Measurement of global spin alignment of K* and φ vector ...K*0 and φ Subhash Singha, QM 2019 5 •...

Measurement of global spin alignment of K*0 and φ vector mesons using the STAR detector at RHIC

Subhash SinghaInstitute of Modern Physics Chinese Academy of Sciences, Lanzhou

and Kent State University, Ohio(For the STAR Collaboration)

This work in part supported by grant from DOE Office of Science

2

Outline

•Motivation

•Analysis method

•Results:

Spin alignment of K*0 Comparison with φ meson (QM 2018) Comparison with ALICE results

•Summary and outlook

Subhash Singha, QM 2019

3

Probe initial stages in HIC

• Initial large angular momentum (L) ~ 104 h

• Initial large magnetic field (B) ~ 1018 Gauss at RHIC

• Can polarize quarks in medium

F. Becattini, et. al., Phys Rev. C. 77, 024906 (2008) D. Kharzeev, Nucl Phys A803, 227 (2008)


Angular momentum Magnetic field

Nature 548, 62 (2017) (STAR Collaboration) Phys Rev C 98, 14910 (2018) (STAR Collaboration)Λ Polarization

• PH(Λ) & PH(Λ) > 0

• PH(Λ) > PH(Λ)

Positive vorticity

Hints of magnetic coupling

‣ First experimental access to study the vorticity of the medium

See talk by J. Adams 06/11, 2.00 pm

4

Vector meson spin alignment (ρ00)


Z. Liang et. al., Phys. Lett. B629, 20 (2005) Y. Yang et. al., Phys. Rev. C 97, 034917 (2018)

dNd(cosθ*)

= N0 × [(1 − ρ00) + (3ρ00 − 1) cos2θ*)]

Observable

nRP

z

K*0

θ*

K+

π-

>

Reac

tion

Plan

e

‣ Deviation of ρ00 from (1/3) indicates spin alignment

K. Schiling et. al., Nucl. Phys. B 15 (1970) 397 Phys. Rev. C 77 (2008) 61902 (STAR Collaboration)

*θcos 1− 0.5− 0 0.5 1

(arb

uni

ts)

*θdc

osdN

0.5

0.6

0.7

Qualitative plot = 1/3

00ρ

= 0.2700ρ

Theoretical expectation of ρ00

Vorticity

Magnetic field

Hadronization

ρ00(ω) < 1/3

ρ00(B) > 1/3

ρ00(B) < 1/3

ρ00(rec) < 1/3

ρ00(frag) > 1/3

Electrically neutral vector mesonsElectrically charged vector mesons

Recombination

Fragmentation

Angular momentum and magnetic field can induce spin alignment of vector mesons

K*0 and φ

5Subhash Singha, QM 2019

• Predominantly produced in primordial production• Negligible feed-down compared to Λ and Λ

• Λ spin polarization (PH): Required knowledge of orientation of the angular momentum vector, estimated by deflection of spectators (can use 1st-order event plane)

• Vector meson spin alignment (ρ00): Polarization direction not required. Not subject to local cancellation. (can use both 1st-order and 2nd-order event plane)

Characteristic of K*0 and φ:

Species K*0 φ

Quark content ds ss

Mass (MeV/c2) 896 1020Lifetime (fm/c) 4 45

Spin (JP) 1- 1-

Decays Kπ KK

Branching ratio 49% 66%

The STAR detector and analysis details


• Uniform acceptance, full azimuthal coverage• TPC: tracking, centrality and event plane• TPC+TOF: particle identification

collision system Au+Au

collision energy 54.4 and 200 GeV

# of good events 520 and 350 M

rapidity |y| < 0.5

background rotation of daughters

polarization axis perpendicular to TPC 2nd-order event plane

consistency check 3D-random event plane

Report K*0 ρ00 as function of transverse momentum and centrality

)2 K (GeV/cπinvariant mass 0.75 0.8 0.85 0.9 0.95 1 1.05

Cou

nts

500

1000

1500

2000

310×

Au+Au 200 GeV, 10-60%DataBW functionResidual bkg function

2 0.2 MeV/c±mass = 891.0 2 0.7 MeV/c±width = 48.2

S/B = 0.0012

STAR Preliminary

* < 0.6θ < 2.0 GeV/c, 0.4 < cos T

1.5 < p

The STAR detector and signal reconstructionK*0 reconstruction:


