DGLAP analyses of nPDF: constraints from data
Abstract
We explain how the constraints from present experimental data can be used to obtain the nPDF in the framework of LO DGLAP evolution. We will also compare the only two available sets of this type and comment on the important information that neutrino factories could provide.
1 Introduction
Parton distribution functions (PDF) are needed to compute hard processes in hadronic and nuclear collisions. The method to obtain the PDF from experimental data is well established in the case of the free proton: the initial distributions at are evolved by the DGLAP equations [1] to larger and fitted to available data. The data from deep inelastic leptonproton scattering (DIS) are of main importance in these analyses. The nuclear structure functions measured in DIS experiments differ from those of the free nucleons. Definining the ratio vs. deuterium, ) at small values of , antishadowing () at intermediate and EMC effect ( again) and Fermi motion at large . The nuclear effects in translate in nuclear PDF (nPDF) which are modified from the ones of the free proton. The goal then is to obtain a set of nPDF following the well established procedure used for the free proton. In practice, a set of ratios of the PDF in bound and free protons, for , are extracted for a known set of the free proton PDF . several nuclear effects can be distinguished: shadowing (
2 EKRS analysis
The main problem in the nuclear case is the lack of experimental data. The DGLAP analysis of EKRS, which lead to the set EKS98 [2], uses several sets of DIS data on (see [2] for the refs.) and data on the DrellYan (DY) process measured in pA collisions [3]. Some other sets of data could be very helpful in constraining the nuclear effects for different parton flavours, e.g. charm production to constrain gluons. However, so far they are not included in [2] because of large error bars (open charm in ) or the presence of final state nuclear effects (charmonium in ). Further constraints which are used are momentum and baryon number sum rules. At an initial scale, chosen as GeV, the ratios for valence quarks (same for and ), sea quarks (same for , and ) and gluons are obtained in the following way:

At large values of () valence quarks dominate, and the data on fix the ratio but do not constrain the ratio . There are no constraints for the nuclear gluons, either, in this region. For consistency of the DGLAP evolution, it is assumed that , and that a similar EMC effect also exists in already at .

At intermediate values of () both DIS and DY data constrain the ratios and . The use of DY data [3] is essential in order to fix the relative strength of the valence and sea quark modifications, as DIS alone cannot distinguish between them. The baryon number sum rule imposes also constraints to . The gluon ratio is constrained at by the NMC data on the dependence of the ratio [4], and by momentum conservation. A 20% antishadowing is found for gluons at .

At small values of (), is dominated by sea quarks, so DIS data constrains mainly . The ratio is fixed by baryon number conservation and turns out to be larger (less shadowing) than . At , where no information from data is obtained in the region GeV, a saturation of the shadowing () is assumed. This phenomenon has been observed but only at GeV. At the initial scale, is assumed at , which leads to positive slopes for (observed at [4]).
For a given initial condition, LO DGLAP evolution is done. Then, comparing with the data at different , the best initial distributions are obtained through a recursive procedure. The resulting initial ratios at can be seen in Figure 1.
3 Comparison with other approaches
For the moment there is only one global DGLAP analysis on the nPDF similar to EKRS [2], that of HKM [6, 7]. Figure 1 shows a comparison of the EKS98 and HKM results for the ratios , and at GeV. The difference between the results follows from the fact that the data on the DY process [3] and on the dependence of [4] are not used as contraints in the HKM analysis.
The DY data set is important in the EKRS analysis in fixing and at intermediate : the DIS data forces at and, as the the DY cross sections show almost no nuclear effects (in ) there, the ratio is bound to be less than one (no antishadowing for sea quarks). In this conference, preliminary results from the HKM analysis with the DY data included were presented [7]. As a result, a better agreement with EKS98 was found.
The dependence of the structure function is very sensitive to the gluon distribution at small values of . LO DGLAP evolution of the nPDF gives [5] . NMC has measured [4] positive slopes for the ratio . This implies that within the DGLAP framework gluon shadowing cannot be much stronger than that in in the measured region . Also too weak a gluon shadowing is outruled [5] by the NMC data.
4 Improvements from neutrino DIS data
DIS experiments with neutrino and antineutrino projectiles could measure [8]
with similar relations for neutrons. Different flavors could then be disentangled and some of the uncertainties discussed above (e.g. valence at small and sea at large ) would become more directly constrained by data. This would allow for a more detailed analysis of the nPDF. Moreover, the valence/sea separation at medium would be measured and could be compared with the results from DY data. This would test the universality of the nPDF. Measuring sea and valence quark distributions in experiments would also shed more light on some open questions of QCD in nuclei, such as the probability interpretation of the (n)PDF [9].
References
 [1] Yu. Dokshitzer, Sov. Phys. JETP 46 (1977) 1649; V.N. Gribov and L. N. Lipatov, Sov. Nucl. Phys. 15 (1972) 438, 675; G. Altarelli, G. Parisi, Nucl. Phys. B 126 (1977) 298.
 [2] K. J. Eskola, V. J. Kolhinen and P. V. Ruuskanen, Nucl. Phys. B 535 (1998) 351; K. J. Eskola, V. J. Kolhinen and C. A. Salgado, Eur. Phys. J. C 9 (1999) 61.
 [3] D. M. Alde et al., Phys. Rev. Lett. 64 (1990) 2479.
 [4] M. Arneodo et al. [New Muon Collaboration], Nucl. Phys. B 481 (1996) 23.
 [5] K. J. Eskola, H. Honkanen, V. J. Kolhinen and C. A. Salgado, Phys. Lett. B 532 (2002) 222.
 [6] M. Hirai, S. Kumano and M. Miyama, Phys. Rev. D 64 (2001) 034003.
 [7] S. Kumano, these proceedings and arXiv:hepph/0204242.
 [8] M. L. Mangano et al., arXiv:hepph/0105155.
 [9] S. J. Brodsky et al., Phys. Rev. D 65 (2002) 114025.