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Recent results from relativistic heavy ion collisions at the LHC Camelia Mironov MIT A ‘teaser’ talk with very few (though recent) results

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Page 1: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Recent results from relativistic heavy ion collisions at the LHC

Camelia MironovMIT

A ‘teaser’ talk with very few (though recent) results

Page 2: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Collision systems

Center of mass colliding energy (TeV)

2.76 (2011, 2013)5.02 (2015)7,13

—5.02 (2013)

2.76 (2010, 2011)5.02 (2015)

LHC Heavy-Ion (HI) Program

2

Page 3: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Characterize HI collisions

➡ ‘Event-activity’ characteristics (Data, Monte Carlo)✓ central collisions: small impact parameter collision (high-multiplicity

events, large energy deposited in calorimeters, etc)✓ peripheral collision: large impact parameter collision

➡ At a certain colliding energy, for a certain impact parameter b✓ <Npart> — number of incoming nucleons participating in the collision✓ <Ncoll> — number of equivalent nucleon-nucleon collisions

- Glauber MC calculation3

5

4

A → ←A

Page 4: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

➡ Particle production✓ transverse momentum: component perpendicular on the beam axis

- pT = p cosθ

✓ pseudorapidity: angular position in detector

Characterize HI collisions

4

⌘ = �ln[tan(✓/2)]

Page 5: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

(GeV)NNs10 210 310 410

⟩η/d

chNd⟨ ⟩

part

N⟨2

0

2

4

6

8

10

12

14), INELppp(p AA, central

ALICE ALICECMS CMSUA5 ATLASPHOBOS PHOBOSISR PHENIX

BRAHMSpA(dA), NSD STARALICE NA50PHOBOS

| < 0.5 η|

0.103(2)s ∝

0.155(4)s ∝

LHC vs RHIC

➡ The charged particle multiplicity per colliding nucleon pair measured at LHC for the most central collisions is ✓ ~2x that measured at RHIC, where the collision energy is factor 14 lower✓ ~2x that measured at LHC in pp or pPb collisions at similar collision energy

5

PRL 116 (2016)

Page 6: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Ini$al-stateinhomogeneity

ΨEP

x

y

Ini$al-stateanisotropy

Ψ2

Ψ3

Analyzing HI collisions: 2-particle correlations

➡ Event-by-event

6

Trigger particlepTtrig,ηtrig, φtrig

Associated particlepTasssoc,ηassoc, φassoc

Δη = ηtrig - ηassoc

ΔΦ = φtrig - φassoc

η∆-4-2

02

4

φ∆ 02

4

φ∆

dη∆d

pair

N2 d

trig

N1 0.160.180.20

< 35trkoffline = 5.02 TeV, NNNsCMS pPb

< 3 GeV/cT

1 < p(a)

η∆-4

-3-2

-10

12

34

(radians)

φ∆

-1

0

1

2

3

4

φ∆

∆d

pair

N2 d

trig

N1 0.14

0.16

0.18

< 35offline

trk = 13 TeV, NsCMS pp

< 3 GeV/cT

1 < p(a)

Back-to-back jet contribution

Single jet contribution

Page 7: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Collective motion: 2-particle correlations

7

Single jet contribution

Back-to-back jet contribution

JHEP 09 (2010)

RIDGE: “collective effect” 2 particles with very different η are “connected”

Page 8: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Collective motion: 2-particle correlations

8

RIDGE: “collective effect” 2 particles with very different η are “connected”

Single jet contribution

Back-to-back jet contribution

RIDGE Also in pPb high-multiplicity events

η∆-4

-2

0

2

4 (radians)

φ∆

0

2

4

φ∆

dη∆d

pair

N2 d

trig

N1 3.1

3.2

3.3

3.4

< 260offlinetrk N≤ = 5.02 TeV, 220 NNs(b) CMS pPb

< 3 GeV/ctrigT

1 < p < 3 GeV/cassoc

T1 < p

PLB 718 (2013)

