The puzzling spin or the spin puzzle - Easy · 2016. 12. 28. · Frontiers and Careers 2015! 31 October - 02 November 2015! Paphos, Cyprus. ... independent of the renormalization

The puzzling spin or the spin puzzle

Charlotte Van Hulse University of the Basque country UPV-EHU

Frontiers and Careers 2015 31 October - 02 November 2015

Paphos, Cyprus

The nucleon and its spin

2

• naïve constituent quark model: 1

2=

1

2�⌃

• add relativistic corrections:

�⌃ ⇡ 0.65

�⌃ = 1


3


2=

1

2�⌃


�⌃ ⇡ 0.65

�⌃ = 1

• First measurement - EMC 1988: �⌃ = 0.14± 0.09± 0.21

= �u+�u+�d+�d+�s+�s


4


2=

1

2�⌃


�⌃ ⇡ 0.65

�⌃ = 1


= �u+�u+�d+�d+�s+�sSpin puzzle


5


2=

1

2�⌃


�⌃ ⇡ 0.65

�⌃ = 1


= �u+�u+�d+�d+�s+�sSpin puzzleSpin crisis!


6


2=

1

2�⌃


�⌃ ⇡ 0.65

�⌃ = 1


= �u+�u+�d+�d+�s+�sSpin puzzleSpin crisis!Birth of new experiments:

SMC, HERMES, COMPASS, JLab

Measurement of quark spin

7

• longitudinally polarised proton, deuteron, … • longitudinally polarised e±, μ± beam • in DIS regime: interaction of γ* with quark of

opposite spin orientation !

• measure , with lepton spin ( ) and proton spin ( ) / � � � ) !) !)

- number of quarks with spin aligned - anti-aligned wrt. proton spin7


8




- number of quarks with spin aligned - anti-aligned wrt. proton spin8


9




- 𝝙q=number of quarks with spin aligned - anti-aligned wrt. proton spin

Inclusive measurement of spin• inclusive measurement

�⌃ = �u+�u+�d+�d+�s+�s

/ � � � ) !)

/ g1(x) =1

2

X

q

e

2q�q(x)

integration over x

) !)� + �

10


�⌃ = �u+�u+�d+�d+�s+�s

/ � � � ) !)

/ g1(x) =1

2

X

q

e

2q�q(x)

integration over x

) !)� + �

flavor nonsinglet cNS‘ and singlet cS‘ Wilson coefficients arecalculable in ‘-loop perturbative QCD. These perturbativeQCD coefficients have been calculated to Oð!3

sÞ precision(Larin, van Ritbergen, and Vermaseren, 1997). For !s ¼ 0:3typical of the deep inelastic experiments one finds f1þP3

‘¼1 cNS‘!‘sðQÞg ¼ 0:85 and f1þP3

‘¼1 cS‘!‘sðQÞg ¼ 0:96.

The term "1 represents a possible leading-twist subtractionconstant from the circle at infinity when one closes thecontour in the complex plane in the dispersion relation(Bass, 2005). The subtraction constant affects just the firstmoment and corresponds to a contribution at Bjorken x equalto zero.

In terms of the flavor-dependent axial charges

2Ms#!q ¼ hp; sj "q$#$5qjp; si; (13)

the isovector, octet, and singlet axial charges are

gð3ÞA ¼ !u% !d;

gð8ÞA ¼ !uþ !d% 2!s;

gð0ÞA jinv=Eð!sÞ & gð0ÞA ¼ !uþ !dþ !s:

(14)

Here

Eð!sÞ ¼ expZ !s

0d~!s$ð~!sÞ="ð~!sÞ (15)

is a renormalization group factor which corrects for the (two-loop) nonzero anomalous dimension $ð!sÞ of the singletaxial-vector current

J#5 ¼ "u$#$5uþ "d$#$5dþ "s$#$5s (16)

which is close to 1 and which goes to 1 in the limit Q2 ! 1.The symbol " denotes the QCD beta function "ð!sÞ ¼%ð11% 2

3 fÞð!2s=2%Þ þ ' ' ' and $ is given by $ð!sÞ ¼

fð!s=%Þ2 þ ' ' ' where f ð¼ 3Þ is the number of active fla-

vors (Kodaira, 1980). The singlet axial charge gð0ÞA jinv isindependent of the renormalization scale # and corresponds

to gð0ÞA ðQ2Þ evaluated in the limit Q2 ! 1. The flavor non-

singlet axial charges gð3ÞA and gð8ÞA are renormalization groupinvariants. We are free to choose the QCD coupling !sð#Þ ateither a hard or a soft scale #. The perturbative QCDexpansion of Eð!sÞ remains close to 1—even for large valuesof !s. If we take !s ( 0:6 as typical of the infrared thenEð!sÞ ’ 1% 0:13% 0:03þ ' ' ' ¼ 0:84þ ' ' ' where %0:13and%0:03 are theOð!sÞ andOð!2

sÞ corrections, respectively.In the naive parton model gð0ÞA is interpreted as the fraction

of the proton’s spin which is carried by the intrinsic spin of itsquark and antiquark constituents. The experimental value of

gð0ÞA is obtained through measuring g1 and combining the first

moment integral in Eq. (12) with knowledge of gð3ÞA and gð8ÞA

from other processes plus theoretical calculation of the per-turbative QCD Wilson coefficients.

The isovector axial charge is measured independently in

neutron " decays [gð3ÞA ¼ 1:270) 0:003 (Beringer et al.,2012)] and the octet axial charge is commonly taken to bethe value extracted from hyperon " decays assuming a two-

parameter SU(3) fit [gð8ÞA ¼ 0:58) 0:03 (Close and Roberts,1993)]. However, it should be noted that the uncertainty

quoted for gð8ÞA has been a matter of some debate (Jaffe and

Manohar, 1990; Ratcliffe, 2004). SU(3) symmetry may be

badly broken and some have suggested that the error on gð8ÞA

should be as large as 25% (Jaffe and Manohar, 1990). Arecent reevaluation of the nucleon’s axial charges in thecloudy bag model taking into account the effect of the one-gluon-exchange (OGE) hyperfine interaction and the pion

cloud plus kaon loops led to the value gð8ÞA ¼ 0:46) 0:05

(Bass and Thomas, 2010). The model reduction of gð8ÞA fromthe SU(3) value comes primarily from the pion cloud with

gð3ÞA taking its physical value.Deep inelastic measurements of g1 have been performed in

experiments at CERN, DESY, JLab, and SLAC. An overviewof the world data on the nucleon’s g1 spin structure function isshown in Fig. 4. These data are published in EMC (Ashmanet al., 1989), SMC (Adeva et al., 1998b), E142 (Anthonyet al., 1996), E143 (Abe et al., 1998), E154 (Abe et al.,1997), E155 (Anthony et al., 2000), E155 (Anthony et al.,1999), HERMES (Airapetian et al., 2007a), JLab (Zheng

p 1xg

−0.03

−0.02

−0.01

0

0.01

0.02

0

0.02

0.04

0.06

0.08EMC

SMC

E143

E155

HERMES

CLAS

COMPASS

d 1xg

0

0.01

0.02

0.03

SMC

E143

E155

HERMES

CLAS

COMPASS

x−210 −110 1

n 1xg

−0.03

−0.02

−0.01

0

0.01

0.02

JLAB Hall A

E142

E154

HERMES

FIG. 4. World data on xg1 as a function of x for the proton (top),the deuteron (middle), and the neutron (bottom) at the Q2 of themeasurement. Only data points for Q2 > 1 GeV2 and W > 2:5 GeVare shown. Error bars are statistical errors only.

Aidala et al.: The spin structure of the nucleon 665

Rev. Mod. Phys., Vol. 85, No. 2, April–June 2013

Rev. Mod. Phys. 85, 655 (2013)

11


�⌃ = �u+�u+�d+�d+�s+�s

/ � � � ) !)

/ g1(x) =1

2

X

q

e

2q�q(x)

integration over x

= 0.33± 0.03(stat)± 0.05(syst)

) !)� + �

flavor nonsinglet cNS‘ and singlet cS‘ Wilson coefficients arecalculable in ‘-loop perturbative QCD. These perturbativeQCD coefficients have been calculated to Oð!3

sÞ precision(Larin, van Ritbergen, and Vermaseren, 1997). For !s ¼ 0:3typical of the deep inelastic experiments one finds f1þP3

‘¼1 cNS‘!‘sðQÞg ¼ 0:85 and f1þP3

‘¼1 cS‘!‘sðQÞg ¼ 0:96.

The term "1 represents a possible leading-twist subtractionconstant from the circle at infinity when one closes thecontour in the complex plane in the dispersion relation(Bass, 2005). The subtraction constant affects just the firstmoment and corresponds to a contribution at Bjorken x equalto zero.

In terms of the flavor-dependent axial charges

2Ms#!q ¼ hp; sj "q$#$5qjp; si; (13)

the isovector, octet, and singlet axial charges are

gð3ÞA ¼ !u% !d;

gð8ÞA ¼ !uþ !d% 2!s;

gð0ÞA jinv=Eð!sÞ & gð0ÞA ¼ !uþ !dþ !s:

(14)

Here

Eð!sÞ ¼ expZ !s

0d~!s$ð~!sÞ="ð~!sÞ (15)

is a renormalization group factor which corrects for the (two-loop) nonzero anomalous dimension $ð!sÞ of the singletaxial-vector current

J#5 ¼ "u$#$5uþ "d$#$5dþ "s$#$5s (16)

which is close to 1 and which goes to 1 in the limit Q2 ! 1.The symbol " denotes the QCD beta function "ð!sÞ ¼%ð11% 2

3 fÞð!2s=2%Þ þ ' ' ' and $ is given by $ð!sÞ ¼

fð!s=%Þ2 þ ' ' ' where f ð¼ 3Þ is the number of active fla-

vors (Kodaira, 1980). The singlet axial charge gð0ÞA jinv isindependent of the renormalization scale # and corresponds

to gð0ÞA ðQ2Þ evaluated in the limit Q2 ! 1. The flavor non-

singlet axial charges gð3ÞA and gð8ÞA are renormalization groupinvariants. We are free to choose the QCD coupling !sð#Þ ateither a hard or a soft scale #. The perturbative QCDexpansion of Eð!sÞ remains close to 1—even for large valuesof !s. If we take !s ( 0:6 as typical of the infrared thenEð!sÞ ’ 1% 0:13% 0:03þ ' ' ' ¼ 0:84þ ' ' ' where %0:13and%0:03 are theOð!sÞ andOð!2

sÞ corrections, respectively.In the naive parton model gð0ÞA is interpreted as the fraction

of the proton’s spin which is carried by the intrinsic spin of itsquark and antiquark constituents. The experimental value of

gð0ÞA is obtained through measuring g1 and combining the first

moment integral in Eq. (12) with knowledge of gð3ÞA and gð8ÞA

from other processes plus theoretical calculation of the per-turbative QCD Wilson coefficients.

The isovector axial charge is measured independently in

neutron " decays [gð3ÞA ¼ 1:270) 0:003 (Beringer et al.,2012)] and the octet axial charge is commonly taken to bethe value extracted from hyperon " decays assuming a two-

parameter SU(3) fit [gð8ÞA ¼ 0:58) 0:03 (Close and Roberts,1993)]. However, it should be noted that the uncertainty

quoted for gð8ÞA has been a matter of some debate (Jaffe and

Manohar, 1990; Ratcliffe, 2004). SU(3) symmetry may be

badly broken and some have suggested that the error on gð8ÞA

should be as large as 25% (Jaffe and Manohar, 1990). Arecent reevaluation of the nucleon’s axial charges in thecloudy bag model taking into account the effect of the one-gluon-exchange (OGE) hyperfine interaction and the pion

cloud plus kaon loops led to the value gð8ÞA ¼ 0:46) 0:05

(Bass and Thomas, 2010). The model reduction of gð8ÞA fromthe SU(3) value comes primarily from the pion cloud with

gð3ÞA taking its physical value.Deep inelastic measurements of g1 have been performed in

experiments at CERN, DESY, JLab, and SLAC. An overviewof the world data on the nucleon’s g1 spin structure function isshown in Fig. 4. These data are published in EMC (Ashmanet al., 1989), SMC (Adeva et al., 1998b), E142 (Anthonyet al., 1996), E143 (Abe et al., 1998), E154 (Abe et al.,1997), E155 (Anthony et al., 2000), E155 (Anthony et al.,1999), HERMES (Airapetian et al., 2007a), JLab (Zheng

p 1xg

−0.03

−0.02

−0.01

0

0.01

0.02

0

0.02

0.04

0.06

0.08EMC

SMC

E143

E155

HERMES

CLAS

COMPASS

d 1xg

0

0.01

0.02

0.03

SMC

E143

E155

HERMES

CLAS

COMPASS

x−210 −110 1

n 1xg

−0.03

−0.02

−0.01

0

0.01

0.02

JLAB Hall A

E142

E154

HERMES

FIG. 4. World data on xg1 as a function of x for the proton (top),the deuteron (middle), and the neutron (bottom) at the Q2 of themeasurement. Only data points for Q2 > 1 GeV2 and W > 2:5 GeVare shown. Error bars are statistical errors only.



