wg1: structure functions and parton densities · 2018-01-09 · wg1: structure functions and parton...

WG1: Structure Functions and Parton Densities

Lucian Harland-Lang∗

Rudolf Peierls Centre for Theoretical Physics, Oxford, UKE-mail: [email protected]

Philip IltenSchool of Physics and Astronomy, University of Birmingham, Birmingham, UKE-mail: [email protected]

Jan KretzschmarOliver Lodge Laboratory, University of Liverpool, Liverpool, UKE-mail: [email protected]

This paper gives a summary of selected highlights discussed in the working group on “Struc-ture Functions and Parton Densities” (WG1) at the DIS 2017 conference. From the many talkspresented we extract some general themes discussed with respect to global PDF fits, new PDF-sensitive measurements from the LHC experiments and elsewhere, exploitation of new ideas,tools to perform PDF fits, PDFs of heavy nuclei, and finally progress in basic theory calculations.

XXV International Workshop on Deep-Inelastic Scattering and Related Subjects3-7 April 2017University of Birmingham, UK

∗Speaker.

c© 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). https://pos.sissa.it/

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WG1: Structure Functions and Parton Densities Lucian Harland-Lang

1. Introduction

The “Structure Functions and Parton Densities” working group (WG1) of the DIS 2017 con-ference featured 45 talks spanning a wide range of interesting topics. The talks were organisedin 10 sessions, including one joint session with “Physics with Heavy Flavours” (WG5) [1] andtwo joint sessions with “Hadronic and Electroweak Observables” (WG4) [2]. In the following wesummarise some selected highlights of these sessions.

2. Global PDF Fits

Updates from three major global fitting collaborations CT [3], MMHT [4], and NNPDF [5]were presented. In all cases, the results shown made use of an increasingly wide range of data fromthe LHC experiments and the LHC data are playing an increasingly important role in global PDFfits. Studies beyond the new LHC data were also presented, for example regarding updates on thephoton PDF from the CT and MMHT groups and intrinsic charm by the CT and NNPDF groups,as discussed further below. Work towards new public releases of PDF sets is ongoing for the CTand MMHT groups, while the updated NNPDF3.1 set based on the work presented here is nowavailable [6].

In Fig. 1 (left) the impact of new data on the gluon, predominately from the LHC, is shownby comparing the new determination to the previous NNPDF3.0 determination; the changes aresignificant, especially at larger x. A similar effect is observed by CT and MMHT. In the latter case,for example, LHC data is found to provide the most important constraints in the latest fit for 21out of the 50 eigenvector directions. In Fig. 1 (right) the constraint that the new high precisionATLAS W and Z production data [7, 8] places on the strange-quark distribution in the proton (theratio of the strange to the light-quark sea is shown here) is demonstrated, within the MMHT fit.The impact is large, with the strange-quark fraction found to be somewhat higher than the previousdetermination, although consistent, and the uncertainties are reduced. A similar trend is seen in theNNPDF analysis.

LHC data certainly represent important opportunities to improve the knowledge on PDFs.However, there are many challenges for the PDF fitters to include such increasingly precise dataeffectively within a PDF fit. Some of these challenges were also highlighted in this conference,and will be discussed below.

3. New Measurements sensitive to PDFs and αS

There has been significant progress in the past year regarding new experimental measurements.The majority of new results were presented by the ATLAS, CMS, and LHCb collaborations at theLHC, but new results are still being made public from the HERA experiments like H1. These datacan be used to further constrain PDFs and measure the strong coupling αS. The results span a widerange of physical observables including jets, vector bosons in association with heavy flavour jets,and high-precision inclusive vector-boson measurements.

Double-differential jet cross sections in DIS have been measured as a function of virtualityQ2 and jet pT by the H1 collaboration [9, 10]. These data have been compared to the latest next-to-next-to-leading order (NNLO) theory calculations for the first time for a Q2 range of 5.5 to

1


6

Impact of new data

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1.153.0 datasetglobal dataset

2 GeV4=102NNPDF3.1 NNLO FC, Q

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Juan Rojo DIS2017, Birmingham, 04/04/2017

Proton strangeness - PDF fitter studies

19

The strangeness content of the proton

!

xFitter analysis of the ATLAS W,Z 2011 inclusive data prefers a symmetric strange sea with small uncertainty, at odds with all other PDF fits!

Actually the ATLAS data suggest that there are more strange than up and down sea quarks in the proton, which is very difficult to understand from non-perturbative QCD arguments !

Can one accommodate the ATLAS W,Z 2011 data in the global fit? What happens to strangeness?


