Open Charm and Beauty Production at HERA

Transcription

1 Nuclear Physics B Proceedings Sulement () Nuclear Physics B Proceedings Sulement Oen Charm and Beauty Production at HERA Olaf Behnke for the ZEUS and H Collaborations DESY, Notkestrasse 85, 67 Hamburg, Germany Abstract A review is rovided of oen charm and beauty roduction at HERA and its descrition by erturbative QCD (QCD). Four years after the end of the data taking there is still a steady flow of new charm and beauty results from HERA. Among the results reorted here are the first combined H and ZEUS measurements on the contribution from charm roduction to dee inelastic scattering (DIS), reresented by the structure function F c c, as well as new recise results on the corresonding structure function for beauty roduction, F b b. Furthermore the situation of charm and beauty roduction in the hotoroduction kinematic regime is reviewed. Since it is a related field also the first hadroroduction results from LHC are resented. A brief outlook is given on oen heavy flavour rosects at ossible future e colliders, with a focus on the LHeC. Keywords: charm, beauty, erturbative QCD, hotoroduction, dee inelastic scattering. Introduction Heavy quark roduction at HERA rovides an exciting testing ground for erturbative QCD (QCD). In leading order, heavy quarks are roduced in e collisions via the Boson Gluon Fusion (BGF) rocess shown in Fig. on the left. his rocess rovides direct ace + γ * Q c, b m c, m b α s g c, b e + γ c, b Figure : Left: Leading order Boson Gluon Fusion (BGF) diagram for charm and beauty roduction in e-collisions. Middle and right: Sketch of the leading order rocesses in the massless aroach, where charm and beauty quarks are treated as massless sea quarks in the roton and in the resolved hoton, resectively. e + γ g c, b cess to the gluon density in the roton. BGF tye rocesses dominate DIS scattering towards lower values of the Bjorken scaling variable x, due to the large gluon density. In the limit of large hoton virtualities Q, the events with charm and beauty quarks are exected to account for 6% and 9% of the BGF rocesses and hence contribute significantly to inclusive DIS. On the theoretical side, the descrition of heavy quark roduction in the framework of erturbative QCD is comlicated due to the resence of several large scales like the heavy quark masses, the transverse momentum of the roduced quarks and Q. Different calculation schemes have been develoed to obtain redictions from QCD. At low scales (or Q ) the fixed-flavour number scheme (FFNS) [] is exected to be most aroriate where the quark masses are fully accounted for. Calculation rograms [, ] are available to Next-to-Leading Order (NLO), which is order O(α s) for the cross sections. An exemlary NLO diagram is shown in Fig. on the left. Comlete Next-to- Next-to-Leading Order (NNLO) redictions are not yet available due to difficulties to determine two loo diagrams with heavy quark lines (see Fig. right). However, some imortant stes have been already undertaken towards an NNLO calculation, including thresh-

2 Olaf Behnke / Nuclear Physics B Proceedings Sulement () old resummation of soft gluon radiation, as discussed in the talk by S. Alekhin [4]. At very high scales the NLO scales, charm in hotoroduction and ending with the largest scales, beauty roduction in DIS. In the outlook e + e + Menu: walk through the scales γ γ Q α s g α s g m Q Photoroduction Q DIS Q GeV Figure : Exemlary diagrams for heavy quark roduction at higher orders: left at Next to Leading Order (NLO) and right at Next to Next to Leading Order (NNLO). he two loo NNLO diagram has not yet been calculated. FFNS scheme redictions are exected to break down since large logarithms ln( /m ) are neglected that reresent collinear gluon radiations from the heavy quark lines. hese logarithms can be resummed to all orders in the alternative Zero-Mass Variable Flavour Number schemes (ZM-VFNS) [5]. Here the charm and beauty quarks are treated above kinematic threshold as massless and aear also as active sea quarks in the roton and in the resolved hoton, as deicted in figure middle and right. Most widesreadly used are nowadays the so-called Generalised Variable Flavour Number Schemes (GM-VFNS) [6]. hese mixed schemes converge to the massive and massless schemes at low and high kinematical scales, resectively, and aly a suitable interolation in the intermediate region. However, the exact modelling of the interolation and in general the treatment of mass deendent terms in the erturbation series are still a highly controversial issue among the various theory grous. he different treatments have rofound imlications for global Parton Distribution Function (PDF) fits and influence the fitted densities of gluons and other quark flavours in the roton. his toic is discussed extensively in the talk by K. Lika [7] as well as the imlications for redictions of many imortant rocesses at the LHC, for instance for Z and W roduction. As it turns out the HERA inclusive charm roduction data in DIS allow to determine the charm quark mass arameter in the different scheme calculations and this hels to stabilise the PDF fits and redictions for the LHC. In the review resented here the focus is on comaring the HERA oen charm and beauty roduction data with QCD calculations in the various schemes, to see how well they are doing. A systematic tour through the hard scales is taken, as indicated in Fig., starting with the smallest quark mass and hoton virtuality c.5 GeV b 4.75 GeV Figure : Ordering scheme of toics in this review, according to the hard scales of quark mass and hoton virtuality Q. also some rosects for heavy quark roduction at ossible future e colliders are briefly