Rev. Mod. Phys. 85, 655 (2013)

12


�⌃ = �u+�u+�d+�d+�s+�s

/ � � � ) !)

/ g1(x) =1

2

X

q

e

2q�q(x)

integration over x

= 0.33± 0.03(stat)± 0.05(syst)

• neutron β decay: g3A = (�u+�u)� (�d+�d) = 1.270± 0.003

hyperon β decay: g8A = (�u+�u) + (�d+�d)� 2(�s+�s)= 0.58± 0.03

) !)� + �

13


�⌃ = �u+�u+�d+�d+�s+�s

/ � � � ) !)

/ g1(x) =1

2

X

q

e

2q�q(x)

integration over x

= 0.33± 0.03(stat)± 0.05(syst)

• neutron β decay: g3A = (�u+�u)� (�d+�d) = 1.270± 0.003

hyperon β decay: g8A = (�u+�u) + (�d+�d)� 2(�s+�s)= 0.58± 0.03

�u+�u = 0.84± 0.01(stat)± 0.02(syst)

�d+�d = �0.43± 0.01(stat)± 0.02(syst)

�s+�s = �0.08± 0.01(stat)± 0.02(syst)

) !)� + �

Semi-inclusive measurement of spin

15

u

du

*γ

π+

(E, p )’ ’

N

e

q

π

hh

(E, p)

distribution function fragmentation function: • e+e- annihilation • semi-inclusive DIS • pp collisions

�

ep!eh =X

q

DF

p!q(xB , Q2)�eq!eq

FF

q!h(z,Q2)DF

p!q(xB , Q2) FF q!h(z,Q2)

LO


16

u

du

*γ

π+

(E, p )’ ’

N

e

q

π

hh

(E, p)


�

ep!eh =X

q

DF


FF

q!h(z,Q2)DF


3

e+e- annihilation and fragmentation functions (FFs)

e-

e+

γ*

q

q

h

h

LO


17

u

du

*γ

π+

(E, p )’ ’

N

e

q

π

hh

(E, p)


�

ep!eh =X

q

DF


FF

q!h(z,Q2)DF


LO


18

COMPASS, Phys. Lett. B 694, 227 (2010)

LO230 COMPASS Collaboration / Physics Letters B 693 (2010) 227–235

Fig. 1. The inclusive asymmetry A1,p [20] and the semi-inclusive asymmetries Aπ+1,p , AK+

1,p , Aπ−1,p , AK−

1,p from the present measurements (closed circles). The bands at the

bottom of each plot show the systematic errors. The A1,p , Aπ+1,p and Aπ−

1,p measurements from HERMES [14,26] open circles) are shown for comparison. The curves show thepredictions of the DSSV fit [1].

Table 1Unfolded asymmetries for charged pions and kaons produced on a proton target. The first error is statistical, the second is systematic.

⟨x⟩ ⟨Q 2⟩(GeV/c)2

Aπ+1,p Aπ−

1,p AK+1,p AK−

1,p

0.0052 1.16 0.008 ± 0.029 ± 0.016 0.020 ± 0.029 ± 0.016 0.078 ± 0.067 ± 0.038 −0.112±0.069±0.0390.0079 1.46 0.041 ± 0.018 ± 0.010 0.016 ± 0.018 ± 0.010 0.126 ± 0.036 ± 0.021 −0.040±0.039±0.0220.0142 2.12 0.040 ± 0.014 ± 0.008 0.049 ± 0.015 ± 0.009 0.046 ± 0.028 ± 0.016 0.038±0.031±0.0180.0245 3.22 0.122 ± 0.022 ± 0.014 0.055 ± 0.023 ± 0.013 0.117 ± 0.041 ± 0.024 0.092±0.048±0.0280.0346 4.36 0.156 ± 0.030 ± 0.019 0.060 ± 0.032 ± 0.018 0.196 ± 0.054 ± 0.033 0.074±0.066±0.0370.0487 5.97 0.141 ± 0.029 ± 0.018 0.118 ± 0.031 ± 0.019 0.174 ± 0.051 ± 0.031 0.027±0.064±0.0360.0765 8.96 0.230 ± 0.031 ± 0.022 0.053 ± 0.033 ± 0.019 0.215 ± 0.054 ± 0.033 0.029±0.071±0.0400.121 13.8 0.243 ± 0.041 ± 0.027 0.096 ± 0.047 ± 0.027 0.315 ± 0.072 ± 0.044 0.212±0.101±0.0580.172 19.6 0.392 ± 0.058 ± 0.040 0.165 ± 0.066 ± 0.038 0.355 ± 0.099 ± 0.059 0.195±0.147±0.0830.240 27.6 0.518 ± 0.060 ± 0.046 0.233 ± 0.069 ± 0.041 0.450 ± 0.101 ± 0.063 0.264±0.157±0.0890.341 40.1 0.549 ± 0.097 ± 0.064 0.134 ± 0.113 ± 0.064 0.512 ± 0.163 ± 0.097 0.375±0.259±0.1470.480 55.6 0.871 ± 0.122 ± 0.086 0.520 ± 0.142 ± 0.085 0.726 ± 0.207 ± 0.124 0.654±0.339±0.194

Table 2Correlation coefficients ρ of the unfolded asymmetries in bins of x.

x-bin 0.004–0.006 0.006–0.01 0.01–0.02 0.02–0.03 0.03–0.04 0.04–0.06 0.06–0.10 0.10–0.15 0.15–0.20 0.2–0.3 0.3–0.4 0.4–0.7

ρ(Aπ+1,p , A1,p) 0.29 0.34 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.43 0.45 0.46

ρ(Aπ−1,p , A1,p) 0.30 0.34 0.37 0.38 0.38 0.39 0.39 0.39 0.38 0.38 0.39 0.40

ρ(Aπ−1,p , Aπ+

1,p ) 0.12 0.15 0.17 0.16 0.15 0.16 0.16 0.15 0.16 0.16 0.19 0.20

ρ(AK+1,p , A1,p) 0.26 0.28 0.28 0.26 0.27 0.28 0.29 0.30 0.29 0.29 0.30 0.30

ρ(AK+1,p , Aπ+

1,p ) −0.17 −0.09 −0.04 −0.02 −0.02 −0.01 −0.02 −0.01 −0.01 −0.02 −0.02 −0.01

ρ(AK+1,p , Aπ−

1,p ) 0.03 0.04 0.04 0.05 0.05 0.05 0.05 0.06 0.05 0.05 0.04 0.03

ρ(AK−1,p , A1,p) 0.12 0.15 0.17 0.17 0.17 0.18 0.17 0.17 0.16 0.16 0.16 0.15

ρ(AK−1,p , Aπ+

1,p ) 0.03 0.03 0.04 0.04 0.04 0.04 0.03 0.04 0.02 0.03 0.02 0.05

ρ(AK−1,p , Aπ−

1,p ) −0.16 −0.09 −0.05 −0.03 −0.03 −0.03 −0.03 −0.03 −0.02 −0.03 −0.04 −0.02

ρ(AK−1,p , AK+

1,p ) 0.05 0.08 0.10 0.10 0.10 0.11 0.11 0.12 0.11 0.11 0.13 0.16

test on the asymmetries made on 23 subsets of data. At the levelof one standard deviation the upper bound of the error due tothese time-dependent effects is found to be 0.56σstat .

The experimental double-spin asymmetries for a proton targetare shown in Fig. 1. They are compared to the predictions of theDSSV fit [1] at the (x, Q 2) values of the data. The HERMES inclu-sive [26] and semi-inclusive [14] measurements for π+ and π−

are also displayed. The agreement with the DSSV parameterisationis good, even for the kaon asymmetries for which no data wereavailable when the prediction was made. In spite of the differentkinematic conditions, the agreement between the COMPASS andthe HERMES values for the pion asymmetries is also good. Thisobservation illustrates the fact that the Q 2 dependence at fixed xis small for semi-inclusive asymmetries.

0.80.60.40.20.0

-0.2

A

h1 (x,Q

2, z) =

Pq e

2q�q(x,Q2)Dh

q (z,Q2)

Pq e

2qq(x,Q

2)Dhq (z,Q

2)

Figure 2: Present status of the nucleon’s NLO helicity distributions according to the global analysisof Ref. [13]. The solid center lines show the best-fit result. The shaded bands provide uncertaintyestimates, using a criterion of ��

2 = 1 (inner bands) or ��

2/�

2 = 2% (outer bands) as allowedtolerance on the �2 value of the fit. Also shown are results from earlier analyses [14, 15] of nucleon spinstructure from lepton scattering data alone.

polarized opposite to the proton. Hence, if such pairs are in a spin singlet, one expects �u > 0 and,by the same reasoning, �d < 0. We note that the uncertainties in SIDIS are still quite large, and it isin particular di�cult to quantify the systematic uncertainty of the results related to the fragmentationmechanism at the relatively modest energies available.

The strange sea quark density shows a sign change. At moderately large x ⇠ 0.1, it is constrainedby the SIDIS data, which prefer a positive �s. On the other hand, the inclusive DIS data combinedwith the constraints from baryon �-decays demand a negative integral of �s. As a consequence, �s

obtains its negative integral purely from the contribution from low-x. Interestingly, there are initiallattice determinations of the integral �⌃

s

[12], which point to small values. It is clearly important tounderstand the strange contribution to nucleon spin structure better.

Constraints on the spin-dependent gluon distribution �g predominantly come from RHIC. As canbe seen from Fig. 2, the gluon distribution turns out to be small in the region of momentum fraction,0.05 . x . 0.2, accessible at RHIC, quite possibly having a node. At Q2 = 10 GeV2, the integral overthe mostly probed x-region is found to be almost zero,

R 0.2

0.05 dx�g(x) = 0.005± 0.06, where the error isobtained for a variation of �2 by one unit. Thus, on the basis of [13], there are no indications of a sizablecontribution of gluon spins to the proton spin. We also note that a way to access �g in lepton-nucleonscattering at HERMES and COMPASS is to measure final states that select the photon-gluon fusionprocess, heavy-flavor production and high-p

T

hadron or hadron-pair production [21, 22]. These datawere not included in the analysis [13], mostly because of the fact that success of the perturbative-QCDhard-scattering description had not been established for these observables in the kinematic regime of

4

Global fit of data

19

• 𝝙u>0

• 𝝙d<0

• sea quarks • ≈0 <-> <0 from inclusive DIS • large uncertainties

combine data from • ep eX and ep ehX • pp hX • e+e- hX (fragmentation)

Figure 2: Present status of the nucleon’s NLO helicity distributions according to the global analysisof Ref. [13]. The solid center lines show the best-fit result. The shaded bands provide uncertaintyestimates, using a criterion of ��

2 = 1 (inner bands) or ��

2/�

2 = 2% (outer bands) as allowedtolerance on the �2 value of the fit. Also shown are results from earlier analyses [14, 15] of nucleon spinstructure from lepton scattering data alone.

polarized opposite to the proton. Hence, if such pairs are in a spin singlet, one expects �u > 0 and,by the same reasoning, �d < 0. We note that the uncertainties in SIDIS are still quite large, and it isin particular di�cult to quantify the systematic uncertainty of the results related to the fragmentationmechanism at the relatively modest energies available.

