This contribution reviews the QCD analysis of the H1 inclusive DIS data. Flavor separated parton densities are extracted in a NLO QCD fit using neutral and charged current HERA I data. The results of a dedicated QCD analysis of the gluon and $\alpha_s$ are also reviewed

Portheault, B

arXiv

Proceedings of the DIS'2004, Strbske Pleso, SlovakiaThis contribution reviews the QCD analysis of the H1 inclusive DIS data. Flavor separated parton densities are extracted in a NLO QCD fit using neutral and charged current HERA I data. The results of a dedicated QCD analysis of the gluon and $\alpha_s$ are also reviewed

Portheault, Benjamin

HAL-IN2P3

H1 QCD analysis of inclusive cross section dataBenjamin PortheaultTo cite this version:Benjamin Portheault. H1 QCD analysis of inclusive cross section data. Apr 2004, StrbskePleso. <hal-00003228>HAL Id: hal-00003228https://hal.archives-ouvertes.fr/hal-00003228Submitted on 5 Nov 2004HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.ccsd-00003228, version 1 - 5 Nov 2004Proceedings of the DIS’2004, Sˇtrbske´ Pleso, SlovakiaH1 QCD ANALYSIS OF INCLUSIVE CROSS SECTION DATABENJAMIN PORTHEAULTOn behalf of the H1 collaborationLaboratoire de l’Acce´le´rateur Line´aireIN2P3-CNRS et Universite´ de Paris Sud,F-91898 Orsay CedexE-mail: portheau@lal.in2p3.frThis contribution reviews the QCD analysis of the H1 inclusive DIS data. Flavorseparated parton densities are extracted in a NLO QCD fit using neutral andcharged current HERA I data. The results of a dedicated QCD analysis of thegluon and αs are also reviewed.At leading order in the electroweak interaction, the double differential crosssection of inclusive Deep Inelastic Scattering (DIS) can be expressed in terms ofstructure functionsd2σ±NCdxdQ2=2piα2xQ4[Y+F˜2 − y2F˜L ∓ Y−xF˜3], (1)for Neutral Currents (NC) where Y± = 1 ± (1 − y)2, and similarly for ChargedCurrent (CC)d2σ±CCdxdQ2=G2F4pix[M2WQ2 +M2W]2 [Y+FCC±2 − y2FCC±L∓ Y−xFCC±3], (2)where the structure functions exhibit a dependency upon the incoming leptoncharge. The QCD factorization theorem allows the separation of the long dis-tance physics and the short distance physics, such that the structure functions canbe expressed as convolutions of universal parton distributions (pdfs) and pertur-batively computable kernels. The QCD analysis (the so-called “QCD fits”) aimsat extracting the pdfs through the QCD evolution. It is also possible to extractany parameter entering in the expression of the cross section, such as the strongcoupling constant αs.1 The H1 inclusive cross section measurementThe published H1 data from the HERA I data taking covers a large range in x andQ2. The inclusive NC DIS cross sections are measured to an accuracy of 1–2 % forstatistical uncertainty and 2–3 % of systematic uncertainty. This gives a stringentconstraint on F2 ∝ 4(u + u¯) + d + d¯ over the low and medium x regions. Large xand Q2 data are sensitive to the valence densities, but further statistics are neededto fully exploit this constraint. The wide Q2 range covered allow to constraint αsgfrom scaling violations. For the inclusive CC cross section, constant progress inc© Institute of Experimental Physics SAS, Kosˇice, Slovakia 12 Benjamin Portheaultunderstanding the detectors helped to reduce the systematic uncertainties to about6 % but the data are still limited by the statistical error at large x and Q2. Onecan define a reduced CC cross sectionσ˜±CC=2pixG2F[Q2 +M2WM2W]2d2σ±CCdxdQ2(3)which reads at the lowest orderσ˜+CC= x[u¯+ c¯+ (1 − y)2(d+ s)]and σ˜−CC= x[u+ c+ (1 − y)2(d¯+ s¯)]. (4)The measured σ˜−CCand σ˜+CCprovide thus a unique constraint on large x for u andd densities, respectively.2 QCD analysis and extraction of parton densitiesAll the H1 high Q2 NC and CC data [1,2,3] together with the low Q2 data [4] areused to extract flavor separated parton densities in a NLO QCD analysis [3] in theso-called massless scheme. The understanding of systematic correlations