given.. Results.. Charm hotoroduction One of the most recise measurements of charm hotoroduction to date are rovided by the ZEUS D meson analysis [8] based on the HERA I data set. he D mesons are identified via full reconstruction of the decay D + D π + with subsequent decay D K π + or D K π + π + π. hroughout this review the charge conjugated states and decay chains are imlicitly included. Figure 4 shows the obtained differential roduction cross sections as a function of the transverse momentum of the D meson. A vast region from.9 GeV to GeV is covered, where the data are falling over four orders of magnitude. he ZEUS data are comared to the FMNR [] massive scheme NLO calculations and to the FONLL [9] redictions which are based on the massive scheme at NLO lus a nextto-leading log resummation of terms of collinear origin. he FMNR rediction describes the data better than FONLL towards the high transverse momenta. his is a surrise since this is the region where one might exect that the massive scheme starts to fail. At the starting oint of the sectrum, where the transverse momenta are not much above the charm quark mass, both calculations are slightly below the data, however still within 6

3 Olaf Behnke / Nuclear Physics B Proceedings Sulement () dσ(e ed*x)/dη[nb] 4 H Preliminary HERA II D* in Photoroduction H data (rel.) GMVFNS (CEQ6.5).5 < µ / m c + < r,f t η(d*) Figure 5: Differential D hotoroduction cross sections as a function of the seudoraidity of the meson. he H measurement [] is comared to the generalised variable flavour number scheme calculation (labelled GMVFNS), for more details of the calculation see []. Figure 4: Differential D hotoroduction cross sections as a function of the transverse momentum of the meson. he ZEUS measurement [8] is comared to two massive scheme NLO redictions: the FMNR [] (labelled NLO QCD) and the FONLL [9] calculation which includes additional collinear gluon radiation terms. on D meson differential roduction cross sections as a function of the meson transverse momentum. he data are comared to different massive NLO lus reasonable agreement considering the estimated rediction uncertainties. hese uncertainties have been obtained by varying the renormalisation and factorisation scales simultaneously by the factors two u and down from the nominal scale µ r, f = m c + t. hey reach a level of about 5% at small transverse momenta. his is no surrise, since α s, which enters the cross section rediction already at leading order (see Fig. left), is large for the relatively small hard scales available in this kinematic domain. hus the redictive ower of the NLO calculations remains limited in the kinematic threshold region. he situation will only change when NNLO redictions will become available, which unfortunately cannot be exected for the near future. Figure 5 shows the results of a similar but more recent D meson measurement [] from H, in this case as a function of the D seudoraidity. he data are reasonably well described by a generalised variable flavour number scheme calculation. In this Figure, due to the linear scale, the large uncertainties of the rediction are very clearly visible. Recently the LHC entered the game of heavy flavour roduction. he dominant roduction mechanism at LHC is gluon gluon fusion into a heavy quark-antiquark air. Figure 6 shows the first ALAS results [] Figure 6: Differential D hadroroduction cross sections as a function of the transverse momentum of the meson. he ALAS measurement [] is comared to various massive scheme calculations (for further details and references see also []. matched arton shower calculations, MC@NLO [] and POWHEG []. he sectrum itself and the quality of the descrition by the calculations bears a striking resemblance to the ZEUS hotoroduction results shown in Fig. 4. Also for collisions the redictions tend to undershoot the data, but are still in reasonable agreement considering the theory uncertainties. hese uncertainties are considerably larger comared to those at HERA, which demonstrates the virtue of having at HERA an electromagnetic hoton robe at hand. In the future one can exect the LHC exeriments to extend the hase sace of charm roduction to much higher

4 Olaf Behnke / Nuclear Physics B Proceedings Sulement () 4 transverse momenta than those covered in Fig. 6. It will be interesting to see how well the various theory models can describe this large momentum domain. he dominant roduction mechanism for charm in hotoroduction at HERA is the BGF rocess (Fig. left), where the hoton enters directly the hard interaction. However, it is known since long that there is a sizeable roduction comonent which can be exlained by resolved hoton rocesses. A leading order diagram for such a rocess is shown in Fig. right. Here the hoton emitted by the electron fluctuates hadronically before the hard interaction, and a arton from this fluctuation enters the hard rocess. In the deicted reaction, which is called charm excitation, this arton is a charm quark. he charm excitation rocess exists only in the massless icture since in the massive scheme only light artons can be constituents of the resolved hoton structure, and the charm quarks can only be roduced in the hard interaction. However, in the massive calculation, excitation like rocesses (but with massive charm quarks) can aear at NLO. he main exerimental hints on contributions from excitation like rocesses were obtained by analyses selecting events containing a reconstructed D meson and at least two jets. he kinematic information from the two leading jets allows to reconstruct (in the leading order icture) the fraction x γ of the hoton energy which is carried into the hard interaction. Recent H results [4] on