Constraining the d PDF at large values of x has traditionally relied, in part, on the use of deeply inelastic lepton deuterium scattering data. The use of such data requires the inclusion of nuclear corrections which account for Fermi motion, binding, and off-shell effects. The impact of these corrections in the context of a global fit is examined. The uncertainties due to these nuclear effects are large

Owens, J. F.

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DOI 10.1393/ncc/i2012-11287-4Colloquia: PAVI11IL NUOVO CIMENTO Vol. 35 C, N. 4 Luglio-Agosto 2012PDFs, nuclear corrections, and the d/u ratioJ. F. OwensPhysics Department, Florida State University - Tallahassee, Florida 32306-4350, USAricevuto il 10 Ottobre 2011; approvato il 5 Maggio 2012pubblicato online il 4 Luglio 2012Summary. — Constraining the d PDF at large values of x has traditionally relied,in part, on the use of deeply inelastic lepton deuterium scattering data. The useof such data requires the inclusion of nuclear corrections which account for Fermimotion, binding, and off-shell effects. The impact of these corrections in the contextof a global fit is examined. The uncertainties due to these nuclear effects are large.PACS 12.38.Bx – Perturbative calculations.PACS 13.60.Hb – Total and inclusive cross sections (including deep-inelastic pro-cesses).PACS 24.85.+p – Quarks, gluons, and QCD in nuclear reactions.1. – IntroductionParton distribution functions (PDFs) are necessary for QCD-based calculations ofobservables involving the scattering of hadrons. Separating the various parton flavorswhen performing global fits for PDFs requires a variety of types of data. In particular,separating the u and d PDFs typically relies on deep inelastic lepton scattering (DIS)data taken with both proton and deuterium targets. However, it is not sufficient to treatdeuterium as a sum of a neutron and a proton; nuclear effects can give rise to significantcorrections, especially at large values of x.Conventional global fits typically rely on data in the region x  0.7 since that isthe region covered by most of the high energy experiments included in the fits. Thisessentially allows one to neglect effects due to target mass corrections and higher twistcontributions, thereby allowing the use of only the twist-two PDFs. In this region thenuclear corrections for deuterium targets are thought to be on the order of a few percentand so they are often ignored in global fits.One unintended result of this procedure is that the PDFs for values of x above about0.7 are extrapolations of the fitted PDFs and are essentially unconstrained by data.Nevertheless, there are times when PDFs in the large-x region are needed. An examplewould be the production of a large mass state at high values of rapidity y. In lowestc© Societa` Italiana di Fisica 219220 J. F. OWENSorder the relevant values of the PDF momentum fractions arex1,2 =M√sexp(±y).Thus, large values of y result in one large value of x and one small value.In a previous study [1], the effects of systematically extending the range in x werestudied. Target mass effects were included along with a parametrization of higher twistterms. It was found that the twist-two PDFs were stable to variations in the techniquesused to calculate the target mass corrections, provided that a sufficiently flexible highertwist parametrization was employed. However, it was observed that the d PDF wasparticularly sensitive to the assumptions used to calculate the nuclear corrections indeuterium.In this talk I describe some results from an analysis whose goal is to study the sensitiv-ity of PDFs to various models of nuclear corrections for DIS data taken with deuteriumtargets. Detailed results, including a description of the issues related to nuclear correc-tions may be found in ref. [2].2. – Fit resultsThe global fits discussed here were performed using the same fitting package andtechniques described in ref. [1]. All of the observables are fitted with theoretical expres-sions calculated to next-to-leading-order in the strong coupling. The new features in thisanalysis are the inclusion of off-shell corrections as well as the use of a range of deuteronwave functions to calculate the nuclear corrections [2].Visualizing the results of this analysis is most easily done by displaying the d/u ratio.This is due to the fact that the u PDF is already well constrained by the proton DISdata and by data from lepton pair production and jet production at collider energies.The main constraint on the d PDF is provided by deuterium DIS data, since the rolesof the u and d PDFs are interchanged when considering a neutron target. Thus, whendifferent models for nuclear corrections are considered, the d PDF is modified by thegreatest amount. Therefore, the effects of the nuclear corrections show up directly inthe d/u ratio. This may be made clearer by considering that it is the convolution of thePDFs with the nuclear smearing function that is constrained when fitting the deuteriumdata. Changes in the nuclear corrections can be compensated by corresponding changesin the d PDF, since the u PDF is already well constrained by other observables.The left-hand panel of fig. 1 illustrates the variation of the d/u ratio for differentmodels of the off-shell corrections based on the off-shell spectator quark model by Kulaginand Petti [3], as described in ref. [2], when the AV18 [4] deuteron wave function is used.A conventional parametrization of the d and u PDFs is employed, wherein the d PDFvanishes as x→ 1 faster than the u PDF, resulting in the vanishing of d/u in this limit.Similar results are shown in the central panel where a modified d PDF has been used:d → d + axbu. This choice has the feature that d/u → a as x approaches 1. Theright-hand panel shows the dependence of the results on the choice of the deuteron wavefunction.The full range of variations of the d/u ratio due to deuteron wave function and off-shellcorrections is shown in fig. 2 along with the PDF fit uncertainties (based on Δχ2 = 1).It is clear that the model-dependent nuclear uncertainties dominate at large values