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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