this observable are shown in Fig. 7 and are comared with redictions by the MC@NLO massive scheme rogramme. he Figure 7: Differential cross sections for D meson lus dijet roduction in hotoroduction as a function of the observable x γ. he H data [4] are comared with the MC@NLO [] massive scheme redictions. calculation rovides a good descrition of the data for values of x γ close to unity, where direct rocesses are dominating, but undershoots the data by far in the small x γ region. his demonstrates that the aforementioned massive NLO contribution to excitation like rocesses cannot account for the charm event yields in this region. A better descrition of the data in this region (not shown) is obtained by the PYHIA [5] Monte Carlo model containing a massless charm excitation comonent. Also, as has been reorted in revious Ringberg workshos, numerous other HERA measurements involving D mesons and jets have added evidence for the resence of a seizable excitation like comonent at small x γ, for instance in the analysis [6], where the dijet angular distributions were investigated... Beauty hotoroduction he relatively large beauty quark mass makes one believe that the QCD redictions for beauty quark roduction should be very reliable. hus it was a surrise when the very first results on beauty roduction in hotoroduction at HERA and also in collisions at EVARON, about fifteen years ago, indicated some excesses of the data over the NLO calculations. However, since then the situation has imroved. Nowadays one can state that there is in general a reasonable agreement of data and NLO redictions, both for HERA and EVARON. he main reasons for the situation change is that much more recise data have become available and simultaneously the theory models have advanced. Figure 8 shows a comilation of all the available beauty hotoroduction results at HERA as a function of the transverse momentum of the beauty quark. (b/gev) b dσ/d σ meas /σ th H 97- D*µ H 99- b jet H 99- b µ jet H (rel) 6/7 µ jet H (rel) b ee ZEUS b e ZEUS 96- b D* µ ZEUS 96- b µ ZEUS 96- b e ZEUS 5 b µ jet ZEUS 4 b bb µµ ZEUS b b jet HERA dσ/d b (e ebx) Q < GeV,. < y <.8, η < b NLO QCD µ =(m + )/4 b µ =m b b (GeV) Figure 8: Summary lot of beauty hotoroduction results at HERA as a function of the transverse momentum of the beauty quark. he H and ZEUS data oints, based on various beauty hadron tagging techniques, are comared to the FMNR [] massive NLO redictions, for more details of the calculation see [7].

5 Olaf Behnke / Nuclear Physics B Proceedings Sulement () 5 he lot contains measurements based on various exerimental techniques. he latest two additions are the ZEUS measurement labelled ZEUS b b jet [7] and the H analysis labelled H (rel) b ee [8]. In the new ZEUS measurement the events containing beauty quarks are tagged by exloiting the signatures of long lifetime and large mass of the beauty hadrons. racks associated to the beauty jet candidate are fitted to a secondary vertex. he significance of the decay length from rimary to secondary vertex and the secondary vertex mass are used as observables to searate the beauty, charm and light flavour contributions to the event yields. With this technique an almost background free subsamle of more than thousand beauty quark events is obtained. he measurement delivers the highest data oint in Fig. 8 lus four other oints. he new H measurement [8] is comlementary, it is based on tagging events where both beauty quarks decay semiletonically with electrons in the final state. his double tagging technique allows to select events with very small beauty quark transverse momenta down to threshold. All the measurements shown in Fig. 8 are comared to the FMNR massive scheme NLO calculation. Both the new ZEUS and H measurements are reasonably well described by the calculation as is the large majority of the other measurements. he calculation is also shown (dashed line) with a factor two smaller renormalisation and factorisation scale µ. It should be noted that this smaller scale was for many years the standard choice and using it gave the imression that there might be some trend of theory undershooting data. However, since the scale choice is arbitrary such a conclusion is not warranted. Figure 9 shows from the same ZEUS analysis [7] as discussed above the measured cross sections as a function of the seudoraidity of the beauty tagged jet. Again a good descrition is observed by the FMNR massive NLO calculation, for both PDF sets tested. As for charm also for beauty roduction the very first results from LHC have become recently available. Figure shows the cross sections for b-jet roduction as measured [9] by CMS, using an inclusive secondary vertex tag method. he results are resented double differentially as function of the transverse momentum and the raidity of the tagged jet. In the covered region of transverse momenta from GeV to about 5 GeV the cross sections fall over seven orders of magnitude. he MC@NLO calculation, which is also shown, rovides a good descrition over most of the hase sace, with the excetion at highest in the not so central raidity bins where it exceeds the data. Figure 9: Differential cross sections for beauty jet roduction in hotoroduction at HERA as a function of the seudoraidity of the jet. he ZEUS data [7] are comared to the FMNR [] massive scheme calculations. dy (b/gev) σ/d b-jet d CMS reliminary, 6 nb MC@NLO ex. uncertainty Anti-k R=.5 PF y <.5 ( 5).5 y < ( 5) y <.5 ( 5).5 y < 4 b-jet s = 7 ev (GeV) Figure : Double differential Beauty-jet hadroroduction cross sections as function of the transverse momentum and the raidity of the tagged jet. he CMS data [9] are comared with the massive scheme MC@NLO [] redictions.

