Heavy Flavour Production at HERA

Kenan Mujkic

University College London (UCL) and Deutsches Elektronen Synchrotron (DESY)On behalf of the ZEUS and H1 collaborations

Abstract

Measurements of heavy-quark production at HERA constrain the structure of the proton, and have provided valuableindications of perturbative QCD. In this publication measurements of heavy-flavour jet cross sections in photoproduc-tion and deep inelastic scattering (DIS), performed by the H1 and ZEUS collaborations, are presented using inclusivetechniques for the signal extraction. The results are compared to next-to-leading order QCD calculations and foundto be in reasonable agreement with theory predictions.

Keywords: Heavy flavour physics, perturbative QCD, proton structure, Fcc̄2 , inclusive techniques

1. Introduction

This proceeding reviews inclusive measurements ofheavy-flavour production at HERA in photoproductionand deep inelastic scattering (DIS) performed by theH1 and ZEUS collaborations. The study of beauty andcharm production in ep collision constitutes a strin-gent test of perturbative Quantum Chromo Dynam-ics (pQCD), since the heavy-quark masses provide ahard scale, thereby allowing precise predictions to bemade [1]. At leading order, the dominant process forheavy quark production at HERA is boson-gluon fusion(BGF), γg → qq with q ∈ b, c. The massive quarks aregenerated in the hard sub-process, and next-to-leading-order (NLO) QCD calculations are expected to providereliable predictions for heavy-quark jet production crosssections.

Provided the negative squared four-momentum ex-changed at the electron vertex, Q2, is small, the scatter-ing process can be treated as photoproduction, where aquasi-real photon emitted by the incoming electron in-teracts with the proton. In this proceeding a measure-ment of heavy-quark jet cross sections in photoproduc-tion will be presented, which is based upon the semi-leptonic decay of heavy-flavoured hadrons into muons,

and which uses the signed impact parameter δ and therelative transverse momentum Prel

T of the muon to theheavy-quark jet axis as variables for the signal extrac-tion. The measured heavy-quark jet cross sections arecompared to NLO QCD predictions and previous mea-surements using exclusive tagging techniques. Further-more, a measurement of heavy-flavour jet cross sectionsbased upon the decay length significance of the decay-ing hadrons and the invariant mass of the tracks associ-ated to the decay vertex will be presented. The resultsare compared to NLO QCD predictions.

In the case of large momentum transfer, Q2 , betweenthe electron vertex and a constituent of the proton, usu-ally referred to as deep inelastic scattering (DIS), theproduction of heavy flavours is of particular interest fortesting pQCD calculations, since the process involvestwo hard scales: the square root of the photon virtu-ality Q2 and the heavy quark mass mb/c . In the finalsection of this proceeding inclusive measurements ofheavy-quark jet cross sections in deep inelastic scatter-ing will be presented. The results will be compared toNLO QCD precdictions, and the charm contribution Fcc̄

2to the proton structure function will be extracted.

Available online at www.sciencedirect.com

Nuclear Physics B (Proc. Suppl.) 233 (2012) 122–127

0920-5632/$ – see front matter © 2013 Published by Elsevier B.V.

www.elsevier.com/locate/npbps

doi:10.1016/j.nuclphysbps.2012.12.065

2. Photoproduction

Beauty and charm has been measured in photopro-duction using various techniques by both the ZEUS andH1 collaborations. In the measurements presented inthis publication the cross sections have been determinedusing semi-leptonic decays into muons, and the decaylength significance and secondary vertex mass of de-caying charm and beauty hadrons. In the muon anal-ysis performed by the H1 collaboration, the fraction ofleptons originating from beauty was determined usingthe large transverse momentum of the muon relative tothe axis of the associated jet, Prel

T , and the impact pa-rameter of the muons. The inclusive analysis performedby the ZEUS collaboration relies upon the reconstruc-tion of secondary vertices of decaying hadrons and usestwo discriminating variables, the significance of the re-constructed decay length and the invariant mass of thecharged tracks associated with the secondary vertex.

Figure 1: Signed impact parameter δ and relative transverse momen-tum Prel

T of muon μ.

The muon analysis performed by the H1 collabora-tion to measure beauty and charm cross sections re-quires events with two jets and a muon, where the muonis associated with one of the jets. The analysis exploitsthe lifetime and the mass of heavy flavoured hadrons.Compared to previous measurements, a more precisetest of pQCD predictions was possible due to increasedstatistics, an extended phase space and reduced system-atics due to an improved understanding of the H1 vertexdetector.