The strange sea quark density shows a sign change. At moderately large x ⇠ 0.1, it is constrainedby the SIDIS data, which prefer a positive �s. On the other hand, the inclusive DIS data combinedwith the constraints from baryon �-decays demand a negative integral of �s. As a consequence, �s

obtains its negative integral purely from the contribution from low-x. Interestingly, there are initiallattice determinations of the integral �⌃

s

[12], which point to small values. It is clearly important tounderstand the strange contribution to nucleon spin structure better.

Constraints on the spin-dependent gluon distribution �g predominantly come from RHIC. As canbe seen from Fig. 2, the gluon distribution turns out to be small in the region of momentum fraction,0.05 . x . 0.2, accessible at RHIC, quite possibly having a node. At Q2 = 10 GeV2, the integral overthe mostly probed x-region is found to be almost zero,

R 0.2

0.05 dx�g(x) = 0.005± 0.06, where the error isobtained for a variation of �2 by one unit. Thus, on the basis of [13], there are no indications of a sizablecontribution of gluon spins to the proton spin. We also note that a way to access �g in lepton-nucleonscattering at HERMES and COMPASS is to measure final states that select the photon-gluon fusionprocess, heavy-flavor production and high-p

T

hadron or hadron-pair production [21, 22]. These datawere not included in the analysis [13], mostly because of the fact that success of the perturbative-QCDhard-scattering description had not been established for these observables in the kinematic regime of

4

DSSV, Phys. Rev. Lett. D101, 072001 (2008)

W production in pp collisions• pure parity violation:

uL dR ! W+

uR dL ! W�d(x1)

u(x2) • no need fragmentation functions • at higher Q2 scale than DIS

W+

ν

l+

20

W production in pp collisions

21

• pure parity violation: uL dR ! W+

uR dL ! W�d(x1)

u(x2)

A

W+

L (x1 � x2) =d

+R(x1)u(x2)� d

�R(x1)u(x2)

d

+R(x1)u(x2) + d

�R(x1)u(x2)

+u

+L(x1) d(x2)� u

�L (x1) d(x2)

u

+L(x1) d(x2) + u

�L (x1) d(x2)

=�d(x1)u(x2)��u(x1) d(x2)

d(x1)u(x2) + u(x1) d(x2)

• no need fragmentation functions • at higher Q2 scale than DIS

W+

ν

l+


22


uR dL ! W�d(x1)

u(x2)

A

W+

L (x1 � x2) =d

+R(x1)u(x2)� d

�R(x1)u(x2)

d

+R(x1)u(x2) + d

�R(x1)u(x2)

+u

+L(x1) d(x2)� u

�L (x1) d(x2)

u

+L(x1) d(x2) + u

�L (x1) d(x2)

=�d(x1)u(x2)��u(x1) d(x2)

d(x1)u(x2) + u(x1) d(x2)

�d(x1)

d(x1)

��u(x1)

u(x1)

x1 >> x2

x1 << x2


W+

ν

l+


23


uR dL ! W�d(x1)

u(x2)

A

W+

L (x1 � x2) =d

+R(x1)u(x2)� d

�R(x1)u(x2)

d

+R(x1)u(x2) + d

�R(x1)u(x2)

+u

+L(x1) d(x2)� u

�L (x1) d(x2)

u

+L(x1) d(x2) + u

�L (x1) d(x2)

=�d(x1)u(x2)��u(x1) d(x2)

d(x1)u(x2) + u(x1) d(x2)

�d(x1)

d(x1)

��u(x1)

u(x1)

x1 >> x2

x1 << x2

the ⌧s from the W ! ⌧⌫ process. Approximately 10 % of the W bosons decay into an electron and a

neutrino.

The LO W boson production mechanism results in the W boson being polarized by means of the V �A

structure of the weak interaction as shown in Fig. 1.7. The top panel shows the helicity configuration

of the incoming quark and anti-quark. The lower panel displays the preferred direction of e± quoting

the scattering angle ✓⇤ in the W center-of-mass system measured with respect to the positive z axis.

The V � A structure means that the weak current couples only to left-handed u and d quarks (or

to right-handed u and d quarks). For ultra-relativistic quarks, helicity 5 and chirality (handedness) are

approximately equivalent, and this results in full polarization of the produced W bosons. The W leptonic

decay process also couples only to left-handed e� and right-handed ⌫ (or right-handed e+ and left-handed

⌫). The conservation of angular momentum favors a decay with the final state lepton at a small angle with

respect to the initial state quark direction (and a similar small angle between the initial state anti-quark

and final anti-lepton). As a result, the W ! l⌫ decay distribution has angle dependence of:

d�W!l�+⌫

d(cos ✓⇤)/ (1± cos ✓⇤)2. (1.23)

Figure 1.7: Helicity configuration of W+ (Left) and W� (Right) production showing on top the helicityconfiguration of the incoming quark and anti-quark. The lower panel displays the preferred direction ofe± quoting the scattering angle ✓⇤ in the W center-of-mass system measured with respect to the positivez axis.

It is necessary to relate the lepton kinematics to yW , so that one can assign the momentum fraction

(x1, x2) of the quark or anti-quark through Eq. 1.22. Only then would it be possible to translate the

measured single spin asymmetry or charge ratio into a determination of the quark or anti-quark PDFs.

The rapidity of the W (yW ) is related to the lepton rapidity in the W rest frame (y⇤l ) and in the lab

frame (yl) by:

yl = yW + y⇤l , where y⇤l =12

ln1 + cos ✓⇤

1� cos ✓⇤

�. (1.24)

5Helicity is the projection of the spin onto the direction of momentum.

16

correlation (x1-x2) with direction of detected lepton


picture from Ph.D. thesis Kenichi Karatsu

W+l+

ν

Results from STAR collaboration

24Figure 7. 2011+2012 W+/− AL as afunction of W decay lepton η (|η| < 1.3) [6].Color lines/band stand for theory predictions,see details in the text. The grey bandpresents the systematic error from the relativeluminosity.

η lepton-2 -1 0 1 2

-0.5

0

0.5

= 2% error2χ/2χ∆DSSV08 L0

STAR Run 2013 Projection

-W

+W

ν + ± e→± W→+pp=510 GeVs < 50 GeVe

T25 < E-1=460pbdeliveredL

<P> = 53%

LA

+W -WDSSV08 RHICBOSDSSV08 CHE NLOLSS10 CHE NLO

Figure 8. Projections of W+/− AL inthe 2013 510 GeV p+p collisions at STARwith 460 pb−1 integrated luminosity andaverage polarization 53%. Central valuesare evaluated by the CHE model with DSSVglobal QCD fit.

the FCS and associated detectors (West, East, EEMC, FCS) and their ALL asymmetries in NLOQCD MC are shown in Figure 5 and Figure 6. Fiducial volume cuts are applied as well for theforward di-jet simulation. The left-top panel is for the FCS and east Barrel di-jet production;the right-top is for the FCS and west Barrel di-jets; the left-bottom panel is for the FCS andEEMC di-jets and the right-bottom panel is for the FCS and FCS di-jets. The FCS-FCS di-jetsprobe the lowest x region which is below 10−3. Reducing the systematic errors will be a primarygoal to realize such measurements for studying gluon helicity distribution at low x .

3. W production at STAR to probe the sea quark helicity distributionThe u and d momentum fraction distributions have been found asymmetric through Drell-Yan process by the E866 experiment [18]. This phenomenon can not be fully described byperturbative QCD and indicates a non-perturbative mechanism may play a role in this field.In the parity violating weak processes, intial u (d) quark and d (u ) quark couple to W+

(W−) in proton-proton collisions. The longitudinally polarized 500 or 510 GeV proton-protoncollisions at RHIC open a path to probe the light sea quark helicity functions via W productions(p+p → W+/−+X → l+/−+X). This process gets rid of the final state fragmentation functionsthat are encountered in semi-inclusive DIS processes. The W boson measured in high energypolarized proton-proton collisions is a unique probe for the polarized sea quark distrubtion atthe W mass scale [2, 19].

STAR has successfully reconstructed W+/W− via their e+/e− decay channels in the mid-

6

Journal of Physics: 535, 012003 (2014)• W+: • consistent with DSSV08 • 𝝙d<0

• W-: • >DSSV08 for η<0 • 𝝙u>0

• possibly 𝝙u>𝝙d

STAR preliminary 2011+2012 data

DSSV08 based on • ep eX and ep ehX • pp hX • e+e- hX

Projected precision with full RHIC W± data

25

-0.04

-0.02

0

0.02

10 -2 10 -1

x6u–

DSSV

DSSV+

DSSV++ with proj. W data

Q2 = 10 GeV2

-0.04

-0.02

0

0.02

10 -2 10 -1

x6d–

Q2 = 10 GeV2

Figure 9. x dependent sea quark polarized PDF (∆u is shown in the left, and ∆d is shown inthe right) extracted from the DSSV global fit. Uncertainties change from the yellow band to thered bands after including the projection of combined 2009 to 2013 RHIC W AL asymmetries.Figure from [16].

rapidity (−1 < η < 1) from 2009 500 GeV proton-proton collisions [20]. Measured mid-rapidityW+/− single spin asymmetries in 2009 data are consistent with predictions of the DSSV08global QCD fit analysis which only include DIS and SIDIS results. But statistics were limitedto separate different theoretical model descriptions. In RHIC runs of 2011 (500 GeV) and2012 (510 GeV) longitudinally polarized proton-proton collisions, STAR collected around 94pb−1 integrated luminosity of data, with average proton beam polarizations of 49% and 56%.The good statistics of this data sample allowed for the measurements of lepton pseudorapiditydependent W single spin asymmetry AL. To obtain this goal, several updates were applied tothe 2011 and 2012 combined data set. The detector acceptance to measure the W has beenextended from −1 < η < 1 to −1.3 < η < 1.3, with the help from the shower maximum detector(SMD) of the EEMC and inner sectors of the TPC. The profile likehood method was used tocombine W AL results which were measured independently in run 2011 and 2012 [6]. W+/−

events are reconstructed from W+/− decays to e+/− with transverse energy 25 < EeT < 50

(GeV). A significant signal to background ratio is seen in the reconstructed W+/− invariantmass distributions.

The STAR W decay lepton pseudorapidity dependent single spin asymmetry AL from the2011+2012 data is shown in Figure 7. Results of the W+/− AL are extracted from the likelihoodfunction with 68% confidence level. The grey band stands for the relative luminosity systematicerror. Colored lines stand for the NLO QCD calculations on the W+/− AL in RHICBOS andCHE models with DSSV08/LSS10 [2, 19] helicty functions as inputs. The green band reflects theDSSV08 ∆χ2/χ2 = 2% uncertainties. This result probes the flavor separated light quark andanti-quark helicity distributions in the 0.05 < x < 0.2 region. The W+ AL which is consistentwith the theory predictions indicates a negative d polarization. The W− AL which is sensitiveto the u quark polarization is larger than the theory predictions for the ηe < 0 range. Thissuggests a positive u helicity distribution. Therefore, a postive u− d helcity dependent functionis favored by this result.

