In this contribution we discuss the impact of PDF uncertainties on t\bar{t}
and t-channel single-top production at the LHC. We present predictions for
total cross-sections computed at NLO accuracy with different PDF sets. For
single- top production, we point out that the uncertainty arising from the
choice of the bottom quark mass is one of the dominant theoretical
uncertainties on the total cross-section. Finally, the possibility of using PDF
induced correlations between top quark and electroweak vector boson production
cross-sections to improve the accuracy of LHC measurements is investigated.Comment: 8 pages, 5 figures. To appear in the Proceedings of the International
  Workshop on Top Quark Physics (top2010), Bruges, Belgium, May 31 - June 4,
  201

Guffanti, Alberto

Rojo, Juan

English

arXiv

In this contribution we discuss the impact of PDF uncertainties on tt̄ and t-channel single-top production at the LHC. We present predictions for total cross-sections computed at NLO accuracy with different PDF sets. For singletop production, we point out that the uncertainty arising from the choice of the bottom quark mass is one of the dominant theoretical uncertainties on the total cross-section. Finally, the possibility of using PDF-induced correlations between top quark and electroweak vector boson production cross-sections to improve the accuracy of LHC measurements is investigated. © Società Italiana di Fisica

Guffanti, A

Rojo, J

Oxford University Research Archive (ORA)

Top production at the LHC: The impact of PDF uncertainties and correlations

Oxford University Research Archive

In this contribution we discuss the impact of PDF uncertainties on t¯t and t-channel single-top production at the LHC. We present predictions for total cross-sections computed at NLO accuracy with different PDF sets. For singletop production, we point out that the uncertainty arising from the choice of the bottom quark mass is one of the dominant theoretical uncertainties on the total

cross-section. Finally, the possibility of using PDF-induced correlations between top quark and electroweak vector boson production cross-sections to improve the

accuracy of LHC measurements is investigated

Guffanti, A.

Rojo, J.