The identification of muon candidates relies upona combination of information from the central silicontracker (CST) and the central tracking detector (CTD).At least two CST hits in the r−φ plane have to be associ-ated with the muon track, and the track segments mustbe well matched to a track reconstructed in the CTD.Jets are reconstructed using the inclusive longitudinallyinvariant kT cluster algorithm in the massless PT recom-bination scheme, with the distance parameter R0 = 1 inthe η−φ plane [2]. The algorithm is applied in the labo-ratory frame using all reconstructed hadronic final state

particles including the muon candidate. A jet is definedas a μ-jet if the selected muon candidate lies within acone of radius 1 about the jet axis in the η − φ plane.

The signal to background separation is performed ex-ploiting the properties of the muon track associated tothe μ-jet [3]. The impact parameter δ of a muon trackis the transverse distance of closest approach (DCA) ofthe muon track to the beam spot point. In case the an-gle α between the azimuthal angle of the μ-jet and theline joining the primary vertex to the point of closest ap-proach is less than 90◦, the impact parameter is definedas positive. It is defined negative otherwise. The trans-verse momentum Prel

T of the muon relative to the μ-jetaxis is also sensitive to the quark content of the eventsample and used together with the impact parameter forthe flavour separation. The distributions used for theflavour separation are shown in Fig. 1.

The fractions of events with beauty, charm and lightquarks are obtained by a binned likelihood fit in theδ − Prel

T plane [4]. In order to extract the differentialcross sections the fit is performed separately for eachindividual differential bin, while the total cross sectionsare determined using the fractions obtained from a fit tothe complete event sample.

Figure 2: Differential cross sections as a function of the average trans-verse momentum P jet1

T of the leading jet, the transverse momentumPμT and pseudorapidity ημ of the muon μ and the azimuthal angulardifference Δφi j.

The beauty and charm cross sections are measureddifferentially as a function of the transverse momen-tum Pjet1

T of the leading jet, the transverse momentumPμT and the pseudorapidity ημ of the muon and the az-imuthal angular difference Δφi j between the two lead-

K. Mujkic / Nuclear Physics B (Proc. Suppl.) 233 (2012) 122–127 123

ing jets. The results are presented in Fig. 2 [5] andcompared to next-to-leading order (NLO) calculationsprovided by MC@NLO [6], a program calculating next-to-leading order QCD predictions in the massive fixedflavour number scheme (FFNS). In general the predic-tions are in reasonable agreement with the beauty andcharm measurements.

Figure 3: Mirrored and subtracted decay length significance distribu-tions S + − S − in bins of the secondary vertex mass Mvtx.

The inclusive analysis performed by the ZEUS col-laboration measured beauty and charm quarks with atleast two jets using the invariant mass of charged tracksassociated with secondary vertices and the decay-lengthsignificance of these vertices [7]. In this context thedecay length, d, was defined as the distance in X − Ybetween the secondary vertex and the interaction point,projected onto the jet axis in the X − Y plane. The signof the decay length was assigned using the axis of thejet to which the vertex is associated. In case the de-cay length vector was in the same hemisphere as the jetaxis, a positive sign was assigned to it; otherwise thesign of the decay length was negative. The decay lengthsignificance, S , is defined as d / δd, where δd is the un-certainty on d.

The shape of the decay-length significance distribu-tion together with the secondary-vertex mass distribu-tion, mvtx, was used to extract the beauty and charmcontent. The invariant mass of the tracks fitted to thesecondary vertex provides a distinguishing variable forjets from beauty and charm quarks, reflecting the differ-ent masses of the beauty and charm hadrons. Aiming tominimise the effect of the light-flavour contribution, thecontents of the negative bin of the significance S distri-bution, N (S −), were subtracted from the contents of thecorresponding positive bin, N (S +), resulting in a sub-tracted decay-length significance distribution shown inFig. 3.

In order to reduce the uncertainty due to remainingdifferences between data and MC in the core region ofthe significance distribution, a cut of |S | > 3 was ap-plied. The beauty and charm contributions were thenextracted using a least-squares fit to the subtracted dis-tributions in the three mass bins. The MC beauty, charmand light-flavour contributions, normalised to the dataluminosity, were scaled by the factors kb , kc and kl f togive the best fit to the observed subtracted distributions.In order to extract the differential cross sections the fit-ting procedure was repeated for every differential bin.

Parton-level jets were found by applying the kT clus-ter algorithm to the generated partonic final state. TheNLO QCD predictions for the parton-level jets werecorrected for hadronisation effects applying a bin-by-bin procedure, where dσ = dσNLO · Chad and dσNLO

is the cross section for partons in the final state of theNLO calculation. The hadronisation-correction factorsChad were obtained from the ratio of the hadron-levelto the parton-level MC jet cross section. In this contextthe parton level is defined as the result of the parton-showering stage of the simulation.

Figure 4: Differential beauty and charm jet cross sections as a functionof the average transverse momentum P jet

T and the pseudo-rapidity η jet .