betweenthe data allows to make reliable error propagation with the Pascaud–Zomer χ2method[5]. To disentangle the different flavors a novel decomposition anzats hasbeen set up which makes use of the flavor combination of the inclusive data: thedistributions U = u + c and D = d + s which appear in the NC and CC inclusivecross section with the gluon and the charge conjugate U,D are parameterized atinput scale Q20 = 4 GeV2 and evolved. A procedure to explore the parameterizationspace has been set up and led to a solution with ten free parameters and χ2/ndof =540/(621− 10) = 0.88. As a result of the fit, the U distribution precision is 1% forx = 0.001 and 7% for x = 0.65. The D distribution precision is 3% for x = 0.001and 30% for x = 0.65. Results for the input distributions atQ2 = 4 GeV2 are shownon Fig. 1. A “model” uncertainty is estimated by variation of the parameters thatenters in the modelisation of the QCD analysis, such as the input scale Q20, thestrange and charm components of D and U , the heavy quark thresholds and thestrong coupling constant αs(M2Z). Further detail about the analysis can be foundin [3].3 Determination of the gluon and αsAnother QCD analysis [4] dedicated to the determination of the strong couplingconstant αs(M2Z) and the gluon density was performed in a NLO massive schemeusing the H1 low Q2 96–97 data [4], the 94–97 high Q2 data [1] and the BCDMSµp DIS data [6]. The results are shown on Fig. 2. The result is αs = 1.1150 ±0.0019(exp)±0.005(th) where the theoretical error corresponds to variations of therenormalisation and factorisation scales. The experimental error is small, ∼ 1%and the theoretical error is expected to be reduced by factor of ∼ 3 in a NNLOQCD analysis.H1 QCD analysis of inclusive cross section data 300.20.40.60.800.20.40.60.810 -3 10 -2 10 -1 1024610 -3 10 -2 10 -1 1xP(x)xuvxUxUxdvxDxxDH1 CollaborationxxgH1 PDF 2000:  Q2 = 4 GeV2Fit to H1 dataexperimental errorsmodel uncertaintiesFit to H1 + BCDMS dataparton distributionFigure 1. Parton distributions xU , xU , xD, xD and xg as determined from the H1PDF2000 fitto H1 data only. The inner error band represents the experimental uncertainty, the outer errorband shows the total uncertainty obtained by adding in quadrature the experimental and modeluncertainty. For comparison, the parton distributions from the fit to H1 ep and BCDMS µp andµd data are shown as solid line.4 ConclusionThe determination of flavor separated parton densities form H1 data only and theextraction of the strong coupling αs and the gluon density are major achievementsof the HERA I physics. Further extension to this work – beside the inclusion ofHERA II data or a future NNLO analysis – could be an inclusion of jet and/orinclusive heavy flavor production data which provide additional constraints on themedium x gluon density.4 Benjamin PortheaultH1 CollaborationH1 CollaborationFigure 2. The left plot shows the total χ2 for the fits of H1 only, BCDMS only and H1+BCDMSfits. The right plot shows the gluon distribution at Q2 = 5 GeV2. Beside the experimental error,one sees the error due to the αs uncertainty and the total uncertainty which include the theoreticaluncertainty coming from variations of the renormalisation and factorisation scale.References1. C. Adloff et al. [H1 Collaboration], Eur. Phys. J. C 13, 609 (2000) [arXiv:hep-ex/9908059].2. C. Adloff et al. [H1 Collaboration], Eur. Phys. J. C 19, 269 (2001) [arXiv:hep-ex/0012052].3. C. Adloff et al. [H1 Collaboration], Eur. Phys. J. C 30 (2003) 1 [arXiv:hep-ex/0304003].4. C. Adloff et al. [H1 Collaboration], Eur. Phys. J. C 21 (2001) 33 [arXiv:hep-ex/0012053].5. C. Pascaud and F. Zomer, LAL 95-05.6. A. C. Benvenuti et al. [BCDMS Collaboration], Phys. Lett. B 223, 485 (1989).

H1 QCD analysis of inclusive cross section data

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H1 QCD analysis of inclusive cross section data

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