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2010-10668-yColloquia: TOP2010IL NUOVO CIMENTO Vol. 33 C, N. 4 Luglio-Agosto 2010Top production at the LHC: The impact of PDF uncertaintiesand correlationsA. Guffanti(1) and J. Rojo(2)(1) Physikalisches Institut, Albert-Ludwigs-Universita¨t - Hermann-Herder-Str. 379104, Freiburg i. Br., Germany(2) Universita` and INFN, Sezione di Milano - via Celoria 16, 20100 Milano, Italy(ricevuto il 25 Agosto 2010; approvato il 25 Agosto 2010; pubblicato online l’11 Ottobre 2010)Summary. — In this contribution we discuss the impact of PDF uncertaintieson tt¯ and t-channel single-top production at the LHC. We present predictions fortotal cross-sections computed at NLO accuracy with different PDF sets. For single-top production, we point out that the uncertainty arising from the choice of thebottom quark mass is one of the dominant theoretical uncertainties on the totalcross-section. Finally, the possibility of using PDF-induced correlations betweentop quark and electroweak vector boson production cross-sections to improve theaccuracy of LHC measurements is investigated.PACS 12.38.-t – Quantum chromodynamics.PACS 14.65.Ha – Top quarks.1. – IntroductionA precise determination of Parton Distribution Functions (PDFs) with reliable esti-mate of their uncertainties is crucial for the success of the physics program at the LHCexperiments. On the one hand, PDF uncertainties are often the dominant theoreticaluncertainties for many relevant signal and background processes [1]. On the other hand,overestimated PDF errors might hinder the discovery of new physics effects, as shown forexample in [2]. Top physics at the LHC is no exception and both top pair and single-topproduction present complementary and interesting properties as far as PDF determina-tion/effects are concerned. This contribution aims to review some of the implications ofPDFs for top quark physics at the LHC.In the first part of the contribution we summarize the present status of the predictionsfor tt¯, t- and s-channel single-top cross-sections, computed using different PDF sets. Weshow how differences in the predictions can directly be traced to both differences in theparton luminosities, and the values of physical parameters used in the PDF analyses,such as the strong coupling constant αs or the the b-quark mass, mb. In particular, wec© Societa` Italiana di Fisica 6566 A. GUFFANTI and J. ROJOTable I. – Top pair cross-section at NLO with different PDF sets at LHC 7TeV.CTEQ6.6 [8] 147.7± 6.4 pbMSTW2008 [9] 159.0± 4.7 pbNNPDF2.0 [6] 160.0± 5.9 pbABKM09 [10] 131.9± 4.8 pbHERAPDF1.0 [11] 136.4± 4.7 pbhighlight the importance to account for the uncertainty on the b-quark mass for accuratepredictions of single-top production at the LHC.In the second part we study PDF-induced correlations between PDFs and tt¯/single-top cross-sections and between top and W±/Z0 cross-sections. We briefly discuss howthese correlations could be used in order to improve the accuracy of top cross-sectionmeasurements with early data at the LHC. These correlation studies are performed withinthe framework of the NNPDF parton analysis [3-6] which, by relying on Monte Carlotechniques for the estimation of uncertainties, provides an ideal tool for such statisticalstudies.The baseline PDF set for the studies presented in this contribution is the recentlyreleased NNPDF2.0 [6], the first NLO global fit using the NNPDF methodology.2. – Top-quark production at the LHC2.1. tt¯ production. – Top pair production is the main channel for top quark productionat Tevatron and LHC. In table I we collect the predictions for the top pair cross-sectionat LHC 7TeV at NLO computed with the MCFM code [7] using different PDF sets.We notice that the predictions from the three global fits, NNPDF2.0, CTEQ6.6 andMSTW08 agree at the 1-sigma level. The differences with PDF sets based on reduceddatasets, ABKM09 and HERAPDF1.0, are larger. We note that top pair productiondepends strongly on the large-x gluon, and thus using sets which do not include Tevatronjet data might lead to rather different predictions for this observable. One should noticethat differences between the predictions from different PDF sets also arise from the useof different values for the strong coupling constant αs. It has been shown that using acommon value of αs brings predictions from different groups for various LHC observables,including top pair production, in better agreement [12,13].Once we subtract the difference introduced by different choices for αs, the remainingdifferences can be directly traced to differences in the PDF luminosities at the typicalscale of the process. This is illustrated in