JHEP 09 (2010)

Page 9: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Collective motion: pPb

9arXiv:1606.08170

PLB 718 (2013) PLB 719 (2013)

arXiv:1512.00439

ALICE

Page 10: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

η∆-4

-2

0

2

4 (radians)

φ∆

0

2

4

φ∆

dη∆d

pair

N2 d

trig

N1 3.1

3.2

3.3

3.4

< 260offlinetrk N≤ = 5.02 TeV, 220 NNs(b) CMS pPb

< 3 GeV/ctrigT

1 < p < 3 GeV/cassoc

T1 < p

Collective motion everywhere!

10

RIDGE: “collective effect” 2 particles with very different η are “connected”

Single jet contribution

Back-to-back jet contribution

RIDGE Also in pp high-multiplicity events

η∆4−

2−

0

2

4

(radians)

φ∆

0

2

4

φ∆

∆d

pair

N2 d

trig

N1 1.65

1.70

1.75

= 13 TeVsCMS pp < 150offline

trk N≤105 < 3 GeV/cassoc

T, ptrig

T1 < p

± - h±h

η∆4−

2−

0

2

4

(radians)

φ∆

0

2

4

φ∆

∆d

pair

N2 d

trig

N1 1.70

1.75

1.80

± - h0SK

η∆4−

2−

0

2

4

(radians)

φ∆

0

2

4

φ∆

∆d

pair

N2 d

trig

N1 1.60

1.65

± - hΛ/Λ

JHEP 09 (2010) CMS-PAS-FSQ-15-002 ATLAS-CONF-2016-026

Page 11: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

LHC: PbPb @ 2.76, 5.02TeV

11

Z

l+l-

h/D/Binclusive jet / identified-jet

inclusive jet / identified-jetZ

l+l-

inclusive jet

A) Individual hadrons B) Reconstructed jets

QQ

r0,ΔE

C) Quarkonia

➡ Questions one addresses with these measurements✓ Is there a difference in how the light partons and heavy (charm and

beauty) quarks interact with the medium?✓ What are the properties of the medium created?

Page 12: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Analyzing HI collisions: RAA

➡ Nuclear modification factor:✓ if = 1 no medium effects✓ if < 1 suppression (e.g. energy loss in the medium)✓ if > 1 enhancement (e.g. kT broadening in the incoming nuclei)

12

RAA

=Y ield(A+A)

Y ield(p+ p) < Ncoll

>

Page 13: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Z boson: in-situ reference

➡ Z boson measured for the first time in HI collisions✓ confirm the Ncoll scaling: RAA = 1

13

partN0 50 100 150 200 250 300 350 400

AAR

0

0.5

1

1.5

2

2.5 = 2.76 TeVNNsCMS

> 0 GeV/cT

ll, |y| < 1.44, p→Z ll, 0-100% centrality→Z

pp luminosity uncertainty

JHEP 03 (2015PRL 110 (2013)

Z

l+l-

Page 14: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Charged hadrons (gluons & u/d/s quarks)

➡ Agreement between experiments at 2.76TeV➡ And same suppression at 2.76TeV and 5TeV

14

(GeV)T

p1 10 210

AAR

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0-5%

and lumi. uncertaintyAAT|<1η|

(5.02 TeV PbPb)-1bµ (5.02 TeV pp) + 404 -125.8 pb

CMSPreliminary

CMS 5.02 TeVCMS 2.76 TeVATLAS 2.76 TeVALICE 2.76 TeV

CMS-PAS-HIN-15-015

h

Page 15: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

)2 (GeV/cKπm1.7 1.75 1.8 1.85 1.9 1.95 2

)2En

tries

/ (5

MeV

/c

0

20

40

60

80

100

120

140

160

180

200

220DataFit

Signal0D+0D swappedπK-

Combinatorial

PreliminaryCMS = 5.02 TeVNNsPbPb

< 30.0 GeV/cT

25.0 < p

Centrality 0-100%

|y| < 1.0

D mesons (charm quarks)

