PANIC05 M. Liu 1

Probing the Gluon Polarization with ALL of J/ at RHIC

Ming X. Liu

Los Alamos National Lab

(PHENIX Collaboration)

PANIC05 M. Liu 2

Spin Crisis and Gluon Polarization• Proton Spin Puzzle:

• Asymptotic limit

Gq

qG

JJ

LG

+=

Δ+Δ+ΔΣ= +21

21

∞→2Q

fGG

f

fqq

nLGQJ

n

nLQJ

316

16

2

1)(

316

3

2

1

2

1)(

2

2

+→Δ+Δ=

+→Δ+ΔΣ=

Gluons may play a significant role !€

Δ˜ Σ exp = ΔΣ − N f

α s

2πΔg

ΔΣ = 0.6 → Δg ~ 3

• PCAC

€

ΔΣ ≈0.3 vs ΔΣQCD ≈ 0.6

PANIC05 M. Liu 3

Gluon Polarization Measurements: (SI)DIS • Semi-inclusive DIS

– HERMES @ DESY• high-pT hadron pairs

– SMC @ CERN• high-pT hadron pairs

– COMPASS @ CERN• high-pT hadron pairs• open charm

lepton beam

or

or nucleon target

*

gluon

heavy flavor

PANIC05 M. Liu 4

@RHIC-SPIN• Polarized hadron collisions

– double longitudinal spin asymmetry

– leading-order gluon interactions• direct-photon production• heavy-flavor production

proton beam

proton beam

or

or

gluon

photon

proton beam

proton beam

or

or gluongluon

heavy flavor

€

ALL =σ ++ −σ +−

σ ++ + σ +−

PANIC05 M. Liu 5

The PHENIX Detectors

• Central Arms– || < 0.35, Δ ~ – , , e, +-, ... –

Identified– Momentum, Energy

• Muon Arms– 1.2 < || < 2.4– Momentum (MuTr)– Open charm, J/ etc

PANIC05 M. Liu 6

A New Probe: Heavy Quarks Sensitive to gluon polarization: Δg(x)

Gluon-gluon interaction dominates at LO

PHYTHA estimate:GeV Charm Beauty200 95:5 85:15500 97:3 92:8

Double spin asymmetry:

€

ALL ≈Δg(x1)

g(x1)

Δg(x2)

g(x2)aLL

gg →J / Ψ +X

Decay modes:

e+e-, +-, e, eX, X1.5

2

5

aLL

Karliner & Robinett,

Phys.Lett.B324 (1994)

J/bbeX

cceX

x

PANIC05 M. Liu 7

J/ production mechanism

• LO NRQCD:

]})()()2

11(

9[)2,

4()2,(

32

15

)()1()2,4

()2,(

{27

01)(/

803)(/

8021

2

1

13)(/

801

2

1

1

1

12

23

))(/(24

><−><−×⋅

Δ⋅Δ+

><−×⋅

Δ⋅Δ

⋅⋅≈Δ

→ ∫

SOPOm

msx

mfmxf

SOmsx

mfmxf

xdx

ms

JJgg

Jqq

sJpp

sm

λλλ

λλ

λ

δ

δ

ασ

mix of various processes

2~ sα

hep-ph/0509335 G. Nayak et al.

PANIC05 M. Liu 8

J/ production mechanism (cont.)

• NLO RNQCD:

gccgg

gccqq

qccqg

+→++→++→+

},{},{},{

“final state” mixture ratios: fixed from other data

)/,/4( max22/ ppxsma TTc

XJggLL ==→

Partonic asymmetry for ggJ/ X3~ sαTeryaev and Tkabladze PRD56(97)7331

PANIC05 M. Liu 9

NLO NRQCD and PHENIX data

Theoretical predictions of J/Ψ production at RHIC are in good agreement with the PHENIX data: COM process dominant

– PRD 68 (2003) 034003 G. Nayak, M. Liu, F. Cooper– PRL 93 (2004) 171801 F. Cooper, M. Liu, G. Nayak

PHENIX, PRL 92, 051802 (2004)

PANIC05 M. Liu 10

ALL Measurement with J/+-

• Experimental approach– Polarization=47% (average)– R is from Beam-Beam-Counter scalers– N_Jpsi Yield

PANIC05 M. Liu 11

J/ Yield Measurements • Fill by fill: (N+- - N++,--)

– Detector efficiency variation canceled out

– Have Open charm, DY and other background (<10%)

• Gaussian+Exponential background

– Used to estimate the background under J/Psi peak

2

2'

2

2?

