Hera Precision Measurements and Impact for LHC Predictions
HHERA PRECISION MEASUREMENTS AND IMPACT FOR LHCPREDICTIONS
V. Radescu on behalf of the H1 and ZEUS Collaborations
Heidelberg Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
A QCD fit analysis to the combined HERA inclusive deep inelastic cross sections measured bythe H1 and ZEUS collaborations for e ± p scattering to extract HERAPDF sets is presented.The results are used for predictions of p ¯ p processes at Tevatron and pp processes at theLHC. The QCD analysis has been extended to include the combined HERA II measurementsat high Q resulting in the HERAPDF1.5 sets, with full estimation of uncertainties. Theprecision of the new PDFs at high x is considerably improved, particularly in the valencesector. In addition, inclusion of the HERA jet data allows for a precise determination of thestrong coupling. Moreover, inclusion of the preliminary combined HERA charm data providesconstraints for the optimal value of the charm mass used in QCD theory models which mayaccount for some of the differences among global PDF fits. The main information on proton structure functions comes from the Deep Inelastic Scattering(DIS) collider experiments H1 and ZEUS at HERA. Measurements at HERA go well beyondthe phase space accessible by fixed target experiments with an extended kinematic range of0 . < Q <
30 000 GeV and 6 × − < x < .
65. To further benefit from the precision of themeasurements the H1 and ZEUS cross sections are combined, resulting in the most consistentand precise DIS inclusive double differential cross-section measurement of neutral and chargedcurrent e ± p scattering to date . The data combination ”procedure” has been repeated toinclude as well the preliminary high precision measurements at high Q from the second runperiod of HERA. Therefore, these accurate measurements can be used as the sole input to theQCD analysis to determine the proton parton distribution functions (PDFs) as described in thefollowing sections, which can be used then for precise predictions for LHC processes. a r X i v : . [ h e p - e x ] J u l QCD Analysis settings
HERA PDFs are determined from QCD fits to HERA data alone. Only the region whereperturbative QCD is valid, data above Q = 3 . are used in the central fit. The HERAdata have a minimum invariant mass of the hadronic system, W , of 15 GeV, such that they arein a kinematic region where there is no sensitivity to non-perturbative effects common to fixedtarget data.The fit procedure starts by parametrising PDFs at a starting scale Q = 1 . , chosento be below the charm mass threshold. The QCD settings are optimised for HERA measure-ments of proton structure functions which are dominated by gamma exchange, therefore theparametrised PDFs are the valence distributions xu v and xd v , the gluon distribution xg , andthe u -type and d -type sea quark distributions x ¯ U , x ¯ D , where x ¯ U = x ¯ u , x ¯ D = x ¯ d + x ¯ s . Us-ing a simple parametrisation form with the normalisation parameters constrained by the QCDsum-rules and relying on additional assumptions the number of free paramaters reduces to 10for the fits to HERA I data. However, the more data become available, the more constrainingassumptions can be released, therefore the number of free parameters once HERA II data areadded is increased, allowing for more freedom to the gluon and valence distributions, HER-APDF1.5f. For example addition of the preliminary combined charm data, or jet data fromH1 , and ZEUS , allows for more flexibility of the gluon distribution. The PDFs are thenevolved using the DGLAP evolution equations at NLO and NNLO in the M S scheme withthe renormalisation and factorisation scales set to Q . The QCD predictions for the structurefunctions are obtained by convoluting the PDFs with the calculable coefficient functions tak-ing into account mass effects for the heavy quarks based on the general mass variable flavourscheme . The PDF uncertainties at HERA are classified in three categories: experimental,model, and parametrisation. The consistency of the input data set and its small systematicuncertainties enables us to calculate the experimental uncertainties on the PDFs using the χ tolerance ∆ χ = 1. The model uncertainties are evaluated by varying the input assumptions,as performed in . The parametrisation uncertainty is estimated as an envelope which is formedas a maximal deviation at each x value from the central fit. The inclusion of the precise high Q preliminary HERA II data in the QCD fits results inHERAPDF1.5. Figure 1 shows the comparison between HERAPDF1.5 and HERAPDF1.0 whichis based on HERA I data alone. The impact is noticeable especially in the high x region, wherethe valence contribution dominates. In addition, a meticulous study has been performed toestimate the uncertainties for the NNLO HERAPDF set, also shown in Figure 1, where the newNNLO set is compared to the HERAPDF1.0 NNLO. To answer the question about implicationsof the new PDF sets on the Higgs exclusion limits from Tevatron, Figure 2 shows a more explicitcomparison of the gluon distribution at high x between HERAPDF and MSTW08 sets at NNLO.The HERAPDF1.5 NNLO set yields a harder gluon at high x compared to the HERAPDF1.0NNLO set, which is prefered by the Tevatron jet data. The differences are mostly due to theuse of a more flexible functional form made possible via the availability of a more precise