Nuclear Physics B Proceedings Supplement 00 (2012) 1–11 Nuclear Physics B Proceedings Supplement Proton structure measurements and PDFs at HERA Katerina Lipka for the H1 and ZEUS Collaborations DESY, Notkestrasse 85, 22607 Hamburg, Germany Abstract Recent measurements of inclusive and semi-inclusive deep inelastic scattering in electron-proton collisions at HERA are reviewed. These measurements are used to determine the parton distribution functions (PDFs) of the proton, a necessary input to almost all theory predictions for hadron colliders. An introduction to the PDF determi- nation with an emphasis on HERA PDFs is presented. Theory predictions based on HERAPDF are compared to a selection of recent LHC and Tevatron measurements. The impact of jet and charm production measurements in DIS at HERA on the PDFs is discussed. Keywords: deep inelastic scattering, parton distribution functions, jets, charm, benchmarking 1. Introduction A deep understanding of proton structure is one of the most important topics in modern particle physics. A precise knowledge of the parton distribution functions of the proton is essential in order to make predictions for the Standard Model and beyond the Standard Model processes at hadron colliders. The cross sections of processes in proton-(anti)proton collisions are factorized by a convolution of the ma- trix element of parton-parton interaction and the pro- ton structure. The latter is described by parton distri- bution functions (PDFs). A PDF, f i ( x, Q 2 ), represents the probability of finding in the proton a parton i (quark or gluon) carrying a fraction x of the proton momen- tum, with Q being the energy scale of the hard interac- tion. In case of proton-(anti)proton interaction PDFs of both hadrons enter multiplicatively into the calculation of the process cross section. Therefore the precision of the PDFs is of particular importance for accurate cross- section predictions. In the last decades, the measure- ments of lepton-nucleon and proton-antiproton scatter- ing have been used to determine the proton PDFs. The kinematic ranges accessible by the different ex- periments where PDFs can be determined are shown in Fig. 1. At low to medium x the PDFs are constrained x Q 2 / GeV 2 Atlas and CMS (7 TeV) Atlas and CMS rapidity plateau D0 Central+Fwd. Jets CDF/D0 Central Jets H1 ZEUS NMC BCDMS E665 SLAC 10 -1 1 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1 Figure 1: The ranges of Q 2 and x accessible by fixed target experi- ments and in ep and proton-(anti)proton collisions. by HERA data. The measurements at fixed target ex- periments and the Tevatron contribute mainly at high x. The recent precise data from the Tevatron and the LHC
Transcript
Nuclear Physics B Proceedings Supplement 00 (2012) 1–11
Nuclear Physics BProceedingsSupplement
Proton structure measurements and PDFs at HERA
Katerina Lipka for the H1 and ZEUS Collaborations
DESY, Notkestrasse 85, 22607 Hamburg, Germany
Abstract
Recent measurements of inclusive and semi-inclusive deep inelastic scattering in electron-proton collisions atHERA are reviewed. These measurements are used to determine the parton distribution functions (PDFs) of theproton, a necessary input to almost all theory predictions for hadron colliders. An introduction to the PDF determi-nation with an emphasis on HERA PDFs is presented. Theory predictions based on HERAPDF are compared to aselection of recent LHC and Tevatron measurements. The impact of jet and charm production measurements in DISat HERA on the PDFs is discussed.
Keywords: deep inelastic scattering, parton distribution functions, jets, charm, benchmarking
1. Introduction
A deep understanding of proton structure is one ofthe most important topics in modern particle physics. Aprecise knowledge of the parton distribution functionsof the proton is essential in order to make predictionsfor the Standard Model and beyond the Standard Modelprocesses at hadron colliders.
The cross sections of processes in proton-(anti)protoncollisions are factorized by a convolution of the ma-trix element of parton-parton interaction and the pro-ton structure. The latter is described by parton distri-bution functions (PDFs). A PDF, fi(x,Q2), representsthe probability of finding in the proton a parton i (quarkor gluon) carrying a fraction x of the proton momen-tum, with Q being the energy scale of the hard interac-tion. In case of proton-(anti)proton interaction PDFs ofboth hadrons enter multiplicatively into the calculationof the process cross section. Therefore the precision ofthe PDFs is of particular importance for accurate cross-section predictions. In the last decades, the measure-ments of lepton-nucleon and proton-antiproton scatter-ing have been used to determine the proton PDFs.