2

)(

2

)(

2

1'

2

1 σσ

σσ

PsipsiJ MMMMMK eNeNeA

dMdN −

−−

−⋅− ⋅+⋅+⋅=

Dimuon mass distributions

+ - +(-) +(-)

PANIC05 M. Liu 12

NJ/ > 10 per fill

2 sigma cut:

2.78 < Mass < 3.42

<RL> = 1.0089(3)

€

ALL (raw) =NJ / Psi

++ − R ⋅NJ / Psi+−

NJ / Psi++ + R ⋅NJ / Psi

+−= −0.007 ± 0.013

Raw Asymmetries Fill by Fill:

PANIC05 M. Liu 13

Statistical Test• Beam polarization shuffling

– random beam polarization values – repeat 10,000 times

LLALL

LL

A

A

δ

PANIC05 M. Liu 14

Background Raw Asymmetry:

Left of the peak: 2.0 < Mass < 2.5

ALL(raw)= 0.0107 0.0220

Under the peak:

ALL(raw) = -0.0351 0.0318

N = 988 31

Background Estimation

018.00041.0)( ±−=RAWABGLL

Dimuon mass distributionsr

ArAA

r

ArAA

BGLL

inclLLPsiJ

LL

BGLL

inclLLPsiJ

LL

−⋅+

=

−⋅−

=

1)()(

1222

/

/

δδδ

+-

++, --

PANIC05 M. Liu 15

ALL vs pT

Log(x)

XJggLLLL a

xg

xg

xg

xgA +→ΔΔ

≈ /

2

2

1

1

)()(

)()(

First spin physics result from J/ - J/: produced via almost pure gluon fusion - sensitive to gluon polarization

PANIC05 M. Liu 16

Summary and Outlook• First measurement of double spin asymmetry with J/Psi from

longitudinally polarized p-p collisions– Almost pure gluon fusion– 10k J/psi, statistically limited– Expect x100 more statistics in the future

• Work in progress– J/Psi polarization measurement– Open charm - much larger statistics from run5 and will tell us more

about gluon polarization• Need more theoretical work

– J/ production mechanism– Polarized gluon PDFs – Excellent QCD test ground with polarization

• Where does the nucleon get its spin?– Still don’t know … but RHIC-SPIN will help us to find the answer– and we will learn a lot more about the nature of strong interactions

PANIC05 M. Liu 17

More on J/ Production Mechanism

- J/Psi polarization - a key probe?- Spin dynamics in pQCD

*cos1*cos

2θαθ

σ+∝

dd

α= +1: transversely polarizedα= -1: longitudinally polarizedα= 0: no polarization

+J/

θ*-

hep-ph/0106120 M. Kramer

PANIC05 M. Liu 18

NRQCD Calculations of ALL

• NRQCD LO Helicity dependent double-spin

asymmetry

]})()()2

11(

9[)2,

4()2,(

32

15

)()1()2,4

()2,(

{27

01)(/

803)(/

8021

2

1

13)(/

801

2

1

1

1

12

23

))(/(24

><−><−×⋅

Δ⋅Δ+

><−×⋅

Δ⋅Δ

⋅⋅≈Δ

→ ∫

SOPOm

msx

mfmxf

SOmsx

mfmxf

xdx

ms

JJgg

Jqq

sJpp

sm

λλλ

λλ

λ

δ

δ

ασ

λ=1

λ=0

GRSV+

J/

θ*-

hep-ph/0509335 G. Nayak et al.