1. Open questions in QCD at high parton density: EIC vs LHeC
Cyrille Marquet
Centre de Physique Théorique
Ecole Polytechnique

2. Contents gluon saturation: status and open questions
- what we know
- what we would like to know
- what questions can(not) be answered with e+A (p+A)
- connections with Quark-Gluon-Plasma physics
e+(p)A measurements: EIC/LHeC highlights
- structure functions F2 and FL
- hard diffraction
- di-hadron production
- exclusive vector meson production
- cold nuclear matter effects

3. Gluon saturation: status and open questions

4. What we know for sure fundamental consequence of QCD dynamics:
at asymptotically small x:
- QCD evolution becomes non-linear
- particle production becomes non-linear
- QCD stays weakly coupled
both in terms of practical applicability
and phenomenological success
the Color Glass Condensate (CGC) has emerged as the best candidate to approximate QCD in the saturation regime
the energy dependence of the saturation scale, and more generally of observables, can be computed from first principles
although in practice, the predictivity will depend on the level of accuracy of the
calculation (LO vs NLO, amount of non-perturbative inputs needed, …)

5. A big open question is this relevant at today’s colliders ?
in other words: can we get away with using such
a gluon distribution (with ad hoc cutoff if necessary) ?
or do we need to properly take into account
the QCD dynamics at kT ~ QS and below ?
the CGC phenomenology is successful
for every collider process that involves
small-x partons and kT ~ QS , i.e. for a
broad range for high-energy observables:
multiplicities in p+p, d+Au, Au+Au and Pb+Pb; forward spectra and correlations
in p+p and d+Au; total, diffractive and exclusive cross sections in e+p and e+A, …
- for each of these observables, there are alternatives explanations
- the applicability of the theory can be questioned when values of QS start to drop below 1 GeV (e.g. p+p and peripheral d+Au at RHIC)
the CGC is not widely accepted because

6. What EICs can do provide golden measurements
EICs = EIC stage 1, EIC stage 2, LHeC
provide golden measurements
the kind that will prove non-linear QCD evolution to be indispensable, or irrelevant
twice one thought one had found such observables
modification of particle production at forward rapidities in p+A versus p+p
EICs would provide smoking guns for saturation, something
that very likely cannot be done with p+A (let alone A+A)
single inclusive
di-hadron correlations

7. Bigger open questions (I)
EICs would also provide data that can help us address the following questions
the impact parameter dependence of the gluon density and of QS
this has always been the main non-perturbative input in CGC calculations
in the case of a proton, using an impact-parameter averaged saturation
scale is enough most of the time, but in the case of a nucleus it is not
modeling
what is done in the most advanced CGC phenomenological
studies, is to treat the nucleus as a collection of Woods-Saxon
distributed CGCs, and to evolve (down in x) the resulting gluon
density at different impact parameters independently
but is this good enough ? (in principle not)

8. Bigger open questions (II)
the transition from the saturation to the high-pT (leading-twist) regime
rcBK evolution (down in x) does not contain
the DGLAP limit, hence after some evolution
(at forward rapidities), RpA predictions reach
unity only at unrealistically large values of pT
Albacete, Dumitru
how RpA goes back towards unity at high-pT ?
the transition from the saturation regime to confinement
how does it happen ? does the coupling run with Qs ?
are classical fields still the right degrees of freedom ?
p+A and e+A collisions offer special opportunities to explore
this many-body system of strongly-correlated gluons
universality properties of the saturation regime
here I focus on what is unique to e+A, p+A provides great possibilities as well
see e.g. Salgado et al,

9. Connections with QGP physics
bulk observables in heavy-ion collisions reflect the properties of the
initial state as much as those of the hydro evolution of the QGP
see François’s talk next
new sources of uncertainties keep
emerging, for instance even two CGC
models predict different eccentricities
the main source of error in the extraction of medium parameters
(e.g. η/s) is our insufficient understanding of initial state fluctuations
QGP properties cannot be precisely extracted from data without a proper
understanding of the initial state; e+A collisions: access to a precise picture

10. e+p and e+A measurements: EIC and LHeC highlights

11. Deep inelastic scattering (DIS)
photon virtuality
Q2 = - (k-k’)2 = - q2 > 0
*A center-of-mass energy
W2 = (q+p)2
EIC
LHeC
NOT all processes require Q2 ~ QS2 in order to probe saturation effects

12. Inclusive structure functions
measures quark distributions gluon distribution
precisely measuring FL is crucial, and this requires an e+A energy ( ) scan
Albacete, Lamont
can NLO DGLAP simultaneously accommodate F2 and FL
data if saturation sets in according to current models ?

13. Hard diffraction in DIS
a surprising QCD feature at HERA: a proton in its rest frame hit by a 25
TeV electron remains intact 15% of the time
clean and unambiguous signal of saturation, already at EIC stage-1
this enhancement is specific to e+A (there is no equivalent in p+A)
Guzey,
Lamont, CM
observable subject to strong non-linear
effects even with Q2 values
significantly bigger than QS2
at HERA the NLO DGLAP description
breaks down already at Q2 ~ 8 GeV2

14. Exclusive Vector Meson production
@ LHeC
energy dependence
momentum transfer dependence
@ EIC
Toll, Ullrich
Newman, Watt
through a Fourier transformation, one can
extract the spatial gluon distribution (and
correlations), this is not feasible in p+A

15. Di-hadrons in DIS
directly sensitive to the kT dependence of the gluon distribution
at the qualitative level:
similar effects as in p+A
Lee, Xiao, Zheng
unique access to Weizsacker-Williams gluon distribution
(a different operator definition is involved in p+A)
but at the quantitative level, this
process involves a different
unintegrated gluon distribution

16. Conclusions all detailed studies can be found in
- the INT report on the Physics case for the Electron-Ion Collider, arXiv:
e+A conveners : A. Accardi, M. Lamont and CM
- the upcoming EIC white paper
e+A conveners: Y. Kovchegov and T. Ullrich
- the LHeC Conceptual Design Report, arXiv:
small-x conveners: N. Armesto, B. Cole, P. Newman and A. Stasto
thanks to the EIC task forces at Brookhaven and Jefferson labs
thanks to the LHeC small-x working group