Status of nuclear PDFs after the first LHC p-Pb run

In this talk, I overview the recent progress on the global analysis of nuclear parton distribution functions (nuclear PDFs). After first introducing the contemporary fits, the analysis procedures are quickly recalled and the ambiguities in the use of experimental data outlined. Various nuclear-PDF parametrizations are compared and the main differences explained. The effects of nuclear PDFs in the LHC p-Pb hard-process observables are discussed and some future prospects sketched.

What is actually parametrized?
The standard definition of nuclear PDFs

Nuclear modifications
Free proton baseline Why the two components?
Much of the data are ratios of the form =⇒ In a global analysis f p i must always be supplied. What is actually parametrized?
The standard definition of nuclear PDFs

Nuclear modifications
Free proton baseline Most (EPS09, DSSZ,...) impose the flavour independence (FI) at Q 2 = Q 2 0 : The FI immediately destroyed by the DGLAP at Q 2 > Q 2 0 =⇒ No reason to assume FI in the first place.
nCTEQ15: flavour variation for the valence quarks.
The standard analysis procedure Based on considering χ 2 figure-of-merit function Hessian matrix

Parameter variations
The zi coordinates (linear combinations of ai) are ∼ uncorrelated and one can use the standard law of error propagation Expand the global χ 2 around the minimum Hessian matrix
The current fits define δz ± i such that they correspond to fixed ∆χ 2 global .
For the parametrization bias, the global fits take ∆χ 2 global 1.
The LHC data opens a previously unexplored kinematic region.
=⇒ Cannot disentangle the effects of proton PDF f p i (∼90%) and nuclear modifications R Pb i (∼10%).  (2011) 071] =⇒ As much as possible of the dependence on the proton PDF f p i cancels. =⇒ Cancel also experimental uncertainties (especially if the correlations are known)... but lose some information also.

=⇒
=⇒ Cannot use the Pb-Pb data in this way. To reduce the theoretical bias & experimental uncertainties a following observable was suggested [PRL 110 (2013) Size of the (x,y) bin A typical pattern of antishadowing + EMC effect clearly visible.
The CHORUS ν-Pb and ν-Pb data included in the EPPS16 analysis in this wayaccounting for the correlated systematics.
The true structure functions (used now in EPPS16): The true structure functions (used now in EPPS16): Both ways have been used -the latter one less sensitive to experimental assumptions. The EPPS16 nuclear modification for 208 Pb at Q 2 = m 2 charm Total uncertainties shown as blue bands, individual error sets in green The EPPS16 nuclear modification for 208 Pb at Q 2 = m 2 charm Total uncertainties shown as blue bands, individual error sets in green The EPPS16 nuclear modification for 208 Pb at Q 2 = m 2 charm Total uncertainties shown as blue bands, individual error sets in green The EPPS16 nuclear modification for 208 Pb at Q 2 = m 2 charm Total uncertainties shown as blue bands, individual error sets in green Total uncertainties shown as blue bands, individual error sets in green The EPPS16 nuclear modification for 208 Pb at Q 2 = 10000 GeV 2

Total uncertainties shown as blue bands, individual error sets in green
Comparison between nCTEQ15 and EPPS16, Q 2 = 10 GeV 2 Typically smaller uncertainties in nCTEQ15 ⇐ more restrictive parametrization Larger high-x gluon uncertainties in nCTEQ15 ⇐ looser cuts and no LHC data Behaviour of the nCTEQ15 valence sector ⇐ isospin-symmetric DIS data + no ν-A DIS  =⇒ compare the averages  :1612.05741] All three consistent (modulo the large-x valence quarks of DSSZ).
Typically larger uncertainties in EPPS16 (more degrees of freedom). More net shadowing for y ± > 0 than for y ± < 0
The mild nuclear effects of DSSZ gluons lead to a result similar with no effects.
Dijets constitute currently the most stringent probe of large-x gluons.
For the new p-p baseline at √ s = 5 TeV direct measurements of nuclear modification R pPb are now possible (more or less also at √ s = 8 TeV Provide theoretically a cleaner sensitivity to R A i (x, Q 2 ) but.... It is important that in such measurements the correlated systematics between p-p and p-Pb are accounted for. Preferably in a common fiducial phase space.
Near-future prospects: The importance of symmetric phase space Fit the coefficient functions to p-p data Neglects all but the gluon-gluon channel Prospects for other probes -ultra peripheral collisions (UPC) It has been argued that UPC vector meson (e.g. J/ψ) production in Pb-Pb collisions is particularly sensitive to nuclear gluon Summary Overviewed the recent progress on the global analysis of nuclear PDFs The most important developments new ingredients in the latest global analysis: LHC Run I data completely novel constraints neutrino DIS data Ru V ∼ R d V full flavour dependence significantly less bias but larger uncertainties The universality of nuclear PDFs now verified up to the electroweak scale.
More (much!) data expected in the near future -e.g. the p-Pb run at √ s = 8 TeV • The availability of correlated systematics would be advantageous.
• Symmetric acceptance in the c.m. frame would reduce theoretical uncertainties.