Transverse Spin Physicswith an Electron Ion Collider
Oleg Eyser4th International Workshop on Transverse
Polarisation Phenomena in Hard ProcessesChia, Cagliari, 2014
Transverse Spin Physics at an EIC
The Path Forward
Nucleon Structure 2020 Collider Kinematics• Semi-inclusive Deep Inelastic Scattering• Deeply Virtual Compton Scattering
Possible Scenarios for an EIC• eRHIC• MEIC
arxiv.org/abs/1212.1701https://indico.bnl.gov/conferenceDisplay.py?confId=727
Transverse Spin Physics at an EIC
How are sea quarks and gluons and their spin distributed in space and momentum inside the nucleon? How are these quark and gluon distributions correlated with the over all nucleon
properties, such as spin direction? What is the role of the motion of sea quarks and gluons in building the nucleon spin?
How does the nuclear environment affect the distribution of quarks and gluons and their interaction in nuclei? How does the transverse spatial distribution of gluons compare to that in the nucleon? How does matter respond to fast moving color charge passing through it?
Is this response different for light and heavy quarks?
Where does the saturation of gluon densities set in? Is there a simple boundary that separates the region from the more dilute quark gluon
matter?How do the distributions of quarks and gluons change as one crosses the boundary?
Does this saturation produce matter of universal properties in the nucleon and all nuclei viewed at nearly the speed of light?
Open Questions
Transverse Spin Physics at an EIC
1D
3D
5D
The Partonic Picture of the Nucleon
Wigner distributions
∫𝑑𝑥 ∫𝑑𝑥𝑥𝑛−1
transverse momentum impact parameter
∫𝑑2𝑘𝑇∫𝑑2𝑏𝑇
∫𝑑2𝑘𝑇 ∫𝑑2𝑏𝑇
parton densities
Fourier trans.
𝜉=0
generalized partondistributions
form factors generalized form factors
TMDs: confined partonic motion inside the nucleon
GPDs: spatial imaging of quarks and gluons
Transverse Spin Physics at an EIC
Deep Inelastic Scattering
Lorentz invariants
In the collider frame
𝑄2=𝑥 ∙ 𝑦 ∙𝑠
Other variables
Electron Ion Collider 𝐸𝑒=10−30GeV 𝐸𝑝=50−250GeV
Transverse Spin Physics at an EIC
Lepton Kinematics𝐸𝑒=10GeV 𝐸𝑒=15GeV 𝐸𝑒=20GeV
𝐸𝑝=50GeV 𝐸𝑝=100GeV 𝐸𝑝=250GeV
𝐸𝑝 =
250GeV
𝐸𝑒 =15GeV
Transverse Spin Physics at an EIC
Semi-inclusive DIS
Additional degrees of freedom:
Transverse momentum
Fragmentation
Azimuthal correlation
Six-fold differential cross section:
multi-scale problem:
TMD framework/factorization
Measure:
spin-orbit correlations
QCD color gauge invariance
EIC: move beyond fixed target data
𝑑𝜎𝑑𝑥𝑑𝑦𝑑𝜑𝑑𝑧𝑑𝜑𝑆𝑑𝑝𝑇
2 ∝𝐹𝑈𝑈 ,𝑇+|𝑆⊥|sin (𝜑−𝜑𝑆 )𝐹𝑈𝑇 ,𝑇sin (𝜑−𝜑 𝑆 )+⋯
𝑓 1𝑇⊥𝑞 (𝑥 ,𝑘𝑇 )
Transverse Spin Physics at an EIC
SIDIS: Hadron KinematicsCuts:Q2>1 GeV, 0.01<y<0.95, z>0.1
𝐸𝑒=10GeV 𝐸𝑒=15GeV 𝐸𝑒=20GeV 𝐸𝑝 =
250GeV
𝐸𝑝=50GeV 𝐸𝑝=100GeV 𝐸𝑝=250GeV 𝐸𝑒 =15GeV
Try 3x3 matrix?
