gluon polarization measurements at...

Gluon Polarization Measurements at STAR

Matthew Walkerfor the STAR Collaboration

February 6, 2011

STAR

Matthew Walker, MITSTAR WWND, Winter Park, COFebruary 6, 2011

Outline

! Brief theoretical motivation

! Inclusive measurements: Jets and pions

! Correlation measurements: Di-Jets

! Status and Prospects

2


Theoretical Motivation

! Polarized DIS tells us that the spin contribution from quark spin is only ~30%.

3

D. de Florian et al., Phys. Rev. D71, 094018 (2005). D. de Florian et al., Phys. Rev. Lett. 101 (2008) 072001

-0.04

-0.02

0

0.02

0.04

-0.04

-0.02

0

0.02

0.04

-0.04

-0.02

0

0.02

0.04

10-2

10-1

DSSV

DNS KRE

DNS KKP

DSSV !"2=1

DSSV !"2=2%

x!u–

x!d–

x!s–

x

GRSV maxg

GRSV ming

x!g

x

-0.2

-0.1

0

0.1

0.2

0.3

10-2

10-1

1

Without RHIC data With RHIC data

Substantial improvement for

0.05 < x < 0.2, but large

uncertainties at low x

x 110-110-2

8

parabola and the 1! uncertainty in any observable would correspond to !"2 = 1. In order to account for unexpectedsources of uncertainty, in modern unpolarized global analysis it is customary to consider instead of !"2 = 1 betweena 2% and a 5% variation in "2 as conservative estimates of the range of uncertainty.

As expected in the ideal framework, the dependence of "2 on the first moments of u and d resemble a parabola(Figures 3a and 3b). The KKP curves are shifted upward almost six units relative to those from KRE, due to thedi"erence in "2 of their respective best fits. Although this means that the overall goodness of KKP fit is poorer thanKRE, #d and #u seem to be more tightly constrained. The estimates for #d computed with the respective best fitsare close and within the !"2 = 1 range, suggesting something close to the ideal situation. However for #u, they onlyoverlap allowing a variation in !"2 of the order of a 2%. This is a very good example of how the !"2 = 1 does notseem to apply due to an unaccounted source of uncertainty: the di"erences between the available sets of fragmentationfunctions.

-0.2

0

0.2

0.4

-0.2

0

0.2

0.4

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

10-2

10-2

x(!u+!u–)

x(!d+!d–)

x!uv

x!dv

x!g–

x!u–

xBj

x!d–

xBj

x!s–

xBj

KRE (NLO)

KKP (NLO)unpolarizedKRE "

2KRE "

min+1

KRE "2

KRE "min

+2%

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

10-2

FIG. 4: Parton densities at Q2 = 10 GeV2, and the uncertainty bands corresponding to !!2 = 1 and !!2 = 2%

An interesting thing to notice is that almost all the variation in "2 comes from the comparison to pSIDIS data.The partial "2 value computed only with inclusive data, "2

pDIS , is almost flat reflecting the fact the pDIS data are

not sensitive to u and d distributions. In Figure 3, we plot "2pDIS with an o"set of 206 units as a dashed-dotted line.

The situation however changes dramatically when considering #s or #g as shown in Figures 3c and 3f, respectively.In the case of the variation with respect to #s, the profile of "2 is not at all quadratic, and the distribution is muchmore tightly constrained (notice that the scale used for #s is almost four times smaller than the one used for lightsea quarks moments). The "2

pDIS corresponding to inclusive data is more or less indi"erent within an interval aroundthe best fit value and increases rapidly on the boundaries. This steep increase is related to a positivity constraints on!s and !g. pSIDIS data have a similar e"ect but also helps to define a minimum within the interval. The preferredvalues for #s obtained from both NLO fits are very close, and in the case of KRE fits, it is also very close to thoseobtained for #u and #d suggesting SU(3) symmetry.

8

parabola and the 1! uncertainty in any observable would correspond to !"2 = 1. In order to account for unexpectedsources of uncertainty, in modern unpolarized global analysis it is customary to consider instead of !"2 = 1 betweena 2% and a 5% variation in "2 as conservative estimates of the range of uncertainty.

As expected in the ideal framework, the dependence of "2 on the first moments of u and d resemble a parabola(Figures 3a and 3b). The KKP curves are shifted upward almost six units relative to those from KRE, due to thedi"erence in "2 of their respective best fits. Although this means that the overall goodness of KKP fit is poorer thanKRE, #d and #u seem to be more tightly constrained. The estimates for #d computed with the respective best fitsare close and within the !"2 = 1 range, suggesting something close to the ideal situation. However for #u, they onlyoverlap allowing a variation in !"2 of the order of a 2%. This is a very good example of how the !"2 = 1 does notseem to apply due to an unaccounted source of uncertainty: the di"erences between the available sets of fragmentationfunctions.