The kinematic ranges accessible by the different ex-periments where PDFs can be determined are shown inFig. 1. At low to medium x the PDFs are constrained
x
Q2 /
GeV
2
Atlas and CMS (7 TeV)
Atlas and CMS rapidity plateau
D0 Central+Fwd. Jets
CDF/D0 Central Jets
H1
ZEUS
NMC
BCDMS
E665
SLAC
10-1
1
10
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1
Figure 1: The ranges of Q2 and x accessible by fixed target experi-ments and in ep and proton-(anti)proton collisions.
by HERA data. The measurements at fixed target ex-periments and the Tevatron contribute mainly at high x.The recent precise data from the Tevatron and the LHC
experiments have the potential to improve the precisionon the PDFs further.
2. Proton Structure and DIS at HERA
The knowledge of the proton PDFs is obtained toa large extent from the measurements of the structurefunctions in deep inelastic scattering (DIS) experiments.In Fig. 2 the diagram for DIS is represented. The lepton
e +_
/Z, W
PDF
+
+
_
_
e , e
p X
Figure 2: Diagram for neutral NC and charged CC current deep in-elastic scattering processes. The symbols denote the particles, thelabel ”X” denotes the hadronic final state.
is scattered off the nucleon via exchange of a γ or Z0-boson (neutral current, NC, process) or via exchange ofa W±-boson (charged current, CC). Here, the scatteringof an electron (or positron) off the proton is discussed.
The NC (and similarly CC) cross section can be ex-pressed in terms of the generalized structure functions:
d2σe±pNC
dxdQ2 =2πα2
xQ4
[Y+F±2 ∓ Y−xF±3 − y2F±L
],
where Y± = 1 ± (1 − y)2 with y being the transferredfraction of the lepton energy. The (generalized) struc-ture function F2 (F2) is the dominant contribution to thecross section, xF3 is important at high Q2 and FL is siz-able only at high y. In the framework of perturbativeQCD the structure functions are directly related to theparton distribution functions, i.e. in leading order (LO)F2 is proportional to the momentum sum of quark andanti-quark distributions, F2 ≈ x
∑e2
q(q + q), and xF3 isrelated to their difference, xF3 ≈ x
∑2eqaq(q − q). At
higher orders, terms related to the gluon density distri-bution (αS g) appear.In analogy to neutral currents, the inclusive CC ep crosssection can be expressed in terms of structure functions,and in LO the e+p and e−p cross sections are sensitive
to different quark densities:
e+ : σe+pCC = x[u + c] + (1 − y)2x[d + s]
e− : σe−pCC = x[u + c] + (1 − y)2x[d + s].
At HERA at DESY in Hamburg, electrons (orpositrons) were collided with protons at centre-of-massenergies
√s = 225−318 GeV. The measurements of the
NC and CC cross sections from HERA extend the kine-matic regime in Q2 by more than two orders of mag-nitude with respect to the fixed target experiments andcover a wide x range from 10−7 to 0.7. At the HERAcollider experiments, H1 and ZEUS, the cross sectionsof NC and CC DIS are measured with high precision.The measurements of the two experiments are com-bined [1] accounting for correlations of the systematicuncertainties. The combined cross sections are furtherused to determine parton distribution functions HERA-PDFs.
2.1. Determination of PDFs
PDFs are determined from the structure functionmeasurements using the corresponding coefficient func-tions calculated to a certain order in perturbative QCD(pQCD). The structure functions, and in turn the PDFs,depend on x and Q. The x-dependence of the parton dis-tributions is not yet calculable in pQCD and has to beparametrized at a certain starting scale Q0. The depen-dence on Q is described by the DGLAP evolution equa-tions [2]. Starting from a parametrization of the non-perturbative PDFs at a starting scale, either by makingad-hoc assumptions on their analytical form or by usingthe neural-net technology, fits to various sets of experi-mental data, with HERA DIS data being the backbone,are performed within the DGLAP evolution scheme.The resulting PDFs depend on the order in which theperturbative QCD calculation is performed, the assump-tions about the PDF parametrization, the treatment ofheavy quarks, the choice for the value of αS (MZ) and thetreatment of the uncertainties. The data sets included inthe PDF fit and the consistency of these data sets deter-mines the experimental uncertainty of the PDFs.
