2.5 < p

0.1 2.5 7.5 15.0 25.0 35.0 45.0 55.0

tracks |<2.4 η |

N

3

10

)

T b

,p

T a

(p

3

r

0.9 1 1.1 1.2 1.3

0.1 2.5 7.5 15.0 25.0 35.0 45.0 55.0

50 ¡ 08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡

Factorization breaking - connection to the PCA

v Initial-state fluctuations à the EP (Ψn) depends on pT and on η  factorization is broken. New observable introduced:

rn = VnΔ(pT1, pT2) VnΔ(pT1, pT1) VnΔ(pT2, pT2) = vn(pT1)vn(pT2)cos n(Ψn(pT1) − Ψn(pT2))

# $ % &

vn 2(pT1)vn 2(pT2) = 1 <1 >1

' ( ) ) * ) ) + , ) )

  • )

)

holds brakes non-flow Phys.Rev. ¡C87 ¡(2013) ¡031901 Phys.Rev. ¡C87 ¡(2013) ¡034913

v If there is only one principal component for each harmonic n à VnΔ(pi,pj) factorizes

  • Phys. Rev. C 92 (2015) 034911

(arXiv:1503.01692)

v rn i.e. VnΔ(pi,pj) results are partially integrated, while mutually orthogonal eigenmodes contain all information

slide-51
SLIDE 51

08.08.2016 ¡ Reimei ¡2016, ¡Tokai, ¡Japan ¡ 51 ¡

Factorization breaking - connection to the PCA

v The PCA can approximately reconstruct two-particle VnΔ(pi,pj) coefficients

VnΔ(pi, pj) ≈ Vn

(α)∗(pi)Vn (α)∗(pj) α=1 k≤Nb

∑

where Nb=7 which can be used to calculate the factorization breaking ratio rn v Note that the PCA uses the whole pT range simultaneously to extract the information on both leading and sub- leading flow modes v The given harmonic order n has also higher (α>2) eigenmodes ordered from largest to smallest, while in rn they are not clearly distinguished

  • 3.0

Phys.Rev.LeQ. ¡114 ¡(2015) ¡152301 ¡ ¡

η

  • 2.0 -1.0

1.0 2.0 3.0

v So, the PCA is a good tool for analysis in hydrodynamics with fluctuations in the initial state