The mid-rapidity W+/− AL asymmetries probe the polarization contributions carried byboth valence quark and sea quark. Extending the pseudorapidity of the reconstructed W+/−

to forward/backward regions will enhance the sensitivity for sea quark polarizations. A forwardtracking system, the Forward GEM Tracker (FGT, 1 < η < 2) was fully installed at STARbefore the 2013 run. This update enhances the charge seperation capabilities of STAR forforward/backward electron/positrons. In 2013, RHIC delivered around 460 pb−1 integrated

7

DSSV+ based on • ep eX and ep ehX • pp hX • e+e- hX (fragmentation)

Aschenauer, E.-C., et al. (RHIC Spin), 2012, ‘‘The RHIC Spin Program: Achievements and Future Opportunities’’, White Paper, http://www.bnl.gov/npp/docs/RHIC-Spin-WriteUp-121105.pdf

http://www.bnl.gov/npp/docs/RHIC-Spin-WriteUp-121105.pdf

= 0.33± 0.03(stat)± 0.05(syst)�⌃ =

Nucleon spin puzzle

26

𝝙q

More quark distributions: Sivers distribution

27

pT pT- distribution of unpolarized quarks in transversely polarized nucleon

28

pT pT-

left-right asymmetry in direction of outgoing hadron

distribution of unpolarized quarks in transversely polarized nucleon



29

3

The nucleon in multiple dimensionsWigner distributions

impact-parameter distributions

generalized parton distributions (GPDs)

GPDs

semi-inclusive deep-inelastic scattering (DIS) hard exclusive reactions

TMDs

Fourier transform

transverse-momentum dependent PDFs (TMDs)

19

Sivers function f1T

┴

● p+/K+: significantly positive non-zero orbital angular momentum

● π-: consistent with zero

● π0: slightly positive (isospin symmetry)

● K-: slightly positive

● u-quark dominance for π+ amplitude:

● π-: u- and d-quark cancellation

● K+>π+

A. Airapetian et al., Phys. Rev. Lett. 103 (2009) 152002Phys. Rev. Lett. 103, 152002 (2009)

semi-inclusive DIS on transversely polarized target

pictures taken from A. Bacchetta and M. Contalbrigo, Il Nuovo Saggiatore 28 (2012) 1-2


30

3

The nucleon in multiple dimensionsWigner distributions

impact-parameter distributions

generalized parton distributions (GPDs)

GPDs

semi-inclusive deep-inelastic scattering (DIS) hard exclusive reactions

TMDs

Fourier transform

transverse-momentum dependent PDFs (TMDs)

19

Sivers function f1T

┴

● p+/K+: significantly positive non-zero orbital angular momentum

● π-: consistent with zero

● π0: slightly positive (isospin symmetry)

● K-: slightly positive

● u-quark dominance for π+ amplitude:

● π-: u- and d-quark cancellation

● K+>π+

A. Airapetian et al., Phys. Rev. Lett. 103 (2009) 152002Phys. Rev. Lett. 103, 152002 (2009)

semi-inclusive DIS on transversely polarized target

pictures taken from A. Bacchetta and M. Contalbrigo, Il Nuovo Saggiatore 28 (2012) 1-2

Transverse-momentum- dependent quark distributions

31

accessible in semi-inclusive DIS, Drell-Yan, pp collisions hX

Pz

xPzkT


32


Pz

xPzkT


33


Pz

xPzkT

= 0.33± 0.03(stat)± 0.05(syst)�⌃ =

Nucleon spin puzzle

34

𝝙q

= 0.33± 0.03(stat)± 0.05(syst)�⌃ =

Nucleon spin puzzle

35

𝝙q𝝙G

LG

Lq

48

Disentangling the proton spin

Where are the other 70% coming from?

● gluon spin?large uncertainties so far...

● orbital angular momentum!● from gluons?● from quarks?

we continue investigating …..

Gluon helicity

36

Gluon helicity

37

(Bass et al., 2002) accuracy. The axial charge measured in!p elastic scattering is independent of any assumptions aboutpossible SU(3) breaking, the presence or absence of a sub-traction at infinity in the dispersion relation for g1 and thex! 0 behavior of g1. A recent suggestion for an experimentusing low-energy neutrinos produced from pion decay at restis discussed by Pagliaroli et al. (2012).

In a recent analysis (Pate, McKee, and Papavassiliou,2008) of parity-violating quasielastic electron and neutrinoscattering data between 0.45 and 1 GeV2 (from the JLabexperiments G0 and HAPPEx and the Brookhaven experi-ment E734), the axial form factor was extrapolated toQ2 ¼ 0and favored negative or zero values of !s with largeuncertainty.

B. Gluon polarization

Polarized proton-proton scattering is sensitive to the ratioof polarized to unpolarized glue !g=g, via leading-orderinteractions of gluons, as illustrated in Fig. 9. The firstexperimental attempt to look at gluon polarization wasmade by the FNAL E581/704 Collaboration using a200 GeV polarized proton beam and a polarized proton target.They measured a longitudinal double-spin asymmetry ALL

for inclusive multi-" and #0#0 production consistent withzero within their sensitivities, suggesting that !g=g is not solarge in the region of 0:05 & xg & 0:35 (Adams et al., 1994).

COMPASS was conceived to measure !g via the study ofthe photon-gluon fusion process, as shown in Fig. 10. Thecross section for this process is directly related to the (polar-ized) gluon distribution at the Born level. The experimentaltechnique consists of the reconstruction of charmed mesons(Alekseev et al., 2009c; Adolph et al., 2012d) or high-pT

hadrons (Ageev et al., 2006) in the final state to access !g.For the charmed meson case COMPASS also performed aNLO analysis which shifts probed xg to larger values. The

high-pT particle method leads to samples with larger statis-tics, but these have higher background contributions from

QCD Compton processes and fragmentation. High-pT hadronproduction was also used in early attempts to access gluonpolarization by HERMES (Airapetian et al., 2000a) andSMC (Adeva et al., 2004) and the most recent HERMESdetermination (Airapetian et al., 2010c) and COMPASSmeasurement (Adolph et al., 2012e).

These measurements in lepton-nucleon scattering are listedin Table III for the ratio of the polarized to unpolarized glue!g=g and shown in Fig. 11 for LO analyses of the data. Thedata cluster is around xg ! 0:1 with the exception of theCOMPASS NLO point from open charm. There is no evi-dence in the data for nonzero gluon polarization at this valueof xg.

The chance to measure !g was a main physics drive forpolarized RHIC. Experiments using the PHENIX and STARdetectors are investigating polarized glue in the proton.Measurements of !g=g from RHIC are sensitive to gluonpolarization in the range 0:02 & xg & 0:3 (

ffiffiffisp ¼ 200 GeV)

and 0:06 & xg & 0:4 (ffiffiffisp ¼ 62:4 GeV) for the neutral pion

ALL measured by PHENIX (Adare et al., 2009a, 2009b) andinclusive jet production measured by STAR at 200 GeVcenter-of-mass energy (Abelev et al., 2008b; Adamczyket al., 2012a). Additional channels sensitive to !g at RHIChave been published as well (Abelev et al., 2009; Adareet al., 2011a, 2012).

Combined preliminary results from PHENIX and STARusing more recent 200 GeV data than those published in

0

0.1

10−2 10−1

x

x∆s

COMPASS

HERMES

FIG. 8 (color online). COMPASS (Alekseev et al., 2010c) andHERMES (Airapetian et al., 2008c) results for the strangenesspolarization x!sðxÞ as a function of x. The data are obtained in aleading-order analysis of SIDIS asymmetries (including thosefor charged kaons) and using the DSS fragmentation functions(de Florian, Sassot, and Stratmann, 2007). The inner error barrepresents the statistical uncertainty; the full bar represents thequadratic sum of statistical and systematic uncertainties.

FIG. 9. Jet production from quark-gluon scattering in polarizedproton-proton collisions.

p

µ

c

cq

γ∗

µ

k

g

FIG. 10. Production of a c "c pair in polarized photon-gluon fusionis being used to measure gluon polarization in the polarized proton.

670 Aidala et al.: The spin structure of the nucleon


• polarized proton-proton collisions

• polarized DIS:
















0

0.1

10−2 10−1

x

x∆s

COMPASS

HERMES



p

µ

c

cq

γ∗

µ

k

g




semi-inclusive DIS: photon-gluon fusion
















0

0.1

10−2 10−1

x

x∆s

COMPASS

HERMES



p

µ

c

cq

γ∗

µ

k

g




high-pT hadron (pairs)

scaling violation from g1(x,Q2)

QCD toolbox

� scale (=DGLAP) evolution

more and more parton-parton splittings resolved as the “resolution” scale P increases

Mertig, van Neerven;Vogelsang

key prediction of pQCD

‘‘resolution scale’’ P

“splitting kernels” known to next-to-leading order (NLO)

NNLO results already on the horizon(crucial for future precision studies)

Moch, Vermaseren, Vogt

r } 1/P charm production

Gluon helicity

38
















0

0.1

10−2 10−1

x

x∆s

COMPASS

HERMES



p

µ

c

cq

γ∗

µ

k

g




• polarized proton-proton collisions

• polarized DIS:
















0

0.1

10−2 10−1

x

x∆s

COMPASS

HERMES



p

µ

c

cq

γ∗

µ

k

g




semi-inclusive DIS: photon-gluon fusion
















0

0.1

10−2 10−1

x

x∆s

COMPASS

HERMES



p

µ

c

cq

γ∗

µ

k

g




high-pT hadron (pairs)

scaling violation from g1(x,Q2)

QCD toolbox









r } 1/P charm production

��

Gluon Spin Contribution ΔG(x) from Scaling Violation of g1(x,Q2) in DIS

!;D3;��$G?3@A��,3;FA�):KE+7H��

9) �J�*��

O �UO �J��6J��S� ��*�� 7/��

��G9GEF��F:�� !7>;5;FK��,FDG5FGD7��JB7D;?7@F�

39

QCD toolbox









r } 1/P

(x

z

, µ)µd

dµ(�q(x, µ)

�g(x, µ) �g

�qZ 1

x

�Pqq �Pqg

�Pgq �Pgg

dz

z(= ( (( (splitting function, known up to NLO

0.8

0.6

0.4

0.2

0.0

-0.20.001 0.01 0.1 1

Phys. Rev. D 74,014015 (2006)

Gluon helicity from polarized DIS: scaling violation

40

Abelev et al. (2008b) and Adare et al. (2009b) are shown inFig. 12. The longitudinal double-spin asymmetry in neutralpion production measured by PHENIX based on combineddata from 2005, 2006, and 2009 is shown as a function of pionpT (upper scale) (Manion, 2011). Figure 12 also shows theasymmetry in single-inclusive jet production as a function ofjet pT (lower scale) measured by STAR based on data taken in2009 (Djawotho, 2011), providing the first evidence for non-zero gluon polarization in the proton. The relationship be-tween the pion and jet pT scales is given by the mean z valueof !0:5 (Adler et al., 2006). The data are shown with acalculation using helicity distributions extracted from aglobal fit to polarized world data from DIS, semi-inclusiveDIS, and proton-proton collisions of de Florian–Sassot–Stratmann–Vogelsang (DSSV) (de Florian et al., 2008,2009) that was updated to include these results (Aschenaueret al., 2012); see Sec. V.C for more details about fits tohelicity distributions. A given pT bin for single-inclusive jetor hadron production generally samples a wide range of xgvalues. However, dijet measurements in pþ p collisionsprovide better constraints on the xg values probed.Preliminary STAR results for dijet production have alsobeen released (Walker, 2011) and confirm the nonzerodouble-spin asymmetry seen in single jet production.

While there is now evidence in the RHIC data that gluonpolarization in the proton is nonzero, the measurements in-dicate that polarized glue, by itself, is not sufficient to resolve

the difference between the small value of gð0ÞA jpDIS and the

naive constituent quark model prediction !0:6 through thepolarized glue term %3ð!s=2"Þ!g. Note, however, thatgluon polarization !g! 0:2–0:3 would still make a signifi-cant contribution to the spin of the proton in Eq. (23).

C. NLO QCD-motivated fits to spin data

Global NLO perturbative QCD analyses are performed onpolarization data sets including both lepton-nucleonand proton-proton collision data. The aim is to extract thepolarized quark and gluon parton distributions. These analy-ses, starting from Ball, Forte, and Ridolfi (1996) and Altarelliet al. (1997), frequently use Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution and are performed in agiven factorization scheme. This QCD fit approach has morerecently been extended to a global analysis of data frompolarized DIS, semi-inclusive polarized DIS, and high-energy

TABLE III. Polarized gluon measurements from deep inelastic experiments.

