aa r X i v : . [ h e p - ph ] J un IL NUOVO CIMENTO
Vol. ?, N. ? ? Parton Distributions and LHC data
J. Rojo ( ) ( ) Dipartimento di Fisica, Universit`a di Milano and INFN, Sezione di Milano, Via Celoria16, I-20133 Milano, Italy
Summary. — In this contribution we briefly report on the progress and open prob-lems in parton distribution functions (PDFs), with emphasis on their implicationsfor LHC phenomenology. Then we study the impact of the recent ATLAS and CMS W lepton asymmetry data on the NNPDF2.1 parton distributions. We show thatthese data provide the first constrains on PDFs from LHC measurements.12.38.-t,12.38.Lg
1. – Progress and open problems in parton distributions
The quantitative control of the Standard Model contribution to collider signal andbackground processes at the few percent level is a necessary ingredient not only for pre-cision physics, but also for discovery at the LHC. The precision determination of partondistribution functions (PDFs) is essential in order to achieve this level of theoreticalaccuracy.There has been substantial progress in PDF analysis in the last years, and it is thusimpossible to review it in detail in this contribution. A recent concise report of thestatus of the field can be found in Ref. [1], while more detailed reviews can be found inRefs. [2-5]. In this contribution we restrict ourselves to highlight some important topicsin PDF determinations. First of all, we will sketch the current status of PDF fits anddiscuss some of the open problems in the field. Then we will discuss how the ATLASand CMS measurements of the W lepton asymmetry data provide the first constraintson PDFs from the LHC, thus paving the way for PDFs based on LHC data.PDF analysis have entered the era in which they can be considered as a quantitativescience. An ideal PDF determination should satisfy several important requirements [2].These include being based on a dataset which is as wide as possible, in order to ensurethat all relevant experimental information is retained, to use a sufficiently general andunbiased parton parametrization and to provide statistically consistent confidence levelsfor PDF uncertainties. Moreover, such ideal set should include heavy quark mass effectsthrough a GM-VFN scheme [6] and be based on computations performed at the highestavailable perturbative order. Finally, PDF sets should be provided for a variety of values c (cid:13) Societ`a Italiana di Fisica J. ROJO
Table
I. –
Summary of the features of the most updated PDF sets from each group. The CT10,MSTW08 and NNPDF2.1 sets include data from a wide variety of physical processes and arethus called global PDF sets. See text for more details.
Ref Dataset Parametrization PDF uncertaintiesABKM09 [14] DIS+DY Polynomial Hessian, standard tol.CT10 [15] DIS+DY+W/Z+jet Polynomial Hessian, dyn. tol.HERAPDF1.0 [16] DIS Polynomial Hessian, standard tol.JR08 [17] DIS+DY+jet Polynomial Hessian, fixed tol.MSTW08 [18] DIS+DY+W/Z+jet Polynomial Hessian, dyn. tol.NNPDF2.1 [12] DIS+DY+W/Z+jet Neural Nets Monte CarloPT order Heavy Quarks Strong couplingABKM09 NLO/NNLO FFNS FittedCT10 NLO S-ACOT- χ Fixed + range of valuesHERAPDF1.0 NLO TR FixedJR08 NLO/NNLO FFNS FittedMSTW08 LO/NLO/NNLO TR Fitted + range of valuesNNPDF2.1 NLO FONLL-A Fixed + range of values of α s , reasonably thinly spaced, similarly for the heavy quark masses, and should includean estimate of uncertainties related to the truncation of the perturbative expansion.While for each of these aspects there has been sizable progress in the recent years, stillno PDF sets fulfills all these conditions.One important development in PDFs in the recent years has been the NNPDF ap-proach [7-11]. Thanks to a combination of Monte Carlo techniques and the use of artificialneural networks, the NNPDF approach avoids some of the drawbacks of the standardapproach like the bias due to the arbitrary choice of input functional forms or the use oflinear approximations for PDF uncertainty estimation. The most updated NNPDF setis NNPDF2.1 [12], an unbiased NLO global fit of all relevant hard scattering data basedon the FONLL-A