fig. 1, where the gluon-gluon luminosity forLHC at 7TeV is plotted for the CTEQ6.6, MSTW2008 and NNPDF2.0 NLO sets. Forexample, the lower value for the cross-section obtained using the CTEQ6.6 set reflectsthe smaller gg luminosity as compared to the other sets at Q2 = m2t .2.2. Single-top production. – Next we present predictions for single-top productionat the LHC at 7TeV. These predictions for various PDF sets are collected in table II,where we present results for both the t- and s-channel single-top cross-sections computedat NLO in QCD with the MCFM code. We have used the Nf = 5 (massless) calculationfor the results presented here, recently the Nf = 4 calculation, which properly takes intoaccount the effects due to finite b-quark mass, also became available [14].TOP PRODUCTION AT THE LHC: THE IMPACT OF PDF ETC. 67Fig. 1. – Gluon-gluon parton luminosities for CTEQ6.6, MSTW2008 and NNPDF2.0 includingthe associated PDF uncertainties. Results are showed as ratios to NNPDF2.0.While at the Tevatron the contributions of t- and s-channel W exchange to single-top production are comparable in size, at the LHC t-channel production is by far thedominant production mechanism.From the point of view of testing the predictions from different PDF sets t-channelsingle-top is also very interesting due to the fact that, in the so-called 5-flavour scheme(i.e. a scheme where the b is assumed to be a parton in the proton) the cross-sectionat LO probes directly the b-quark PDF, which in turn is closely related to the gluondistribution from which it is generated radiatively.From table II one notices that the central predictions from the various PDF setscan differ by several times the quoted 1-sigma PDF uncertainty(1). There are differentcontributions to this discrepancy. The first stems from the different values of the strongcoupling constant αs which are used by different parton sets. Since single-top productionis mediated by electroweak gauge bosons, αs enters only in radiative corrections, unlikethe case of tt¯ production discussed above, this effect is rather small.In order to separate the differences in the single-top production cross-section whicharise from the differences in the PDFs themselves and those from other physical param-eters (like mb or αs) which also enter in the PDF analyses and in the computation ofthe partonic matrix element, we plot in fig. 2 the b-gluon parton luminosity, which de-termines the LO cross-section, for the CTEQ6.6, MSTW2008 and NNPDF2.0 NLO sets.It is clear that parton luminosities in the kinematic region relevant for single-top pro-duction differ by an amount much smaller than the cross-sections themselves, suggestingthat the differences indeed come from variations of other physical parameters which enterthe PDF analysis.Indeed, it can be seen that the bulk of this difference is related to the differentvalues of the b-quark mass used in the fits by the different collaborations. The NNPDFCollaboration sets mb = 4.3GeV, CTEQ uses mb = 4.5GeV while the MSTW08 fit isperformed setting mb = 4.75GeV. In order to substantiate our claim that the differentvalues used the b-quark mass explain the bulk of the difference for the t-channel single-top(1) Note that for the ABKM09 prediction the uncertainty includes the associated αs, mc andmb uncertainties, which cannot be disentangled from the PDF uncertainties, and is thus muchlarger than the one obtained using other PDF sets.68 A. GUFFANTI and J. ROJOTable II. – Single-top cross-section at NLO with different PDF sets at LHC 7TeV.t-channel s-channelCTEQ6.6 [8] 40.85± 0.50 pb 2.33± 0.05 pbMSTW2008 [9] 41.96± 0.26 pb 2.38± 0.04 pbNNPDF2.0 [6] 44.33± 0.32 pb 2.38± 0.06 pbABKM09 [10] 43.17± 1.98 pb 2.40± 0.03 pbHERAPDF1.0 [11] 40.04± 0.33 pb 2.38± 0.05 pbcross-section, we produced two NNPDF2.0 sets with mb = 3.7GeV and mb = 5.0GeV,respectively. The results for the b-gluon parton luminosities for these modified sets areshown in the right plot in fig. 2 and the corresponding cross-sections for the t-channelsingle-top cross-section are collected in table III. It is clear that the value of mb isanti-correlated with the bg luminosity and the t-channel single-top cross-section.From table III one sees that variations of the b-quark mass of the order or δmb ∼0.7GeV induce an uncertainty in the cross-section of δσ ∼ 3 pb. If we take the PDGaverage as the best available determination of the b-quark mass and convert it fromthe MS scheme to the pole mass scheme we obtain an uncertainty of approximatelyδmb(PDG) ∼ 0.2GeV. Rescaling errors, we are still left with an uncertainty in thet-channel single-top cross-section of δσ ∼ 0.8 pb, still larger than the typical nominalPDF uncertainties quoted in table II. It is also clear from table III and fig. 2 that usinga similar value of mb would bring the predictions from different PDF sets into muchbetter agreement. The uncertainty due to mb should thus always be accounted for in thetheoretical predictions for LHC single-top production.3. – PDF-induced correlationsIt is well known (see for example the discussion in ref. [8, 4]) that parton densitiesinduce correlations among different observables measured at hadron colliders. These canbe the PDFs themselves, one PDF and a physical observable or two physical observables. 