Experiment Process hxgi h#2i (GeV2) !g=g

HERMES (Airapetian et al., 2000a) Hadron pairs 0.17 !2 0:41& 0:18& 0:03HERMES (Airapetian et al., 2010c) Inclusive hadrons 0.22 1.35 0:049& 0:034& 0:010þ0:125

%0:099SMC (Adeva et al., 2004) Hadron pairs 0.07 %0:20& 0:28& 0:10COMPASS (Ageev et al., 2006; Procureur, 2006) Hadron pairs, Q2 < 1 0.085 3 0:016& 0:058& 0:054COMPASS (Adolph et al., 2012e) Hadron pairs, Q2 > 1 0.09 3 0:125& 0:060& 0:063COMPASS (Adolph et al., 2012d) Open charm (LO) 0.11 13 %0:06& 0:21& 0:08COMPASS (Adolph et al., 2012d) Open charm (NLO) 0.20 13 %0:13& 0:15& 0:15

−210 −110

g/g

∆

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

gx

, 2002−20062>1 GeV2, QT

New COMPASS, high p, 2002−20032<1 GeV2, Q

TCOMPASS, high p

COMPASS, open charm, 2002−2007 2>1 GeV2, Q

TSMC, high p

2, all QT

HERMES, high p

2=3 GeV2µDSSV fit, 2=2.5 GeV2µG>0,∆LSS fit with

2=2.5 GeV2µG changing sign, ∆LSS fit with

FIG. 11 (color online). Gluon polarization !g=g from leading-order analyses of hadron or hadron-pair production as a function ofthe probed gluon momentum fraction xg. Also shown are NLO fits

from de Florian et al. (2009) and Leader, Sidorov, and Stamenov(2010). The inner error bar represents the statistical uncertainty; thefull bar represents the quadratic sum of statistical and systematicuncertainties. The horizontal bar indicates the xg range of the

measurement. Adapted from Adolph et al., 2012e.

(GeV)T

Jet p0 10 20 30

LLA

0

0.02

0.04

(GeV)T

p0π0 5 10 15

, Run 2005-20090πPHENIX Prelim. PHENIX shift uncertainty

0πDSSV++ for STAR Prelim. jet, Run 2009STAR shift uncertaintyDSSV++ for jet

PHENIX / STAR scale uncertainty 6.7% / 8.8% from pol. not shown

FIG. 12 (color online). The longitudinal double-spin asymmetryin "0 production measured by PHENIX (Manion, 2011) and in jetproduction measured by STAR (Djawotho, 2011), shown withcalculations based on the DSSV polarized parton distributionsthat were updated to include these results. The relationship betweenthe pion and jet pT scales is given by the mean z value of !0:5(Adler et al., 2006). Error bars represent the statistical uncertainty.From Aschenauer et al., 2012.



Gluon helicity from polarized DIS: photon-gluon fusion

Rev. Mod. Phys. 85, 655 (2013)

41











−210 −110

g/g

∆

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

gx

, 2002−20062>1 GeV2, QT


TCOMPASS, high p


TSMC, high p

2, all QT

HERMES, high p






(GeV)T

Jet p0 10 20 30

LLA

0

0.02

0.04

(GeV)T

p0π0 5 10 15







• DIS: • 𝝙G compatible with zero • limited x range • poor constraints on 𝝙G

Gluon helicity from polarized DIS: photon-gluon fusion

Rev. Mod. Phys. 85, 655 (2013)

Gluon helicity from polarized pp collisions

42

Probing ΔG in Polarized pp Collisions

pp → hX

hf

fXff

baba

hf

fXffLL

fXff

baba

LL Ddff

Dadff

ddddA

ba

baba

⊗⊗⊗

⊗⋅⊗Δ⊗Δ

=+

−= →

→→

−+++

−+++

∑

∑σ

σ

σσσσ

ˆ

ˆˆ

,

,

�AG4>7�>A@9;FG6;@3>�EB;@�3EK??7FDK��%%�;E�E7@E;F;H7�FA�Δ �


Probing ΔG in Polarized pp Collisions

pp → hX

hf

fXff

baba

hf

fXffLL

fXff

baba

LL Ddff

Dadff

ddddA

ba

baba

⊗⊗⊗

⊗⋅⊗Δ⊗Δ

=+

−= →

→→

−+++

−+++

∑

∑σ

σ

σσσσ

ˆ

ˆˆ

,

,

�AG4>7�>A@9;FG6;@3>�EB;@�3EK??7FDK��%%�;E�E7@E;F;H7�FA�Δ �


= + + …

�q

q

�q

qALL /

ps = 200GeV

ps = 500GeV

�g

g

�g

g

�g

g

�q

q

data sensitive to 0.05<x<1

Inclusive jet asymmetries in pp collisions

43











−210 −110

g/g

∆

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

gx

, 2002−20062>1 GeV2, QT


TCOMPASS, high p


TSMC, high p

2, all QT

HERMES, high p






(GeV)T

Jet p0 10 20 30

LLA

0

0.02

0.04

(GeV)T

p0π0 5 10 15







ps = 200GeV

Aschenauer, E.-C., et al. (RHIC Spin), 2012, ‘‘The RHIC Spin Program: Achievements and Future Opportunities’’, White Paper, http://www.bnl.gov/npp/docs/RHIC-Spin-WriteUp-121105.pdf

http://www.bnl.gov/npp/docs/RHIC-Spin-WriteUp-121105.pdf

Gluon helicity from inclusive jet asymmetries in pp collisions

44

Figure 1. STAR 2009 inclusive jet ALL

versus parton jet pT in 200 GeV p+pcollisions [4]. ALL of inclusive jets with|η| < 0.5 is shown in the top panel, and theresults with 0.5 < |η| < 1.0 are shown inthe bottom panel. Error bars are statisticaland gray boxes stand for systematic errors.

Figure 2. Recent global analysis fromthe DSSV group. Top panel: the gluonhelicity distribution ∆g at Q2 = 10GeV2, the red line is the newest fitincluding the 2009 RHIC data. Bottompanel: Truncated integral of ∆g for0.001 ≤ x ≤ 0.05 and 0.05 ≤ x ≤ 1at Q2 = 10 GeV2. Figure from [5].

STAR inclusive jet double spin asymmetry ALL in 200 GeV p+p collisions, extracts a non-zero gluon spin contributions (∆g(x,Q2)/g(x,Q2)) to the proton in 0.05 < x < 1 [4, 5]. Wproduction in polarized proton-proton collisions which avoids the parton fragmentation processesis a cleaner probe than hadrons to detect the light sea quark u and d polarization contribution(∆u(x,Q2)/u(x,Q2), ∆d(x,Q2)/d(x,Q2)) to the proton. The first lepton rapidity dependentW+/− single spin asymmetry AL in 500/510 GeV proton-proton collisions indicates a sizableand positive u quark polarization [6]. The latest released inclusive jet and W spin results atSTAR promote our understanding of the gluon, u and d polarized distributions in the probed0.05 < x < 1 region. Details about the jet and W spin analyses and projections for the futuremeasurments will be discussed in the following sections.

2

�G =

Z 1

0.05�g(x,Q2) dx ⇡ 0.2

Journal of Physics: 535, 012003 (2014)

More to come from pp collisions• analyse data extend range to lower x values • analyse di-jets • di-jet invariant mass M: M2=x1x2s • pseudo-rapidities η: ln(x1/x2)=η3+η4

ps = 500GeV

45


ps = 500GeV

vary rapidity to probe different x range

Bernd SurrowQCD Evolution Workshop 2014 QCD2014

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

-0.8 < �3 (4) < 0 / -0.8 < �4 (3) < 0

(EAST / EAST)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

-0.8 < �3 (4) < 0 / 0 < �4 (3) < +0.8

(EAST / WEST)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

-0.8 < �3 (4) < 0 / 1.2 < �4 (3) < 1.8

(EAST / EEMC)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

ET3 > 5GeV ET4 > 8GeV

0 < �3 (4) < 0.8 / 0 < �4 (3) < 0.8

(WEST / WEST)

Cone alg. (R=0.7) /

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

0 < �3 (4) < 0.8 / 1.2 < �4 (3) < 1.8

(WEST / EEMC)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

1.2 < �3 (4) < 1.8 / 1.2 < �4 (3) < 1.8

(EEMC / EEMC)

√

s = 500GeV

Figure 3. x1 (red) and x2 (blue) of initial partons probed by di-jets reconstructed within theSTAR detector acceptance (−1 < η < 2) in MC based on NLO thoery calculations. [13]

�R =

5·1

0-4

x 10-2

ET3 > 5GeV ET4 > 8GeVCone alg. (R=0.7) /

0

0.002

0.004

0.006

0.008

0.01

10 15 20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EAST / EAST)

-0.0010

0.0010.0020.0030.0040.0050.0060.0070.008

10 15 20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EAST / WEST)

-0.1-0.05

-00.05

0.10.15

0.20.25

0.30.35

20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EAST / EEMC)

0

0.002

0.004

0.006

0.008

0.01

10 15 20 25 30 35 40 45 50 55 60M (GeV)

A LL

DSSVGRSV STD

(WEST / WEST)

Delivered Luminosity = 1000pb-1

Polarization = 60%

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

10 15 20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(WEST / EEMC)

-0.0010

0.0010.0020.0030.0040.0050.0060.0070.008

10 15 20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EEMC / EEMC)

√

s = 500GeV

Figure 4. Di-jet ALL versus invariant mass with different configurations in the STAR detectoracceptance, −1 < η < 2 from MC based on NLO thoery calculations. [13]

luminosity in 2012 and 2013. Gluon polarization in lower x region will be probed by the ongoing2012/2013 jet analysis in higher center of mass collision energy.

2.2. Di-jet production at STARInclusive jets measured in 200 and 500 GeV proton-proton collisions can be used to probethe gluon polarization integral over a broad range in x. In the leading order QCD withcollinear approximations, the momentum fractions of inital hard scattering partons x1 and x2

4

op 2014 - QCD2014 �2014

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

-0.8 < �3 (4) < 0 / 2.8 < �4 (3) < 3.7

(EAST / FCS)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2


0 < �3 (4) < 0.8 / 2.8 < �4 (3) < 3.7

(WEST / FCS)

Cone alg. (R=0.7) /

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

1.2 < �3 (4) < 1.8 / 2.8 < �4 (3) < 3.7

(EEMC / FCS)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

2.8 < �3 (4) < 3.7 / 2.8 < �4 (3) < 3.7

(FCS / FCS)

√

s = 500GeV

Figure 5. x1 (red) and x2 (blue) ofinitial partons probed by forward di-jet witha proposed forward hadrnoinc calorimeterupgrade at STAR. [13]

�R = 5·10-4 E T3 >

5G

eV E

T4 >

8G

eVC

one

alg.

(R=0

.7) /

x 10-2

x 10-2

x 10-2

x 10-2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EAST / FCS)

-0.1

-0.05

-0

0.05

0.1

0.15

x 10-2

20 25 30 35 40 45 50 55 60M (GeV)

A LL

DSSVGRSV STD

(WEST / FCS)


Polarization = 60%

-0.1

-0.05

0

0.05

0.1

0.15

0.2

10 15 20 25 30 35 40M (GeV)

ALL

DSSVGRSV STD

(EEMC / FCS)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

10 11 12 13 14 15 16 17 18 19 20M (GeV)

ALL

DSSVGRSV STD

(FCS / FCS)

√

s = 500GeV

Figure 6. Projection of forward di-jet ALL

asymmetries in 500 GeV proton-proton collisionsof 1000 pb−1 delivered luminoisty with beampolarization of 60%. [13]

are correlated with the di-jet invariant mass M and the jet pseudo-rapidities η3, η4 (M2 = x1x2s,ln(x1/x2) = η3 + η4). Therefore, a certain x region can be selected by the di-jet productionby varying the pseudorapidities of the jets. In the asymmetric partonic scattering, lower xgluons can be probed by forward di-jet correlations. Uncertainties of the truncated momentof ∆g(x,Q2 = 10 GeV2) in the 0.001 ≤ x ≤ 0.05 region (shown in the bottom panel ofFigure 2) remain large compared to the fitted results in the 0.05 ≤ x ≤ 1 region. Achievingmeasurements which can probe this low x region will help contribute to our understanding ofthe proton gluon spin distributions. STAR has nearly continuous, full azimuthal acceptanceof electromagnetic calorimeters in −1.0 < η < 4.0: the Barrel ElectroMagnetic Calorimeter(BEMC: −1.0 < η < 1.0), the End-cap ElectroMagnetic Calorimeter (EEMC: 1.07 < η < 2.0)and the Forward Meson Spectrometer (FMS: 2.3 < η < 4.0). The electromagnetic calorimeters(and a possible forward hadronic calorimeter in the STAR upgrade plan [13]) together with theTime Projection Chamber (TPC: −1.3 < η < 1.3) provide a broad ∆η ×∆ϕ coverage for di-jetmeasurements.