GM-VFN scheme [13].Several groups provide regular updates of their PDF sets: in alphabetic order theseare ABKM, CT, HERAPDF, JR, MSTW and NNPDF. In Table I we summarize someof the features of the most updated PDF sets from each collaboration. We consider onlythose sets available in the LHAPDF library. We compare the dataset, parametrization,method to estimate PDF uncertainties, perturbative order at which PDFs are available,the theoretical schemes adopted to include heavy quark mass effects and the treatment ofthe strong coupling α s . More details on each of these issues can be found in Refs. [2,4,5],as well as in the original publications of each group.The main difference arises from the data sets used in each of the various analysis.The CT10, MSTW08 and NNPDF2.1 sets include data from a wide variety of physicalprocesses and are thus called global PDF sets. Other PDF sets use more restrictivesubsets, like ABKM09, which excludes Tevatron jet and weak vector production dataand HERAPDF1.0, that is based solely on HERA data.PDFs are typically parametrized with relatively simple functional forms like q ( x, Q ) ∼ x a (1 − x ) b P ( x, c, d, . . . ) with P a polynomial that interpolates between the small and ARTON DISTRIBUTIONS AND LHC DATA Fig. 1. – Comparison of the NLO total cross sections for W + and t ¯ t production and theircombined PDF+ α s uncertainties at the LHC 7 TeV between the most updated PDF sets ofeach group. Plots from G. Watt. ) (M S a ) ( nb ) n + l fi + B ( W (cid:215) + W s
68% C.L. PDFMSTW08CTEQ6.6CT10NNPDF2.1HERAPDF1.0ABKM09GJR08 = 7 TeV)s at the LHC ( n + l fi + NLO W S a Outer: PDF+Inner: PDF onlyVertical error bars G . W a tt ( A p r il ) ) (M S a ) ( nb ) n + l fi + B ( W (cid:215) + W s ) (M S a ( pb ) tt s
68% C.L. PDFMSTW08CTEQ6.6CT10NNPDF2.1HERAPDF1.0ABKM09GJR08 = 7 TeV)s cross sections at the LHC (tNLO t S a Outer: PDF+Inner: PDF onlyVertical error bars G . W a tt ( A p r il ) ) (M S a ( pb ) tt s large– x regions. These unjustified theoretical assumptions introduce a potentially largefunctional form bias in PDF determinations. The NNPDF approach bypasses this prob-lem using neural networks as universal unbiased interpolants. Related techniques forgeneral PDF parametrizations like Chebishev polynomials have also been discussed inthe literature [19, 20].PDF uncertainties are estimated by all groups (but NNPDF) using the Hessianmethod. However, different choices for the tolerance T = p ∆ χ adopted to define1–sigma PDF uncertainties are used. For example, while HERAPDF1.0 and ABKM08are based on a textbook tolerance ∆ χ = 1, MSTW08 and CT10 adopt a dynamicaltolerance criterion that results in tolerances ∆ χ ≥
1, which are moreover different foreach eigenvector direction. The need for large tolerances has been suggested to partlyarise when restrictive input functional forms are used [20]. NNPDF, on the other hand,is based on the Monte Carlo approach, that is, a sampling in the space of experimentaldata, that allows an exact uncertainty propagation from data to PDFs and from theseto physical observables.Recently, a detailed benchmarking of the predictions for relevant LHC observablesfrom modern NLO PDF sets was performed in the context of the PDF4LHC workinggroup [5]. In Fig. 1 we compare the NLO predictions for different PDF sets for twoimportant LHC observables, the total W + and t ¯ t cross sections. One of the conclusionsfrom that study is that the agreement between global PDF sets is reasonable for mostLHC processes, much better than for sets based on restrictive datasets. However, it wasalso clear that even within global sets there are important discrepancies whose originneeds still to be understood, related for example to the large- x gluon and to strangeness.Another recent benchmark study, this time at NNLO, was presented in [21].The PDF4LHC exercise allowed to elucidate differences and similarities between PDFsets. In particular it showed that the most important source of difference between setsis the choice of fitted data. This study was the basis of the PDF4LHC recommenda-tion [22], that suggests to take the envelope of the combined PDF+ α s uncertainties fromthe three global PDF sets, CT10, MSTW08 and NNPDF2.1, to estimate the PDF+ α s uncertainty on LHC processes. The PDF4LHC has been adopted by ATLAS and CMS inthose analysis sensitive to PDFs, and in particular the LHC Higgs cross section working J. ROJO