15

K

π

D0

D0 decay vertex

Primary

JHEP 09 (2012) CMS-PAS-HIN-16-001

D

Page 16: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Charm vs Light

➡ At high-pT (~4-5GeV/c) light partons (quarks and gluons) and charm quarks ‘products’ have same RAA

16

(GeV/c)T

p1 10 210

AA R0 D

0

0.2

0.4

0.6

0.8

1

1.2

1.4

(5.02 TeV PbPb)-1bµ (5.02 TeV pp) + 404 -125.8 pb

CMSPreliminary

Centrality 0-100%|y| < 1

0 DAAR

charged hadronsAAR and lumi.AAT

uncertainty

2.76 TeV 5.02 TeV CMS-PAS-HIN-16-001 CMS-PAS-HIN-15-015

JHEP 03 (2016)

Page 17: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

B(J/𝜓X) mesons (beauty quark)

➡ First b-quark products measurement✓ B→J/𝜓+X

➡ First exclusive B reconstructed in pA collisions✓ B→J/𝜓+K17

(mm)ψJ/l-1 -0.5 0 0.5 1 1.5 2

Even

ts /

(0.0

35 m

m)

1

10

210

310

410CMS Preliminary

= 2.76 TeVNNsPbPb -1bµ = 150 intL |y| < 2.4

< 30 GeV/cT

6.5 < pCent. 0-100%

datatotal fitbkgd + non-promptbackground

BLxy

J/ψ µ+µ−

�J/� = LxymJ/�

pT

B+ Decay Vertex

J/ψ

B+ cτ = 492 µm

µ+

µ-

K+

m = 3.10 GeV/c2

)2 (GeV/cµµm2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5

)2Ev

ents

/ ( 0

.02

GeV

/c

0

500

1000

1500

2000

2500

3000

CMS Preliminary = 2.76 TeVNNsPbPb

-1bµ = 150 intL|y| < 2.4

< 30 GeV/cT

6.5 < pCent. 0-100%

177±: 8525 ψJ/N2 1 MeV/c± = 35 σ

datatotal fitbkgd + non-promptbackground

)2 (GeV/cBm5 5.2 5.4 5.6 5.8 6

)2En

tries

/ (2

0 M

eV/c

0

50

100

150

200

DataFitSignalCombinatorial

Xψ J/→B

(pPb 5.02 TeV)-134.6 nbCMS

-+B+B < 15 GeV/c

T10 < p

| < 2.4lab

|y

)2 (GeV/cBm5 5.2 5.4 5.6 5.8 6

)2En

tries

/ (3

0 M

eV/c

0

10

20

30

40

50

60

70

DataFitSignalCombinatorial

Xψ J/→B

(pPb 5.02 TeV)-134.6 nbCMS

0B+0B < 15 GeV/c

T10 < p

| < 2.4lab

|y

)2 (GeV/cBm5 5.2 5.4 5.6 5.8 6

)2En

tries

/ (4

0 M

eV/c

0

10

20

30

40

50

60

70

DataFitSignalCombinatorial

(pPb 5.02 TeV)-134.6 nbCMS

0sB+0

sB < 60 GeV/c

T10 < p

| < 2.4lab

|y

CMS-PAS-HIN-12-014

PRL 116 (2016)

Page 18: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Beauty vs Charm vs Light

➡ Smaller measured suppression between the b-quark products and charm or gluon/light-quarks products

18

B→J/𝜓

D, h

JHEP 11 (2015)

Page 19: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Fully reconstructed jets

19… in the kinematic regions where we can

Page 20: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Z+jet: in-situ reference