6 Olaf Behnke / Nuclear Physics B Proceedings Sulement () 6.. Charm roduction in DIS For charm roduction in dee inelastic scattering at HERA, in general a good descrition of the data by the massive NLO scheme redictions has been observed. Figure shows the recent H measurements [] of D meson roduction as a function of Q. Over the [nb/gev dσ / dq norm R ] H D* in DIS H data H D* (high Q ) HVQDIS (MSW8f) HVQDIS (Cf) Q [GeV ] Figure : Differential cross sections for D meson roduction in DIS as a function of the hoton virtuality Q. he H measurements [] are comared to the HVQDIS [] massive NLO calculations erformed with two different PDF sets. whole kinematic range, 5 GeV < Q < GeV, the data are well described by the HVQDIS [] massive NLO calculation, for both sets of roton PDFs tested. Figure resents for the same H analysis the obtained cross sections as a function of z(d ), which denotes the fraction of the hoton energy transferred in the roton rest frame to the D meson. At low z the HVQDIS re- dσ / dz(d*) [nb] norm R 5 5 H D* in DIS H data HVQDIS (MSW8f) HVQDIS (Cf) z(d*) Figure : Differential cross sections for D meson roduction in DIS as a function of the observable z (for exlanation see main text). he H measurements [] are comared to the HVQDIS [] massive NLO calculations erformed with two different PDF sets. diction clearly undershoots the data. his deficiency is the most significant one observed for charm roduction in DIS and has been observed in many analyses. he interretation of this effect is involved since the z observable is sensitive to both higher order erturbative corrections and to the hardness of the fragmentation rocess. Figure shows results from the same H analysis as a function of the event inelasticity y. Additional cuts dσ / dy [nb] norm R 5 5 H D* in DIS H data ZM-VFNS (CEQ6.6M) HVQDIS (Cf) y Figure : Differential cross sections for D meson roduction in DIS as a function of the event inelasticity y. he H measurements [] are comared to the HVQDIS [] massive NLO calculation and also to a zero mass variable flavour number scheme rediction []. have been alied here on the D transverse momentum in the γ centre-of-mass frame (D ) >. GeV. his facilitates a comarison of the data also to a rediction [] based on the zero mass variable flavour number scheme. As one can see this calculation redicts significantly too high cross sections at low values of y, corresonding to the threshold region. he massive NLO scheme calculation rovides a much better descrition of the data. Further interesting new measurements [] of charm and beauty jets in dee inelastic scattering using a secondary vertex tag are available from H. hey show that the massive scheme NLO QCD redictions (and testing several PDF sets used for the calculation) describe the data also in the resence of an additional hard scale rovided by the jet. From all charm analyses at HERA, the determination of the contribution of charm roduction to the total DIS rates is the one which is most in the focus of interest. his contribution is usually reresented by the structure function F c c, which is defined as the art of F due to events with charm quarks in the final state. Exerimentally one can measure charm roduction only in the accetance range of the detectors, which is limited to rather central raidities and usually to some minimum

7 Olaf Behnke / Nuclear Physics B Proceedings Sulement () 7 transverse momentum of the tagged charmed hadron. hus, in order to determine F c c, the measurements are extraolated from the visible to the total hase sace. he extraolation causes inevitably a further systematic uncertainty. he extraolation factors are determined using the NLO theory calculations and are tyically of order.5 or larger. Recently, the H and ZEUS collaborations combined [] their available F c c measurements based on various tagging techniques (using fully reconstructed charm mesons, muons from semiletonic decays or inclusive secondary vertex tags). For the combination a method of weighted averaging was alied, where arameters reresenting exerimental systematic uncertainties (e.g. calorimeter energy scales) are also fitted. his leads to an effective cross calibration of the two exeriments and thus to greatly reduced uncertainties. Figure 4 shows the F c c inut data and also the combined results, as a function of the Bjorken scaling variable x for various Q values. he imrovement of _ F cc. H and ZEUS Q = GeV Q = 4 GeV.5 Q = GeV Q = GeV Q = 6.5GeV.5 Q = 6GeV Q =GeV Q =GeV.5 Q =4GeV Q =GeV x Q = 5GeV HERA (rel.) October 9 HERA Heavy Flavour Working Grou MSW8 NNLO MSW8 NLO CEQ 6.6 