K*0 Kπ

•Rotational background subtraction•mass/width consistent with

published value• K* yield is the area under the Breit-

Wigner function

• Uniform acceptance, full azimuthal coverage• TPC: tracking, centrality and event plane• TPC+TOF: particle identification


Analysis method• Raw yield of K*0 is extracted from 5 cos θ* bins

nRP

z

K*0

θ*

K+

π-

>

Reac

tion

Plan

e

• Here polarization axis (nRP) is the direction perpendicular to the TPC 2nd-order event plane (Ψ2)

• θ* is the angle between the daughter (K+) momentum of K*0 in its rest frame and nRP

<

<

*θcos 0.0 0.2 0.4 0.6 0.8 1.0

*θd

cos ra

wdN

ev

ent

N1

31

32

33

34

35

3−10×

< 2.0 GeV/cT

Au+Au 200 GeV, 10-60%, 1.5 < p

Data

STAR Preliminary

*θcos 0.0 0.2 0.4 0.6 0.8 1.0

*θd

cos co

rrdN

ev

ent

N1

55

60

65

3−10×

< 2.0 GeV/cT

Au+Au 200 GeV, 10-60%, 1.5 < pData

*)]θ(2 - 1) Cosobs00ρ) + (3 obs

00ρ[(1-

0p

STAR Preliminary


Analysis method• Yield of K*0 is corrected for efficiency and acceptance

• Observed ρ00obs is calculated from fitting the yield with function:

• Observed ρ00obs is corrected for TPC event plane resolution (R)

ρ00 −13

=4

1 + 3R(ρobs

00 −13

)

A. Tang et. al., Phys Rev C 98, 044907 (2018)

dNd(cosθ*)

= N0 × [(1 − ρobs00 ) + (3ρobs

00 − 1) cos2θ*)]

(GeV/c)T

p1 2 3 4 5

00ρ *0 K

0.25

0.30

0.35

0.40Au+Au 200 GeV, 10-60%STAR Preliminary

-sub event, TPC-EPηfull event, TPC-EP3D-random

(GeV/c)T

p1 2 3 4 5

00ρ *0 K

0.25

0.30

0.35

0.40Au+Au 54.4 GeV, 10-60%STAR Preliminary


10

K*0 ρ00 (pT)

• Significant deviation of ρ00 from 1/3 is observed at low pT for both 54.4 and 200 GeV• ρ00 from TPC η-sub and full event plane are consistent despite of different event

plane resolutions


• ρ00 results from 3D-random plane consistent with 1/3 as expected

For Au+Au 200 GeV, 10-60% centrality:TPC (Ψ2) resolution ~ 0.55 for η-sub event planeTPC (Ψ2) resolution ~ 0.77 for full event plane

(GeV/c)T

p1 2 3 4 5

00ρ *0 K

0.25

0.30

0.35

0.40Au+Au, 10-60%

54.4 GeV200 GeV

STAR Preliminary

(GeV/c)T

p0 1 2 3 4 5

00ρ φ

0.25

0.30

0.35

0.40Au+Au 200 GeV, 20-60%

TPC EPZDC EP

STAR Preliminary

11

ρ00 (pT): K*0 vs. φ

• Νοn-trivial and opposite pT dependence observed for K*0 and φ


Κ*0 φA

QM 2018

(GeV/c)T

p1 2 3 4 5

00ρ *0 K

0.25

0.30

0.35

0.40Au+Au, 10-60%

54.4 GeV200 GeV

STAR Preliminary

(GeV/c)T

p0 1 2 3 4 5

00ρ φ

0.25

0.30

0.35

0.40Au+Au 200 GeV, 20-60%

TPC EPZDC EP

STAR Preliminary

12

ρ00 (pT): K*0 vs. φ

• Trend for K*0 ρ00 is qualitatively consistent with the naive expectation from recombination/fragmentation of polarized quarks [1] but the magnitude is much larger