19


!

xFitter analysis of the ATLAS W,Z 2011 inclusive data prefers a symmetric strange sea with small uncertainty, at odds with all other PDF fits!

Actually the ATLAS data suggest that there are more strange than up and down sea quarks in the proton, which is very difficult to understand from non-perturbative QCD arguments !

Can one accommodate the ATLAS W,Z 2011 data in the global fit? What happens to strangeness?


20


!

Confirmed the strange symmetric fit preferred by the ATLAS W,Z 2011 measurements, though we find PDF uncertainties larger by a factor 2!

The global fit accommodates both the neutrino data and the ATLAS W,Z 2011 ( !2nutev=1.1, !2AWZ11=2.1 ) finding a compromise value for RS=0.62+-0.12!

Mild tension in the global fit (1.5-sigma level at most) when simultaneously included neutrino data, CMS W+charm and ATLAS W,Z 2010+2011


0

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2 = 1.9GeV2

x

MMHTMMHT16 + ATLAS WZ

MMHT + ATLAS WZ (µ)MMHT + ATLAS WZ (µ/2)

Ratio of (s + s) to u + d, i.e. R

s

at Q

2 = 1.9 GeV2.

At x = 0.023 R

s

⇠ 0.83± 0.15. Compare to ATLAS with R

s

= 1.13+0.08�0.13

R

s

exceeds unity at lower x, but essentially an extrapolation.Comfortably consistent with unity.

DIS2017 – Birmingham – April 2017 27

µF,R/2

• First studies of impact of high precision ATLAS W, Z data in fits. MMHT and NNPDF studies confirm ATLAS finding of increased proton strangeness,

• Caveat - fit quality not great (~ 2 per dof). Though taking improves things with little impact on PDFs.

Juan Rojo

Robert Thorne18Figure 1: (Left) Impact of new data on the gluon PDF, predominately from the LHC, in the new NNPDF3.1fit as compared to the previous NNPDF3.0 analysis [5]. (Right) Impact of the high precision 7 TeV ATLASW and Z production data on the strange-quark contribution to the proton in the MMHT fit [4].

15000 GeV2 and a jet pT range of 5 to 40 GeV. As seen in Fig. 2 (left), the NNLO predictionsprovide a better description of the cross section shape as compared to NLO predictions, as wellas a reduction in the theoretical uncertainties as estimated by scale variations. Double-differentialinclusive jet cross sections in pp collisions at 8 TeV in jet y and pT have been performed by theATLAS and CMS collaborations [11, 12, 13, 14, 15]. The CMS result also provides ratios betweenthe cross sections measured at

√s = 8 and 2.76 TeV [15], resulting in a partial cancellation of sys-

tematic uncertainties and greater sensitivity to PDFs. As shown in Fig. 2 (right), the HERAPDF1.5and MMHT14 PDF sets describe this ratio well, while the ABM11, CT10, and NNPDF3.0 PDFsets systematically under-estimate the cross section ratio at lower jet pT. Analyses of the ATLASmeasurement at

√s = 8 TeV [14] within the framework of global PDF fits have reported difficulties

in describing the measurement across all jet y bins, similar to the previous√

s = 7 TeV ATLASmeasurement [16]. However, decorrelating two of the jet energy scale systematics has been foundto significantly improve the description of the 7 TeV data [4, 17]. Further studies of the 8 TeV dataare therefore required to fully assess its impact on PDFs.

Differential cross section measurements for dijet and trijet events have also been made bythe H1 and CMS collaborations [9, 10, 12, 13, 18, 15]. The H1 dijet results are again comparedto NNLO theory predictions. While the NNLO predictions describe the shape well, they consis-tently overestimate the cross section. The H1 trijet measurement is more limited by statisticaluncertainties and found to be in good agreement with the NLO predictions. A ratio between theCMS inclusive trijet and dijet cross sections at

√s = 8 TeV as a function of the average pT of

the two highest pT jets in the event is particularly sensitive to αs [12, 19]. Fits of this ratio, aswell as the dijet and trijet cross sections, were performed using a variety of PDF sets to determineαS(Mz). The extraction of αS(MZ) from the ratio fit typically resulted in lower values of αS(Mz),giving 0.1139±0.0032 with CT14, than the simultaneous dijet and trijet cross section fits, whichgives 0.1161± 0.0029 with CT14, where the quoted uncertainties exclude QCD scale variations.Electroweak corrections were calculated for the dijet fits but not the trijet fits. However, thesecorrections are assumed to have a minor effect in the cross section ratio, and so the αs(MZ) valueextracted from the ratio is considered as the nominal result in this analysis, leading to the central

