Polarized electron-deuteron deep-inelastic scatteringwith spectator nucleon taggingWim Cosyn

Ghent University, BelgiumINPC 2019

in collaboration with Ch. Weiss,JLab LDRD project on spectator taggingWC, C. Weiss, arXiv:1906.11119

Electron-ion collider� World’s first polarised electron-proton/light ion and electron-nucleuscollider. Two sites under consideration: Jefferson Lab and BrookhavenNational Lab, USA. → talks by S. Fazio, P. Rossi on Fri.

� 2012 EIC White Paper Accardi et al., Eur. Phy. J. A 52, 9

(2016)� 2015 Nuclear Physics Long Range Plan: “[EIC] as the highest priority fornew facility construction following completion of FRIB”� 2017-18 National Academies of Science (NAS) Review� Next stage: CD0 (formally establishing mission need), expected this year� User meeting in Paris last week: https://indico.in2p3.fr/event/18281/

Wim Cosyn (UGent) INPC 2019 July 28, 2019 2 / 15

Why focus on light ions at an EIC?� Measurements with light ions address essential parts of the EICphysics program

I neutron structureI nucleon interactionsI coherent phenomena

� Light ions have unique featuresI polarized beamsI breakup measurements & taggingI first principle theoretical calculations of initial state

� Intersection of two communitiesI high-energy scatteringI low-energy nuclear structure

Use of light ions for high-energy scattering and QCD studies remainslargely unexploredWim Cosyn (UGent) INPC 2019 July 28, 2019 3 / 15

EIC design characteristics (for light ions)� CM energy √seA = √Z /A 20− 100GeVDIS at x ∼ 10

−3 − 10−1, Q2 ≤ 100GeV2

� High luminosity enables probing/measuringI exceptional configurations in targetI multi-variable final statesI polarization observables

� Polarized light ionsI 3He, other @ eRHICI d, 3He, other @ JLEIC(figure 8)I spin structure, polarizedEMC, tensor pol, ...

� Forward detection of target beamremnantsI diffractive and exclusive processesI coherent nuclear scatteringI nuclear breakup and taggingI forward detectors integrated indesigns

Wim Cosyn (UGent) INPC 2019 July 28, 2019 4 / 15

Light ions at EIC: physics objectives� Neutron structure

I flavor decomposition of quark PDFs/GPDs/TMDsI flavor structure of the nucleon seaI singlet vs non-singlet QCD evolution, leading/higher-twisteffects

� Nucleon interactions in QCDI medium modification of quark/gluon structureI QCD origin of short-range nuclear forceI nuclear gluonsI coherence and saturation

� Imaging nuclear bound statesI imaging of quark-gluon degrees of freedom in nucleithrough GPDsI clustering in nuclei

Need to control nuclear configurations that play a role inthese processesWim Cosyn (UGent) INPC 2019 July 28, 2019 5 / 15

Theory: high-energy scattering with nuclei2

..

.A

eQ, x

D

q

Xn

p

x+= const

� Interplay of two scales: high-energy scattering andlow-energy nuclear structure. Virtual photon probesnucleus at fixed lightcone time x+ = x0 + x3

� Scales can be separated using methods oflight-front quantization and QCD factorization� Tools for high-energy scattering known from ep

� Nuclear input: light-front momentum densities,spectral functions, overlaps with specific final statesin breakup/tagging reactionsI framework known for deuteronI still low-energy nuclear physics, just formulateddifferently

Frankfurt, Strikman '80s

Kondratyuk, Strikman, NPA '84

Wim Cosyn (UGent) INPC 2019 July 28, 2019 6 / 15

Neutron structure measurementsNeeded for flavor separation, singlet vs non-singlet evolution etc.

