Summary of Structure Functions and PDFs Working Group
SSummary of Structure Functions and PDFs WorkingGroup
R. McNulty
School of Physics, University College Dublin,Dublin 4, IrelandE-mail: [email protected]
R. S. Thorne ∗ Department of Physics and Astronomy,University College London, WC1E 6BT, UKE-mail: [email protected]
K. Wichmann † Deutsches Elektronen Synchrotron DESY, Hamburg, GermanyE-mail: [email protected]
This summary presents personal highlights from the Structure Functions and PDFs WorkingGroup (WG1).
XXIV International Workshop on Deep-Inelastic Scattering and Related Subjects11-15 April, 2016DESY Hamburg, Germany ∗ Speaker. † Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ h e p - ph ] O c t G1 summary
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1. Introduction
The Structure Functions and PDFs Working Group (WG1) consisted of 43 presentations spreadover 10 sessions, three of which were held jointly with QCD and Hadronic Final States (WG2),Electroweak Physics and Beyond the Standard Model (WG3), and Future Experiments (WG7).This summary presents personal highlights from these sessions, with the exception of the jointsession with WG7 that is presented elsewhere.
2. PDF Fits including HERA combined data
The publication of the HERA combined inclusive data [1] is a legacy document that is at thecore of all PDF extractions. A number of groups considered the impact of this data on differentPDF sets.The HERAPDF2.0 set [1], derived only from the HERA data, describes the neutral data wellfor Q > but there are discrepancies at low- x and low- Q (Fig. 1). A possible resolutionis provided by the inclusion of higher twist effects. [2, 3]. Another approach using the Bartels-Golec-Kowalski dipole model was shown to describe the HERA data very well, but only if sizeablesaturation effects are included [4]. Figure 1:
HERA neutral current data with HERAPDF2.0 NNLO fit superimposed [1].
A fit within the MMHT framework [3] was shown to be in good agreement with the MMHT2014PDFs that used previous HERA cross-section data. There is a very small change in central valuesand the uncertainties reduce a little – at most by 20% e.g. the cross-section for gg → H at 14 TeVchanges from 47 . + . − . to 47 . + . − . pb. A comparison with HERAPDF2.0 showed broad agree-ment but there were some marked differences e.g. in the down valence quark and gluon at high x as shown in Fig. 2. 1 G1 summary
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Figure 2:
Down valence (left) and gluon PDF (right) compared to MMHT2014 for: a global fit includingthe new HERA combined data; a fit just using the HERA data; HERAPDF2.0 [3] .
Both MMHT and CT groups find tension between the HERA combined e − p charged currentdata and other data sets. In a CT14-like fit [5] a shift in the up quark near x = . W + production at the LHC. Figure 3:
Up and down valence PDF compared to CT14NNLO including HERA data with different weights[5].
3. Analysis and comparison of global PDF sets
There was a lively discussion on how to synthesise the results of the various PDF global fits inorder to obtain a theoretical uncertainty on an observable. An extreme example was provided bythe H + t ¯ t production cross-section which changes by 13% depending on which PDF set is used.Various approaches were discussed as expounded in [6] and [7].There is an open question on the form of ¯ d − ¯ u at small x and d / u as x →
1. Strong claimsabout ¯ d − ¯ u at small x being non-zero and d / u as x → W + asymmetry data from D W + , W − data fromLHCb. However, the CJ15 fit [10] includes D G1 summary
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Figure 4:
Ratio of down to up valence PDF for various PDF sets. The label ’present analysis’ refers to [9]. but with a poorer fit), and see no requirement for any small- x ¯ d − ¯ u difference. Similarly, MMHT14compares very well [13] to data on high rapidity W production at LHCb at 7 TeV [14] and manyPDF sets give predictions which compare well to W production at LHCb at 8 TeV [15]. Fits tomore precise vector boson data is an obvious area for further study.A number of talks addressed the flavour decomposition of the proton from another direction.One of the measures of ¯ d − ¯ u is the Gottfried Sum Rule. It was described how one can effectivelymeasure free neutron PDFs using the BONUS (Barely Off-shell Neutron Structure) experiment[16], where in electron deuteron scattering one measures the scattered electron in coincidence witha proton tag. This study allows for a re-examination of the Gottfried sum rule from NMC deuteronscattering data [17] down to x = .