• φ ρ00 does not fit into naive recombination/fragmentation picture [1]• But it can be explained by the existence of coherent φ meson field [2]


[1] Z. Liang et. al., Phys. Lett. B629, 20 (2005) [2] X. Sheng et. al., arXiv:1910.13684 (2019)

QM 2018 Κ*0 φ

〉 part N〈0 100 200 300

00ρ *0 K

0.25

0.30

0.35

0.40 < 1.5 GeV/c

TAu+Au, 1.0 < p 54.4 GeV

200 GeV

STAR Preliminary TPC-EP


K*0 ρ00 (centrality)

• For peripheral collisions ρ00 ~ 1/3• For midcentral collisions ρ00 < 1/3 • For central collisions ρ00 close to 1/3

〉 part N〈0 100 200 300

00ρ *0 K

0.25

0.30

0.35

0.40 < 1.5 GeV/c

TAu+Au, 1.0 < p 54.4 GeV

200 GeV




• For peripheral collisions ρ00 ~ 1/3• For midcentral collisions ρ00 < 1/3 • For central collisions ρ00 close to 1/3• Trend similar to angular momentum vs. centrality

Angular momentum vs. impact parameter

〉 part N〈0 100 200 300 400

00ρ φ

0.30

0.32

0.34

0.36

< 5.4 GeV/cT

Au+Au 200 GeV, 1.2 < pZDC EP

STAR Preliminary

〉 part N〈0 100 200 300

00ρ *0 K

0.25

0.30

0.35

0.40 < 1.5 GeV/c

TAu+Au, 1.0 < p 54.4 GeV

200 GeV


15

ρ00 (centrality): K*0 vs. φ


QM 2018 Κ*0 φ

Mesons

τ(fm/c)Φ 45K*0 4

• K*0 ρ00 < 1/3 • φ ρ00 > 1/3 • For midcentral collisions

(GeV/c)T

p1 2 3 4 5

00ρ *0 K

0.15

0.20

0.25

0.30

0.35

0.40

ALICE, Pb+Pb, 10-50%

2.76 TeV

Au+Au, 10-60%54.4 GeV200 GeV

STAR Preliminary

〉 part N〈0 100 200 300 400

00ρ *0 K

0.1

0.2

0.3

0.4

< 1.2 GeV/cT

ALICE, 0.8 < pPb+Pb 2.76 TeV

< 1.5 GeV/cT

Au+Au, 1.0 < p54.4 GeV200 GeV

STAR Preliminary

16

K*0 ρ00 : RHIC vs. LHC

•pT and centrality dependence of ρ00 at RHIC is similar to LHC energies but with much better precision

•At low pT and midcentral collisions hint that LHC measurements are lower than RHIC by 1-1.5σ

Subhash Singha, QM 2019 arXiv: 1910.14408 (2019) (ALICE Collaboration)

17

Summary of ρ00/PH measurements from RHIC and LHC


Species Quark content JP ρ00/PH at top-RHIC ρ00/PH at LHC

K*0 ds 1- ρ00 < 1/3 (~4σ ) ρ00 < 1/3 (~3σ )

φ ss 1- ρ00 > 1/3 (~3σ ) ρ00 < 1/3 (~2σ )

Λ uds 1/2+ PH > 0 (~4σ ) PH ~ 0 (~1σ )

For midcentral collisions

• From current theoretical understanding PH Pq, while ρ00 Pq2• Given the small PH values observed at top RHIC and LHC energies, ρ00 expected to

be close to 1/3• Hence, the current ρ00 measurements are surprising!

• ρ00 can depend on hadronization, vorticity, electromagnetic and mesonic field• More theoretical input is needed to understand the data Z. Liang et. al., Phys. Lett. B629, 20 (2005)

Y. Yang et. al., Phys. Rev. C 97, 034917 (2018) X. Sheng et. al., arXiv:1910.13684 (2019)

∝ ∝ Pq: quark polarization

Nature 548, 62 (2017) (STAR Collaboration) Phys Rev C 98, 14910 (2018) (STAR Collaboration) arXiv: 1909.01281 (2019) (ALICE Collaboration) arXiv: 1910.14408 (2019) (ALICE Collaboration)

18

•We presented pT and centrality dependence of ρ00 of neutral K* from 54.4 GeV and 200 GeV.