GJR8 ABKM BMSN ABKM FFNS NLO ABKM FFNS NNLO _ F cc.5 Q =GeV -4 - Q =4GeV -4 - Q =6.5GeV -4 - October 9 Figure 5: he structure function F c c as a function of x for various Q values. he HERA combined results [] are comared to various QCD based redictions (for further details and references for the redictions see also []) Q = GeV - Q =6 GeV - - Q =4GeV - Q = GeV - - Q =GeV - - Q = GeV x Q =5 GeV - - Q =GeV HERA Heavy Flavour Working Grou - HERA (rel.) H D* HERA II (rel.) H D* HERA I H L HERA II (rel.) H L HERA I ZEUS µ 5 ZEUS D + 5 ZEUS D 5 ZEUS D* 99- ZEUS D* Figure 4: he structure function F c c as a function of x for various Q values. he HERA combined results are shown as well as the various searate inut data from H and ZEUS used for the combination. For better visual clarity the different inut data sets are offset horizontally from each other by small amounts. the uncertainties for the combined oints is evident, and a recision of about 5% is obtained over a large art of the hase sace. In Fig. 5 the combined F c c oints are comared to various theory models, using different schemes and orders in erturbation theory. It is obvious that the data have some ower to discriminate be- tween the various redictions. A dominant source of uncertainty for the calculations is the value of the charm quark mass arameter, which affects the F c c redictions esecially at low Q. As discussed in the talk [7] and documented in [4], the combined F c c data can be used to determine for the various schemes their otimal charm quark mass arameter values. his turns out to be helful to stabilise the PDF fits to the HERA inclusive neutral and charged current data such that the different scheme redictions for imortant LHC rocesses, e.g. W roduction, become much more consistent with each other. In Fig. 6 further recent F c c measurements [5] by ZEUS are shown, which have not yet been used in the combination with H. he data are comared to the redictions based on the HERAPDF. [6] PDF set. his set was obtained from fitting the flavour inclusive neutral and charged current data from the HERA I eriod, i.e. without using any F c c measurements. Within the theory uncertainties, dominated by the charm quark mass value, the rediction describes the F c c data very well. In the first lace this demonstrates the universality of the gluon density obtained from the scaling violations of F with the one that drives charm roduction. his universality is exected from the QCD factorisation theorem. From the new F c c results one can ex-

8 Olaf Behnke / Nuclear Physics B Proceedings Sulement () 8 ZEUS (b / GeV) jet dσ / de ZEUS (rel.) 54 b HVQDIS hadr rad Raga x.6 e e bbx e jet X jet E (GeV) Figure 6: he structure function F c c as a function of x for various Q values. he new reliminary ZEUS data [5], based on D and D + meson tags are shown together with the HERA combined results resented already in Fig. 5. Also shown are the QCD redictions based on the HERAPDF. [6] set. ect another significant imrovement towards the final HERA combined F c c data which will rovide one of the most imortant legacies from HERA in the domain of heavy flavour hysics..4. Beauty roduction in DIS he domain of beauty roduction in DIS concludes our survey of oen heavy flavour roduction at HERA. Figure 7 shows new ZEUS results [7] on beauty jet roduction, as a function of the jet transverse momentum. he analysis is based on the same inclusive secondary vertex tagging method as used in the hotoroduction measurement (see Fig. 9). he resulting measurements are the most recise ones so far. As shown in Fig. 7 the massive scheme HVQDIS calculation describes the data adequately over the large momentum range covered. Also for beauty roduction the contribution to the total DIS cross section, reresented by the structure function F b b, is at the centre of attention. Of articular interest are high values of Q where one can measure with F b b an effective beauty sea quark density in the roton. his can be used for redictions of many interesting rocesses at LHC with beauty quarks in the initial state. For instance, as discussed in [9], in the minimal suersymmetric extension of the standard model the roduction data / HVQDIS jet E (GeV) Figure 7: Differential cross sections for beauty roduction in DIS as a function of the transverse energy of the beauty hadron jet. he ZEUS data [7] are comared to the HVQDIS [] massive NLO calculations as well as to scaled RAPGAP [8] MC redictions. of the neutral Higgs boson A is driven by b b A and for the calculation of this rocess the PDF uncertainties dominate over the theoretical uncertainties of the erturbative calculation. Figure 8 shows a comilation [] of the HERA F b b results, based on semiletonic and/or inclusive secondary vertex tags of beauty hadrons in the final state. he data are described by the various model redictions. It is a most imortant task, to be yet erformed, to combine the various F b b data from H and ZEUS. his will allow to achieve the best recision and thus to test the theory redictions at a new level of quality.. Conclusion and outlook In this review it was shown that oen charm and beauty roduction rovide a most intriguing testing ground for erturbative QCD. he extra hard scale ro-