of x.PDFs, NUCLEAR CORRECTIONS, AND THE d/u RATIO 221Fig. 1. – The d/u ratio at Q2 = 10GeV2 obtained with different choices of d-quark parametriza-tion and nuclear corrections. Left panel: standard d-quark parametrization [1] and AV18deuteron wave function for several off-shell correction models; middle panel: modified d-quarkparametrization for the same nuclear corrections; right panel: dependence on the deuteron wavefunction for a fixed off-shell correction (mKP). The shaded bands and bottom panels show theΔχ = 1 PDF errors and the relative PDF errors on the d/u ratio, respectively. The thinnerlines above x ≈ 0.8 denote extrapolations into unmeasured regions.Moreover, even when one employs cuts on Q2 and W 2 that limit x to values below 0.7,the deuteron nuclear corrections are potentially substantial.An interesting feature of the results is summarized in fig. 3. Here the extremes ofthe fitted u, d, and g PDFs are shown relative to those obtained with a set of choiceswhich lies roughly midway between the extremes of the d PDF. As expected, the u PDFis relatively insensitive to the nuclear models, since it is well constrained by proton data.However, the d and g PDFs appear to be strongly anticorrelated, although the errors oneach PDF must be kept in mind when evaluating the significance of this anticorrelation.This effect is due primarily to the influence of the high-pT collider jet data. As the dPDF is reduced the gluon contribution (and to a very much lesser extent, that of theu PDF) must be increased in order to describe the data. This variation is substantialfor values of x even as low as x = 0.5, which strongly suggests that nuclear correctionsshould be included in global fits whenever deuterium data are utilized.Another interesting feature discussed in ref. [2] is the existence of tension betweenthe deuterium data and data for the W rapidity charge asymmetry [5]. The d/u ratiochanged significantly in the low x region when a fit without the deuterium data wasperformed. This fit showed a marked reduction in the χ2 for the W asymmetry data.This is particularly interesting since the nuclear corrections in this region are expected222 J. F. OWENSFig. 2. – Full range of variations of the d/u ratio due to deuteron wave function and off-shell cor-rections (cross-hashed band) and PDF fit uncertainties (diagonal hashed). The arrow indicatesthe extrapolation region at large x.Fig. 3. – The extremes of the variations of the u (left panel), d (middle panel), and gluon (rightpanel) PDFs, relative to reference PDFs extracted using the smearing function with the AV18deuteron wave function and mKP (central) off-shell corrections.PDFs, NUCLEAR CORRECTIONS, AND THE d/u RATIO 223to be small. For relatively small values of the W rapidity, the asymmetry is proportionalto the slope of the d/u ratio. Without the constraints provided by the deuterium DISdata, the program was able to increase the d PDF at low values of x while keeping it thesame at higher values. This resulted in a steepening of the d/u ratio at small values of xwhich, in turn, resulted in a better description of the W asymmetry data. However, inthe context of nuclear corrections, it would require a low-x shadowing correction muchlarger than expected in order to replicate this effect when the deuterium target data areincluded in the fit.In the longer term, the issue of the dependence of the d PDF on the choice of nu-clear models may be resolved by data which are sensitive to the d/u ratio but whichdo not depend sensitively on nuclear corrections. Examples include the BoNuS [6],MARATHON [7], and PVDIS [8] experiments which are scheduled to run after the com-pletion of the 12GeV upgrade at Jefferson Lab. If the d/u ratio were known indepen-dently of the nuclear corrections, then the problem could be turned around —pinningdown the d PDF would enable one to determine which nuclear model gave the bestresults.This analysis is being extended [9]. The data sets are being updated as new onesbecome available, including new DIS data, Z rapidity distributions, and high-pT jetdata. The range of nuclear models being considered is under review to insure thatrepresentative examples are included without expanding the model dependence to anunwarranted extent. Different choices for the PDF parametrizations are being studiedin order to better ascertain the effects of extrapolations beyond the fitted regions. PDFerror sets will be generated using the Hessian technique and the software for this isunder construction. The goal is to produce NLO PDF sets with errors for each of threechoices of nuclear corrections. These sets will allow users to judge whether or not theuncertainties due to nuclear corrections will contribute to the overall PDF uncertaintiesin regions where their observables are measured.Although the nuclear corrections needed for deuterium target DIS are largest in thehigh-x region, their influence on the fitted PDFs can extend to values of x as low as0.5. Therefore, even calculations for observables measured at collider energies can beaffected. These nuclear corrections provide an additional source of uncertainty for thePDFs which should be taken into account when error bands are estimated.REFERENCES[1] Accardi A., Christy M. E., Keppel C. E., Monaghan P., Melnitchouk W., Morf´ınJ. G. and Owens J. F., Phys. Rev. D, 81 (2010) 034016.[2] Accardi A., Melnitchouk W., Owens J. F., Christy M. .E, Keppel C. E., Zhu L.and Morf´ın J. G., Phys. Rev. D, 84 (2011) 014008.[3] Kulagin S. A. and Petti R., Nucl. Phys. A, 765 (2006) 126.[4] Wiringa R. B., Stoks V. G. J. and Schiavilla R., Phys. Rev. C, 51 (1995) 38.[5] Aaltonen T. et al. (The CDF Collaboration), Phys. Rev. Lett., 102 (2009) 181801.[6] http://www.jlab.org/~kuhn/BoNuS Welcome.html.[7] http://www.jlab.org/exp prog/PACpage/PAC30/talks/pac30-petratos.pdf.[8] http://hallaweb.jlab.org/experiment/E05-007.[9] Accardi A. et al., in preparation.

PDFs, nuclear corrections, and the d/u ratio

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PDFs, nuclear corrections, and the d/u ratio

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