Figure 3 shows the measured intial parton x1 and x2 by final di-jets with six different detectorconfigurations in 500 GeV proton-proton collisions from MC based on NLO QCD framework [13].The BEMC acceptance is divided into separate coverages: “East” (−1.0 < η < 0) and “West”(0 < η < 1). Jets are reconstructed using the Mid-point cone algorithm with cone radius R=0.7.In the di-jet pair, the leading jet pT is required to be larger than 8 GeV/c and the sub-leading jetpT should be larger than 5 GeV/c. The current RHIC sensitive x region extends to around 10−2

when both jets are reconstructed in the EEMC. The projected di-jet ALL for the West-West,West-East, East-East, West-EEMC, East-EEMC and EEMC-EEMC combinations are shown inFigure 4 assuming the beam polarization is 60% and 1000 pb−1 delivered luminosity [13]. Thedominant systematic error is the relative luminosity error δR = 5·10−4, the same value as cited inthe 2009 inclusive jet ALL results. The statistical and systematic errors of the projected ALL asshown in Figure 4 are much smaller than the separation between DSSV [5] and GRSV-STD [17]theory calculations, and both predict non-zero gluon helicity distribution. A forward hadroniccalorimeter (FCS) is proposed in the STAR forward upgrade plan [16]. Installation of thisforward instrument will allow the di-jet measurements to go to the forward pseudorapidity andreach lower x values. Projected initial parton x1, x2 values probed by forward di-jets detected in

5

46

proposed upgrade for STAR

Journal of Physics: 535 (2014) 012003


ps = 500GeV

vary rapidity to probe different x range

Bernd SurrowQCD Evolution Workshop 2014 QCD2014

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

-0.8 < �3 (4) < 0 / -0.8 < �4 (3) < 0

(EAST / EAST)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

-0.8 < �3 (4) < 0 / 0 < �4 (3) < +0.8

(EAST / WEST)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

-0.8 < �3 (4) < 0 / 1.2 < �4 (3) < 1.8

(EAST / EEMC)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2


0 < �3 (4) < 0.8 / 0 < �4 (3) < 0.8

(WEST / WEST)

Cone alg. (R=0.7) /

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

0 < �3 (4) < 0.8 / 1.2 < �4 (3) < 1.8

(WEST / EEMC)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

1.2 < �3 (4) < 1.8 / 1.2 < �4 (3) < 1.8

(EEMC / EEMC)

√

s = 500GeV

Figure 3. x1 (red) and x2 (blue) of initial partons probed by di-jets reconstructed within theSTAR detector acceptance (−1 < η < 2) in MC based on NLO thoery calculations. [13]

�R =

5·1

0-4

x 10-2

ET3 > 5GeV ET4 > 8GeVCone alg. (R=0.7) /

0

0.002

0.004

0.006

0.008

0.01

10 15 20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EAST / EAST)

-0.0010

0.0010.0020.0030.0040.0050.0060.0070.008

10 15 20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EAST / WEST)

-0.1-0.05

-00.05

0.10.15

0.20.25

0.30.35

20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EAST / EEMC)

0

0.002

0.004

0.006

0.008

0.01

10 15 20 25 30 35 40 45 50 55 60M (GeV)

A LL

DSSVGRSV STD

(WEST / WEST)


Polarization = 60%

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

10 15 20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(WEST / EEMC)

-0.0010

0.0010.0020.0030.0040.0050.0060.0070.008

10 15 20 25 30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EEMC / EEMC)

√

s = 500GeV

Figure 4. Di-jet ALL versus invariant mass with different configurations in the STAR detectoracceptance, −1 < η < 2 from MC based on NLO thoery calculations. [13]

luminosity in 2012 and 2013. Gluon polarization in lower x region will be probed by the ongoing2012/2013 jet analysis in higher center of mass collision energy.

2.2. Di-jet production at STARInclusive jets measured in 200 and 500 GeV proton-proton collisions can be used to probethe gluon polarization integral over a broad range in x. In the leading order QCD withcollinear approximations, the momentum fractions of inital hard scattering partons x1 and x2

4

op 2014 - QCD2014 �2014

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

-0.8 < �3 (4) < 0 / 2.8 < �4 (3) < 3.7

(EAST / FCS)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2


0 < �3 (4) < 0.8 / 2.8 < �4 (3) < 3.7

(WEST / FCS)

Cone alg. (R=0.7) /

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

1.2 < �3 (4) < 1.8 / 2.8 < �4 (3) < 3.7

(EEMC / FCS)

1

10

10 210 310 410 510 610 710 8

10-5

10-4

10-3

10-2

10-1

1x1 (x2)

d�/d

x 1 (d�

/dx 2)

(pb)

x1

x2

2.8 < �3 (4) < 3.7 / 2.8 < �4 (3) < 3.7

(FCS / FCS)

√

s = 500GeV

Figure 5. x1 (red) and x2 (blue) ofinitial partons probed by forward di-jet witha proposed forward hadrnoinc calorimeterupgrade at STAR. [13]

�R = 5·10-4 E T3 >

5G

eV E

T4 >

8G

eVC

one

alg.

(R=0

.7) /

x 10-2

x 10-2

x 10-2

x 10-2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

30 35 40 45 50 55 60M (GeV)

ALL

DSSVGRSV STD

(EAST / FCS)

-0.1

-0.05

-0

0.05

0.1

0.15

x 10-2

20 25 30 35 40 45 50 55 60M (GeV)

A LL

DSSVGRSV STD

(WEST / FCS)


Polarization = 60%

-0.1

-0.05

0

0.05

0.1

0.15

0.2

10 15 20 25 30 35 40M (GeV)

ALL

DSSVGRSV STD

(EEMC / FCS)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

10 11 12 13 14 15 16 17 18 19 20M (GeV)

ALL

DSSVGRSV STD

(FCS / FCS)

√

s = 500GeV

Figure 6. Projection of forward di-jet ALL

asymmetries in 500 GeV proton-proton collisionsof 1000 pb−1 delivered luminoisty with beampolarization of 60%. [13]

are correlated with the di-jet invariant mass M and the jet pseudo-rapidities η3, η4 (M2 = x1x2s,ln(x1/x2) = η3 + η4). Therefore, a certain x region can be selected by the di-jet productionby varying the pseudorapidities of the jets. In the asymmetric partonic scattering, lower xgluons can be probed by forward di-jet correlations. Uncertainties of the truncated momentof ∆g(x,Q2 = 10 GeV2) in the 0.001 ≤ x ≤ 0.05 region (shown in the bottom panel ofFigure 2) remain large compared to the fitted results in the 0.05 ≤ x ≤ 1 region. Achievingmeasurements which can probe this low x region will help contribute to our understanding ofthe proton gluon spin distributions. STAR has nearly continuous, full azimuthal acceptanceof electromagnetic calorimeters in −1.0 < η < 4.0: the Barrel ElectroMagnetic Calorimeter(BEMC: −1.0 < η < 1.0), the End-cap ElectroMagnetic Calorimeter (EEMC: 1.07 < η < 2.0)and the Forward Meson Spectrometer (FMS: 2.3 < η < 4.0). The electromagnetic calorimeters(and a possible forward hadronic calorimeter in the STAR upgrade plan [13]) together with theTime Projection Chamber (TPC: −1.3 < η < 1.3) provide a broad ∆η ×∆ϕ coverage for di-jetmeasurements.

Figure 3 shows the measured intial parton x1 and x2 by final di-jets with six different detectorconfigurations in 500 GeV proton-proton collisions from MC based on NLO QCD framework [13].The BEMC acceptance is divided into separate coverages: “East” (−1.0 < η < 0) and “West”(0 < η < 1). Jets are reconstructed using the Mid-point cone algorithm with cone radius R=0.7.In the di-jet pair, the leading jet pT is required to be larger than 8 GeV/c and the sub-leading jetpT should be larger than 5 GeV/c. The current RHIC sensitive x region extends to around 10−2

when both jets are reconstructed in the EEMC. The projected di-jet ALL for the West-West,West-East, East-East, West-EEMC, East-EEMC and EEMC-EEMC combinations are shown inFigure 4 assuming the beam polarization is 60% and 1000 pb−1 delivered luminosity [13]. Thedominant systematic error is the relative luminosity error δR = 5·10−4, the same value as cited inthe 2009 inclusive jet ALL results. The statistical and systematic errors of the projected ALL asshown in Figure 4 are much smaller than the separation between DSSV [5] and GRSV-STD [17]theory calculations, and both predict non-zero gluon helicity distribution. A forward hadroniccalorimeter (FCS) is proposed in the STAR forward upgrade plan [16]. Installation of thisforward instrument will allow the di-jet measurements to go to the forward pseudorapidity andreach lower x values. Projected initial parton x1, x2 values probed by forward di-jets detected in

5

47

proposed upgrade for STAR

Journal of Physics: 535 (2014) 012003

= 0.33± 0.03(stat)± 0.05(syst)�⌃ =

Nucleon spin puzzle

48

𝝙q𝝙G

LG

Lq

48

Disentangling the proton spin

Where are the other 70% coming from?

● gluon spin?large uncertainties so far...

● orbital angular momentum!● from gluons?● from quarks?

we continue investigating …..

�G ⇡ 0.2 ?

subtracting 𝝙q quark orbital angular momentum Lq

Access to quark orbital angular momentum

49

X. Ji, Phys. Rev. Lett. 78, 610 (1997)

➡

• Ji relation:

Jq = limt!0

1

2

Z 1

�1dx x[Hq(x, ⇠, t) + Eq(x, ⇠, t)]

JG = limt!0

1

2

Z 1

�1dx x[HG(x, ⇠, t) + EG(x, ⇠, t)]

50

Generalized parton distributions (GPDs)

x=average longitudinal momentum fraction

2ξ=average longitudinal momentum transfer t=squared momentum transfer to nucleon

four quark helicity-conserving GPDs at twist-2

proton-helicity non-flip proton-helicity flip

spin independent

spin dependent

Hq(x, ⇠, t)

Hq(x, ⇠, t) E

q(x, ⇠, t)

E

q(x, ⇠, t)

50

51


18


parton distributionsform factors

probability to findquark with longitudinal

momentum fraction x at transverse location b

┴

GPDs

Z 1

¡1

dxEq(x; »; t) = Fq2(t)

Z 1

¡1

dxHq(x; »; t) = Fq1(t) Hq(x; 0; 0) = q(x)

~Hq(x; 0; 0) =¢q(x)

Form factors Parton distributions GPDsprobability to find quark with longitudinal momentum fraction x at transverse location b⊥

52


18





┴

GPDs

Z 1

¡1


Z 1

¡1

dxHq(x; »; t) = Fq1(t) Hq(x; 0; 0) = q(x)

~Hq(x; 0; 0) =¢q(x)


53


18





┴

GPDs

Z 1

¡1


Z 1

¡1

dxHq(x; »; t) = Fq1(t) Hq(x; 0; 0) = q(x)

~Hq(x; 0; 0) =¢q(x)


54

helicity-(in)dependent probability distribution of quarks as a function of their longitudinal fractional momentum and transverse position M. Burkardt, Phys. Rev. D 62, 071503 (2000)

distortion of quark probability distribution compared to unpolarized nucleon M. Burkardt, Phys. Rev. D 66 114005 (2002)


55

DVCS

Deeply virtual Compton scattering

t

�⇤(q) �(q0)

x+ ⇠ x� ⇠

p(p) p(p0)

Q2 ⌘ �q2

xB ⌘ Q

2

2pq

⇠ ⇡ xB

2� xB

56

DVCS

Exclusive lepto-production of real photons

t

�⇤(q) �(q0)

x+ ⇠ x� ⇠

p(p) p(p0)

57

DVCS Bethe-Heitler

d� / |⌧BH |2 + |⌧DV CS |2+ ⌧BH⌧⇤DV CS + ⌧DV CS⌧⇤BH

|⌧BH | calculable with knowledge form factors

access to interference term through cross-section differences or azimuthal asymmetries

Exclusive lepto-production of real photons

t

�⇤(q) �(q0)

x+ ⇠ x� ⇠

p(p) p(p0)

Charge-separated beam-helicity asymmetry

58

CLAS, Phys. Rev. Lett. 100, 162002 (2008)

I / !e‘

!X3

n¼0

cIn cosðn!Þ þ "X2

n¼1

sIn sinðn!Þ": (35)

The proportionality involves a kinematic factor and the leptonpropagators of the BH process; " is the helicity of theincoming lepton. The Fourier coefficients cIn provide anexperimental constraint on the real part of the Comptonform factor and sIn on the imaginary part. Their relation tolinear combinations of Compton form factors and hence tothe respective GPDs is listed in Table VI. A specific Fouriercoefficient can be accessed experimentally by weighting thecross section with the respective azimuthal modulation.