data.Another important result is related to the determination of the strong coupling. New resultsfrom HERA based solely on the inclusive DIS measurements can not yet pin down the value of α S as shown in Figure 2 (right), where a scan in χ as function of strong coupling is shown.However, as soon as the jet data are included in the QCD fit, resulting in HERAPDF1.6, itcan be seen that the strong coupling is well constrainted. In fact, the addition of the HERAjet data into the fit allows the strong coupling and gluon to be simultaneously constrained.Figure 3 shows the impact of the inclusion of the jet data on the gluon distribution when the fits performed with the strong coupling as a free parameter. As a result, the HERA data prefer arather larger value for α S ( M Z ) = 0 . ± . ± . ± . +0 . − . (th).In addition, the inclusion of the preliminary HERA charm data provides constraints for theoptimal value of the charm mass used in theory models. It has been observed that QCD fitswithout charm data have only a small sensitivity to the value of the charm mass. However,there is a strong preference for a particular m c once charm data is included. This study hasbeen performed for various schemes, such as those used in the global fit analyses of MSTW08and CTEQ. The results conclude that each scheme describes the data well at the correspondingbest value of the m c . It is interesting to observe that differences in the PDF sets correspond todifferences in the charm mass used in different schemes .All HERAPDF sets derived solely from ep measurements are able to give a good predictionof the Z and W at Tevatron from the p ¯ p processes, and provide a competitive description to pp processes at the LHC as well. -4 -3 -2 -1
10 100.20.40.60.81 HERAPDF1.0 (HERA I) HERAPDF1.5 (HERA I+II) x x f = 10 GeV Q v xu v xd 0.05) × xS ( 0.05) × xg ( H E R A S t r u c t u r e F un c ti on s W o r k i ng G r oup J u l y H1 and ZEUS Combined PDF Fit -4 -3 -2 -1
10 100.20.40.60.81 HERAPDF1.5 NNLO (prel.) exp. uncert. model uncert. parametrization uncert. HERAPDF1.0 NNLO(prel.) x x f = 10 GeV Q v xu v xd 0.05) × xS ( 0.05) × xg ( H E RA P D F S t r u c t u re F un c t i o n W o r k i n g G r o up M a rc h H1 and ZEUS HERA I+II PDF Fit
Figure 1: On the left hand side: the comparison between HERAPDF1.0 (light colour) based on the HERA I dataand HERAPDF1.5 (dark colour) based on the HERA I and II data, using the total uncertainty band at Q = 10GeV with gluon, sea (which are scaled by a factor of 0.05) and valence distributions. On the right hand side: thesummary plot for HERAPDF1.5 at Q = 10 GeV at NNLO with the uncertainties including the experimental(red), model (yellow) and the PDF parametrisation (green), compared to the central fit for HERAPDF1.0 atNNLO. HERA provides accurate determinations of the proton structure and can predict related Stan-dard Model processes. Additional preliminary combined measurements from HERA II allow thehigh x region to be better constrained resulting in a more precise HERA PDF set, HERAPDF1.5at NLO and NNLO in α S with a detailed analysis of the uncertainties. The HERAPDF sets,which are based solely on ep data also describe the Tevatron data well and provide competitivepredictions to the LHC processes. Inclusion of the HERA jet data allows for a precise deter-mination of the strong coupling, for which HERA data prefers a rather larger value of α S . Inaddition, inclusion of the preliminary combined HERA charm data provides constraints on theoptimal value for the charm mass used in theory models and it may account for some of thedifferences among global PDF fits. Therefore, HERAPDF provides a large variety of meticulousstudies based on new measurements from HERA for accurate predictions at the LHC . Z (M S (cid:95) m i n (cid:114) - (cid:114) H1 and ZEUS (prel.)HERAPDF1.5fHERAPDF1.6 H E RA P D F S t r u c t u r e Fun c t i on W o r k i ng G r oup M a r c h Figure 2: On the left hand side: the gluon distribution from the HERAPDF sets (based on HERA I only -HERAPDF1.0, and based on HERA I+II, HERAPDF1.5) to MSTW08 at NNLO in the high x region. On theright hand side: the ∆ χ distribution as a function of the value of α S ( M Z ) in the PDF fits for HERAPDF1.5f(dashed line) without jet data and HERAPDF1.6 (solid line) with jet data. -4 -3 -2 -1
10 100.20.40.60.81 HERAPDF1.5f (prel.) ) Z (M s (cid:95) free exp. uncert. model uncert. parametrization uncert. x x f = 10 GeV Q v xu v xd 0.05) × xS ( 0.05) × xg ( H E RA P D F S t r u c t u re F un c t i o n W o r k i n g G r o up M a rc h H1 and ZEUS HERA I+II PDF Fit -4 -3 -2 -1
10 100.20.40.60.81 HERAPDF1.6 (prel.) ) Z (M s (cid:95) free exp. uncert. model uncert. parametrization uncert. x x f = 10 GeV Q v xu v xd 0.05) × xS ( 0.05) × xg ( v xu v xd 0.05) × xS ( 0.05) × xg ( H E RA P D F S t r u c t u re F un c t i o n W o r k i n g G r o up M a rc h H1 and ZEUS HERA I+II PDF Fit with Jets
Figure 3: Summary plot for HERAPDF1.5f (left) and HERAPDF1.6 (right) as a function of x for Q = 10 GeV .The strong coupling constant α S ( M Z ) is a free parameter in both fits. The central values of the PDFs (solidlines) are shown together with the experimental, model and parametrisation uncertainties represented by the red,yellow and green shaded bands, respectively. References
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9. The LHAPDF grid files are located at9. The LHAPDF grid files are located at