➡ Central PbPb xJZ distributions shifted to lower values wrt pp at all Z-pT : the back-parton suffers energy loss in the medium✓ theoretical models: energy loss directly related to the medium density

20

Z

l+l-

Jet

CMS-PAS-HIN-15-013

Page 21: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

-weighted)coll

(N⟩partN⟨0 50 100 150 200 250 300 350 400

⟩ Jx⟨

0.56

0.58

0.6

0.62

0.64

0.66

0.68

0.7

0.72

0.74pp

30-100%

10-30%0-10%

(5.02 TeV PbPb)-1bµ (5.02 TeV pp) + 404 -125.8 pb

CMSPreliminary

Inclusive dijets

Data

pp-based reference

Beauty vs Light

➡ Blue: Inclusive-dijets imbalance increases from peripheral to central PbPb collisions➡ Red: Imbalance of b-dijets measured for the first time

✓ similar to that of inclusive jets (red vs blue)21

-weighted)coll

(N⟩partN⟨0 50 100 150 200 250 300 350 400

⟩ Jx⟨

0.56

0.58

0.6

0.62

0.64

0.66

0.68

0.7

0.72

0.74pp

30-100%

10-30%0-10%

(5.02 TeV PbPb)-1bµ (5.02 TeV pp) + 404 -125.8 pb

CMSPreliminary

b dijets

Data

pp-based reference

Jet 2

Jet 1

b-Jet 2

b-Jet 1CMS-PAS-HIN-16-005

xJ =p

Jet2T

p

Jet1T

pJet2T > 40GeV/c

pJet1T > 100GeV/c

Page 22: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

LHC: the full picture

➡ Probes ‘blind’ to the medium: photons, Z, W➡ Probes affected by the medium:

✓ low-pT: different suppression pattern for b-quark vs c/q/gluon products✓ high-pT: similar suppression pattern no matter the color of the pattern

22

) [GeV]T

(mT

p0 20 40 60 80 100

AAR

0

0.5

1

1.5

2

2.5

| < 1ηCharged particles (0-5%) | (0-100%) |y| < 2.4ψ J/→*B

*Z (0-100%) |y| < 2| < 2.1µη, | > 25 GeV/cµ

TW (0-100%) p

| < 1.44ηIsolated photon (0-10%) |

[GeV]T

p100 150 200 250 3000

0.5

1

1.5

2

2.5 = 2.76 TeVNNsCMS *PRELIMINARY PbPb

-1bµ L dt = 7-150 ∫| < 2η*Inclusive jet (0-5%) |

| < 2η*b-jet (0-10%) |

Photons, W, Z

h , B→J/𝜓 Inclusive jet, b-jet!, h , D

Page 23: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Quarkonia

➡ Onia in a deconfined partonic medium: color screening at different medium temperatures for different states (depending on binding energy) ✓ sequential melting/destruction of the states

➡ Onia: thermometer of the medium

23

A. Mocsy Eur.Phys.J.C61,2008

T

QQ

r0,ΔE

Page 24: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

partN0 50 100 150 200 250 300 350 400

AAR

0

0.2

0.4

0.6

0.8

1

1.2

1.4 = 2.76 TeVNNsCMS PbPb -1bµ = 150 PbPb

intL-1 = 230 nbpp

intL

0-5%5-10%10-20%

20-30%

30-40%

40-50%

50-100%

(1S)ϒ

(2S)ϒ

(3S), 95% upper limitϒ

0 0.5 1

AAR

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0-100%

Sequential melting: ϒ(1S, 2S, 3S)

➡ Sequential melting (proposed as key proof for existence of a QGP), first experimental proof of color screening picture

24

A. Mocsy Eur.Phys.J.C61,2008

T

RAAΥ(1S) > RAA

Υ(2S) > RAAΥ(3S)

PRL 109 (2012)