-0.2

0

0.2

0.4

-0.2

0

0.2

0.4

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

10-2

10-2

x(!u+!u–)

x(!d+!d–)

x!uv

x!dv

x!g–

x!u–

xBj

x!d–

xBj

x!s–

xBj

KRE (NLO)

KKP (NLO)unpolarizedKRE "

2KRE "

min+1

KRE "2

KRE "min

+2%

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

10-2

FIG. 4: Parton densities at Q2 = 10 GeV2, and the uncertainty bands corresponding to !!2 = 1 and !!2 = 2%

An interesting thing to notice is that almost all the variation in "2 comes from the comparison to pSIDIS data.The partial "2 value computed only with inclusive data, "2

pDIS , is almost flat reflecting the fact the pDIS data are

not sensitive to u and d distributions. In Figure 3, we plot "2pDIS with an o"set of 206 units as a dashed-dotted line.

The situation however changes dramatically when considering #s or #g as shown in Figures 3c and 3f, respectively.In the case of the variation with respect to #s, the profile of "2 is not at all quadratic, and the distribution is muchmore tightly constrained (notice that the scale used for #s is almost four times smaller than the one used for lightsea quarks moments). The "2

pDIS corresponding to inclusive data is more or less indi"erent within an interval aroundthe best fit value and increases rapidly on the boundaries. This steep increase is related to a positivity constraints on!s and !g. pSIDIS data have a similar e"ect but also helps to define a minimum within the interval. The preferredvalues for #s obtained from both NLO fits are very close, and in the case of KRE fits, it is also very close to thoseobtained for #u and #d suggesting SU(3) symmetry.

1

2=

1

2!"+ Lq +!G+ Lg


Theoretical Motivation

! Extracting gluon polarization

4

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1aLL

cos!*

gg ! gg

qg ! qg

qq ! qq qq̄ ! qq̄

gg ! qq̄

=!f1 ! !f2 ! !h · aLL ! Dh

f

f1 ! f2 ! !h ! Dhf

ALL =d!!

d!

long-range short-range long-range

!f1

!f2

!h

!G(Q2) =! 1

0!g(x,Q2)dxExtract !g(x,Q2) using a global fit

1

2=

1

2!"+ Lq +!G+ Lg


STAR Detector

! = 1

! = 2

! = 0! = -1

East

Time Projection Chamber (TPC)

Endcap Electro

Magnetic

Calorimeter

(EEMC)

Barrel Electro Magnetic Calorimeter (BEMC)

Magnet

0.5T

West

5

Not shown:Trigger detectors or polarimeters


Inclusive Measurements

! Inclusive measurements have:

! High statistics

! Simple triggers

! Simple reconstruction

! Multiple subprocesses contribute

! Wide range of xgluon in each reconstructed bin

6

0.2

0.4

0.6

0.82/c2=100GeV2Q

-310 -210-110 1

0

X gluon

p =28 GeV/cT

p = 5.6 GeVT

/c

a)

1

!G

x10 5

0.25

0.5

0.75

1.0

0

frac

dN/d

(log

x)

-410

-310

-210

10

CL

/c ) 2 = 0.4 GeV2 G (Q! 20

-1 -0.5 0 0.5 1

-1

1

STARjet+X"pp

g=-g

!G

RSV

g=0

!G

RSV

GRS

V-st

d g=g

!G

RSV

b)

Pol. uncertainty

ALL =1

PBPY

(N++ +N!!)!R(N+! +N!+)

(N++ +N!!) +R(N+! +N!+)


Inclusive Jets

! STAR is well suited for Jet measurements with large acceptance (2" in azimuth)

! TPC provides charged tracking (|#| < 1.3)

! B/EEMC provide electromagnetic energy reconstruction (-1 < # < 2)

! Jets reconstructed using a midpoint cone algorithm

7

part

onpa

rtic

ledete

ctor

Jet

"0

"+

g

q


Inclusive Jets! Shape comparison between Run 6

Data and simulation shows good agreement

! Motivates use of correction based on PYTHIA MC

8

pT [GeV]

(Da

ta -

MC

) /

MC

-1

0

1

20 30 40 50 60

pT [GeV]