The DVCS-BH interference term was extracted by varyingthe electric charge of the incident lepton (HERMES) andstudying polarization observables, varying the beam or targethelicity (JLab and HERMES). JLab experiments focused onstudying their accessible observables fully differentially.HERMES explored the advantages of using simultaneouslypolarization and charge observables to cleanly isolate theinterference term and obtained the most complete set ofDVCS observables measured so far providing access to allinterference terms listed in Eq. (34).

Figure 16 shows a summary of the HERMES DVCSmeasurements with polarized proton and deuterium targetsat their average kinematics (Airapetian et al., 2008b, 2009c,2010b, 2010d, 2011a, 2011b, 2012b, 2012c). Here AC is thecharge asymmetry and AXY are the polarization-dependentasymmetries with X and Y indicating the beam and targetpolarization, respectively, which could be longitudinal (L) ortransverse (T). The subscript I indicates an extraction of thepure interference term. The measured asymmetries are sub-ject to a harmonic expansion with respect to the azimuthalangle(s) as given by the superscript of AXY in the figure.These data denoted by squares in Fig. 16 show results ex-tracted from a DVCS sample with kinematically completeevent reconstruction (Airapetian et al., 2012c). The depen-dence on the kinematic variables t, Q2, and xB was exploredfor each observable.

An example of the high statistics data from JLab is shownin Fig. 17 for the beam-spin asymmetry ALU measured fullydifferentially by CLAS (Girod et al., 2008). The presented

data contain an admixture of the Asin!LU;I and Asin!

LU;DVCS contri-

butions from the interference and pure DVCS terms, which

TABLE VI. Linear combinations of Compton form factors (CFF)in the DVCS-BH interference terms. Here F1 and F2 are theelectromagnetic form factors. Subleading terms not shown aresuppressed in a wide range of kinematics.

Target polarization CFF combination

Unpolarized, charge F1H þ #ðF1 þ F2Þ ~H ! ðt=4m2ÞF2ELongitudinal F1

~H þ #ðF1 þ F2ÞH ! & & &Transverse / sinð!!!SÞ F2H! F1Eþ & & &Transverse / cosð!!!SÞ F2

~H ! F1# ~Eþ & & &

Amplitude Value−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3

)φcos(2LLA

φcosLLA

)φcos(0LLA

)φsin(2ULA

φsinULA

φcos)s

φ−φcos(

LT,IA

φsin)s

φ−φsin(

LT,IA

)s

φ−φcos(

LT,BH+DVCSA

)s

φ−φcos(

LT,IA

φsin)s

φ−φcos(

UT,IA

φcos)s

φ−φsin(

UT,IA

)s

φ−φsin(

UT,DVCSA

)s

φ−φsin(

UT,IA

)φsin(2LU,IA

φsinLU,DVCSA

φsinLU,IA

)φsin (2LUA

φsinLUA

)φcos(3CA

)φcos(2CA

φcosCA

)φcos(0CA

HERMES DVCSHydrogenDeuteriumHydrogen Pure

FIG. 16 (color online). Overview of all DVCS azimuthal asym-metry amplitudes measured at HERMES with proton and deuteriumtargets, given at the average kinematics. The inner error barrepresents the statistical uncertainty; the full bar represents thequadratic sum of statistical and systematic uncertainties.

0

0.1

0.2

0.3 = 2.82Q

= 0.45Bx

0

0.1

0.2

0.3 = 2.32Q

= 0.35Bx

0

0.1

0.2

0.3 = 1.72Q

= 0.25Bx

0 0.5 1 1.5

0

0.1

0.2

0.3 = 1.22Q

= 0.13Bx

= 3.32Q = 0.46Bx

= 2.72Q = 0.36Bx

= 1.92Q = 0.25Bx

0 0.5 1 1.5

= 1.42Q = 0.17Bx

= 3.72Q = 0.46Bx

= 3.02Q = 0.36Bx

= 2.22Q = 0.25Bx

0 0.5 1 1.5

= 1.62Q = 0.18Bx

)2−t (GeV00

a(t)

FIG. 17 (color online). The leading beam-spin asymmetry ampli-tude aðtÞ ¼ Asin!

LU differential in t, x, and Q2 as measured by CLAS,from Girod et al. (2008). An earlier CLAS measurement(Stepanyan et al., 2001) is indicated by the square. The opentriangles represent the cross-section data from Hall A (Camachoet al., 2006). Error bars are statistical errors only.



DVCS at HERMES

59Amplitude Value

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 )φcos(2

LLA

φcos LLA

)φcos(0LLA

)φsin(2ULA

φsin ULA

φcos )sφ - φcos(LT,IA

φsin )sφ - φsin(LT,IA

)sφ - φcos(

LT,BH+DVCSA

)sφ - φcos(

LT,IA

φsin )sφ - φcos(UT,IA

φcos )sφ - φsin(UT,IA

)sφ - φsin(

UT,DVCSA

)sφ - φsin(

UT,IA

)φsin(2LU,IA

φsin LU,DVCSA

φsin LU,IA

)φcos(3CA

)φcos(2CA

φcos CA

)φcos(0CA

HERMES DVCS HydrogenDeuterium

beam-charge asymmetry

JHEP 07 (2012) 32Nucl. Phys. B 829 (2010) 1

beam-helicity asymmetry

JHEP 07 (2012) 32Nucl. Phys. B 829 (2010) 1

transverse target-spin asymmetry

JHEP 06 (2008) 066

double spin (LT) asymmetry

Phys. Lett. B 704 (2011) 15

longitudinal target-spin asymmetry

JHEP 06 (2010) 019Nucl. Phys. B 842 (2011) 265double spin (LL) asymmetry

JHEP 06 (2010) 019Nucl. Phys. B 842 (2011) 265

GPD

GPD

GPD

H

E

H

Access to GPDs

60

• DVCS

• hard exclusive vector meson production:

• sensitive to different flavour combinations of GPDs

• sensitive to gluon GPDs

• amplitudes: Compton form factors

!

!

!

• constrain models from data

• lattice calculations

F(⇠, t) =X

q

e

2q

Z 1

�1dxF

q(x, ⇠, t)(1

⇠ � x� i✏

� 1

⇠ + x� i✏

)

F

q(x, ⇠, t) = GPD

Access to GPDs

61

• DVCS

• hard exclusive vector meson production:

• sensitive to different flavour combinations of GPDs

• sensitive to gluon GPDs

• amplitudes: Compton form factors

!

!

!

• constrain models from data

• lattice calculations

F(⇠, t) =X

q

e

2q

Z 1

�1dxF

q(x, ⇠, t)(1

⇠ � x� i✏

� 1

⇠ + x� i✏

)

F

q(x, ⇠, t) = GPD

• lattice calculations (arXiv.:1312.4816)

•

•

• Fit to data

• - Eur. Phys. J. C 59, 809 (2009)

• - Eur. Phys. J. C 73, 2397 (2013)

• - Eur. Phys. J. C 88, 065206 (2013)

Quark angular momentum

62

Ju = 0.24 Jd = 0.02

Jvalu = 0.230+0.009

�0.024 Jvald = �0.004+0.010

�0.016

Jvalu = 0.286± 0.011 Jval

d = �0.049± 0.007

Jvalu = 0.335 Jval

d = �0.052

Lu = �0.025± 0.080 Lu � Ld = �0.22± 0.11Ld = 0.19± 0.07

63

𝝙q𝝙G

LG

Lq

What are we actually measuring?

64

𝝙q𝝙G

LG

Lq

Spin decomposition

65

• Ji decomposition

1

2=

1

2�⌃+

X

q

Lq + JG

M0xy =X

q

1

2q†⌃zq +

X

q

q†[~r ⇥ 1

i(~@ � ig ~A)]zq + [~r ⇥ ( ~E ⇥ ~B)]z

�⌃ LQ JG

• each term from manifestly gauge invariant local operator • partonic interpretation • mixing with gluons (through ) • and accessible experimentally

�⌃

LQ ~A�⌃ JQ

LQ

JG

Spin decomposition

66


1

2=

1

2�⌃+

X

q

Lq + JG

M0xy =X

q

1

2q†⌃zq +

X

q

q†[~r ⇥ 1

i(~@ � ig ~A)]zq + [~r ⇥ ( ~E ⇥ ~B)]z

�⌃ LQ JG


�⌃

LQ ~A�⌃ JQ

LQ

JG

Spin decomposition

67


1

2=

1

2�⌃+

X

q

Lq + JG

M0xy =X

q

1

2q†⌃zq +

X

q

q†[~r ⇥ 1

i(~@ � ig ~A)]zq + [~r ⇥ ( ~E ⇥ ~B)]z

�⌃ LQ JG


�⌃

LQ ~A�⌃ JQ

LQ

Spin decomposition

68

• Jaffe-Manohar decomposition

1

2=

1

2

X

q

�q +X

q

Lq +�G+ LG

�⌃

M+12 =1

2

X

q

q†+�5q+ +X

q

q†+(~r ⇥1

i~@)zq+ + ✏+�ijTrF+iAj + 2TrF+j(~r ⇥ 1

i~@)zAj

LQ LG�G

�⌃• only term in common with Ji decomposition • in A+=0 gauge: partonic interpretation for quark, gluon spin and OAM • and accessible experimentally, and not clear • interpretation of quark OAM (Phys. Rev. D 88, 014014 (2013))

�⌃ �G LQ LG

LQ quark OAM before quark struck by γ*LQ quark OAM after quark struck by γ* and moved away from nucleon remnant

• only term in common with Ji decomposition • in A+=0 gauge: partonic interpretation for quark, gluon spin and OAM • and accessible experimentally, and not clear • interpretation of quark OAM (Phys. Rev. D 88, 014014 (2013))

Spin decomposition

69

• Jaffe-Manohar decomposition

1

2=

1

2

X

q

�q +X

q

Lq +�G+ LG

�⌃

M+12 =1

2

X

q

q†+�5q+ +X

q

q†+(~r ⇥1

i~@)zq+ + ✏+�ijTrF+iAj + 2TrF+j(~r ⇥ 1

i~@)zAj

LQ LG�G

�⌃

�⌃ �G LQ LG

LQ quark OAM before quark struck by γ*LQ quark OAM after quark struck by γ* and moved away from nucleon remnant

I / !e‘

!X3

n¼0

cIn cosðn!Þ þ "X2

n¼1

sIn sinðn!Þ": (35)

The proportionality involves a kinematic factor and the leptonpropagators of the BH process; " is the helicity of theincoming lepton. The Fourier coefficients cIn provide anexperimental constraint on the real part of the Comptonform factor and sIn on the imaginary part. Their relation tolinear combinations of Compton form factors and hence tothe respective GPDs is listed in Table VI. A specific Fouriercoefficient can be accessed experimentally by weighting thecross section with the respective azimuthal modulation.

The DVCS-BH interference term was extracted by varyingthe electric charge of the incident lepton (HERMES) andstudying polarization observables, varying the beam or targethelicity (JLab and HERMES). JLab experiments focused onstudying their accessible observables fully differentially.HERMES explored the advantages of using simultaneouslypolarization and charge observables to cleanly isolate theinterference term and obtained the most complete set ofDVCS observables measured so far providing access to allinterference terms listed in Eq. (34).