0.85 0.9 0.95 1 1.05 1.1 100  120  140  160  180  200  220  240Ratio to NNPDF2.0MX [GeV]bg luminosityS = (7 TeV)2mt=173.1 GeVNNPDF2.0CTEQ6.6MSTW08Fig. 2. – (Left) b-gluon parton luminosities for CTEQ6.6, MSTW2008 and NNPDF2.0, nor-malized to the NNPDF2.0 value. (Right) b-gluon parton luminosities for NNPDF2.0 fits withdifferent values of the b-quark mass normalized to the standard NNPDF2.0.TOP PRODUCTION AT THE LHC: THE IMPACT OF PDF ETC. 69Table III. – t-channel single-top cross-section at NLO computed using NNPDF2.0 sets withdifferent values of the b-quark mass.NNPDF2.0 (mb = 3.7GeV) 46.77± 0.36 pbNNPDF2.0 (mb = 4.3GeV) 44.33± 0.32 pbNNPDF2.0 (mb = 5.0GeV) 41.04± 0.32 pbThe latter case is especially important from the experimental point of view, since itallows to define measurement strategies in which the PDF uncertainties between twoobservables cancel, for example in the case in which this correlation between the twoobservables is maximal.In the case of a PDF set based on the Monte Carlo method, like NNPDF, the cor-relation coefficient ρ[A,B] for two observables A and B which depend on PDFs is givenby the standard expression for the correlation of two stochastic variables [4, 12](1) ρ[A,B] =〈AB〉rep − 〈A〉rep〈B〉repσAσB,where the averages are taken over the ensemble of the Nrep values of the observablescomputed with the different replicas of the PDF set, and σA,B are the standard deviationsfor the observables as computed from the MC ensemble. The value of ρ characterizeswhether two observables are correlated (ρ ≈ 1), anti-correlated (ρ ≈ −1) or uncorrelated(ρ ≈ 0). In the following we present results for the NNPDF2.0 set, the LHC cross-sectionshave been obtained as before using the MCFM code.As a first example, we compute the correlation between the tt¯ and t-channel single-topcross-section at the LHC (7TeV) and different PDFs at the factorization scale μf = mtopas a function of x. The results are plotted in fig. 3. The most remarkable features are thatthe tt¯ cross-section at the LHC at 7TeV is mostly correlated to the gluon distribution atx ∼ 0.1 and anti-correlated with it at small-x, with the same behaviour present for seaquark PDFs, generated radiatively from the gluon. We note also that the u- and d-quarkdistributions are anti-correlated with the cross-section at medium/large x.-1-0.5 0 0.5 1 1e-05  0.0001  0.001  0.01  0.1ρxPDF-ttbar cross-section correlationguubarddbarssbarcb-1-0.5 0 0.5 1 1e-05  0.0001  0.001  0.01  0.1ρxPDF-single-top cross-section correlationguubarddbarssbarcbFig. 3. – Correlation between parton densities and tt¯ (left) and t-channel single-top (right)cross-sections at the LHC 7TeV. The PDF set used is NNPDF2.0 and cross-sections have beencomputed with MCFM.70 A. GUFFANTI and J. ROJO[nb]-Wσ3.88 3.90 3.92 3.94 3.96 3.98 4.00 4.02 4.04 4.06[pb]ttσ154156158160162164166-W[nb]+Wσ5.65 5.70 5.75 5.80 5.85 5.90 5.95[pb]ttσ154156158160162164166+W [nb]0Zσ0.890 0.895 0.900 0.905 0.910 0.915 0.920 0.925 0.930 [pb]ttσ1541561581601621641660ZFig. 4. – Correlation between tt¯ and Electroweak Vector Boson cross sections at the LHC 7TeV.The cross-sections have been computed with MCFM and the NNPDF2.0 parton set.As for the case of the t-channel single-top cross-section, we point out that the strongcorrelation with the gluon (and therefore with the c- and b-quark distributions) presentfor tt¯ is now milder and peaked at medium x, x ∼ 0.01, and now we find a moderatecorrelation at medium/small x with the u and d PDFs, of the opposite sign as in the tt¯cross-section. We would like to stress as well the correlation of single-top cross-sectionand the s-,s¯-quark PDFs at medium/small x, which is notably absent in the tt¯ case.As previously pointed out, the correlation coefficient eq. (1) can also be computedbetween two cross-sections, which is potentially relevant since in the case of a sizablecorrelation the measurement of one of these observables would provide useful informationon the value of the other one. In this respect we have computed the correlation betweenthe tt¯ and t-channel single-top cross-sections