1. Physics of the EIC
Cyrille Marquet
Theory Division - CERN

2. The Electron-Ion Collider
Two possible options: eRHIC-(1)2 and (m)EIC
although at the beginning (~ 5 years ago) this was not the case, now the
two designs have converged towards similar energy and luminosity
at Jefferson lab
at Brookhaven lab
10 x (up-to) 100 GeV e+p 5 x (up-to) 250 GeV e+p
stage cm-2s-1
10 x 40 GeV e+A 5 x 100 GeV e+A
10-20 x (up-to) 250 GeV e+p 5-30 x (up-to) 325 GeV e+p
stage 2 few 1034 cm-2s-1
10-20 x 100 GeV e+A x 130 GeV e+A
What I will discuss today
not all the possible physics that one can do with the EIC (see INT report on arXiv: )
but rather selected measurements, identified by the community, with undeniable physics deliverables (golden measurements)

3. Contents e+A physics at small x e+A physics at higher x
proton spin physics
proton transverse imaging
transverse imaging in momentum space

4. e+A physics at small x

5. Inclusive structure functions
this is fundamental knowledge about the
nuclear wave function that is still lacking
the most basic observables from the theory side, they will be the first
observables for which non-linear QCD evolution will be available at NLO F2
measurement with the smallest x reach, but there is a cancelation
of non-linear effects in F2 (from summing FT and FL)
this is presumably why the leading-twist approximation is able to describe F2 down to 2 GeV2 at HERA, if we had as precise FL data, we might see the collinear approach fail already at 5-10 GeV2
also, the heavy-ion program at the LHC would benefit a lot from a precise determination
of nuclear pdfs over a large x-Q2 range (similar to the impact of HERA on the p+p program) FL
F2c
better access to the gluon distribution, but can’t reach x as small
because of an energy scan is needed for the measurement
better access to the gluon distribution, but can’t reach x
as small because of the large charm quark mass
we should aim, for all of these, to get the same precision
that was reached at HERA with the F2 combined data

6. Diffractive structure functions
they have never been measured in e+A
the sensitivity to saturation is
better in diffraction, in fact many
hints from saturation at HERA
come from diffraction:
the constant ratio, with increasing energy, of
the diffractive to inclusive cross section does
not reflect the x dependence expected in the
linear regime: ,
quantitatively, DGLAP fits for the inclusive structure function F2 become problematic for Q2 below 4 GeV2 while for the diffractive structure function
F2D they become problematic at a much higher Q2 around 8 GeV2
the data feature geometric scaling which is
not explained in the DGLAP approach
at HERA % of events are diffractive, at an EIC we expect %

7. Semi-inclusive DIS Q zh Q SIDIS
measured only at high x and for light nuclei
at small x hadronization happens outside the nuclear matter
the kT dependence of the gluon distribution can be extracted from the PT dependence of the SIDIS cross-section
for saturation physics the relevant regime is low PT (~ Qs)
unique opportunity to study non-linear effects, while staying away from non-perturbative physics
CM, Xiao and Yuan (2009)
even if Q2 is much bigger than Qs2, the saturation regime is important when
in fact, thanks to the existence of Qs, the limit is finite

8. Di-hadron angular correlations
comparisons between d+Au → h1 h2 X (or p+Au → h1 h2 X ) and p+p → h1 h2 X
p+p collisions
central d+Au collisions
Df=0
(near side)
Df=p
(away side)
(rad) ~p
however, when y1 ~ y2 ~ 0 (and therefore xA ~ 0.03),
the p+p and d+Au curves are almost identical

9. Di-hadron correlations in e+A
never been measured, we expect to see the same effect in e+A vs e+p
Dominguez, Xiao and Yuan (2010)
at small x, multi-gluon distributions
are as important as single-gluon
distributions, they contribute to
such di-hadron correlations
the description of the RHIC data is
therefore subject to uncertainties
the same gluon correlations are
involved in the d+Au case but the e+A
measurement can constrain them better
the non-linear evolution of (kT-dependent) multi-gluon
distributions is different from that of the single-gluon
distribution, and it is equally important to understand it

