EIC prospects for SIDIS and ΔG

Thomas BurtonBNL

RHIC and AGS Users’ Meeting 2010

Overview

• What do we currently know about spin?

• What do we need to learn & improve?

• How does an EIC allow us to do this?

‣ ΔG

‣ SIDIS - longitudinal & transverse spin

Spin of the nucleon

• Ultimate goal: disentangle quark, gluon and orbital contributions to nucleon spin

• Understand spin-dependent parton dynamics (Sivers, Boer-Mulders...).

• Many quantities/distributions are still poorly known.

12h= P, 12 | JQCD

z |P, 12 = 12q

∑ Sqz + Sgz + Lqzq∑ + Lgz

Deep inelastic scattering

x = Q2/2M(E-E`) Q2 = -q2 = -(e - e`)2

F1(x) = Σq q+(x) + q-(x)

Longitudinal spin in DIS

F1(x) = Σq q+(x) + q-(x)

g1(x) = Σq q+(x) - q-(x)

A1 = g1 / F1

5

Quark (spin ½)absorbs

photon (spin 1)and flips helicity

Δq = q+ - q-

vs

HERAScaling violations

HERA F2

0

1

2

3

4

5

1 10 102

103

104

105

F2

em-l

og

10(x

)

Q2(GeV

2)

ZEUS NLO QCD fit

H1 PDF 2000 fit

H1 94-00

H1 (prel.) 99/00

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102

x=0.000161x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

DIS

• Exquisite control of parton kinematics.

• Clean and precise determination of parton distributions

• We would like the same precision for spin-dependent distributions

➡ Detailed understanding of nucleon spin structure

• Where do we currently stand with this aim?

Gluon contribution to the nucleon helicity: ΔG

• ΔG = ∫dx Δg(x)

• Δg = g+ - g-

12h= P, 12 | JQCD

z |P, 12 = 12q

∑ Sqz + Sgz + Lqzq∑ + Lgz

1) Inclusive DIS spin asymmetries

Inclusive world data

g1 scaling violations

Scaling violations (Q2-dependence) give indirect access to the gluon distribution via DGLAP evolution.

2) ΔG from p + p

RHIC p + p collisions at midrapidity directly involve gluons

Rule out large ΔG for 0.05 < x < 0.2

RHIC

DISEIC

Small at currently accessible xΔG = -0.084

5fb-1 integrated luminosity

Access to ΔG at small x where

uncertainties are very large

5fb-1 integrated luminosity

Access to ΔG at small x where

uncertainties are very large

ΔG via charm• Measure charm

prodution via D0 → K- π+

• High energy → theoretically clean

10 fb-1 at 10+250

2.5 fb-1 at 5+50

Gluon polarisation

• EIC will provide precise g1 to small x

➡ Determination of Δg at small x

➡ Reduced uncertainty on ΔG due to low-x extrapolation

➡ Precise test of the Bjorken sum rule

∫01dx (g1p(x,Q2) - g1n(x,Q2)) = 1/6gA(1 + O(αs) + O(1/Q2))

inclusive DIS

The hadronic final state is not measured

X

Semi-inclusive DIS: SIDIS

Tag a hadron ➜ access to quark flavour

12h= P, 12 | JQCD

z |P, 12 = 12q

∑ Sqz + Sgz + Lqzq∑ + Lgz

inclusive DIS

Longitudinal spin

Semi-inclusive DIS asymmetries

ProtonHelium

Deuteron

Sea uncertainties remain large

Δu = 0.813Δd = -0.459Δu = 0.036Δd = -0.115Δs = -0.057ΔΣ = 0.242

@ Q2 = 10 GeV2

Flavour-dependence

Flavour-dependenceeRHIC projections for:

• 10 + 250 GeV

• 9fb-1

0.2

-0.8

0.

0.8

X

Current

Transverse spin

Transverse spin asymmetries

• First seen in p + p

• What is their origin?

Transverse-momentum-dependent functions (TMDs)

ransverse spin topics

Transversity distribution δq = q↑ - q↓

“Sivers” parton distributionsParton distributions depend on S⊥

“Collins” fragmentation functionsFragmentation depends on S⊥

S⊥

Transverse spin in SIDIS• Collins & Sivers - different azimuthal dependence

➡ Disentangle the effects

25

Transverse spin in SIDIS• Collins & Sivers - different azimuthal dependence

➡ Disentangle the effects

25

Phys. Rev. Lett. 103 (2009)

152002

Current status

26

Sivers functions

Transversity

Uncertainties remain large

Sivers at EIC

• High luminosity

➡ x, Q2 & momentum dependence

➡multi-dimensional binning

27

Transverse spin at EIC

• Uncertainties remain large compared to helicity distributions

• Precision measurements of TMDs, including their momentum and Q2 dependence

• Sivers, Collins, Boer-Mulders...

• Precise measure of transversity

• High energy → theoretically interpretable

28

EIC summary

• Complementary x, Q2, energy range to past & existing experiments

• High luminosity → precise

➡ Will advance our knowledge of all aspects of the spin puzzle

• Also see talks by:

• Elke: GPDs

• Thomas Ullrich: EIC physics case

• Vladimir: eRHIC machine design