3. HERAPDF
Starting from the first published HERA PDF setHERAPDF1.0 [1], the parton distributions HERAPDFare determined using combined HERA DIS data, wherethe correlations of the systematic uncertainties are prop-erly taken into account. This allows the usage of theconventional χ2 tolerance of ∆χ2 = 1. Since this QCD
analysis is solely based on ep data, the PDFs do not de-pend on the approach for nuclear corrections needed forfixed target data. Several phenomenological schemes ofheavy quark treatment can be used in the HERAPDFapproach. Therefore direct tests of these schemes arepossible.
The full statistics of the HERA inclusive CC and NCdata are used for NLO and NNLO QCD fits result-ing in HERAPDF1.5 [3]. The combined NC and CCcross sections are shown in Fig. 3 and Fig. 4, respec-tively, together with QCD prediction based on HERA-PDF1.5NLO.
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Figure 3: Inclusive DIS cross sections for NC in e±p collisionsat HERA. The measurements of the H1 and ZEUS experiments arecombined. Open (closed) symbols represent e−p (e+p) scatter-ing. The shaded curves represent QCD prediction based on HERA-PDF1.5NLO.
The QCD analysis HERAPDF1.5 makes use of thesame formalism, model and paramatrisation assump-tions as used in the HERAPDF1.0. The QCD predic-tions for the structure functions are obtained by solv-ing the DGLAP evolution equations at NLO (or NNLO)in the MS scheme with the renormalisation and factor-ization scales chosen to be Q2. The DGLAP equationsyield the PDFs at all values of Q2 above the input scaleQ2
0 at which they are parametrized as a functions of x.The starting scale Q2
0 is chosen to be 1.9 GeV2 suchthat the starting scale is below the charm mass thresh-old. The QCD predictions for the structure functions areobtained by the convolution of the PDFs with the NLOcoefficient functions calculated using the general mass
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Figure 4: Inclusive DIS cross sections for CC in e−p scatter-ing. The measurements of the H1 and ZEUS experiments are com-bined. The shaded curves represent QCD prediction based on HERA-PDF1.5NLO.
variable flavour number RT scheme [4].For the parametrisation of PDFs at the input scale the
generic form x f (x) = AxB(1− x)C(1+Ex2) is used. Theparametrised PDFs are the gluon distribution xg, the va-lence quark distributions xuv, xdv, and the u-type andd-type anti-quark distributions xU, xD. At the startingscale Q2
0 = 1.9 GeV2 the following relations for quarkand antiquark distributions are used: xU = xu andxD = xd + xs. The central fit parametrisation is:
The normalisation parameters A are constrained by thequark number and momentum sum-rules, extra con-straints for the small-x behaviour of d− and u−typequarks are Buv = Bdv , BU = BD and AU = AD(1− fs)( fs is the strange quark fraction), which ensures thatxu→ xd as x→ 0.
The parton distributions HERAPDF1.5 at NLO at ascale of Q2 = 10 GeV2 and at NNLO at Q2 = 10000GeV2 are shown in Fig. 5 and Fig. 6, respectively.In addition to the experimental uncertainties, variationof model inputs and parametrization in the determina-
Figure 5: The parton distribution functions from HERAPDF1.5 NLOat Q2 = 10 GeV2. The gluon and sea distributions are scaled downby a factor of 20. The experimental, model and parametrisation un-certainties are shown.