004 (relying on an extrapolation at higher Q ). There is no signin this of ¯ d − ¯ u changing sign or being large at low x . It was also shown how by performing asimultaneous study of precision proton and deuteron data one can fit and also verify predictions fordeuteron corrections [10], e.g. DO W asymmetry data and deuteron DIS probe the down quark forsimilar x so a simultaneous fit largely determines the deuteron correction. Figure 5:
Jet cross-section ratios to ME calculations using CT14 PDFs. The effect of other PDFs is shownby different coloured lines [18]. G1 summary
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4. Experimental inputs to PDFs
Several new experimental results that will help to further constrain the PDFs were shown.The CMS collaboration presented inclusive jet cross-sections at 13 TeV [18]. Fig. 5 shows theirdata compared to CT14 and various other PDF sets. The other end of the energy spectrum wasrepresented by results from H1 [19] who showed inclusive jet cross-sections at low- Q , some ofwhich are shown in Fig. 6. The experimental uncertainties are dominated by the jet energy scaleand modelling and are significantly smaller than the theory uncertainties, which have large scaleuncertainties. Figure 6:
Preliminary results from H1 on inclusive jet cross-section (solid points). The open points are aprevious analysis that just used HERA-I data. The coloured band represents the NLO predictions [19].
The ATLAS collaboration presented results on Drell-Yan production including a recent analy-sis of 8 TeV data [20]. Fig. 7 (left) shows the cross-section for electron-positron pairs with massesbetween 116 and 1500 GeV, compared to different PDFs. It was demonstrated that these data havesensitivity to the poorly known photons PDFs and can thus be used to constrain them.
Figure 7:
Left: ATLAS results on Drell-Yan production at 8 TeV [21]. Right: LHCb results on Z bosonproduction at 13 TeV [22]. Both are compared to predictions with various PDF sets. G1 summary
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Results on W boson production at 13 TeV were shown by ATLAS [21], while Z boson produc-tion at 13 TeV was shown by the ATLAS and LHCb [22] collaborations. Fig. 7 (right) shows thedifferential cross-section for Z production in the forward region as measured by LHCb, comparedto predictions using various PDFs.
5. Nuclear PDFs
There were various presentations of nuclear PDFs in the light of new LHC data. The updatednCTEQ15 PDFs [23] include the impact of some new LHC data on p − Pb scattering via thereweighting technique, but this provides little impact on the PDFs yet. No neutrino data is includedin this fit. There was also an update on Kulagin-Petti nuclear PDFs (see e.g. [24, 25]), whichmodel the nuclear corrections rather than primarily fit them to data. This includes account ofFermi motion, off-shell effects, nuclear meson exchange current corrections and contributions fromcoherent nuclear interactions (nuclear shadowing). So far predictions for LHC p − Pb data appearto be successful. The difference between neutral and charged current nuclear data was investigatedfor iron targets [26]. As seen in Fig. 8 (left), very good agreement between the two is found athigh x , but there is evidence for less suppression in the neutrino nuclear structure functions at low x . There were also a couple of detailed studies in nuclear collisions at the LHC. For example, thecentrality dependence of nuclear modifications was investigated [27] by looking at W production asa function of rapidity in three centrality bins, with some evidence for centrality dependence seen.Another topic is the so called neutron skin effect. The neutron distribution is expected to be broaderthan that of the proton in the nucleus [28], i.e. the neutron tail extends further. This can potentiallybe seen by looking at the charged hadron ratio in Pb − Pb collisions where deviations from unityare expected with increasing p T and rapidity. Fig. 8 (right) shows the effect at mid-rapidity: atforward rapidities, deviatinos set in at lower p T , although the uncertainties are larger. Figure 8:
Left: Comparison of F Fe measured in neutral and charged current data [26]. Right: Ratio ofcharged hadrons normalised with minimum bias events for two fragmentation functions. No skin effectcorresponds to a value of one [28]. We also saw a presentation of the angular distributions of Drell-Yan dimuons at E906/SeaQuesttesting the correlation of the azimuthal and polar angles of leptonic products relative to the initial5
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K. Wichmann hadronic plane[29], and a study of the ability of pion exchange models to describe both leadingneutron electroproduction at HERA and to extract the ¯ d (cid:54) = ¯ u flavour asymmetry in the proton [30].