Fig. 2. – Left plot: Comparison of the NLO Higgs production cross section with the combinedPDF+ α s uncertainties from NNPDF2.0, MSTW08 and CTEQ6.6, and the resulting PDF4LHCrecipe [22] envelope, from Ref. [1]. Right plot: comparison of the MSTW08 and the preliminaryNNPDF2.1 NNLO predictions for the NNLO Higgs production cross section. For the MSTW08prediction two values of α s have been used. [GeV] H M100 150 200 250 300 350 400 450 500 R L HC H I GG S XS W G LHC 7 TeV 68% C.L. s a PDF+normalized to MSTW2008nlo) Z (m s a different values of uncertainties s a exact PDF+ PDF4LHC recipeNNPDF2.0CTEQ6.6MSTW08nlo [ GeV ] H M100 150 200 250 300 350 400 ( H - > gg ) ) s R ( NNLO gg->H production, Ratio to NNPDF2.1 (TMP) =0.119 S a NNPDF2.1 NNLO(TMP) =0.119 S a MSTW08 NNLO =0.1171 S a MSTW08 NNLO
NNLO gg->H production, Ratio to NNPDF2.1 (TMP) group [1] uses the PDF4LHC recipe to estimate the combined PDF+ α s uncertainty intheir theoretical predictions, see Fig. 2. The same recipe has been used to derive themost updated Tevatron Higgs exclusion limits [23].Let us now turn to discuss some open problems in PDF fits: the treatment of α s ,Higgs production at hadron colliders and deviations from DGLAP in HERA data. Thetreatment of the strong coupling in PDF fits is a source of differences between sets, assummarized in Table I. Some groups, like MSTW or ABKM, determine α s simultane-ously with the PDFs, while others, like CT or NNPDF, take for α s a fixed value closeto the PDG average [24], α s ( M Z ) = 0 . ± . α s is used, as shown also in thecomparison plots of Fig. 1.Let us emphasize that the choice of fixing α s to the PDG value in the reference PDFset is not necessarily related to the sensitivity of a given PDF analysis to α s . Rather, itreflects the idea than the average of α s from a wide range of processes, including somelike τ decays unrelated to the proton structure, is necessarily more accurate than thedetermination from a single PDF fit. For example, NNPDF [25] has recently performeda NLO determinations of the strong coupling, finding good consistency with the PDGvalue: α s ( M Z ) = 0 . ± . α s is closely related to one of the most important process at theLHC, the Higgs production cross section in its dominant production channel of gluonfusion. This process is very sensitive to α s [26], since the partonic cross section dependsas O (cid:0) α s (cid:1) already at leading order, and has received a lot of attention recently dueto claims that theoretical uncertainties were being underestimated. Preliminary NNLOresults from NNPDF, shown in Fig. 2, suggest a reasonable agreement with the MSTW08NNLO prediction, as was already the case at NLO, thus confirming the PDF4LHC recipeestimates. It is also clear how the use of a common value of α s improves further theagreement between the two sets. ARTON DISTRIBUTIONS AND LHC DATA Fig. 3. – The kinematic coverage in the ( x, Q ) plane for W production at the LHC in the central(ATLAS and CMS) and forward (LHCb) regions. Another open problem in PDF determinations are the potential departures from fixed-order DGLAP evolution in small- x and Q HERA data. The analysis of Refs. [27,28] found evidence for deviations from NLO DGLAP in the small- x combined HERA-Idata, consistent with small- x resummation and non-linear dynamics but not with NNLOcorrections. This effect has been confirmed by the HERAPDF analysis, which also findsa worse fit quality at NNLO for the small- x data. A related CT10 [29] analysis foundsome hints as well but it was restricted to the use of few functional forms for the small- x PDFs. If deviations from DGLAP for low- x HERA data are confirmed, this suggeststhat small- x resummation [30] is a necessary ingredient in order to use all the potentialof HERA data for precision LHC physics.