2


(GeV)T

Jet p80 100 200 300 400 500

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eV)

dyT

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(2.7

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V)

/ dy

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Data/NPCT10 Theo. predictionCT10 PDF uncertaintyNNPDF3.0ABM11HERAPDF1.5MMHT14

|y| < 0.5

CMS

Figure 2: (Left) Inclusive differential jet cross sections from H1 [9]. (Right) Ratio between the inclusive jetcross sections at

√s = 2.76 and 8 TeV from CMS [15].

result of αS(Mz) = 0.1150± 0.0023+0.0050−0.0000 using the MSTW2008 PDF set without LHC jet data.

The second uncertainty is from QCD scale variations while the the first includes all other remaininguncertainties.

Larger datasets and progress in tagging of heavy-flavour jets has allowed new measurementsof vector bosons in association with heavy flavour jets from both CMS and LHCb to be made. TheCMS collaboration presented differential Z+c cross sections measured at

√s= 8 TeV as a function

of the pT for both the Z-boson and c-jet [20, 21]. This is in principle sensitive to intrinsic charmcontributions to the PDFs, but so far large statistical and c-tagging efficiency uncertainties do notallow for strong constraints. The differential Z + c and ratio of Z + c to Z + b cross sections arecompared to theory predictions from MADGRAPH, aMC@NLO, and MCFM in Fig. 3. While theMADGRAPH and aMC@NLO predictions are found to be in good agreement with data, the MCFMpredictions are consistently lower than the measured result, independent of the PDF set used, andfurther work is required to fully understand the implications of this measurement. A combinedmeasurement of the W + cc, W + bb, and tt cross sections was performed by LHCb [22] using√

s = 8 TeV data with an electron or muon final state in association with two jets tagged to containheavy-flavour hadrons. While this measurement is statistically limited, future updates will providevaluable information on the strange-quark PDF. Further measurements of the W + c final state bythe ATLAS, CMS, and LHCb collaborations will help constrain the size and possible asymmetryof the strange-quark PDF, and resolve the current mild tensions between different datasets.

New precise differential measurements of inclusive vector-boson production have been madeby the ATLAS, LHCb, and STAR collaborations. Integrated and differential W and γ∗/Z crosssections at

√s = 7 TeV were measured by the ATLAS collaboration [7, 8] using both electron and

muon final states with systematic uncertainties well below the percent level and negligible statisticaluncertainty, testing lepton universality at the percent level. A PDF analysis was performed using

3


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p0 50 100 150 200

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/Data

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Figure 4: (Left) Differential W+/W− cross section ratio from STAR as a function of electron pseudorapid-ity. (Right) Isolated photon cross section from ATLAS compared to NLO theory predictions.

these data combined with HERA data, and the strange-to-light sea-quark ratio was found to be nearunity, a result confirmed in global PDF analyses performed by MMHT [4] and NNPDF [5], albeitwith a reduced fit quality. The MMHT study and an ATLAS study demonstrated that halving thenominal factorisation and renormalisation scale, the di-lepton mass, improves the fit quality buthas only a small impact on the strange-quark PDF [4, 8]. New ATLAS measurements of high-mass Drell-Yan cross sections were presented in [24, 25], which are generally well described bydifferent PDF sets, but were found to reduce significantly the variations of the photon PDF in theNNPDF2.3QED set.

Similar precision measurements of γ∗/Z at√

s = 13 TeV and W at√

s = 8 TeV were per-formed by LHCb [26, 23, 27], which is sensitive to PDFs at both lower and higher x due to the

4


forward rapidity coverage of the detector. These results were found to be in good agreement withNNLO predictions using a variety of PDF sets. However, the charge asymmetry at forward leptonpseudorapidity was found to be systematically underestimated by all PDF sets tested, see Fig. 3(right). The W+/W− ratio using W -boson decays into an electron final state was measured differ-entially in pseudorapidity by the STAR collaboration using RHIC pp data at

√s between 500 and

510 GeV [28]. The results are shown in Fig. 4 (left), where a slight tension between theory anddata at large and small electron pseudorapidity is visible.

Finally, measurements of isolated photon production differential in photon ET and pseudora-pidity, were performed by ATLAS at

√s = 13 TeV [29, 30]. The NLO predictions were found to

systematically underestimate the photon cross section, particularly at lower ET as shown in Fig. 4(right), demonstrating the need for NNLO predictions that have recently become available [31].