9 Olaf Behnke / Nuclear Physics B Proceedings Sulement () 9 +. i bb F HERA. ZEUS (rel.) vtx 54 b x=. i=7 x=. i=6 x=.5 i=5 x=. i=4 x=. i= x=.5 i= x=. i= x=. i= ZEUS e 6 b ZEUS µ 4 b ZEUS µ+vtx 6 b H vtx 46 b ZEUS-S+HVQDIS ABKM NNLO MSW8 NLO MSW8 NNLO CEQ6.6 NLO JR9 Q (GeV Figure 8: he structure function F b b as a function of Q for various x values. he measurements [] from H and ZEUS, based on various beauty hadron tagging techniques, are comared to different QCD redictions (for references see also []). vided by the heavy quark masses comlicates the theory calculations since it leads to mixed terms in the erturbation series such as (α s ln(q /m )) n which aear at all orders n. At HERA it was ossible to study this battle of the scales over a wide range, from the threshold region, where the kinematic scales Q and/or the transverse momenta of the roduced heavy quarks are close to zero GeV, u to the region of about 5 GeV, much above the charm and beauty quark masses. Across the full kinematic range, the massive scheme NLO calculations rovide a reasonable descrition of the charm and beauty roduction data with excetions in some hase sace corners. hat the massive calculations have not yet been observed to break down in the HERA kinematic region was anticiated by many the- ) orists, see for instance the discussion in []. Unfortunately, to this day, NLO rograms are available (FMNR and HVQDIS) only for the massive scheme, which can calculate differential cross sections for any kinematical configuration of the outgoing hard artons (u to three artons at NLO). he redictions based on these arton level calculations have one weakness that should be mentioned here. So far the hadronisation rocess for these calculations has been modelled by rather simle models, such as the Peterson [] fragmentation function with fixed arameters indeendent of the hard scale. he resent calculations in the massless or generalised variable flavour number schemes can either rovide redictions for total DIS cross sections (see next aragrah) or for single inclusive article sectra. Where alicable, such NLO or NNLO redictions did in most cases not lead to an imrovement but rovided a similar or sometimes even worse descrition of the HERA data. he measurements of the charm and beauty quark roduction contributions to the total DIS cross sections, reresented by the structure functions F c c and Fb b, rovide the most imortant legacy of all heavy flavour measurements at HERA. hey contain most valuable information for the PDF fits at HERA, for instance F c c is imortant for determining values of the charm quark mass arameters used in the fits. After the very successful hysics rogram at HERA there are ideas for future electron-roton colliders. One of them is the Electron-Ion Collider (EIC) [] which is at resent under discussion in the US. he EIC is lanned to be oerated with a factor or lower centreof-mass energy comared to HERA, but with times larger luminosity and with olarised rotons and nuclei. Heavy flavour roduction at the EIC will be helful as a secific hard robe that can be used to test arton saturation effects that are exected at low x, in articular in heavier nuclei. Another intriguing roject is the LHeC [4] collider. Here the idea is to collide the LHC rotons with electron beams of energies between 5 and 5 GeV, deending on the accelerator design. he LHeC would be a worthy successor of HERA with a factor -5 higher centre-of-mass energy and also much larger integrated luminosity. On to of this the heavy flavour measurements will greatly benefit from the advanced detector design at LHeC with high recision (Silicon or similar) trackers all over the lace. At HERA, the tagging of heavy flavours was restricted to central raidities and effective efficiencies of he effective efficiency takes the background ollution into account. It is defined as the efficiency of an equivalent background free samle with the same signal recision as that obtained in the data.

