THE DEEP INELASTIC

SCATTERING ON THE

POLARIZED NUCLEONS AT EIC

E.S.Timoshin, S.I.Timoshin

We have two pictures about the nucleon spin:

Jaffe-Manohar, 1990

It is simple parton picture for longitudinal polarization

X.Ji, 1996

It is relate to the partons in transverse polarized nucleon

gq LLG 2

1

2

1

Quark

helicity Gluon

helicity Orbital

momentumof quarks and

gluons

gqgq JLJJ 2

1

2

1

Total

angular momentum

of quarks

Total

angular momentum

of gluons

What do we know?

We know fairly well the quark contribution

~ 30%

However, the information on polarization of the flavor and sea are still sketchy.

Contribution from small ?

We know with large uncertains about the gluon contribution

~ 20% (with RHIC data)

There not have direct information on the quark and gluon orbital angular momentum.

Lattice QCD → and are large, but ~ 0

ssdduudx

)x(gdxG

uL dL du LL

x

Major advance since 2007:

We have new phenomenology to study nucleon structure:

Generalized Parton Distributions (GPDs) (3D “imaging”) that provide access to orbital angular momentum in DVCS and Exclusive production.

These studies will require high luminosity and polarized beams.

Electron–Ion Collider (EIC)

High luminosity

Low regime

High polarization 70% electron and nucleon beams

Ion beams from deuteron to the heaviest nuclei

Center mass energies 20-100 GeV (upgradable 150 GeV)

,,/J

410xx

123410 scm

What can to explore at EIC:

Sea/gluon (inclusive DIS, SIDIS at low ), flavor separation.

GPD (DVCS, Exclusive meson production) => angular momentum

The first constraint on quark orbital contribution to proton spin

by combining the sea from EIC and valence from JLab 12

42 1010 ~x

.J,J gq

x

qqqt

q Lt,,xEt,,xHxdxlimJ 2

1

2

10

GPD

The inclusive DIS with charged current

Here are 2 independent polarized structure functions (SF)

flavor separation

In contrast with SIDIS here not have the fragmentation functions that give essential uncertains.

XNl

qq~g

,qq~g

6

1

q,q

The polarization asymmetries through SF are

,

)Q,x(Fy

)Q,x(Fy

)Q,x(gy)Q,x(gy

dd

dd)Q,x(A

l,ll,l

l,ll,l

,l,l

,l,l

,l,l

,l,l

l,l

23

1211

211

261

22

222

2

Where

.

)Q,x(F)Q,x(Fy

)Q,x(F)Q,x(Fy

)Q,x(g)Q,x(gy)Q,x(g)Q,x(gy

dddd

dddd)Q,x(A

llll

llll

llll

llll

23

23

121

211

21

211

26

261

2222

22222

2

.yy,yy 11 1211

The polarized SF in leading order QCD (improved parton model)

where and for

lepton (antilepton).

q q

q q

),Q,x(q)Q,x(q)Q,x(g

),Q,x(q)Q,x(q)Q,x(g

2226

2221

b,s,dqt,c,uq t,c,uqb,s,dq

The first moment polarized SF

where is the quark

(antiquark) contribution to the nucleon spin

dx)x(q)x(q)q(q 1

0

,qqdx)Q,x(g)Q(q,q

,, 1

0

261

261

The proton

where

We use also the measurable quantity – the axial charge that in parton model:

,qdu

),ss()dd()uu(

VVVplpl

plpl

66

66

.ddd,uuu VV

.du

),ss()dd()uu(

VVplpl

plpl

11

11

00350267013 ..DFa

.dduua 3

The quark contributions to the nucleon spin:

The quark flavors

.ass

),a(dd

),(uu

plpl

plplplpl

plplplpl

366

36611

6611

22

1

2

1

The valence quarks

The sea quarks

.)(d

,)(u

plplplplV

plplplplV

6611

1166

2

12

1

).a(s

)a(d

),(u

plpl

plpl

plpl

366

361

61

2

12

12

1

We are obtained the quark contributions for the neutron and the deutron.

The deutron

where is the probability D-state in the wave function of the deuteron.

.,

du

,,

ss

dldl

VV

dldl

511

511

66

66

,,

dldl

51111

050.

Fig. 1. The asymmetries and p

eA

neA

neA

p

eA

Fig. 2. The asymmetries and

pAnA

pA

nA

Fig. 3. The asymmetries and

deA

deA

deA

Fig. 4. The asymmetries and

dAdA

dA

Fig.5. QED correction to asymmetry in leading log approximation (LLA)

A. De Rujula et al. Nucl. Phys. 1979. V. B154 P.394.

J. Blŭmlein. Prog. Part. Nucl. Phys. 2013. V.69. P.28.

(%)l p

eA

Fig.6. QED correction to asymmetry in LLA

NLO QCD correction to the asymmetries CC DIS are small and LO accuracy is very good approximation ( E.C.Aschenauer et al. Phys. Rev. D 88(2013) 114025).

(%)n,l n

eA

CONCLUSION

Data from CC DIS experiments provide complementary

information on the spin structure nucleon as they probe

combinations of quark flavours different from those accessible

in purely electromagnetic DIS.

CC DIS can only be studied in high-energy lepton-nucleon

collisions (EIC).

The quark contributions to the nucleon spin are obtained

through the first moments of the polarized SF that

can be to extract from the measurable asymmetries CC DIS.

61 g,g