Transverse Spin Physics at an EIC
SIDIS: Hadron Coverage Plot with Logz()
Transverse Spin Physics at an EIC
Particle Distribution
Transverse Spin Physics at an EIC
Pseudodata
Binned in 4 dimensions:
Simulator: gmc_transhttps://wiki.bnl.gov/eic/
are fromEur. Phys. J. A39, 89-100 (2009)
No TMD evolution included yet
Statistical uncertainties are not scaled with asymmetries
https://indico.bnl.gov/conferenceDisplay.py?confId=727
Transverse Spin Physics at an EIC
Projection for Quark Sivers TMD
�⃗� 𝒛
𝑺𝑻
QCD dynamics in the hard process Evolution Resummation Matching of factorization - TMD vs. collinear
Anselmino et al.J. Phys. Conf. Ser. 295, 012062 (2011)
EIC pseudo data
𝑥=0.1
Transverse Spin Physics at an EIC
Gluon Sivers from Charm
N⇑
e
Measure correlations of D-meson pairs
: in correlation limit
𝑨(𝒌⊥′ ,𝝋𝑺)
Transverse Momentum of HadronsPossible contributions to hadron :
Intrinsic, non-perturbative Parton showers soft factors in TMDs Hard scattering Fragmentation
𝑘𝑇
How to disentangle different contributions?
Appropriate probes Multi-dimensional data: High precision
Transverse Spin Physics at an EIC
Primordial
scattered partontarget remnant
sensitive to intrinsic TMD inspired fit fails available data
Different underlying subprocesses
Transverse Spin Physics at an EIC
eRHIC
per bunch
https://indico.bnl.gov/conferenceDisplay.py?confId=727
Transverse Spin Physics at an EIC
A Model Detector for eRHIC
ROMANPOTS
LOW-Q2
TAGGER
GEMTRACKER
TPC
SILICON VTXTRACKER
Transverse Spin Physics at an EIC
Particle Rates
Transverse Spin Physics at an EIC
ePHENIX / eSTARwww.phenix.bnl.gov/plans.htmlarxiv.org/abs/1402.1209
https://drupal.star.bnl.gov/STAR/future
Transverse Spin Physics at an EIC
MEIC
Warm large booster(3 to 25 GeV/c)
Warm electron collider ring (3-12 GeV) Medium-energy IPs with
horizontal beam crossing
Injector
12 GeV CEBAF
Pre-booster
SRF linac
Ionsource
Cold ion collider ring (25 -100 GeV)
Three Figure-8 rings stacked vertically
arxiv:1209.0757
Transverse Spin Physics at an EIC
MEIC Detector
Bunch spacing:
collisions per bunch crossing
Asynchronous trigger with L2 tracking to suppress background
Transverse Spin Physics at an EIC
SummaryLu
min
osity
1032
1033
1034
50 100 150
Internal landscape
of the nucleus
QCD at extremeparton
densities
Spin and flavor structureof the nucleon
Tomography of the nucleon
Electroweak
An electron ion collider will combine: Kinematic reach into the gluon
dominated region Precision from electromagnetic
interaction Accuracy from high luminosity Polarized nucleons and light/heavy
ions
This will provide decisive measurements to answer many open questions in QCD.
arxiv:1212.1701
Transverse Spin Physics at an EIC
Spatial Imaging of Nucleons
𝑓 ⇑ (𝑥 ,𝑏𝑇 )= 𝑓 (𝑥 ,𝑏𝑇2 )+
(𝑆𝑇 ×𝑏𝑇 )𝑧
𝑀𝜕
𝜕𝑏𝑇2 𝑒 (𝑥 ,𝑏𝑇
2 )
𝐸 (𝑥 , 𝜉 , 𝑡 )𝐻 (𝑥 ,𝜉 ,𝑡 )
Fourier transform of at 𝜉=0𝑒 (𝑥 ,𝑏𝑇
2 )𝑓 (𝑥 ,𝑏𝑇
2 )
Exclusive processes to measure generalized parton distribution functions:
Resolution scale 𝑄2 𝑀𝑉2 +𝑄2
𝑉
Transverse Spin Physics at an EIC
DVCS Kinematics
𝐸𝑝=50GeV 𝐸𝑝=100GeV 𝐸𝑝=250GeV 𝐸𝑒 =15GeV
𝜂>4.5
Too crowded…?
Transverse Spin Physics at an EIC
Pseudodata Single Spin Asymmetrieshttp://arxiv.org/abs/1304.0077
Transverse Spin Physics at an EIC
GPDs & Spatial Imaginghttp://arxiv.org/abs/1304.0077
Only show the 2D part of the bottom
Transverse Spin Physics at an EIC
Gluon Distributions
Requires high luminosities at different energies to map out the spatial distribution