2. – Constraining PDFs with LHC W asymmetry data We now turn to discuss the first constraints on PDFs from LHC data, provided by theATLAS [31] and CMS [32] measurements of the leptonic W asymmetry( ). As it is wellknown, W production at hadron colliders is sensitive to the light quark and antiquarkPDFs at medium and small- x . The kinematic coverage of W production at the LHC issummarized in Fig. 3. We have studied the impact of the W asymmetry data using theBayesian reweighting method of Ref. [33]. Bayesian reweighting is a powerful techniqueto efficiently determine the impact of new data into PDFs without the need of refitting.This method also allows to determine the internal consistency of the data sets and theircompatibility with the global fit.A detailed discussion of the impact of LHC data on NNPDF will be presented else- ( ) There exist as well preliminary data from LHCb that will be sensitive to even smaller andlarger values of x , see Fig. 3. J. ROJO
Fig. 4. – The ATLAS and CMS W lepton asymmetry data compared to the NNPDF2.1 predic-tions before and after reweighting. m y0 0.5 1 1.5 2 2.5 ) m ( y m A Preliminary Results
NNPDF2.1NNPDF2.1 + ATLAS+CMS W asyATLAS W asy Data
Preliminary Results l y0 0.5 1 1.5 2 2.5 ) l ( y l A Preliminary Results
NNPDF2.1NNPDF2.1 + ATLAS/CMS W asyCMS W asy Data - ElectronsCMS W asy Data - Muons
Preliminary Results where. In this contribution we restrict ourselves to some selected preliminary results.We will show results for the impact of the combined ATLAS and CMS data. In thecase of CMS we consider the more inclusive dataset (with the cut in lepton transversemomentum of p lt ≥
25 GeV) and both electrons and muons. For ATLAS only the muonasymmetry has been presented. The theoretical predictions have been computed withthe DYNNLO generator [34] at NLO accuracy for NNPDF2.1. The kinematic cuts arethe same as in the respective experimental analyses.In Fig. 4 we compare the ATLAS and CMS lepton asymmetry data with the NNPDF2.1predictions before and after including the effect of these data sets. We notice that thedata is already nicely consistent with the NNPDF2.1 prediction within the respectiveuncertainties. After including the LHC measurements, one finds that the W asymmetrydata constraints the PDF uncertainties and leads to an even better agreement with thedata. A more detailed statistical analysis confirms that the ATLAS and CMS data areconsistent between them and with the experiments included in the global PDF analysis.After reweighting, the χ per data point of the combined CMS and ATLAS data is ∼ W asymmetry data. We find that the PDF uncertainties are reducedfor medium and small- x light quark and antiquarks, by a factor that can be as large as ∼ W asymmetrymeasurements with the global fit. At large- x the constrains are weaker, as expected fromthe kinematic coverage shown in Fig. 3. Upcoming measurements of this asymmetry byLHCb might help in reducing PDF uncertainties in the large- x region.Note that these preliminary results have been derived from a sample of only N rep =100 Monte Carlo replicas. This means that there can be non–negligible fluctuations andexplains why PDF uncertainties are apparently reduced even at very small- x , outside thekinematic coverage of the ATLAS and CMS data.To summarize, we have shown that the W lepton asymmetry is the first dataset fromthe LHC that has the precision to constrain PDFs and thus improve the accuracy ofStandard Model computations for LHC processes. We have quantified this impact onthe light quark and antiquark PDFs, and found that PDF uncertainties can be reducedby factors up to ∼
40% at medium and small- x . More constrains on PDFs should soon ARTON DISTRIBUTIONS AND LHC DATA Fig. 5. – The impact of the ATLAS and CMS lepton asymmetry data on the relative uncertaintyof the light quark and antiquark NNPDF2.1 PDFs. x -5 -4 -3 -2 -1 R e l E rr [ x u ( x , Q ) ] , ratio to NNPDF2.1 -- Preliminary Results = M Q NNPDF2.1NNPDF2.1 + ATLAS/CMS LASY , ratio to NNPDF2.1 -- Preliminary Results = M Q x -5 -4 -3 -2 -1 R e l E rr [ x db a r ( x , Q ) ] , ratio to NNPDF2.1 -- Preliminary Results = M Q NNPDF2.1NNPDF2.1 + ATLAS/CMS LASY , ratio to NNPDF2.1 -- Preliminary Results = M Q be available from upcoming LHC measurements.
3. – Outlook
In this contribution we have briefly reviewed recent developments and open problemsrelated to PDFs, with emphasis on their implications for the LHC physics program.While our understanding of the proton structure has seen a huge progress in the recentyears, there are still open questions that need to be answered, and that are important toimprove even further the accuracy of theoretical predictions at the LHC. We have alsopresented preliminary results on the impact of the LHC W lepton asymmetry data onthe NNPDF2.1 set. We have shown that these data provide the first constraints on PDFsfrom LHC measurements, in particular they help to pin down with better accuracy themedium and small x light quarks and antiquarks.In the medium term, LHC measurements will provide very important constraints onmost PDF combinations. This will allow parton distributions to be derived solely fromcollider data: HERA, Tevatron and the LHC. Collider data is more robust theoreticallyand experimentally than low-energy fixed target data, that now provide basic constrainsin global PDF analysis. In order to achieve this program, several measurements will beprovided by the LHC: Z –boson rapidity distributions, low mass Drell-Yan differentialdistributions, high E T jets and photons, and W/Z production in association with heavyquarks. The increased experimental and theoretical accuracy on PDFs determined thisway will provide a solid ground for precision Standard Model predictions and searchesfor new physics at the LHC. ∗ ∗ ∗
I would like to thank the La Thuile 2011 organizers for their kind invitation to presentthis review. I thank all the members of the NNPDF Collaboration for endless discussionson PDFs, specially S. Forte. I thank G. Watt for providing the plots in Fig. 1.
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