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Figure 6: The parton distribution functions from HERAPDF1.5NNLO. The gluon and sea distributions are scaled down by a fac-tor of 20. The experimental, model and parametrisation uncertaintiesare shown.
tion of HERAPDF are performed and provided as addi-tional eigenvectors. The model uncertainties are evalu-ated by varying the input assumptions on the minimumQ2 of the data used in the fit, Q2
min, the strangenessfraction, and the masses of heavy quarks, mc and mb.The parametrization uncertainty is formed by an enve-
lope of the maximal deviations from the central fit vary-ing parametrization assumptions. HERAPDF1.5NLOand NNLO sets are the recommended HERA PDFs tobe used for the predictions of processes at the LHC.The corresponding eigenvectors are available in theLHAPDF library [5].
4. Benchmarking HERAPDF
The PDFs are intrinsic properties of the proton andare therefore process-independent. Cross section pre-dictions for processes in proton-(anti)proton collisionscan be obtained using HERAPDF, evolved in Q2 us-ing the DGLAP equations. In the following, compar-isons of the QCD predictions based on HERAPDF1.5to measurements at Tevatron and the LHC experimentsare presented.
The measurements of jet production at hadron col-liders is an important instrument for testing the under-standing of the PDFs at high x, and they also provideadditional constraints on the value of αS (MZ). In Fig. 7the jet production cross sections as measured by the D0experiment [6] are presented. The measurements areconfronted with the QCD prediction at NLO [7, 8] basedon HERAPDF1.5NLO. The data are very well describedby this prediction.
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| < 1.2 jet0.8 < |y
)-3| < 1.6 (x 10jet1.2 < |y
)-6| < 2.0 (x 10jet1.6 < |y
)-9| < 2.4 (x 10jet2.0 < |y
+ nonperturbative corr.
Tevatron inclusive jet cross sections
Figure 7: Jet production cross sections as a function of jet transversemomentum for different ranges of pseudorapidity, as measured by theD0 collaboration. The data are represented by closed symbols. Themeasurements are compared to the QCD calculations at NLO basedon HERAPDF1.5NLO. The total PDF uncertainty and hadronisationcorrection uncertainty on the predictions are shown as shaded bands.
Jet production at the LHC is particularly interestingfor constraining the parton distribution functions at high
x. In Fig. 8 the jet measurement from the ATLAS ex-periment [9] in a central rapidity bin is shown in com-parison with NLO predictions using HERAPDF1.5NLOand several other PDFs. The QCD prediction usingHERAPDF1.5NLO describes the data very well.
[GeV]T
p210 310
/d|y
|T
(CTE
Q 6
.6)/d
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|y|/d
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2(CL90)PDF jets. R =0.4 (0.0<|y|<0.3) tanti-k
DataCTEQ 6.6HERAPDF 1.0
HERAPDF 1.5
GJR 2008
ATLAS Preliminary
Figure 8: Inclusive jet production cross section as a function of the jettransverse momentum, as measured by the ATLAS collaboration in therapidity range 0 < y < 0.3 The jets are identified using the anti-kt al-gorithm with R = 0.4. The data are represented in a ratio (stars) to theQCD prediction, using CTEQ6.6 [10] as reference PDFs. The centralvalue for the QCD calculation at NLO based on HERAPDF1.5NLOis represented by closed circles surrounded by the error band shownas the hashed area.
Production of electroweak bosons provides importantconstraints on the light quark distributions. The highprecision LHC data can be used not only to comparewith theory predictions to differentiate between differ-ent PDF sets but also to put constraints on them. For ex-ample, the W lepton charge asymmetry Al(W) can helpto constrain the u to d quark ratio. This asymmetry canbe represented as
Al(W) =(σW+ − σW− )(σW+ + σW− )
≈(uv − dv)
uv + dv + 2usea
and is sensitive to the valence u and d quark ratio.The W-boson muon asymmetry as measured by the
CMS experiment [11] is shown in Fig. 9. The mea-surement is compared to the NLO predictions [12] ob-tained using MSTW08 [13], CT10W[14] and HERA-PDF1.5 parton densities. The prediction based on HER-APDF1.5NLO describes the data very well.