� EIC will measure inclusive DIS on light nuclei [d ,3He, 3H(?)]I Simple, no FSI effectsI Compare n from 3He ↔ p from 3HI Comparison n from 3He, d

� Uncertainties limited by nuclear structure effects→ binding, Fermi motion, non-nucleonic dof

� 3He is in particular affected because of intrinsic ∆sIf we want to aim for precision, use tools that avoid these complications

Wim Cosyn (UGent) INPC 2019 July 28, 2019 7 / 15

Neutron structure with tagging� Proton tagging offers a way of controlling the nuclear configuration

pD

pR

pR pD

q

X

R RTpα ,

proton

neutron

t = ( − ) 2

pn

� Advantages for the deuteronI active nucleon identifiedI recoil momentum selects nuclear configuration(medium modifications)I limited possibilities for nuclear FSI, calculable

� Allows to extract free neutron structure withpole extrapolationI Eliminates nuclear binding and FSI effects

[Sargsian,Strikman PLB '05]

� Suited for colliders: no target material (pp → 0), forward detection,polarization.fixed target CLAS BONuS limited to recoil momenta ∼ 70 MeVWim Cosyn (UGent) INPC 2019 July 28, 2019 8 / 15

Theoretical Formalism� General expression of SIDIS for a polarized spin 1 target

I Tagged spectator DIS is SIDIS in the target fragmentation region~e + ~T → e ′ + X + h

� Dynamical model to express structure functions of the reactionI First step: impulse approximation (IA) modelI Results for longitudinal spin asymmetriesI FSI corrections (unpolarized Strikman, Weiss PRC '18)

� Light-front structure of the deuteronI Natural for high-energy reactions as off-shellness of nucleons in LFquantization remains finite

Wim Cosyn (UGent) INPC 2019 July 28, 2019 9 / 15

Polarized deuteron tagged DIS: cross section� Spin 1 particle has density matrix with 8 parameters: 3 vector, 5 tensor

� SIDIS cross section: unpolarized + vector polarized can be copiedfrom spin 1/2 [Bacchetta et al., JHEP ('07)]Tensor part has 23 additional structure functions, each with theirunique azymuthal dependence [WC, C. Weiss, in prep.]

� In the impulse approximation all SF can be written asF kij = {kin. factors} × {F1,2(x̃ ,Q2)or g1,2(x̃ ,Q2)} × {bilinear formsin deuteron radial wave function f0(k), f2(k)}

� In the IA the following structure functions are zero → sensitive to FSII beam spin asymmetry [F sinφh

LU ]I target vector polarized single-spin asymmetry [8 SFs]I target tensor polarized double-spin asymmetry [7 SFs]

Wim Cosyn (UGent) INPC 2019 July 28, 2019 10 / 15

Polarized structure function: longitudinal asymmetry� On-shell extrapolation of double spin asymmetry

d1/2− λ+λ

e d

=e+−1, 0=

I Nominatordσ|| ≡ 1

4

[dσ (+ 1

2,+1)− dσ (− 1

2,+1)− dσ (+ 1

2,−1) + dσ (− 1

2,−1)]

I Two possible denominators: 3-state and 2-statedσ3 ≡ 1

6

∑Λe[dσ (Λe ,+1) + dσ (Λe ,−1) + dσ (Λe , 0)]

dσ2 ≡ 1

4

∑Λe[dσ (Λe ,+1) + dσ (Λe ,−1)]

I Asymmetries: tensor polarization enters in 2-state oneA||,3 = dσ||

dσ3[φh avg] = FLSL

FT + εFL

A||,2 = dσ||dσ2

[φh avg] = FLSL

FT + εFL + 1√6(FTLLT + εFTLLL)

� Impulse approximation yields in the Bjorken limit [αp = 2p+p

p+D

]A||,i ≈ D i (αp, |ppT |)A||n = D i (αp, |ppT |) D||g1n(x̃ ,Q2)

2(1 + εRn)F1n(x̃ ,Q2)Wim Cosyn (UGent) INPC 2019 July 28, 2019 11 / 15

Nuclear structure factors D 2, D 3� D 2 has physical interpretation as ratio of nucleon helicity density tounpolarized density in a deuteron with polarization +1. D 3 has nosuch interpretation.