Finally, inclusive beauty and charm cross sectionhave been measured as functions of the transverse mo-mentum, p jet

T , and the pseudo-rapidity, η jet , of the jet,and compared to NLO QCD predictions generated withthe FMNR program [8]. The NLO calculations werebased on the fixed-flavour-number scheme, using threelight flavours for charm predictions and four flavoursfor beauty predictions. In order to allow for compar-

K. Mujkic / Nuclear Physics B (Proc. Suppl.) 233 (2012) 122–127124

ison with previous measurements the Parton DensityFunctions (PDFs) were taken from CTEQ6.6 [9] forthe proton and GRV-G HO[10] for the photon. Theheavy-quark masses were set to mb = 4.75 GeV andmc = 1.5 GeV, and the QCD scale, ΛQCD , to 0.226GeV. The renormalization scale, μR , and the factori-sation scale, μF , were chosen to be equal and set toμR = μF =

12 ( p̂2

T + m2b/c)

12 , where p̂T is the average

transverse momentum of the heavy quarks.

Figure 5: Differential beauty jet cross sections as a function of theaverage transverse momentum pb

T of the b-quark.

The results are shown in Fig. 4 and 5 [7]. In gen-eral a good agreement between the measured beauty andcharm cross sections and the NLO predictions is ob-served. Compared to previous measurements of specificdecay chains, this analysis has increased statistics andreduced the uncertainty originating from the branchingfractions. Furthermore, the measurement presented inthis proceeding extends the kinematic region to higherpb

T values than previous measurements and representsthe most precise measurement of b-quark photoproduc-tion at HERA.

3. Deep Inelastic Scattering

The measurement of beauty and charm jet cross sec-tions in DIS at HERA performed by the H1 collabora-tion uses an inclusive lifetime technique to distinguishjets containing beauty and charm flavoured hadronsfrom those containing light flavoured hadrons only [11].The most important of these inputs are the transversedisplacement of tracks from the primary vertex andthe reconstructed position of a secondary vertex in thetransverse plane. Typically, heavy flavoured hadronshave longer life times than light flavoured hadrons and

therefore produce tracks with a significant displacementfrom the primary vertex. For jets with three or moretracks in the vertex detector the reconstructed variablesare used as input to a neural network to discriminatebeauty from charm events.

In the analysis presented in this proceeding theflavour of the event is defined as the flavour of the jetwith the highest transverse energy, E jet

T , in the labora-tory frame. The separation of beauty, charm and lightflavour jets is performed using the properties of trackswithin a cone of radius 1 from the jet axis in the η − φplane [2]. The tracks are reconstructed in the CTD,must have at least 2 CST hits and transverse momen-tum greater than 300 MeV. The signed impact param-eter δ is defined as the distance of closest approach ofthe track to the beam spot. Tracks with δ > 0.1 cm arerejected to suppress contributions from decays of long-lived strange particles.

The track significance S is defined as S = δ/σ(δ),where σ(δ) is the uncertainty on the signed impact pa-rameter δ. The tracks are ordered according to theirabsolute track significance, and the sign of the highestabsolute significance track is used as reference. In thetrack selection the remaining tracks will only be consid-ered, if they have the same sign like the highest signif-icance track. The significances S 1, S 2 and S 3 are thendefined as the significance of the track with the highest,second highest and third highest absolute significanceafter the described track selection. The number of tracksin the jet after this selection is called Ntrack , and the se-lected tracks are also used to reconstruct the position ofthe secondary vertex associated with the jet.

In order to obtain statistically independent distribu-tions for the signal extraction, the jets are separated intothree independent samples. For each sample a differ-ent distribution is used to separate the beauty, charmand light flavour jets. The S 1 distribution is used forjets, where only one track has passed the cuts, and theS 2 distribution for jets, where two tracks have passedthe cuts. For jets with Ntrack ≥ 3, where S 1, S 2 and S 3all have the same sign an artificial neural network (NN)is used to produce a distribution that combines severalvariables in order to provide an optimal discriminationbetween beauty and charm jets.

The input to the NN are S 1, S 2, S 3 , the significanceof the transverse distance between the secondary andprimary vertex, the transverse momenta of the trackswith the highest and second highest transverse momen-tum, Ntrack , and the number of reconstructed tracks atthe secondary vertex [11]. The NN is trained usinga sample of inclusive heavy flavour DIS Monte Carloevents, with beauty events as “signal” and charm events

K. Mujkic / Nuclear Physics B (Proc. Suppl.) 233 (2012) 122–127 125

as “background”. The output of the neural network issigned according to the sign of S 1.

Given that the S 1 , S 2 and NN output distributions forlight flavour jets are nearly symmetric around zero thesensitivity to the modelling of the light jets can be re-duced by subtracting the contents of the negative binsfrom the contents of the corresponding positive bins.The subtracted distributions are dominated by beautyand charm jets, and the fraction of events with charm,beauty and light jets is extracted using a least squaressimultaneous fit to the subtracted S 1, S 2 and NN outputdistributions and the total number of events after DISand jet selection.