6. Transverse Momentum Dependent (TMD) PDFs
The session devoted to TMD PDFs highlighted the importance of including resummations andnonperturbative information, particularly at low k t , and a proper simulation of parton showers. Itincluded various updates on a new large scale and ambitious project including full coupled quarkand gluon evolution using the Monte Carlo approach in a form applicable over all x and Q . Resultson the fully integrated PDFs obtained in the framework were successfully compared to HERA in-clusive cross section data, and updates on the considerable ongoing work for the fully unintegratedPDFs were presented [31]. Saturation effects in the same framework were discussed [32], andTMDlib libraries and a plotter were introduced for the first time [33], also produced by the samegroup. There was also a contribution studying the role of the nonperturbative input to the (TMD)gluon density in hard processes at the LHC, and deriving the input distribution from a fit of inclu-sive hadron spectra measured at low transverse momenta in pp collisions at the LHC [34].
7. Theoretical topics
There were a variety of updates on specific theoretical topics relevant for PDF studies. Therewas a presentation of intrinsic charm based on [35], which looked at the impact on the differential γ + c cross section, showing this could be significant. Intrinsic charm was also discussed as partof a NNPDF study [36], where it is determined from a fit to heavy flavour distributions, on top ofthat generated dynamically from the gluon and light quarks via evolution. The inclusion of EMCdata [37] significantly reduces the uncertainties and the fitted charm is lower than purely dynamicalcharm for x ∼ .
05 (see Fig. 9). This has implications for predictions of W , Z + c data at the LHC. Figure 9:
NNPDF fitted charm compared to dynamical charm (left) and to the fit without EMC data(right) [36].
The NNPDF group also presented PDFs with threshold resummations [38], whose effects aremuch larger at NLO than NNLO, as NNLO already includes much of the effect present at NLO.Data sets for which the threshold corrections are unknown are not used in the fit. The resummed6
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K. Wichmann cross-sections are closer to the fixed order predictions, although the effect at NNLO is arguably nobigger than that due to the missing data.Another study concentrated on the extreme limits of the PDFs [39], comparing the effectivelysmall- x powers and high- x powers of ( − x ) for different PDF sets, finding some significant vari-ation in the latter for the gluon. Improvements to the low- x gluon for NNPDF were shown [40],obtained by incorporating charm production data from LHCb. This allows improved predictionsfor the prompt atmospheric neutrino flux up to 10 GeV, which are consistent with IceCube bounds.There was an investigation of different methods to incorporate the effect of photons in hardprocesses [41]. Two different approaches were used for calculating cross sections: either the photonis treated as a collinear parton in the proton, or alternatively the k T factorization method is used.Also we had a discussion of a method to obtain the double gluon distribution from the single gluondistribution using sum rules [42].There was s discussion of exclusive J / Ψ and ϒ production [43], which in principle can con-strain the gluon PDF that is related to generalised parton distributions. The one-loop corrections tothe cross section have been calculated but lead to large, opposite sign corrections, particularly for J / Ψ . Theoretical improvements are needed for these processes to be a precision constraint on thegluon distribution.A procedure for calculating PDFs on the Lattice [44] was presented, using quasi-distributionsat finite longitudinal momentum rather than exact distributions in the infinite momentum frame.One can then try to transform the quasi-distributions to the correct limit. Longitudinal momentum P = π / L on available lattices corresponds to about 0 . .
8. Tools for PDFs
There were a number of updates on various tools used to study and present PDFs. APFEL [45]showed a plotting procedure for changing the transition point for heavy flavours in variable flavourschemes, which demonstrates diminished sensitivity to this in PDFs at NNLO compared to NLO.The HERAFitter collaboration, now called XFitter [46], presented theoretical improvements andthe inclusion of new data sets. The effect of asymmetric uncertainties was discussed in the CT14replica PDFs presentation [47], along was the χ distribution of the global fit quality for 1000CT14 replicas, which use 28 PDF eigenvectors and tolerance ∼
40 for one sigma. Remarkably, thisis extremely similar to the equivalent χ distributions for 1000 NNPDF replicas (see e.g. [48]),despite the fact these are obtained from a very different approach. This supports the use of atolerance criterion in global fits based on the eigenvector approach.7 G1 summary
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