4. New Ideas to constrain PDFs

While many of the discussions in WG1 were centred around existing fit frameworks and theinclusion of data traditionally used to constrain PDFs, many new ideas and approaches were alsodiscussed. Novel possibilities to constrain the gluon PDF at low x were introduced in [32] and [33].In [32, 34], data of open-charm hadron production from pp collisions in the forward region takenby the LHCb experiment was demonstrated to have significant constraining potential. These con-straints have implications for the production of neutrinos though heavy-flavour production in ultrahigh-energy cosmic ray collisions and for physics at a possible

√s = 100 TeV FCC. In [33, 35] the

exclusive photoproduction of heavy quarkonia (J/ψ , ϒ), where both protons remain intact after thecollision, was also shown to have a significant impact on the gluon PDF in the very low x region.However, both processes are affected by large theoretical uncertainties estimated from varying thefactorisation and renormalisation scales. In [32] the impact was minimised by choosing suitablynormalised observables and assuming that these variations are largely correlated, while in [33] aphysically motivated scale choice was taken.

The high x gluon was considered in two separate contributions, [36] and [37]. In [36] a PDFfit was described that utilises the new NNLO QCD theory calculation combined with the recentATLAS and CMS data for differential top-quark production; these measurements are differentialin mtt , yt , ytt and pt

T, see [38] for details. Although there are tensions in some distributionsbetween the ATLAS and CMS data, the impact on the gluon distribution of the individual distri-bution choices was mostly consistent. A recommendation was made to use a combination of thenormalised top and top pair rapidity distributions, for which no tension was apparent. Addition-ally, the sensitivity in the high mtt region, where beyond-the-standard-model effects may enter, issmaller. A clear impact on the gluon PDF at high x, comparable to the effect of inclusive jet data,was demonstrated, as shown in Fig. 5 (left). The CMS collaboration has also recently exploredthe impact of double-differential tt measurements as presented in [12, 39], although here the the-oretical calculation is only available at NLO so far. ATLAS presented a study that correlates ttand Z production in pp collisions at various

√s = 7,8,13 TeV to improve the impact on PDF

constraints [24, 40].In [37, 42] the impact of measurements of the Z-boson transverse momentum distribution on

the determination of PDFs was explored. The theoretical calculations are now available at up to

5


Constraining the gluon at high x

• Emanuele Nocera: Probing the large x gluon at NNLO with top-pair differential data

Data/Theory comparison: mtt

0

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PDF set ATLAS d�/dmtt CMS d�/dmtt ATLAS (1/�)d�/dmtt CMS (1/�)d�/dmtt

NNPDF3.0 0.77 (0.38) 5.73 (4.36) 1.57 (0.10) 10.6 (3.87)MMHT14 0.58 (0.24) 7.32 (5.74) 1.01 (0.05) 13.5 (4.93)CT14 0.61 (0.19) 7.28 (6.06) 1.09 (0.05) 13.5 (4.82)

Emanuele R. Nocera (Oxford) The large-x gluon with tt di↵erential data April 5 2017 8 / 19

• Take advantage of recent NNLO differential top pair calculation and precise ATLAS/CMS data. Sensitivity to gluon at high x, comparable to inclusive jets.

• Apparent tension between ATLAS + CMS in some distributions- pick observable where this is not/less apparent.

• However all choices pull gluon in same direction.

Our optimal fit: features

0.7

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Distributions not included in the fit not well described, except companion absolute distr.

Charm and bottom quark PDFs (generated radiatively) a↵ected similarly as the gluon


Procedural suggestionobservational facts

Impact of data on PDF central values appears relatively insensitive of distribution choiceall distributions are equal in the pool on the gluon PDF central value

While some distributions exhibit tensions, some appear perfectly compatibleselect distributions whose inclusion in the global fit leads to �2/Ndat ⇠ 1

Normalised distributions + total cross sections exhibit the largest constraining powerthey lead to the largest reduction of the gluon PDF uncertainties

Di↵erent distributions have their largest impact on a slightly di↵erent region of xchoose di↵erent distributions from ATLAS and CMS in order to maximise the kinematic coverage

Rapidity distributions have the weakest dependence on the value of mt

and on potential BSM contaminations (kinematic suppression of heavy resonances)

our recommendation for including 8 TeV `+jets tt distributions in a fit

the normalized top rapidity distribution (1/�)d�/dyt

from ATLASthe normalized top-pair rapidity distribution (1/�)d�/dy

tt

from CMSthe corresponding total cross section �

tt

from ATLAS and CMS

Selection minimisestension between ATLAS/CMStension with existing data

sensitivity to m

t

/BSM contaminations

Balanced againstoptimal fit quality

PDF constraining powervaried kinematic coverage


Procedural suggestionobservational facts

Impact of data on PDF central values appears relatively insensitive of distribution choiceall distributions are equal in the pool on the gluon PDF central value