• K*0 ρ00 < 1/3 is observed for both 54.4 and 200 GeV

• Observation of K*0 spin alignment at RHIC energies

• pT and centrality dependence of ρ00 similar between RHIC and LHC

Summary


〉 part N〈0 50 100 150 200 250 300 350

00ρ *0 K

0.25

0.30

0.35

0.40 < 1.5 GeV/c

TAu+Au 54.4 GeV, 1.0 < p

54.4 GeV200 GeV

STAR Preliminary

• For midcentral collisions, ρ00 (K*0) < 1/3, while ρ00 (φ) > 1/3• Need quantitative estimation from models to better

understand the data

(GeV/c)T

p1 2 3 4 5

00ρ *0 K

0.25

0.30

0.35

0.40Au+Au, 10-60%

54.4 GeV200 GeV

STAR Preliminary

19

OutlookFor Au+Au 200 GeV data:• STAR has collected more than 2 B events during 2014,

2016 and 2018. We expect to reach better statistical precision• Analysis of charged K* ρ00 with high statistics 200 GeV

data is underway


GeVNNs10 210

00ρ *0 K

0.1

0.2

0.3

0.4

< 5.0 GeV/c T

Au+Au, Centrality: 20-60 %, 1.2 < pSTAR Preliminary

Energy (GeV) # events (M)7.7 1009.1 16011.5 20014.5 32019.6 58027 500

(BES-II)

For lower energy Au+Au data (< 39 GeV):•High statistics and detector upgrades in 2nd phase of BES

will improve precision of vector meson ρ00 measurements


Thank you

21

Backup slides


)2 K (GeV/cπinvariant mass 0.75 0.8 0.85 0.9 0.95 1 1.05

Cou

nts

500

1000

1500

2000

310×

Au+Au 200 GeV, 10-60%DataBW functionResidual bkg function

2 0.2 MeV/c±mass = 891.0 2 0.7 MeV/c±width = 48.2

S/B = 0.0012

STAR Preliminary

* < 0.6θ < 2.0 GeV/c, 0.4 < cos T

1.5 < p

)2 K (GeV/cπinvariant mass 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Cou

nts

0.05

0.10

0.15

0.20

910×

Au+Au 200 GeV, 10-60% K pairπSame event

K pairπRotated event

STAR Preliminary

* < 0.6θ < 2.0 GeV/c, 0.4 < cos T

1.5 < p

22

Invariant mass signal reconstruction

• K*0 signal is extracted by using rotational background subtraction method• Signal fitted with Breit Wigner function plus second order polynomial as residual

background• K*0 mass and width consistent with published values• K*0 yield is the area under the Breit Wigner function

Before background subtraction After background subtraction


Breit Wigner function

BW =1

2πAΓ

(m − m0)2 + (Γ/2)2 Κ*0 Κ*0

23

Invariant mass signal reconstruction

•φ signal is extracted by using mixed event background subtraction method•Signal fitted with Breit Wigner function plus first order polynomial as residual

background• φ yield is the area under Breit Wigner function

Before background subtraction After background subtraction

Au+Au 200 GeV, centrality: 40-50%, pT: 1.2-1.8 GeV/c, cos θ*: 1/7- 2/7

φ meson

φ meson


BW =1

2πAΓ

(m − m0)2 + (Γ/2)2

Centrality (%)0 10 20 30 40 50 60 70 80

-sub

EP

reso

lutio

nη

0

0.2

0.4

0.6

0.8

2ΨTPC event plane 54.4 GeV200 GeV

24

Event plane reconstruction

• Second order event plane (ψ2) is measured using TPC

Ψ2 =12

∑ wisin(nϕi)∑ wicos(nϕi)