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.1 0.2 0.3 0.4 0.5 0.6

D3,

D2

ppt [GeV]

αp = 1

three-state D3

two-state D2

WC, C. Weiss, arXiv:1906.11119; in preparation

� Bounds: −1 ≤ D 2 ≤ 1

� Due to lack of OAM D 2 ≡ 1 for pT = 0

� Clear contribution from D-wave at finiterecoil momenta� D 3 violates bounds due to lack of tensorpol. contribution� D 3 6= 0 for pT = 0

� D 2 closer to unity at small recoilmomenta� 2-state asymmetry is also easierexperimentally!!

Wim Cosyn (UGent) INPC 2019 July 28, 2019 12 / 15

Nuclear structure factors D 2, D 3� D 2 has physical interpretation as ratio of nucleon helicity density tounpolarized density in a deuteron with polarization +1. D 3 has nosuch interpretation.

0.8

0.9

1

1.1

0.9 1 1.1

D3,

D2

αp

ppt = 0

three-state D3

two-state D2

WC, C. Weiss, arXiv:1906.11119; in preparation

� Bounds: −1 ≤ D 2 ≤ 1

� Due to lack of OAM D 2 ≡ 1 for pT = 0

� Clear contribution from D-wave at finiterecoil momenta� D 3 violates bounds due to lack of tensorpol. contribution� D 3 6= 0 for pT = 0

� D 2 closer to unity at small recoilmomenta� 2-state asymmetry is also easierexperimentally!!

Wim Cosyn (UGent) INPC 2019 July 28, 2019 12 / 15

Tagging: simulations of pole extrapolation of A||

-0.06

-0.04

-0.02

0

0.02

0.001 0.01 0.1 1

Neu

tro

n s

pin

as

ym

met

ry

A||

n (

x,

Q2)

x

Neutron spin structure with tagged DIS →e +

→D → e’ + p(recoil) + X

EIC simulation, seN = 2000 GeV2, Lint = 100 fb

−1

Nuclear binding eliminated through on-shell extrapolation in recoil proton momentum

Q2 = 10−16

6−10

4−6

2.5−4

16−25

25−40

40−63

Error estimates include

extrapolation uncertainty

JLab LDRD arXiv:1407.3236, arXiv:1409.5768https://www.jlab.org/theory/tag/

� Statistics requirementsI Physical asymmetries∼ 0.05− 0.1

I Effective polarizationPePD ∼ 0.5

I Luminosity required∼ 10

34cm−2s−1� As depolarization factor

D = y (2−y )2−2y+y2

and y ≈ Q2

xseN,wide range of seN required!

� Precise measurement of neutron spin structureI separate leading- /higher-twistI non-singlet/singlet QCD evolutionI pdf flavor separation ∆u,∆d . ∆G through singlet evolutionI non-singlet g1p − g1n and Bjorken sum rule

Wim Cosyn (UGent) INPC 2019 July 28, 2019 13 / 15

Extensions� Final-state interactions modify cross section away fromthe pole

I studied for unpolarized case at EIC kinematics, poleextrapolation still feasible[Strikman, Weiss PRC '18]

I dominated by slow hadrons in target fragmentationregion of the struck nucleonI extend to ~e + ~dI constrain FSI modelsI non-zero azimuthal and spin observables throughFSI

e’

p

e

p

fast

slow

q

� Tensor polarized observables� Tagging with complex nuclei A > 2

I isospin dependence, universality of bound nucleon structureI A− 1 ground state recoil

� Resolved final states: SIDIS on neutron, hard exclusive channelsWim Cosyn (UGent) INPC 2019 July 28, 2019 14 / 15

Conclusions� Light ions address important parts of the EIC physics program� Tagging and nuclear breakup measurements overcome limitations dueto nuclear uncertainties in inclusive DIS → precision machine

� Unique observables with polarized deuteron: free neutron spinstructure, tensor polarization� Clear advantages in using two-state asymmetry to extract g1n� Extraction of nucleon spin structure in a wide kinematic range� Lots of extensions to be explored!

Wim Cosyn (UGent) INPC 2019 July 28, 2019 15 / 15