1

10

102

103

104

105

20 40 60 80

Run-6

Data

MC

Preliminary Run 6

STAR

Preliminary Run 6

STAR

!r/r from Jet Axis

Je

t P

rofile

!(!r)

0.2

0.4

0.6

0.8

1.0

0.2 0.4 0.6 0.8

11.44 < pT < 17.31 GeV

0.2 0.4 0.6 0.8

17.31 < pT < 26.19 GeV

0.2

0.4

0.6

0.8

1.0

26.19 < pT < 39.63 GeV 39.63 < pT < 59.96 GeV

Data

MC

Preliminary Run 6

STAR

MC: Pythia 6.4 + Geant 3


Inclusive Jets

! Data agrees well with NLO pQCD calculation after hadronization and underlying event correction is applied

9

pT [GeV]

(Data

- T

heory

) / T

heory

-1.0

-0.5

0.0

0.5

1.0

15 20 25 30 35 40 45 50 55

Systematic Uncertainty

Theoretical Uncertainty

STAR Run-6

Data-theory Comparison

of Inclusive Jet Cross Section

pp @ 200 GeV

Cone Radius = 0.7

-0.8 < ! < 0.8

!!Ldt = 5.39 pb

!1

Preliminary Run 6

STAR

pT [GeV]

d2!

/ 2!dpTd!

[pb/G

eV

]

0.1

1

10

102

103

104

105

15 20 25 30 35 40 45 50 55


Theory

NLO pQCD + CTEQ6M

Had. and UE. Corrections

STAR Run-6

Inclusive Jet Cross Section

pp @ 200 GeV

Cone Radius = 0.7

-0.8 < ! < 0.8

!!Ldt = 5.39 pb

!1

d2!

2!dpTd!

Preliminary Run 6

STAR

pT [GeV]

-1.0

-0.5

0.0

0.5

1.0

20 30 40 50

Pileup

20 30 40 50

Timebin

20 30 40 50

Luminosity

20 30 40 50

-1.0

-0.5

0.0

0.5

1.0

JES

STAR

Preliminary Run6


Inclusive Jets

! Run 6 results: GRSV-MAX/GRSV-MIN ruled out, a gluon polarization between GRSV-std and GRSV-zero favored

10

ALL systematics (x 10 -3)

Reconstruction +

Trigger Bias

[-1,+3]

(pT dep)

Non-longitudinal

Polarization

~ 0.03

(pT dep)

Relative

Luminosity0.94

Backgrounds1st bin ~ 0.5

else ~ 0.1

pT systematic ± 6.7%

D. de Florian et al. PRL 101 (2008) 072001.


Run 9 Projected Precision

! Projected statistical precision of 0.001 in several pT bins

! Several systematic studies underway

11


Neutral Pions! STAR is able to measure neutral pions over a wide

pseudorapidity range using its electromagnetic calorimeters

! Forward rapidity collisions dominated by qg collisions with a low x gluon

! GRSV-Max ruled out by Run 6 result

12


Correlation Measurements

! Reconstructing multiple physics objects (di-jets, photon/jet) provides information about initial parton kinematics

! Adds information about the shape of !g(x,Q2)

13

M =!x1x2s

!3 + !4 = lnx1

x2

! STAR well suited for correlation measurements with its large acceptance x1 =

1!s(pT3e

!3 + pT4e!4)

x2 =1!s(pT3e

!!3 + pT4e!!4)


Charged Pions

! Comparison of ALL("+) to ALL(" -) can give the sign of !g(x,Q2)

! Calculating ALL as a function of z alleviates problems of trigger bias

14

14

FIG. 11: Asymmetries measured by STAR at RHIC for !! (left) and !+ (right) compared to the prediction

from di!erent sets of polarized pdfs. The theoretical predictions were corrected to account for the jet trigger

e"ciency.

of the trigger is to enhance the contribution from large pjetT with respect to the small pjet

T events

and, therefore, increase the average !x" resulting in larger asymmetries.

With the present experimental accuracy it is not yet possible to perform a precise extraction

of the polarized gluon density from this observable. Nevertheless, the data can already rule out

any possible scenario with a large gluon polarization in the range 0.05 ! x ! 0.3. For that

purpose we include in Fig. 11 the prediction from the set GRSV-max set, where the polarized

gluon distribution is assumed to be equal to the unpolarized density at the very low intial scale of

µ2 = 0.4 GeV2. That set completely overestimates the experimental data at small z. Therefore,

in line with other measurements performed at RHIC, the preliminary data confirms the results

from the global analysis in [6] and points out to a small gluon polarization in the proton.