Phys. Rev. C 58 (1998) 1671

Event plane from TPC:STAR Preliminary


25

nRP

z

K*0

θ*

K+

π-

>

Reac

tion

Plan

e


Analysis method

• K*0 efficiency x acceptance (εrec) from embedding data

*θcos 0.0 0.2 0.4 0.6 0.8 1.0

)re

c∈

Acc

epta

nce

(×

Effic

ienc

y

0.2

0.4

0.6

0.8

< 2.0 GeV/cT

Au+Au 200 GeV, 10-60%, 1.5 < p

rec∈

STAR PreliminaryMC embedding

〉 part N〈0 50 100 150 200 250 300 350

00ρ *0 K

0.15

0.20

0.25

0.30

0.35

0.40 < 1.5 GeV/c

TAu+Au 200 GeV, 1.0 < pSTAR Preliminary


〉 part N〈0 50 100 150 200 250 300

00ρ *0 K

0.15

0.20

0.25

0.30

0.35

0.40 < 1.5 GeV/c

TAu+Au 54.4 GeV, 1.0 < pSTAR Preliminary


26


• Deviation of ρ00 from 1/3 is observed for mid-central collisions for both 54.4 and 200 GeV

• ρ00 results in peripheral collisions consistent with 1/3• ρ00 results from 3D random plane consistent with 1/3


GeVNNs10 210

00ρ *0 K

0.1

0.2

0.3

0.4

< 5.0 GeV/c T

Au+Au, Centrality: 20-60 %, 1.2 < pSTAR Preliminary

27

Energy dependence of K*0 ρ00

• No beam energy dependence observed in ρ00 with current precision• High statistics data from STAR BES-II can improve precision in ρ00 measurements in lower

beam energiesSubhash Singha, QM 2019

28

φ Κ*0

Results shown at QM 2018

• ρ00 (φ) > 1/3 for √sNN =39 and 200 GeV with >~ 3σ significance

• ρ00 (K*0) < 1/3 for √sNN = 11.5 - 39 GeV within ~ 1-2σ significance

High statistics data in 54.4 and 200 GeV allow precision measurement for centrality and transverse momentum dependence of ρ00 for K*0 and φ


〉 part N〈0 100 200 300 400

00ρ *0 K

0.15

0.20

0.25

0.30

0.35

0.40

< 1.2 GeV/cT

ALICE Preliminary, 0.8 < pPb+Pb 2.76 TeV

< 1.5 GeV/cT

Au+Au, 1.0 < p54.4 GeV200 GeV

STAR Preliminary

(GeV/c)T

p0 1 2 3 4 5

00ρ *0 K

0.20

0.25

0.30

0.35

0.40

ALICE Preliminary, Pb+Pb, 10-50%2.76 TeV

Au+Au, 10-60%54.4 GeV200 GeV

STAR Preliminary

29

K*0 ρ00 (centrality): RHIC vs. LHC


In ALICE Preliminary results, EP resolution correction with “1/R” term as a correction

〉 part N〈0 50 100 150 200 250 300 350

00ρ *0 K

0

0.1

0.2

0.3

0.4

0.5

0.6 < 1.5 GeV/c

TAu+Au, 1.0 < p

54.4 GeV200 GeV

STAR Preliminary

< 2.0 GeVT

Au+Au, p

200 GeV, PRC77

30

K*0 : comparison with published results


STAR(200 GeV) Published(Run-04) Preliminary(Run-11)

Event statistics 20 M 370 M

PID TPC only (poor S/B ratio) TPC+TOF

EP resolution correction

ρ00 −13

=4

1 + 3R (ρobs00 −

13 )1

R

• K*0 results are consistent with published results within 1-1.5σ considering systematic uncertainties

Phys. Rev. C 77 (2008) 61902 (STAR Collaboration)

A. Tang et. al., Phys. Rev. C 98 044907 (2018)

(GeV/c)T

p0 1 2 3 4 5

00ρ *0 K

0.1

0.2

0.3

0.4

0.5

0.6

0.7 Au+Au, 10-60%54.4 GeV200 GeV

STAR PreliminaryAu+Au, 20-60%200 GeV, PRC77

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Measurement of global spin alignment of K* and φ vector ...K*0 and φ Subhash Singha, QM 2019 5 •...

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