While some distributions exhibit tensions, some appear perfectly compatibleselect distributions whose inclusion in the global fit leads to �2/Ndat ⇠ 1

Normalised distributions + total cross sections exhibit the largest constraining powerthey lead to the largest reduction of the gluon PDF uncertainties

Di↵erent distributions have their largest impact on a slightly di↵erent region of xchoose di↵erent distributions from ATLAS and CMS in order to maximise the kinematic coverage

Rapidity distributions have the weakest dependence on the value of mt

and on potential BSM contaminations (kinematic suppression of heavy resonances)

our recommendation for including 8 TeV `+jets tt distributions in a fit

the normalized top rapidity distribution (1/�)d�/dyt

from ATLASthe normalized top-pair rapidity distribution (1/�)d�/dy

tt

from CMSthe corresponding total cross section �

tt

from ATLAS and CMS

Selection minimisestension between ATLAS/CMStension with existing data

sensitivity to m

t

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Balanced againstoptimal fit quality

PDF constraining powervaried kinematic coverage


25

• Jacob Ethier: First simultaneous extraction of spin PDFs and FFs from a global QCD analysis

Progress in spin

• Tanmay Maji: Proton structure in a light-front quark diquark model: Single spin asymmetry

• Fit polarized PDFs and Kaon/Pion frag. functions at the same time in DIS, Semi-inclusive DIS and e+e- data.

• Use ‘iterative MC’ fitting.• Changes strange polarization shape -

consistent with zero.

21

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S=0, 1

In the parton model, the flavor singlet scalar diquark and the flavor triplet axial-vectordiquark are combined to a symmetric spin-flavor wave function of SU(4) structure. Theproton state is written as1

|P ;±i = CS |u S0i± + CV |u A0i± + CV V |d A1i±

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|u Si± =

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Collins Asymmetry with x

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−0.05

0

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)UT

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• Red continuous lines(yellow error region): h1

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1

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H?1

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= 2.5 GeV 2.

14

27

Figure 5: (Left) Impact on the gluon PDF with respect to the global baseline of ATLAS and CMS dif-ferential top production data at NNLO [38]. The “optimal” fit corresponds to the recommended choice ofobservables described in the text. (Right) The polarised strangeness ∆s+ distribution extracted from theJAM17 preliminary combined fit to polarised PDFs and fragmentation functions [41].

NNLO in QCD and NLO in EW [43]. To achieve a good description of the data, an additional 1% ofbin-to-bin uncorrelated uncertainty was included, which it was argued was necessary to account forstatistical uncertainties on the theory calculations and a possible underestimation of experimentaluncertainties. The impact of these ad-hoc uncertainties on the extracted PDFs was found to berelatively minor. The analysis found some tension when including the normalised distributions, e.g.the ATLAS 7 TeV data. This is believed to be a feature of either the treatment of the experimentalcorrelations or the theory, in the case of normalised distributions, where both the high pZ

T regionand the integral over the full distributions enter the fit. A fit to the 8 TeV unnormalised distributionswas found to give a significant reduction in PDF uncertainties in comparison to a HERA-only PDFset.

Progress in the determination of polarised PDFs was also presented. In [41, 44] the first simul-taneous extraction of both polarised PDFs and fragmentation functions from DIS, semi-inclusiveDIS (for which the pion and kaon fragmentation functions are required), and semi-inclusive an-nihilation data at NLO within the JAM17 framework was discussed. To achieve this, an iterativeMonte Carlo fitting method was used. A good description of the data was achieved, and as shownin Fig. 5 (right), a ∆s+ consistent with zero across the entire x range within fairly large uncertaintieswas found, in contrast to some earlier studies. In [45, 46] a theoretical calculation of the transversemomentum dependent PDFs within the light-front quark di-quark model was presented. The resul-tant PDFs were found to be consistent with global fits, and were able to successfully describe theCollins asymmetry in semi-inclusive DIS.

The determination of the intrinsic charm content of the proton was discussed in [47, 5]. Inmost PDF analyses the charm PDF is generated extrinsically from perturbative g→ cc splittings,and is therefore determined from the other PDFs with no additional freedom. However, the pos-sibility of some intrinsic non-perturbative charm content in addition to this extrinsic content hasbeen a subject of debate for some time. Two different approaches to this problem were presentedhere. In a CT study [47, 48] physically motivated models for sea- and valence-like componentswere considered. While these models determined the intrinsic charm x dependence, the normal-

6

WG1: Structure Functions and Parton Densities Lucian Harland-LangImpact of IC on the PDFs and their ratios

15

22

Charm content of proton revisited!