V. CONCLUSIONS

It is shown that the perturbative stability of the hadron+jet cross section improves considerably

after including the NLO contributions. The corrections are found to be nontrivial: K#factors are

larger for the unpolarized cross section than for the polarized one, resulting in a reduction of the

asymmetry at NLO. The possibility of looking at charged pions accompanied by a back-to-back

jet is studied phenomenologically in detail, finding that the asymmetries for ! prodution, in terms

D. deFlorian, Phys. Rev. D 79 (2009) 114014.


Di-Jets Run 6

15

! Run 6 data and simulation agreement is good

! Run 6 cross section and asymmetry analyses are progressing


2006 Cross Section

16

Mjj [GeV]

d3!/dMd!3d!4 [

pb

/Ge

V]

1

10

102

103

104

105

30 40 50 60 70 80 90


Theory

NLO pQCD + CTEQ6M

Had. and UE. Corrections

STAR Run-6

Dijet Cross Section

pp @ 200 GeV

Cone Radius = 0.7

max(pT) > 10 GeV, min(pT) > 7 GeV

-0.8 < ! < 0.8, |!!| < 1.0

|!!| > 2.0

!!Ldt = 5.39pb

!1

d3!

dMd!3d!4

! Unpolarized differential cross section between 24 and 100 (GeV/c2)

! NLO theory predictions using CTEQ6M provided by de Florian with and without corrections for hadronization and underlying event from PYTHIA

! Statistical Uncertainties as lines, systematics as rectangles

STAR Preliminary


2006 Cross Section

! Comparison to theory (including hadronization and underlying event correction) shows good agreement within systematic uncertainties

17

Mjj [GeV]

(Da

ta -

Th

eo

ry)

/ T

he

ory

-1.0

-0.5

0.0

0.5

1.0

30 40 50 60 70 80 90


Theoretical Uncertainty

STAR Run-6

Theory:

CTEQ6M

NLO pQCD

Had. UE. Corrections

Data-theory Comparison

of Dijet Cross Section

pp @ 200 GeV

Cone Radius = 0.7

max(pT) > 10 GeV, min(pT) > 7 GeV

-0.8 < ! < 0.8, |!!| < 1.0, |!!| > 2.0

!!Ldt = 5.39 pb

!1 STAR Preliminary


2006 Asymmetry

! Run 6 Longitudinal double helicity asymmetry

! Systematic uncertainties show effects on trigger efficiency from different theory scenarios

! Scale uncertainty (8.3%) from polarization uncertainty not shown

18

Mjj [GeV]

ALL

-0.02

0.00

0.02

0.04

0.06

0.08

30 40 50 60 70 80

Dijet ALL

pp @ 200 GeV

Cone Radius = 0.7

max(pT) > 10 GeV

min(pT) > 7 GeV

-0.8 < ! < 0.8, |!!| < 1.0

|!!| > 2.0

Data Run-6

Sys. Uncertainty

GRSV STD

DSSV

GRSV !g = 0

GRSV !g = !g !!Ldt = 5.39pb

!1

STAR Preliminary

ALL =1

PBPY

N++ !RN+!

N++ +RN+!


2009 Simulation

19

! Different detector, different trigger, updated geometry

! 9 STAR MC productions with partonic pT > 2 GeV

! PYTHIA 6.4.23, proPt0 (PYTUNE 329)

! Virtual Machine prepared with STAR software stack and deployed to over 1000 machines

! Run using cloud computing resources at Clemson University in South Carolina (Ranked #85 best supercomputer)

DateJul17 Jul24 Jul31

N M

ach

ines

0

200

400

600

800

1000

1200

1400

Available Machines

Working Machines

Idle Machines

! Over 12 billion events generated by PYTHIA, filtered to allow only 36 million to undergo detector simulation (GEANT3), and 10 million through full reconstruction

! Took over 400,000 CPU hours and generated 7 TB of files transferred to BNL

! Largest physics simulation on cloud, largest STAR simulation in CPU hours


Data/Simulation Run 9

! Run 9 data simulation agreement is good

20

20 30 40 50 60 70 80 90 100

No

rma

lize

d Y

ield

s

310

410

510

610

Data

Simulation

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

410

510

0 0.1 0.2 0.3 0.4 0.5 0.6

510

)2Invariant Mass (GeV/c20 30 40 50 60 70 80 90 100

(Da

ta-S

imu

)/S

imu

lati

on

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

34!

