transverse spin physics with an electron ion collider

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


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


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


Deep Inelastic Scattering

Lorentz invariants

In the collider frame

𝑄2=𝑥 ∙ 𝑦 ∙𝑠

Other variables

Electron Ion Collider 𝐸𝑒=10−30GeV 𝐸𝑝=50−250GeV


Lepton Kinematics𝐸𝑒=10GeV 𝐸𝑒=15GeV 𝐸𝑒=20GeV

𝐸𝑝=50GeV 𝐸𝑝=100GeV 𝐸𝑝=250GeV

𝐸𝑝 =

250GeV

𝐸𝑒 =15GeV


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 )


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?


SIDIS: Hadron Coverage Plot with Logz()


Particle Distribution


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


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


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


Primordial

scattered partontarget remnant

sensitive to intrinsic TMD inspired fit fails available data

Different underlying subprocesses


eRHIC

per bunch

https://indico.bnl.gov/conferenceDisplay.py?confId=727


A Model Detector for eRHIC

ROMANPOTS

LOW-Q2

TAGGER

GEMTRACKER

TPC

SILICON VTXTRACKER


Particle Rates


ePHENIX / eSTARwww.phenix.bnl.gov/plans.htmlarxiv.org/abs/1402.1209

https://drupal.star.bnl.gov/STAR/future


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


MEIC Detector

Bunch spacing:

collisions per bunch crossing

Asynchronous trigger with L2 tracking to suppress background


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


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


DVCS Kinematics

𝐸𝑝=50GeV 𝐸𝑝=100GeV 𝐸𝑝=250GeV 𝐸𝑒 =15GeV

𝜂>4.5

Too crowded…?


Pseudodata Single Spin Asymmetrieshttp://arxiv.org/abs/1304.0077


GPDs & Spatial Imaginghttp://arxiv.org/abs/1304.0077

Only show the 2D part of the bottom


Gluon Distributions

Requires high luminosities at different energies to map out the spatial distribution

transverse spin physics with an electron ion collider

Documents

nucleon spin

gluons transverse spin

distribution of quarks

distributions of quarks

heavy quarks

nucleon properties

motion of sea quarks

spatial imaging of quarks