Top quark pair production at the LHC probes thegluon density at high x. In Fig. 10 the cross-sectionmeasurement of top pair production [15, 16] is shownas a function of the top-quark pole mass in compar-ison to the approximate NNLO calculations [17] and[18] based on HERAPDF1.5NNLO. The theory uncer-tainty accounts for the variation of renormalisation and
| Muon Pseudorapidity |0 1 2
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HERAPDF1.5 (prel.)MSTW2008NLOCT10W
> 25 GeV µ T
p
= 7 TeVs at -1CMS preliminary 234 pb
MCFM:
Figure 9: The W-boson muon charge asymmetry as measured by theCMS experiment. The measurement (closed symbols) is comparedto the NLO prediction [12] using HERAPDF1.5NLO (shaded band),MSTW08NLO (dotted line) and CT10W (dashed line).
mtpole (GeV)
σ t t_
(pb)
mtpole (GeV)
σ t t_
(pb)
CMS Preliminary, √s=7 TeV, L=1.14 fb-1
approx. NNLO × HERAPDF15NNLO
errors: scale variations × 68% CL PDFexp × αS(MZ)
Langenfeld et al.
Ahrens et al.
Measured cross section dependence on mtMC
Measured cross sectionCross section corrected for m
tpole (Langenfeld et al.)
0
200
400
600
140 150 160 170 180 190
Figure 10: The top-pair production cross section measured by theCMS experiment (open square) shown at the value of the top massdetermined in the analysis. The mass dependence of the tt cross sec-tion according to approximate NNLO QCD predictions [17] and [18]is represented by the shaded and hashed band, respectively. The de-pendence of the experimental measurement on the assumption on mtin the simulation used for efficiency and detector corrections is shownby the light shaded band. The closed circle represents the cross sec-tion measurement, corrected for the top pole mass, extracted using thecalculation [17].
factorisation scales, PDFs error and the variation ofαS (MZ) in the PDF. For the PDF uncertainty of HER-
APDF1.5NNLO, only the eigenvectors for experimen-tal errors are used. The predictions describe the datavery well and are used to extract the value of the topmass from the cross section measurement, as describedin [16].
Furthermore, the precision of the top pair productionmeasurements at the LHC is essential for studies of theassumptions on parametrization and model parametersin the PDFs. In Fig. 11 the CMS measurement [15] ofthe tt cross section is shown with the prediction [17]using HERAPDF1.5NNLO. In contrast to Fig. 10, alsomodel and parametrization eigenvectors are used in thePDF uncertainty estimation.
mtpole (GeV)
σ t t_
(pb)
approx. NNLO (Langenfeld et al.) × HERAPDF15NNLO
only PDF uncertainties (68% CL):experimentalparametrizationmodel variations: Q2 > 5 GeV2
CMS (Prel.) CMS-PAS-TOP-11-005 (2011)
0
200
400
600
140 150 160 170 180 190
Figure 11: The top-pair production cross section measured by theCMS experiment (open square) shown at the value of the top massdetermined in the analysis, compared to the approximate NNLO pre-diction [17] for the tt cross section dependence on the pole mass ofthe top quark. The shaded band represents the PDF uncertainty ofthe prediction, broken down into experimental (dark shaded), model(light shaded) and parametrization (covered by the line width) uncer-tainties.
5. Global benchmarking excercise
Presently, the determination of PDFs is carried outby several groups, namely MSTW [19], CTEQ [20],NNPDF [21], HERAPDF [1], AB(K)M [22] andGJR [23]. The large number of PDF parameters andtheir treatment in the fitting procedure within the differ-ent groups results in differences of the PDFs provided.In order to study these differences, a benchmarking ex-ercise is being carried out by the PDF4LHC working
group [24] formed by the members of the PDF fittinggroups mentioned above. As an example, the NLO pre-diction for the Higgs cross section (MH = 120 GeV) atthe LHC is shown in Fig. 12 for different PDF sets as afunction of αS (MZ). For the different PDF groups notonly the value of αS (MZ), but also the running of thestrong coupling is different, resulting in different crosssection predictions.
)2Z(MS
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SOuter: PDF+Inner: PDF onlyVertical error bars
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Figure 12: NLO Higgs cross section predictions (MH = 120 GeV)using different PDFs at the LHC with
√s = 7 TeV.