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8

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-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

*)"cos(0 0.1 0.2 0.3 0.4 0.5 0.6

-1

-0.8

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0

0.2

0.4

0.6

0.8

1

STAR Run 9 Data Preliminary

Jet + Jet + X#p+p

= 200 GeVs

= 0.7coneR

< 0.8!-0.8 <

| < 1.0!$ |

| > 2.0%$|

STAR Preliminary

M =!x1x2s !34 =

1

2ln

x1

x2cos !!

Matthew Walker, MITSTAR SPIN 2010October 1, 2010

2009 Projections

21

East West East West

Wed Sep 22 15:18:55 2010 ]2M [GeV/c

20 30 40 50 60 70 80

LL

A

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

east barrel - east barrel and west barrel - west barrel

MC

GRSV std

GRSV m03

GRSV zero

GS-C(pdf set NLO)

2009 STAR Data

]2M [GeV/c

20 30 40 50 60 70 80

LL

A

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

east barrel - west barrel

Scale uncertainty

GRSV std

DSSV

Projected PrecisionSTAR

! 8 pb-1 processed so far

! Average polarization: 59%

! Figure-of-merit: 0.96 pb-1


Prospects-Inclusive Jets

! First look at 500 GeV data in Run 9

! Future 500 GeV runs will significantly surpass statistical precision of current constraints, including the upcoming Run 11

22


Prospects: Di-Jets 500 GeV

! Dijets at 500 GeV can access the gluon polarization at lower x

! Expectations are for smaller asymmetries

! Larger luminosities should improve statistical uncertainties

23

500 GeV Projections for 390 pb-1 at 50% polarization

]2M [GeV/c

20 30 40 50 60 70 80 90 100 110

LL

A

-0.005

0

0.005

0.01

0.015

0.02

STAR: east barrel - endcap

< 0.04! < 2.0, -1.0 <

3!1.0 <

(P = 50%)-1390 pb NLO

GRSV std

DSSV

]2M [GeV/c

20 30 40 50 60 70 80 90 100 110

LL

A

-0.005

0

0.005

0.01

0.015

0.02

STAR: west barrel - endcap

< 1.04! < 2.0, 0.0 <

3!1.0 <

]2M [GeV/c

20 30 40 50 60 70 80 90 100 110

LL

A

-0.005

0

0.005

0.01

0.015

0.02

STAR: east barrel - east barrel and west barrel - west barrel

< 0.04! < 0.0, -1.0 <

3!-1.0 <

< 1.04! < 1.0, 0.0 <

3! 0.0 <

]2M [GeV/c

20 30 40 50 60 70 80 90 100 110

LL

A

-0.005

0

0.005

0.01

0.015

0.02

STAR: east barrel - west barrel

< 0.04! < 1.0, -1.0 <

3!0.0 <

Scale uncertainty

GRSV std

DSSV


Prospects-Prompt Photons! Material removed before Run 9 significantly reduces conversion

backgrounds

! Forward photons measure lowest x

! Correlation with mid-rapidity jet provides cleanest identification of initial parton kinematics

24

Gluonx

-310 -210 -110

G/G

!

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

EEMC Photon + BEMC Jet

Norm. from Pythia v8 with trigger simulation

subtraction assumes DSSVLL

Background A

25%" 70% and purity "LDA Efficiency

COMPASS

HERMES

SMC

2 = 100 GeV2DSSV Q

2 = 100 GeV2GRSV STD Q

=200 GeVs, Pol=0.60, -1

Ldt=50 pb#STAR

=500 GeVs, Pol=0.50, -1

Ldt=300 pb#STAR

TPhoton x

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

LL

A

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Photon + Jet, Full EEMC+BEMC

Norm. from Pythia v8 with trigger simulation

subtraction assumes DSSVLL

Background A

0.40! 0.74 and purity !Analysis efficiency

=200 GeVsDSSV

=200 GeVsGRSV STD

=500 GeVsDSSV

=500 GeVsGRSV STD

=200 GeVs, Pol=0.60, -1

Ldt=50 pb"STAR

=500 GeVs, Pol=0.50, -1

Ldt=300 pb"STAR


Summary

! 2006 results improved precision at mid-rapidity and new techniques used to limit systematics

! First global analysis including RHIC Spin data suggest small gluon polarization (0.05 < x < 0.2)

! Correlations measurements provide constraints on parton kinematics

! Run 9 provides the largest 200 GeV data sample to date and first look at lower x with 500 GeV data

! Expanded 500 GeV analyses will be possible with Run 11 data

25

gluon polarization measurements at...

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