on one side and W± or Z0 cross-sections atthe LHC on the other. The values for the correlation coefficients for the different pairsof observables are collected in table IV and the correlation ellipses are plotted in fig. 4for the tt¯ cross-section and in fig. 5 for t-channel single-top.Both the values of ρ and the shape of the correlation ellipses show a significant anti-correlation between the tt¯ cross-section and the W± and Z0 ones. Given the fact that thevector boson cross-sections at the LHC are O(10) times larger than the tt¯ cross-sectionand more accurately known from the theoretical point of view, it is foreseeable to usethose in order to better calibrate the top pair cross-section measurement in early data.On the other hand, the single-top cross-section shows a very mild correlation to thevector boson one thus rendering a similar approach based on the precision measurement ofEW bosons difficult. However, if one is able to identify other observables which should bemeasured with a similar precision and that are correlated to the single-top cross-section,the discussion of the tt¯ case would also apply here.Table IV. – Correlation coefficients between tt¯ or t-channel single-top and W± or Z0 cross-sections at the LHC 7TeV in the NNPDF2.0 analysis.ρ σW+ σW− σZ0σtt¯ −0.716 −0.694 −0.773σt 0.330 0.140 0.240TOP PRODUCTION AT THE LHC: THE IMPACT OF PDF ETC. 71 [nb]-Wσ3.883.903.923.943.963.984.004.024.044.06[pb]t+Xσ43.743.843.944.044.144.244.3-W[nb]+Wσ5.65 5.70 5.75 5.80 5.85 5.90 5.95[pb]t+Xσ43.743.843.944.044.144.244.3+W[nb]Z^0σ0.890 0.895 0.900 0.905 0.910 0.915 0.920 0.925 0.930[pb]t+Xσ43.743.843.944.044.144.244.30ZFig. 5. – Correlation between t-channel single-top and Electroweak Vector Boson cross-sectionsat the LHC 7TeV. The cross-sections have been computed with MCFM and the NNPDF2.0parton set.4. – ConclusionsThe quality of top physics resulting from the LHC experiments will be affected, amongother factors, by our knowledge of Parton Distribution Functions and their uncertainties.In this contribution we have reviewed the present status of predictions for tt¯ and single-top cross-sections evaluated at NLO in QCD with different PDF sets and pointed outdifferences among them, trying to elucidate the reasons for these differences. For the caseof single-top production, we have shown that one important source of difference amongpredictions obtained using different PDF sets is the value of the b-quark mass mb usedby the different collaborations.In the second part we briefly discussed PDF-induced correlations between partondensities and top cross-sections and between the latter and electroweak vector bosonproduction cross-sections at the LHC at 7TeV. These correlations could be useful todefine experimental strategies to measure the top quark cross-section in a way in whichPDF uncertainties are reduced.∗ ∗ ∗AG would like to thank the organizers, and in particular F. Maltoni, for the kindinvitation to participate in a very nice and stimulating Workshop and the HEPTOOLSEuropean Network for providing the financial support for his participation.REFERENCES[1] Campbell J. M., Huston J. W. and Stirling W. J., Rep. Prog. Phys., 70 (2007) 89.[2] Ferrag S. (ATLAS Collaboration), arXiv:hep-ph/0407303.[3] Del Debbio L., Forte S., Latorre J. I., Piccione A. and Rojo J. (NNPDFCollaboration), J. High Energy Phys., 0703 (2007) 039.[4] Ball R. D., Del Debbio L., Forte S., Guffanti A., Latorre J. I., Piccione A.,Rojo J. and Ubiali M. (NNPDF Collaboration), Nucl. Phys. B, 809 (2009) 1.[5] Ball R. D., Del Debbio L., Forte S., Guffanti A., Latorre J. I., Piccione A.,Rojo J. and Ubiali M. (NNPDF Collaboration), Nucl. Phys. B, 823 (2009) 195.[6] Ball R. D., Del Debbio L., Forte S., Guffanti A., Latorre J. I., Rojo J. andUbiali M. (NNPDF Collaboration), Nucl. Phys. B, 838 (2010) 136.72 A. GUFFANTI and J. ROJO[7] Campbell J. and Ellis K., Phys. Rev. D, 62 (2000) 114012, http://mcfm.fnal.gov.[8] Nadolsky P. M. et al., Phys. Rev. D, 78 (2008) 013004.[9] Martin A. D., Stirling W. J., Thorne R. S. and Watt G., Eur. Phys. J. C, 63 (2009)189.[10] Alekhin S., Blu¨mlein J., Klein S. and Moch S., Phys. Rev. D, 81 (2010) 014032.[11] Aaron F. D. et al. (H1 Collaboration and ZEUS Collaboration), JHEP, 1001(2010) 109.[12] Demartin F., Forte S., Mariani E., Rojo J. and Vicini A., Phys. Rev. D, 82 (2010)014002.[13] Ubiali M., Ball R. D., Del Debbio L., Forte S., Guffanti A., Latorre J. I. andRojo J., arXiv:0903.0005.[14] Campbell J. M., Frederix R., Maltoni F. and Tramontano F., Phys. Rev. Lett.,102 (2009) 182003.

Top production at the LHC: the impact of PDF uncertainties and correlations

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