10 Olaf Behnke / Nuclear Physics B Proceedings Sulement () F cc x 4 i only.% (few%) for charm (beauty) were reached. At LHeC much higher efficiencies can be exected. Figure 9 shows the LHeC exected results for the structure function F c c, obtained with the RAPGAP [8] Monte Carlo rogram. he rojected LHeC data are LHeC F cc (RAPGAP MC, 7 ev x GeV, fb, ε c =.) Q = GeV,i=4 Q = GeV,i= Q = 4 GeV,i= Q = GeV,i= Q = GeV,i=6 Q = 6 GeV,i=5 Q = GeV,i=8 Q = 4 GeV,i=7 HERA combined data LHeC θ c > LHeC θ c > LHeC θ c > Q = 5 GeV,i= Q = GeV,i=9 Q = GeV,i= Figure 9: F cc rojections for LHeC comared to a subset of the combined HERA data [], as a function of x for various Q values. he exected LHeC results obtained with the RAPGAP MC simulation are shown as oints with error bars reresenting the statistical uncertainties. he dashed lines are interolating curves between the oints. For the oen oints the detector accetance is assumed to cover the whole olar angular range. For the grey shaded and black oints, events are only acceted if at least one charm quark is found with olar angles θ c > and θ c >, resectively. he combined HERA results from H and ZEUS are shown as triangles with error bars reresenting their total uncertainty. resented as oints with error bars which (where visible) indicate the estimated statistical uncertainties. For the oen oints the detector accetance is assumed to cover the whole olar angle range. For the grey shaded and black oints events are only acceted if at least one charm quark is found with olar angles θ c > and θ c >, resectively. Also shown in the Figure is a large subset of the combined HERA F c c results [], which were already resented above (see Fig. 5). As one can see, the LheC will allow easily a large extension in hase sace towards much smaller x values. he statistical uncertainties are in a large region smaller than %. he reach towards large x deends crucially on the caability to detect charm quarks in the very forward region. Similar hase sace increases are exected for x F bb x 4 i the measurement of F b b as shown in Fig.. Here the rojected LHeC data are comared to the H measurements [5] LHeC F bb (RAPGAP MC, 7 ev x GeV, fb, ε b =.5) Q = 5 GeV,i=4 Q = GeV,i= Q = 5 GeV,i= Q = GeV,i= Q = GeV,i=6 Q = 6 GeV,i=5 H vtx DAA LHeC θ b > LHeC θ b > LHeC θ b > Q = GeV,i=8 Q = 65 GeV,i=7 Q = 5 GeV,i= Q = GeV,i= Q = GeV,i= Figure : F bb rojections for LHeC comared to H data [5], as a function of x for various Q values. he exected LHeC results obtained with the RAPGAP MC simulation are shown as oints with error bars reresenting the statistical uncertainties. he H results are shown as triangles with error bars reresenting their total uncertainty. For further details see the cation of Fig. 9. LHeC will be also the first e-collider where the roduction of to quarks can be studied. For more hysics study results see the web ages [4]. 4. Bibliograhy References [] E. Laenen, S. Riemersma, J. Smith and W.L. van Neerven, Nucl. Phys. B 9 (99) 6; E. Laenen, S. Riemersma, J. Smith and W.L. van Neerven, Nucl. Phys. B 9 (99) 9; S. Riemersma, J. Smith and W.L. van Neerven, Phys. Lett. B 47 (995) 4 [he-h/944]. [] S. Frixione, P. Nason and G. Ridolfi, Nucl. Phys. B 454 (995) [he-h/9566]; S. Frixione, M. Mangano, P. Nason and G. Ridolfi, Phys. Lett. B 48 (995) 6. [] B.W. Harris and J. Smith, Nucl. Phys. B 45 (995) 9 [he-h/95484]. [4] S. Alekhin, these roceedings. [5] B.A. Kniehl, M. Krämer, G. Kramer and M. Sira, Phys. Lett. B 56 (995) 59 [he-h/9554]; B.A. Kniehl, G. Kramer and M. Sira, Z. Phys. C 76 (997) 689 [he-h/9667]; x