The HERAPDF is an active participant in the bench-marking exercise. In contrast to other PDF groups,HERAPDF is not restricted to one particular heavyflavour treatment scheme, several schemes are imple-mented and can be tested. Also, by providing the PDFeigenvectors for model parameter and parametrizationvariations, HERAPDF allows for tests of specific pa-rameterisation and model assumptions during the QCDanalysis of different data sets. In the following, the in-clusion of semi-inclusive DIS data in the QCD analysisof the HERAPDF and the impact of these data on as-sumptions on αS (MZ) and the charm quark mass valuein the PDF fit is discussed.
6. Semi-inclusive data in HERAPDFs
Semi-inclusive measurements in DIS like jet andheavy flavour production, provide additional constraintson the PDFs when included into the QCD analysis to-gether with inclusive DIS data. Jet production is directlysensitive to both the gluon distribution in the proton andthe strong coupling αS . Therefore, including jet datain the QCD analysis can help disentangling the effectsfrom the gluon and αS in the PDF fit. Similarly, charmand beauty production in ep collisions provide direct
access to the gluon distribution in the proton, whichalso depends on the assumption of the charm and beautymass values used in the PDF fit.
6.1. Including jet data in the PDF fit: HERAPDF1.6In addition to the combined HERA inclusive DIS
cross sections as used in the QCD analysis HERA-PDF1.5, H1 and ZEUS measurements [25] of jet pro-duction cross sections are included in the PDF fit. Theresulting parton distributions HERAPDF1.6 [26] are de-termined using a fixed value of αS (MZ) and also usingαS (MZ) as a free parameter in the fit. In Fig. 13 the par-ton distributions for HERAPDF1.6 using a fixed valueof αS (MZ) are compared to those of HERAPDF1.5.Only small changes in the parton distributions, wellwithin the PDF uncertainties, are observed.
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Figure 13: The parton distribution functions from HERAPDF1.6 us-ing a fixed αs(MZ ) compared to those from HERAPDF1.5 at Q2 =
10 GeV2. The uncertainties of each PDF are presented in the corre-sponding lower panels.
The impact of the inclusion of jet data in the PDF fiton the gluon distribution and the value of αS is demon-strated in Fig. 14. Here, the PDFs obtained using the in-clusive data only (HERAPDF1.5) and the PDFs result-ing from including the jet data (HERAPDF1.6) are de-termined using αS (MZ) as a free parameter in the QCDanalysis. In case of the simultaneous fit of PDFs and αS
in HERAPDF1.5, the uncertainties on the gluon PDFbecomes large at low x but as soon as the jet data areincluded, the correlation between the gluon PDF andαS (MZ) is reduced, resulting in significantly reduceduncertainties on the gluon PDF.
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Figure 14: Upper panel: The parton distribution functions from HER-APDF1.5. Lower panel: the parton distribution functions from HER-APDF1.6 (with HERA jet data included in the fit). In both cases, theQCD analysis is performed treating αs(MZ ) as a free parameter inthe fit. The PDFs are presented for Q2 = 10 GeV2.
In Fig. 15 the quality of the PDF fit in terms of χ2 isrepresented as a function of the assumption on the valueof αS (MZ). In case of HERAPDF1.5, where only inclu-sive data are used, a very shallow minimum in the χ2
distribution is observed. The inclusion of the jet mea-surements in the fit results in a distinct minimum, whichallows the simultaneous determination of the PDFs andαS (MZ). The value of αS (MZ) = 0.1202±0.0013 (exp)± 0.0007 (mod/param) ± 0.0012 (hadronisation) +0.0045
−0.0036(scale) is determined [26]. This result is in very good
Figure 15: Distribution of χ2 for the PDF fit as a function of the as-sumption on the αs(MZ ) value. The dashed line corresponds to HER-APDF1.5, where only inclusive DIS data are used. The solid linerepresents HERAPDF1.6, where jet data from DIS at HERA are in-cluded.