Page 25: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

(GeV/c)T

p0 5 10 15 20 25 30

AAR

0

0.2

0.4

0.6

0.8

1

1.2

1.4 CMS Preliminary = 2.76 TeVNNsPbPb

Cent. 0-100%|y| < 2.4

ψPrompt J/

Quarkonium phenomena: J/𝜓

➡ Experimental confirmation of (old) theoretical ideas

25

Regeneration Parton/jet fragmentation and en loss

Low-pT

High-pT

Puts back some QQbar Destroys and/or shifts the kinematics via partonic/hadronic interactions

CMS-PAS-HIN-12-014JHEP 05 (2016)

Page 26: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

pp, pPb, PbPb

➡ Sequential patterns also in pp & pPb✓ not clear whether it was the “medium” affecting the states (as in PbPb),

or the state affecting the “medium”26

JHEP 04 (2014)

|<2.4η|tracksN

10 210 310

(1S)

ϒ(2

S)/

ϒ

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

CMS

= 2.76 TeVNNspp

| < 1.93CM

|y

= 5.02 TeVNNspPb

| < 1.93CM

|y

= 2.76 TeVNNsPbPb

| < 2.4CM

|y

(1S)ϒ(2S)ϒ

0 < pT < 20 GeV/c

Low Track Multiplicity

High Track Multiplicity

Page 27: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

|<2.4η|tracksN

0 20 40 60 80 100 120 140

(1S)

Υ(2

S)/

Υ

0

0.1

0.2

0.3

0.4

0.5(1S)Υ(2S)/Υ

)-1< 5 GeV (0.3 fbT

p≤0

)-1< 7 GeV (1.9 fbT

p≤5 < 9 GeV

T p≤7

< 11 GeVT

p≤9

< 13 GeVT

p≤11

< 18 GeVT

p≤13

< 25 GeVT

p≤18

50 GeV≤ T

p≤25

(7 TeV)-14.8 fbCMSPreliminary

)|<1.2µµ(y|

pp@7TeV

➡ Decrease of the excited/ground state ratio confirmed at 7TeV➡ The ratio decreases strongly at lower pT

✓ in PAS: stronger indications that it is not the state affecting the “medium”27

CMS-PAS-BPH-14-009

25 < pT < 50 GeV/c

0 < pT < 5 GeV/c

Low Track Multiplicity

High Track Multiplicity

Page 28: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

LHC heavy-ions: Summary➡ Precision, Diversity and Surprises

✓ Precision: - charged hadrons measured up to 400GeV/c- separate measurements of charm & beauty quarks products

✓ Diversity- identified hadrons AND fully reconstructed jets

✓ Surprises: - collectivity also in pPb and pp collisions- ‘sequential’ pattern for onia also observed in pp and pPb collisions

28

Page 29: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

Extra stuff

29

Page 30: MIT at the LHC - University of Adelaide...Analyzing HI collisions: 2-particle correlations Event-by-event 6 Trigger particle p T trig,ηtrig, φtrig Associated particle p Tasssoc,ηassoc,

➡ 4 (6, 8) -particle cumulant (average over all events)✓ .

LHC: … collective motion EVERYWHERE

30

offlinetrkN

0 50 100 150

2v 0.05

0.10 = 13 TeVspp

< 3.0 GeV/cT

0.3 < p| < 2.4η|

PreliminaryCMS

|>2}η∆{2, |sub2v{4}2v{6}2v{8}2v{LYZ}2v

offlinetrkN

0 100 200 300

2v

0.05

0.10 = 2.76 TeVNNsPbPb

< 3.0 GeV/cT

0.3 < p| < 2.4η|

offlinetrkN

0 100 200 300

2v

0.05

0.10 = 5 TeVNNspPb

< 3.0 GeV/cT

0.3 < p| < 2.4η|

4 ≈ cos n φ1 +φ2 −φ3 −φ4( )#$ %&

1 2

z

3 4

cn{4} = 4 − 2 22, vn{4} = −cn{4}4

arXiv:1606.06198