10. Diffractive vector meson production
Stage 1: precise transverse imaging of the gluons, from light to heavy nuclei
Stage 2: how the small-x evolution modifies the transverse distribution of gluons
Toll and Ullrich (2011)
as a function of t
exclusive production (coherent):
the target undergoes elastic
scattering, dominates at small |t|
→ steep exp. fall at small |t|
target dissociation (incoherent): the target undergoes inelastic scattering, dominates at large |t|
breakup into the nucleons → slower exp. fall at 0.02 < -t < 0.7 GeV2
breakup of the nucleons → power-law tail at large |t|

11. Coherent vs incoherent
coherent diffraction
measured only at high x and for light nuclei
the b dependence of the gluon distribution is obtained from the t dependence of the cross section by Fourier transformation
it is often assumed that gluons from different nucleons are independent, the EIC allows to study how this changes with the non-linear QCD evolution towards small x
incoherent diffraction
has never been measured
gives access to gluon correlations in the transverse plane
the distribution and correlations of small-x gluons in the transverse plane are poorly known, without this knowledge for instance one cannot achieve a quantitative understanding of important RHIC results
the initial nuclear wave functions in relativistic heavy-ion collisions are the source of large uncertainties, their descritption is based on expectations which need to be checked and constrained with e+A data

12. e+A physics at higher-x

13. Nuclear quarks and gluons
the EIC can reveal the nuclear structure throughout the (x,Q2) plane, from
gluon saturation at low x to the gluon EMC effect and its Q2 evolution at high x
QCD fits on e+A pseudo-data
with
allows to estimate nuclear quark and gluon distributions and their uncertainties
the EIC has constraining power, it will be to nuclei what HERA is to the proton
Nuclear GPDs, nuclear TMDs

14. In-medium fragmentation
unprecedented ν range
small v :
in-medium hadronization
the EIC can study the dynamics of confinement: the stages of hadronization (parton, pre-hadron, hadron) and their time scales
SIDIS/jet production
large v : in-medium parton propagation
from the energy loss and pT-broadening of leading partons as well as jet-shape modifications, the EIC can measure fundamental properties of cold nuclear matter: , , modifications of angular ordering
heavy quarks
for the first time, the in-medium hadronization and propagation of heavy quarks
can be studied, and the pQCD description of cold nuclear matter can be tested

15. Proton spin physics

16. Origin of the proton spin
angular momentum
~ 0.3
spin contributions : 0.15 < 0.1
low x behavior unconstrained
significant polarization still possible
no reliable error estimate
for 1st moment
(entering spin sum rule)
find
current
status of
Δg(x,Q2):
DSSV global fit:
de Florian, Sassot,
Stratmann, Vogelsang x
RHIC pp
DIS
&

17. What the EIC will bring
Sassot and
Stratmann,
expect to determine at about 10% level (or better – more studies needed)
kinematic reach down to x = 10-4 essential to determine integral

18. Proton transverse imaging

19. GPDs and b-dependent pdfs
probabilistic interpretation of GPDs
as FTs of impact parameter dependent pdfs
GPDs accessible from DVCS
there are different GPDs

20. GPDs and angular momentum
probabilistic interpretation of GPDs
E → transverse deformation of pdfs when the target is transversely polarized
sign and magnitude of the average shift model independent O(0.2 fm)
Ji relation for the angular momentum carried by quarks
proton polarization

21. Transverse imaging in momentum space

22. TMD quark distributions
TMDs are accessible through hard processes
(un)polarized DY and SIDIS
8 leading-twist TMDs
nucleon polarization
Sivers function
correlation between transverse spin of the nucleon and transverse momentum of the quark
quark polarization
Boer-Mulders function
correlation between transverse spin and transverse momentum of the quark in unpolarized nucleon
goal: make the extraction of these quantities a quantitative science

23. Conclusions
very little is known about the structure of nuclei at small x
- only for inclusive structure functions we have data at moderate x
- SIDIS and exclusive VM production data are at high x or for light nuclei
- diffractive structure functions have never been measured
crucial measurements at an EIC (e+A)
- inclusive and diffractive structure functions: integrated gluons
- semi-inclusive DIS: the kT dependence of the gluon distribution
- di-hadron correlations: the kT dependence of the gluon correlations
- (in)coherent diffraction: distribution (and correlations) in transverse plane
- unprecedented ν range to study in-medium fragmentation (access to HQs)
crucial measurements at an EIC (polarized e+p)
- determination of gluon spin contribution ΔG at 10% level
- 2+1 D imaging of the proton and estimation of quark angular momentum
- crucial tests of TMD factorization