)Z
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World averageS. Bethke, Eur. Phys. J. C64, 689 (2009)
jets 98-00TZEUS incl. kPhys. Lett. B 649, 12 (2007)
jets 96-97TZEUS incl. kPhys. Lett. B 547, 164 (2002)
multijetsT k2H1 low QEur. Phys. J. C67, 1 (2010)
multijetsT norm. k2H1 high QEur. Phys. J. C65, 363 (2010)
HERAPDF1.6Preliminary
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Figure 16: The summary of αs(MZ ) determination results using jetproduction at HERA as compared to the world average [27]. Theupper point corresponds to the simultaneous determination of αs(MZ )and the PDF, as described in the text. The experimental uncertainty isrepresented by solid lines, the theory uncertainty is shown by dashedlines.
agreement with different results of αS determination atHERA from jets measurements and the world averageas indicated in Fig. 16. It is important to note, thatthe dominant uncertainty arises from the variation of therenormalization and factorisation scales in the NLO cal-culation for the jet cross sections. This variation is usedto mimic the effect of the missing contribution from thehigher orders. Once the NNLO QCD calculations for jetproduction in ep collisions are provided, a very precisesimultaneous determination of αS (MZ) and PDFs will
be achievable using the DIS data.
6.2. Charm quark measurements in the PDF fit
The assumption on the number of flavours defines thefactorization scheme, used for the PDF determination.The number of flavours in the proton varies dependingon the value of the scale, which has to be compared tothe threshold, at which charm and beauty quarks can betreated as partons in the proton. This threshold is deter-mined by the mass of charm and beauty quarks. There-fore, the treatment of heavy quarks and the assumptionson their masses have particular importance in the QCDanalysis of the proton structure. Different approaches totreat heavy quarks (heavy quark schemes) are used bydifferent PDF fitting groups, corresponding to a differ-ent treatment of mass terms in the perturbative calcu-lations, but also implying differences in the interpreta-tion and assumptions on the values of the heavy quarkmasses. Measurements of charm and beauty productionin ep collisions can help to constrain some of these as-sumptions.
The effect of including the HERA charm data in theQCD PDF fits is studied at HERA. The charm contri-bution, Fc
2, to the proton structure function F2 is mea-sured at H1 and ZEUS using different charm taggingtechniques. These measurements are combined takinginto account the correlations of the systematic uncer-tainties [28] and the result is shown in Fig. 17.
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compared to the predictions [29] of the ABKM group.
The combined Fc2 data are included in the QCD anal-
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the parton distributions using different assumptions onthe charm quark mass, mc, is studied [30]. In Fig. 18 theparton distributions HERAPDF1.0 are shown togetherwith the result of the QCD analysis including the com-bined charm measurements. The best fit quality is ob-tained using mc closest to the pole mass value [31].
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Figure 18: The parton distribution functions from HERAPDF1.0(shaded bands) at Q2 = 10 GeV2. The result from the QCD analysisincluding combined charm measurements is shown for mc = 1.35 GeV(dashed line) and mc = 1.65 GeV (dash-dotted line).
The sensitivity of the PDF fit to mc when using com-bined Fc
2 was used to constrain assumptions on mc indifferent heavy quark schemes [32]. The charm dataare used together with different implementations of thevariable flavour number schemes (VFNS). The χ2 of thePDF fit including the charm data was determined as afunction of the input values of the charm quark mass,mmod
c , using different heavy quark schemes. The resultis shown in Fig. 19. It is observed that the minimumvalues of χ2 are comparable for all schemes in spite ofthe different optimal values of mmod
c , corresponding tothe χ2 minima.
Although this study is not interpreted as a measure-ment of the charm quark mass, it provides an importantconstraint on the assumptions of the mc value by differ-ent PDF groups. The important question of a measure-ment of mc using DIS data is addressed by the ABKMgroup [29], where the MS definition for heavy quarkmasses in the PDF fit is used. Therefore, the runningcharm quark mass mc(mc) can be determined to NLOor NNLO together with the PDF. Important constraintson mc(mc) from including combined HERA Fc
2 in thisanalysis are expected.