Figure 6: Differential charm jet cross sections as a function of theaverage transverse energy E jet

T , photon virtuality Q2, pseudo-rapidityη jet and number of jets N jet .

Differential charm and beauty jet cross sections weremeasured as a function of E jet

T , η jet , Q2 and N jet. Themeasured cross sections have been compared to NLOQCD predictions generated with the HVQDIS program[12]. The predictions are based on a fixed flavour num-ber scheme (FFNS) which uses the massive PGF O(α2

s)matrix element [13] and provides weighted events withtwo or three partons, i.e. a heavy quark pair and possi-bly an additional light parton.

In order to investigate the dependence of the NLOpredictions on the renormalisation and factorisationscale two different choices for the scale have been made.Firstly, the scale μr = μ f =

√(Q2 + p2

T + m2c/b)/2 was

used, where pT is the highest heavy quark transversemomentum in the virtual photon-parton centre of massframe. This choice of scale was motivated by the com-parison of NLO QCD predictions with recent measure-ments of inclusive jet data by the H1 collaboration. Sec-ondly, the scale μr = μ f =

√Q2 + 4m2 was chosen,

which has been used previously in the comparison ofHVQDIS predictions with H1 inclusive and dijet D∗DIS data [14], [15].

Figure 7: Differential beauty jet cross sections as a function of theaverage transverse energy E jet

T , photon virtuality Q2, pseudo-rapidityη jet and number of jets N jet .

The charm cross sections are shown in Fig. 6 togetherwith the NLO predictions generated with the HVQDISprogram [12] that is based on the fixed-flavour-numberscheme (FFNS), in which the heavy quarks are pro-duced in the interaction. In general the NLO predictionsdescribe the data reasonably well in all differential dis-tributions, although the predictions generated with thefirst renormalisation and factorisation scale fall some-what below the data at low Q2 , low E jet

T and in theforward η jet region. On the other hand, the differen-tial beauty jet cross sections presented in Fig. 7 are inreasonable agreement with NLO predictions with littledependence on the choice of scale.

The inclusive measurement of charm jet cross sec-tions in deep inelastic scattering performed by theZEUS collaboration uses the same technique like themeasurement in photoproduction, and relies upon the

K. Mujkic / Nuclear Physics B (Proc. Suppl.) 233 (2012) 122–127126

significance of the reconstructed decay length and theinvariant mass of the charged tracks associated to thedecay vertex. The measurement is kept fully inclusiveaiming to extract the heavy quark content to the protonstructure function with high precision.

For this purpose differential cross sections as func-tions of the photon virtuality Q2 and the Bjoerken scal-ing variable x have been measured. The results werecompared to NLO QCD predictions and the heavy-quark contribution to the proton structure function wasextracted. Theory predictions were obtained from theHVQDIS program using ZEUS-S [16] and ABKM [17]as proton PDFs, and setting the value of the strong cou-pling constant αs (MZ) = 0.118 and the heavy-quarkmasses mc = 1.5 GeV and mb = 4.75 GeV. The renor-malisation and factorisation scale were chosen to beequal and set to μr = μ f =

√Q2 + 4m2

c/b .

Figure 8: Charm contribution Fcc̄2 to the proton structure function as a

function of Bjoerken x in various bins of Q2.

The heavy quark contribution to the proton structurefunction can be defined in terms of an inclusive double-differential cross section:

d2 σqq̄

dx dQ2 =2πα2

em

xQ4

{[1+(1−y2)

]Fqq̄

2 (x,Q2)−y2Fqq̄L (x,Q2)

},

where Fqq̄L is the heavy-quark contribution to the

structure function FL.

In order to extract Fqq̄2 from the visible cross sections,

σqq̄, an extrapolation from the measured range in E jetT

and η jet to the full phase space was performed. Themeasured values of Fqq̄

2 at a reference point in the x−Q2

plane were calculated using

Fqq̄2 (x,Q2) =

d2σqq̄

dx dQ2 ·Fqq̄,NLO

2 (x,Q2)

d2σNLOqq̄ /dxdQ2

,

where Fqq̄,NLO2 and d2σNLO

qq̄ /dxdQ2 were calculatedat NLO in the FFNS using the HVQDIS program cor-rected for hadronisation and QED radiation effects.

The charm contribution Fcc̄2 to the proton structure

function extracted in this way is shown in Fig. 8 as afunction of x for various values of Q2. The measure-ment is compared to the NLO QCD predictions gener-ated with HVQDIS and HERAPDF1.0 [18], and foundto be in agreement with theoretical predictions withinthe statistical and systematic uncertainties. The mea-surement is in agreement with the HERA combinedmeasurements and particularly competitive at high Q2.

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