The new LHC experiments provide additional constraints on non-perturbative charm !

Including the EMC charm data, we find evidence for non-perturbative charm at the 1.5 sigma level. Even without EMC data, non-perturbative charm bounded < 1.0 % at the 90% CL


Figure 6: (Left) Ratio of the CT14 charm quark PDF with different model fits of intrinsic charm, to thebaseline extrinsic only PDF [47]. (Right) Ratio of the NNPDF fitted charm quark PDF, including andexcluding the EMC data in the fit, to the baseline extrinsic only PDF [5]. In both cases the scale Q= 100 GeVis taken.

isation was left free and fitted to data. Alternatively, in the NNPDF study [5, 49] a completelyagnostic approach was taken and the charm PDF was fitted in the same fashion as the light quarks.Excluding the early EMC data, for which questions have been raised with respect to the reliabilityof the experimental systematic uncertainties, both studies place a limit on the momentum fractioncarried by intrinsic non-perturbative charm of 1(2)% for NNPDF (CT). Including the EMC data,NNPDF finds evidence for non-perturbative charm at the 1.5σ level. Future Z + c, open-charm,and J/ψ measurements from the LHC should help further constrain or discover intrinsic charm.The extracted charm quark PDFs are shown in Fig. 6.

In [50] the resummation of logk(x) terms in the QCD splitting functions, which are particularlyimportant at low x, was presented. This was applied for the first time within a PDF fit to a range offixed-target and HERA DIS data. Interestingly, some improvement in the description, in particularat NNLO, was found. The impact on the PDFs at low x is found to be quite large, and a ∼ 1%change in the Higgs gluon-fusion production cross section is observed. However, this can onlybe taken as an indication of possible effects, as low x resummation should also be included inthe cross-section calculations themselves, which may reduce the effect. The outlook for includingfurther processes in the context of a more global fit was discussed, and has subsequently beenpresented in [51].

5. Tools for PDF fits

In recent years there has been a large increase in theory calculations for standard-candle pro-cesses at NNLO in perturbative QCD. These now cover, in addition to inclusive W/Z/γ∗ produc-tion, various 2→ 2 processes, e.g. W/Z+ jet [52, 53], tt [54], and inclusive jets [55], in both ep andpp collisions. However, each calculation requires a large computational effort and thus they are notdirectly usable in PDF fits. The APPLfast project [56] works on extending the grid-technologyfor NLO calculations known from FastNLO and APPLgrid [57, 58] to the calculations providedby the NNLOJET program. While significant computations of about 200,000 CPU-hours must be

7


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Figure 7: (Left) Extraction of the photon PDF from ATLAS high-mass Drell-Yan data [64, 65]. (Right)Transverse momentum dependent PDFs evolved using the parton branching model [66].

performed initially, any subsequent convolution with an arbitrary PDF is completed in much lessthan one second. Recently, work on FastNLO tables for NNLO tt calculations has been com-pleted [59]. The availability of fast NNLO calculations will be an important ingredient to improvethe precision of PDF fits with hadron-collider data.

The APFEL package [60, 61] is a library for the computation of collinear PDF evolution andDIS structure functions. In the current version, the package supports evolution at up to NNLO inQCD and NLO in QED, various options for heavy-quark contributions (e.g. fixed/variable-flavour-number schemes, pole masses, MS masses), and a fast computation of DIS observables. APFEL isthe main evolution code used by the NNPDF collaboration [6] and is also available in the xFitterpackage [62, 63]. APFEL features flexible interfaces to Fortran, C/C++, and Python code.

Finally, the xFitter package [62, 63] is the major platform used for PDF fits and analysesoutside the dedicated PDF collaborations. It is open source and integrates several other programsthat are necessary to perform a PDF analysis. The xFitter team has recently developed a newmajor release, 2.0.0, with significant improvements. There are more than 30 public results obtainedwith xFitter since the start of the project. Members of the LHC experiments are currently themain developers and users of xFitter, using the program to assess data sensitivity to PDFs andcompatibility with QCD predictions. Two recent results by the xFitter team were featured atthis workshop. The first was an extraction of the photon PDF using high-mass Drell-Yan datafrom the ATLAS experiment at the LHC [64, 65]. The second result explored a new approachto performing the evolution of transverse momentum dependent PDFs using the parton branchingmodel [66]. These two results are showcased in Fig. 7 (left) and (right), respectively.