11 Olaf Behnke / Nuclear Physics B Proceedings Sulement () J. Binnewies, B.A. Kniehl and G. Kramer, Z. Phys. C 76 (997) 677 [he-h/9748], Phys. Rev. D 58 (998) 44 [he-h/9748]; M. Cacciari and M. Greco, Phys. Rev. D 55 (997) 74 [he-h/9789]. [6] F.I. Olness and W.K. ung, Nucl. Phys. B 8 (988) 8; M.A.G. Aivazis, J.C. Collins, F.I. Olness and W.K. ung, Phys. Rev. D 5 (994) [he-h/99]; M.A.G. Aivazis, F.I. Olness and W.K. ung, Phys. Rev. D 5 (994) 85 [he-h/98]; M. Kramer, F.I. Olness and D.E. Soer, Phys. Rev. D 6 () 967 [he-h/5]; R.S. horne and R.G. Roberts, Phys. Rev. D 57 (998) 687 [he-h/97944], Phys. Lett. B 4 (998) [he-h/97]; Eur. Phys. J. C 9 () 9 [he-h/44]; G. Kramer and H. Siesberger, Eur. Phys. J. C 8 (4) 9; B.A. Kniehl, G. Kramer, I. Schienbein and H. Siesberger, Phys. Rev. D 7 (5) 48. [7] K. Lika, these roceedings. [8] ZEUS Collaboration, Submitted to st International Conference on High Energy Physics, ICHEP,, Amsterdam, Abstract 786. [9] M. Cacciari, M. Greco and P. Nason, JHEP 985 (998) 7 [he-h/984]; M. Cacciari, S. Frixione and P. Nason, JHEP () 6 [he-h/4]. [] H Collaboration, Hrelim-8-7, web age: htt://www-h.desy.de/sfiles/confa/dis8 /Hrelim-8-7.s. [] ALAS Collaboration, Conference note ALAS-CONF- 7. [] S. Frixione, P. Nason and B.R. Webber, JHEP 8 () 7 [he-h/55]. [] P. Nason, JHEP 4 (4) 4 [he-h/4946]. [4] H Collaboration, Hrelim--7, web age: htt://www-h.desy.de/h/www/ublications/ htmlslit/hrelim--7.long.html. [5]. Sjöstrand, Comut. Phys. Commun. 9 (986) 47;. Sjöstrand and M. Bengtsson, Comut. Phys. Commun. 4 (987) 67;. Sjöstrand et al., Comut. Phys. Commun. 5 () 8 [he-h/7]. [6] S. Chekanov et al. [ZEUS Collaboration], Phys. Lett. B 565 () 87 [he-ex/5]. [7] H. Abramowicz et al. [ZEUS Collaboration], Eur. Phys. J. C 7 () 659 [arxiv: [he-ex]]. [8] H Collaboration, Hrelim-7, web age: htt://www-h.desy.de/h/www/ublications /htmlslit/hrelim-7.long.html. [9] CMS Collaboration, Conference note CMS-PAS-BPH--9. [] F.D. Aaron et al. [H Collaboration], Eur. Phys. J. C 7 () 769 [arxiv:6.8 [he-ex]]. [] G. Heinrich and B.A. Kniehl, Phys. Rev. D 7 (4) 945 [he-h/49]. [] F.D. Aaron et al. [H Collaboration], Eur. Phys. J. C 7 () 59 [arxiv:8.7 [he-ex]]. [] H and ZEUS Collaborations, Hrelim-97, ZEUS-rel- 95, web age: htts:// heavy_flavours/h_zeus_fc_relim.s. [4] H and ZEUS Collaborations, Hrelim-4, ZEUS-rel- 9, web age: htt:// heavy_flavours/mcscan/charmfit.df. [5] ZEUS Collaboration, ZEUS-rel, web age: htt://www-zeus.desy.de/hysics/hfla/ublic/ PublicPlots/Zeus-rel/es_charm.df. [6] F.D. Aaron et al. [H and ZEUS Collaboration], JHEP () 9 [arxiv:9.884 [he-ex]]. [7] ZEUS Collaboration, ZEUS-rel--4, web age: htt://www-zeus.desy.de/hysics/hfla/ublic/ PublicPlots/Zeus-rel--4/fb_iche.df. [8] H. Jung, Comut. Phys. Commun. 86 (995) 47. [9] A. Belyaev, J. Pumlin, W.K. ung and C.P. Yuan, JHEP 6,(6) 69 [arxiv:he-h/58]. [] R. Shehzadi [for the ZEUS Collaboration], arxiv:9.478 [he-ex]. [] A. Chuvakin, J. Smith and W.L. van Neerven, Phys. Rev. D 6 () 964 [he-h/995], Phys. Rev. D 6 () 64 [he-h/]. [] C. Peterson, D. Schlatter, I. Schmitt and P.M. Zerwas, Phys. Rev. D 7 (98) 5. [] EIC Collaboration, web age: htt://web.mit.edu/eicc/ [4] he LHeC roject web age: htt:// [5] F.D. Aaron et al. [H Collaboration], Eur. Phys. J. C 65 () 89 [arxiv:97.64 [he-ex]].