Different assumptions on mmodc in VFN schemes im-
/ GeV modelcm
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Figure 19: Comparison of the χ2 distributions of fits to the inclusiveHERA I + Fcc
2 data using different heavy flavour schemes representedas lines of different styles.
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Figure 20: NLO prediction of σW+ at the LHC for√
s = 7 TeV as afunction of mmod
c in the input PDF. The lines show predictions for dif-ferent VFN schemes. The stars show the predictions obtained with theoptimal value of mmod
c used in a given scheme. The dashed horizontallines indicate the range of σW+ , determined for mmod
c = mmodc (opt).
pact the charm contribution to the sea quark distribu-tion and thus affect the composition of xU(x) from thexu(x) and the xc(x) contributions. These in turn influ-ence the value of the W± and Z cross section predictionsat LHC. In Fig. 20 the NLO prediction [12] for the W+
production cross section is shown, using parton distri-butions evaluated with different assumptions on mmod
c invarious heavy quark schemes. Taking into account thewhole spread of cross section predictions using the stud-ied schemes, an uncertainty of 7% on the W+ productioncross section arises due to assumption on mmod
c in thePDF. However, when using the values of mmod
c corre-sponding to the minima from Fig. 19 as constrained byHERA charm data, this uncertainty is reduced to 1%.
6.3. HERAPDF1.7
Finally, a QCD fit is performed which includes allcurrently available HERA NC and CC inclusive, charm,low energy and jet data (HERAPDF1.7 [33]). In thisQCD analysis the studies, performed for including jetand charm data separately, as described above, are re-peated. Very consistent results are obtained. This HER-APDF1.7 fit prefers the same αS value as obtained witha fit using only inclusive and jet data (HERAPDF1.6).Similarly, the same optimal mc value is found, as thatobtained in a fit when only inclusive and charm data arefitted. A somewhat steeper gluon distribution with re-spect to the HERAPDF1.6 is obtained, although wellwithin PDF uncertainties, as shown in Fig. 21.
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Figure 21: The parton distribution functions from HERAPDF1.7 atQ2 = 10 GeV2. The gluon and sea distributions are scaled down bya factor of 20. The experimental, model and parametrisation uncer-tainties are shown separately. For comparison, the central values ofHERAPDF1.6 are also shown.
7. Summary
Precision of the parton distribution functions is es-sential for accurate predictions of cross sections of pro-cesses at hadron colliders. The proton PDFs are deter-mined using the experimental data of DIS and proton-proton collisions. Combined data of HERA colliderexperiments provide the most precise constraint on thePDFs at small and medium x. HERAPDF is one ofthe modern QCD analyses in which PDFs are deter-mined. HERAPDFs are based only on the HERA data.The advantages of these PDFs are: no need for nu-clear corrections (in contrast to PDFs using the fixedtarget data), consistent treatment of the systematic un-certainties of the experimental data, and implementationof several phenomenological approaches of the heavyflavour treatment. Currently, HERAPDF1.5 at NLO andNNLO are among the recommended parton densities forpredictions of the LHC cross sections. The QCD predic-tions based on the HERAPDF1.5 describe the measure-ments at Tevatron and the LHC very well. With increas-ing precision of the LHC data, particular processes likeW-boson, jet or top-pair production will provide addi-tional constraints on the PDFs.
Recent developments in the HERAPDF fits includethe QCD analyses of HERA inclusive DIS data togetherwith jet and charm measurements. The inclusion of thejet measurements in the HERAPDF analysis reducesthe correlation between the gluon distribution and thestrong coupling constant. In such a fit, the PDF is de-termined together with the αS (MZ) value. The resulton αS (MZ) is in very good agreement with the worldaverage, and the precision is limited by the missingNNLO calculation for jet production. Inclusion of thecharm data reduces the correlation between the gluondensity and the value of the charm mass used in differ-ent schemes of heavy flavour treatment in the PDF fit.In particular, a proper choice of the charm quark massvalue is important for accurate QCD predictions of Wand Z boson production at the LHC. With the propertreatment of the charm mass in the QCD analysis, in-clusion of charm measurements should help constrain-ing the running charm quark mass and the PDFs.
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