6. PDFs and effects in heavy Nuclei

The study of PDFs for heavy atomic nuclei continues to be an interesting topic with a steadylevel of activity. As has been known for some time, a nucleus is more than the sum of free nu-cleons, due to nuclear dynamics. Recent new data on heavy ion collisions have increased both theinterest in predictions and expanded the available datasets. Traditionally νN scattering has been

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an important source of information on the strange-quark density, which requires an understand-ing of the nuclear corrections, as discussed in [67]. While the EMC effect has been known since1983, work is ongoing to describe this theoretically as a combination of several effects, includingdynamic short range correlations, as discussed in [68].

The extraction of nuclear PDFs typically proceeds with a model to parameterise the nucleareffects. The new EPPS16 fit was presented in [69, 70, 71], which relies on a parametrisation ofthese effects that is fitted to data. For the first time, this fit includes LHC data, which has allowedthe parametrisation to be more flexible to reduce the impact of initial assumptions. The inclu-sion of pion-nucleus Drell-Yan data show some sensitivity to nuclear valence-quark modifications.The approach by the nCTEQ collaboration was presented in [67], which features a generalised A-dependent parameterisation of nuclear effects. Fig. 8 shows an overlay of the most recent EPPSand nCTEQ results regarding the modification factor for lead nuclei. A general agreement on thecentral values can be seen. However, the uncertainties are large and their estimation is typicallydriven by model choices rather than the data. The Kulagin-Petti approach was presented as wellin [72], which uses a microscopic model incorporating Fermi motion.

Another topic of continued interest is the combination d− u at x≈ 0.1, which was found to besignificantly larger than zero by the E866 Drell-Yan experiment. Explanations for this effect werediscussed in [73, 74]. These typically use models based on pion exchange, which can be obtainedfrom QCD and calculated in chiral effective field theory. New data by the SeaQuest collaborationhas recently disfavoured a possible change of sign change at x > 0.3, as shown in Fig. 9 (left). Inthe future, leading neutron analyses and Drell-Yan data with pion beams will constrain pion PDFsat low and high x in an upcoming neutron tagged DIS experiment at JLAB [75].

Several LHC measurements sensitive to nuclear effects were presented by the experiments [76,77] or discussed further by the fit collaborations [69, 72, 67]. These included most prominently dataon the production of jets or W/Z bosons in LHC pPb collisions. Comparisons of jet productionbetween pp and pPb collisions have been made, and while they are similar when integrated in

9


Figure 9: (Left) Data from the E866 and SeaQuest experiments on d− u [73]. (Right) An example of pPbLHC data, here W+ production, that is used to differentiate between nuclear models and constrain modelparameters [72].

rapidity, CMS data show significant modification as a function of jet rapidity. Indeed, this dataalready provides some constraints on the EPPS16 fit. An example of data on W+ production inpPb collisions compared to a variety of predictions is shown in Fig. 9 (right); not all nuclear modi-fications improve the description of the W± and Z data. Similar to the high precision pp case, cor-relations in these pPb data are starting to be exploited, e.g. by analysing the forward/backward andW+/W− asymmetries. More precise measurements in the near future will significantly improveour knowledge. New νN cross-section data is expected in the near future from the MINERvAexperiment [78], although the reach in Q2 will be limited.

7. New Theory Developments

A number of new theoretical ideas and developments were also discussed at the conference.In [81] a summary of the first joint PDF and lattice QCD workshop, which took place in Oxford,March 2017, was presented. The aim is to explore the possibility for lattice QCD calculations tobe used as constraints for global PDF fits. Many topics were discussed at this workshop, includingthe need to identify benchmarks that are well constrained by global fits and can therefore be usedto validate the lattice inputs, the choice of observables that could benefit from lattice constraints,and the understanding of various sources of systematic uncertainty in the lattice calculations. Thishas subsequently been summarised in the form of a white paper [82], which serves as a basis forfuture work in the area.

In [79, 83], a novel approach to performing PDF fits was described. Markov Chain MonteCarlo techniques were used to extract the probability density functions of PDFs, allowing for fur-ther information on the PDF uncertainties. The minimisation was performed using a hybrid (orHamiltonian) Monte Carlo technique, first applied in lattice QCD applications. The implemen-tation used the xFitter package and a validation was performed using the HERA DIS dataset

10


First results PDFs probability distribution functions

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output (left) for xuval and xg, at Q

2 = 10 GeV

2. The bands show the 68% confidence interval around the most probable

value for the MCMC PDFs, and the standard �‰

2= 1 deviation for HERAPDF.