Figure 16 shows a summary of the HERMES DVCSmeasurements with polarized proton and deuterium targetsat their average kinematics (Airapetian et al., 2008b, 2009c,2010b, 2010d, 2011a, 2011b, 2012b, 2012c). Here AC is thecharge asymmetry and AXY are the polarization-dependentasymmetries with X and Y indicating the beam and targetpolarization, respectively, which could be longitudinal (L) ortransverse (T). The subscript I indicates an extraction of thepure interference term. The measured asymmetries are sub-ject to a harmonic expansion with respect to the azimuthalangle(s) as given by the superscript of AXY in the figure.These data denoted by squares in Fig. 16 show results ex-tracted from a DVCS sample with kinematically completeevent reconstruction (Airapetian et al., 2012c). The depen-dence on the kinematic variables t, Q2, and xB was exploredfor each observable.

An example of the high statistics data from JLab is shownin Fig. 17 for the beam-spin asymmetry ALU measured fullydifferentially by CLAS (Girod et al., 2008). The presented

data contain an admixture of the Asin!LU;I and Asin!

LU;DVCS contri-

butions from the interference and pure DVCS terms, which

TABLE VI. Linear combinations of Compton form factors (CFF)in the DVCS-BH interference terms. Here F1 and F2 are theelectromagnetic form factors. Subleading terms not shown aresuppressed in a wide range of kinematics.

Target polarization CFF combination

Unpolarized, charge F1H þ #ðF1 þ F2Þ ~H ! ðt=4m2ÞF2ELongitudinal F1

~H þ #ðF1 þ F2ÞH ! & & &Transverse / sinð!!!SÞ F2H! F1Eþ & & &Transverse / cosð!!!SÞ F2

~H ! F1# ~Eþ & & &

Amplitude Value−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3

)φcos(2LLA

φcosLLA

)φcos(0LLA

)φsin(2ULA

φsinULA

φcos)s

φ−φcos(

LT,IA

φsin)s

φ−φsin(

LT,IA

)s

φ−φcos(

LT,BH+DVCSA

)s

φ−φcos(

LT,IA

φsin)s

φ−φcos(

UT,IA

φcos)s

φ−φsin(

UT,IA

)s

φ−φsin(

UT,DVCSA

)s

φ−φsin(

UT,IA

)φsin(2LU,IA

φsinLU,DVCSA

φsinLU,IA

)φsin (2LUA

φsinLUA

)φcos(3CA

)φcos(2CA

φcosCA

)φcos(0CA

HERMES DVCSHydrogenDeuteriumHydrogen Pure

FIG. 16 (color online). Overview of all DVCS azimuthal asym-metry amplitudes measured at HERMES with proton and deuteriumtargets, given at the average kinematics. The inner error barrepresents the statistical uncertainty; the full bar represents thequadratic sum of statistical and systematic uncertainties.

0

0.1

0.2

0.3 = 2.82Q

= 0.45Bx

0

0.1

0.2

0.3 = 2.32Q

= 0.35Bx

0

0.1

0.2

0.3 = 1.72Q

= 0.25Bx

0 0.5 1 1.5

0

0.1

0.2

0.3 = 1.22Q

= 0.13Bx

= 3.32Q = 0.46Bx

= 2.72Q = 0.36Bx

= 1.92Q = 0.25Bx

0 0.5 1 1.5

= 1.42Q = 0.17Bx

= 3.72Q = 0.46Bx

= 3.02Q = 0.36Bx

= 2.22Q = 0.25Bx

0 0.5 1 1.5

= 1.62Q = 0.18Bx

)2−t (GeV00

a(t)

FIG. 17 (color online). The leading beam-spin asymmetry ampli-tude aðtÞ ¼ Asin!

LU differential in t, x, and Q2 as measured by CLAS,from Girod et al. (2008). An earlier CLAS measurement(Stepanyan et al., 2001) is indicated by the square. The opentriangles represent the cross-section data from Hall A (Camachoet al., 2006). Error bars are statistical errors only.













−210 −110

g/g

∆

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

gx

, 2002−20062>1 GeV2, QT


TCOMPASS, high p


TSMC, high p

2, all QT

HERMES, high p






(GeV)T

Jet p0 10 20 30

LLA

0

0.02

0.04

(GeV)T

p0π0 5 10 15







230 COMPASS Collaboration / Physics Letters B 693 (2010) 227–235

Fig. 1. The inclusive asymmetry A1,p [20] and the semi-inclusive asymmetries Aπ+1,p , AK+

1,p , Aπ−1,p , AK−

1,p from the present measurements (closed circles). The bands at the

bottom of each plot show the systematic errors. The A1,p , Aπ+1,p and Aπ−

1,p measurements from HERMES [14,26] open circles) are shown for comparison. The curves show thepredictions of the DSSV fit [1].

Table 1Unfolded asymmetries for charged pions and kaons produced on a proton target. The first error is statistical, the second is systematic.

⟨x⟩ ⟨Q 2⟩(GeV/c)2

Aπ+1,p Aπ−

1,p AK+1,p AK−

1,p

0.0052 1.16 0.008 ± 0.029 ± 0.016 0.020 ± 0.029 ± 0.016 0.078 ± 0.067 ± 0.038 −0.112±0.069±0.0390.0079 1.46 0.041 ± 0.018 ± 0.010 0.016 ± 0.018 ± 0.010 0.126 ± 0.036 ± 0.021 −0.040±0.039±0.0220.0142 2.12 0.040 ± 0.014 ± 0.008 0.049 ± 0.015 ± 0.009 0.046 ± 0.028 ± 0.016 0.038±0.031±0.0180.0245 3.22 0.122 ± 0.022 ± 0.014 0.055 ± 0.023 ± 0.013 0.117 ± 0.041 ± 0.024 0.092±0.048±0.0280.0346 4.36 0.156 ± 0.030 ± 0.019 0.060 ± 0.032 ± 0.018 0.196 ± 0.054 ± 0.033 0.074±0.066±0.0370.0487 5.97 0.141 ± 0.029 ± 0.018 0.118 ± 0.031 ± 0.019 0.174 ± 0.051 ± 0.031 0.027±0.064±0.0360.0765 8.96 0.230 ± 0.031 ± 0.022 0.053 ± 0.033 ± 0.019 0.215 ± 0.054 ± 0.033 0.029±0.071±0.0400.121 13.8 0.243 ± 0.041 ± 0.027 0.096 ± 0.047 ± 0.027 0.315 ± 0.072 ± 0.044 0.212±0.101±0.0580.172 19.6 0.392 ± 0.058 ± 0.040 0.165 ± 0.066 ± 0.038 0.355 ± 0.099 ± 0.059 0.195±0.147±0.0830.240 27.6 0.518 ± 0.060 ± 0.046 0.233 ± 0.069 ± 0.041 0.450 ± 0.101 ± 0.063 0.264±0.157±0.0890.341 40.1 0.549 ± 0.097 ± 0.064 0.134 ± 0.113 ± 0.064 0.512 ± 0.163 ± 0.097 0.375±0.259±0.1470.480 55.6 0.871 ± 0.122 ± 0.086 0.520 ± 0.142 ± 0.085 0.726 ± 0.207 ± 0.124 0.654±0.339±0.194

Table 2Correlation coefficients ρ of the unfolded asymmetries in bins of x.

x-bin 0.004–0.006 0.006–0.01 0.01–0.02 0.02–0.03 0.03–0.04 0.04–0.06 0.06–0.10 0.10–0.15 0.15–0.20 0.2–0.3 0.3–0.4 0.4–0.7

ρ(Aπ+1,p , A1,p) 0.29 0.34 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.43 0.45 0.46

ρ(Aπ−1,p , A1,p) 0.30 0.34 0.37 0.38 0.38 0.39 0.39 0.39 0.38 0.38 0.39 0.40

ρ(Aπ−1,p , Aπ+

1,p ) 0.12 0.15 0.17 0.16 0.15 0.16 0.16 0.15 0.16 0.16 0.19 0.20

ρ(AK+1,p , A1,p) 0.26 0.28 0.28 0.26 0.27 0.28 0.29 0.30 0.29 0.29 0.30 0.30

ρ(AK+1,p , Aπ+

1,p ) −0.17 −0.09 −0.04 −0.02 −0.02 −0.01 −0.02 −0.01 −0.01 −0.02 −0.02 −0.01

ρ(AK+1,p , Aπ−

1,p ) 0.03 0.04 0.04 0.05 0.05 0.05 0.05 0.06 0.05 0.05 0.04 0.03

ρ(AK−1,p , A1,p) 0.12 0.15 0.17 0.17 0.17 0.18 0.17 0.17 0.16 0.16 0.16 0.15

ρ(AK−1,p , Aπ+

1,p ) 0.03 0.03 0.04 0.04 0.04 0.04 0.03 0.04 0.02 0.03 0.02 0.05

ρ(AK−1,p , Aπ−

1,p ) −0.16 −0.09 −0.05 −0.03 −0.03 −0.03 −0.03 −0.03 −0.02 −0.03 −0.04 −0.02

ρ(AK−1,p , AK+

1,p ) 0.05 0.08 0.10 0.10 0.10 0.11 0.11 0.12 0.11 0.11 0.13 0.16

test on the asymmetries made on 23 subsets of data. At the levelof one standard deviation the upper bound of the error due tothese time-dependent effects is found to be 0.56σstat .

The experimental double-spin asymmetries for a proton targetare shown in Fig. 1. They are compared to the predictions of theDSSV fit [1] at the (x, Q 2) values of the data. The HERMES inclu-sive [26] and semi-inclusive [14] measurements for π+ and π−

are also displayed. The agreement with the DSSV parameterisationis good, even for the kaon asymmetries for which no data wereavailable when the prediction was made. In spite of the differentkinematic conditions, the agreement between the COMPASS andthe HERMES values for the pion asymmetries is also good. Thisobservation illustrates the fact that the Q 2 dependence at fixed xis small for semi-inclusive asymmetries.

0.8

0.6

0.4

0.2

0.0

-0.2

70

𝝙q𝝙G

LG

LqFigure 7. 2011+2012 W+/− AL as afunction of W decay lepton η (|η| < 1.3) [6].Color lines/band stand for theory predictions,see details in the text. The grey bandpresents the systematic error from the relativeluminosity.

η lepton-2 -1 0 1 2

-0.5

0

0.5

= 2% error2χ/2χ∆DSSV08 L0

STAR Run 2013 Projection

-W

+W

ν + ± e→± W→+pp=510 GeVs < 50 GeVe

T25 < E-1=460pbdeliveredL

<P> = 53%

LA

+W -WDSSV08 RHICBOSDSSV08 CHE NLOLSS10 CHE NLO

Figure 8. Projections of W+/− AL inthe 2013 510 GeV p+p collisions at STARwith 460 pb−1 integrated luminosity andaverage polarization 53%. Central valuesare evaluated by the CHE model with DSSVglobal QCD fit.

the FCS and associated detectors (West, East, EEMC, FCS) and their ALL asymmetries in NLOQCD MC are shown in Figure 5 and Figure 6. Fiducial volume cuts are applied as well for theforward di-jet simulation. The left-top panel is for the FCS and east Barrel di-jet production;the right-top is for the FCS and west Barrel di-jets; the left-bottom panel is for the FCS andEEMC di-jets and the right-bottom panel is for the FCS and FCS di-jets. The FCS-FCS di-jetsprobe the lowest x region which is below 10−3. Reducing the systematic errors will be a primarygoal to realize such measurements for studying gluon helicity distribution at low x .

3. W production at STAR to probe the sea quark helicity distributionThe u and d momentum fraction distributions have been found asymmetric through Drell-Yan process by the E866 experiment [18]. This phenomenon can not be fully described byperturbative QCD and indicates a non-perturbative mechanism may play a role in this field.In the parity violating weak processes, intial u (d) quark and d (u ) quark couple to W+

(W−) in proton-proton collisions. The longitudinally polarized 500 or 510 GeV proton-protoncollisions at RHIC open a path to probe the light sea quark helicity functions via W productions(p+p → W+/−+X → l+/−+X). This process gets rid of the final state fragmentation functionsthat are encountered in semi-inclusive DIS processes. The W boson measured in high energypolarized proton-proton collisions is a unique probe for the polarized sea quark distrubtion atthe W mass scale [2, 19].

STAR has successfully reconstructed W+/W− via their e+/e− decay channels in the mid-

6

Thank you.

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