Mariane Mangin-Brinet MCMC PDFs DIS2017 - April 4th, 2017 27 / 30

a) b)

c) d)

Figure 12: The structure-function F2(Q2) for selected values of xBj, extracted with the BKSmodel for Q2 2 GeV2 and with results from the HHT NNLO analysis for Q2 > 2 GeV2. Eachof the four plots contains data for four xBj values from 0.013 to 5 · 10�4 and one additional xBj

value, ranging from xBj = 2·10�4 in a) to xBj = 5·10�5 in d). Also shown are the predictions fromthe HHT-REGGE fit and the HHT NNLO analysis, together with the HHT-ALLM prediction.Dotted lines indicate extrapolations beyond the fitted regions. The width of the bands representsthe uncertainty on the HHT NNLO predictions. No uncertainties were computed for the HHT-REGGE and HHT-ALLM predictions. For xBj = 0.00005 and Q2 = 2 GeV2, two points areshown, extracted from data with

ps = 318 and 300 GeV, respectively.

35

Figure 10: (Left) Up valence quark distribution extracted using the Markov Chain Monte Carlo tech-nique [79]. (Right) The structure function F2(Q2) for selected values of xB j, compared to the Regge andNNLO DGLAP based predictions [80].

with the zero-mass variable-flavour number scheme. The results were found to be consistent withthe corresponding HERAPDF set, thus serving as a proof-of-concept. The extracted u-valence isshown in Fig. 10 (left).

In [84, 85] the determination of CTEQ-TEA MC replica sets was discussed. Alternative tech-niques for converting from the Hessian to MC PDFs were considered, either sampling directly inthe PDF f , or in ln f . The latter case guarantees PDF positivity, provided the original Hessian set ispositive within its uncertainty. In addition, a shift is introduced to guarantee that the central valueof the MC replicas corresponds exactly to the central Hessian set, something which is otherwisenot guaranteed. The MC sets using these techniques were compared to the original Hessian PDFs,and found to agree well. These are now publicly available in LHAPDF format.

In [86, 87], a new calculation of certain contributions to the 4-loop splitting functions wasdiscussed. In particular, a lattice basis reduction technique was applied to reconstruct the large nF

contributions to the splitting functions from the calculated Mellin moments. These results havebeen validated against a range of known results in various limiting regions, and are an importantstep towards a consistent treatment of PDFs at N3LO.

The description of HERA DIS data in the low x and Q2 region was discussed in two talks [88,89]. In [89, 80] the HERA data was fit using a two-component approach, with standard perturbativeQCD DGLAP applied above a Q2 of 2 GeV2, and a Regge-inspired model applied below. The dataagrees well with these approaches in their expected regions of validity, but not in the transitionregion. However, as shown in Fig. 10 (right) the data shows a smooth transition between the tworegions, prompting the conclusion that nature does not “know” about perturbation theory. In [88,90] a QCD-inspired model of higher-twist corrections was used to supplement standard DGLAPevolution, with the parameters of these corrections determined in a simultaneous fit to the HERAdata. A large improvement in the fit quality at low Q2

min was found upon the inclusion of thesecorrections, providing possible evidence for the important contribution of higher twists at HERA.

11


8. Conclusions

The structure of hadrons, specifically PDF dynamics, is an interesting topic that continuesto attract attention from the larger nuclear and particle physics communities. From a practicalperspective, experiments at the current and future energy frontiers using hadron beams need PDFinformation to exploit their data. Without improved DIS data, much of the attention has now turnedto data from the LHC experiments, with a continuous effort to measure and predict standard-candleprocesses at the highest possible precision, and include these data into global PDF fits. Many ofthe talks in this working group revolved around these topics. For the case of heavy nuclei the rangeof datasets is more scarce than for protons, giving the new data from LHC and elsewhere a moreprominent role.

Beyond the topic of the LHC data and applications, fundamental topics raise interest, includingthe validity of the framework of collinear factorisation, the treatment of heavy-quark contributions,non-perturbative effects and techniques, resummation effects, and the nature of PDFs at very smallor large x.

Many of these topics were debated lively in the working groups sessions, demonstrating thatthe DIS conference is one of the focal points of the community for these discussions.

Acknowledgements

We would like to thank all the speakers and participants that contributed to the success of theworking group 1 programme with interesting presentations and lively discussions. We also thankthe organisers for a well-organised and interesting DIS 2017 conference, and for giving us theopportunity to convene this session.

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