NLO QCD Fit Research Articles

COMPASS results on proton longitudinal spin structure function g1and quark fragmentation functions

We present a few recent highlights from the COMPASS experiment at CERN, related to the nucleon spin and structure: the proton spin structure function g1 p (x) measured using 200 GeV polarized muons, together with a QCD fit of g1 world data; pion and kaon multiplicities in DIS in view of constraining quark fragmentation functions.The statistical precision on g1 p is improved by a factor of ~2 at low x. A reevaluation of the Bjorken sum rule based on COMPASS data alone confirms its validation within 9% accuracy. An NLO QCD fit to g1 world data leads to a value of the quark spin contribution to the nucleon spin ΔΣ, between 0.26 and 0.36 at Q2 = 3 (GeV/c)2 , the size of the uncertainty being driven by the unknown shape of the polarized parton distributions.The results on pion and kaon multiplicities produced in DIS of muons off an isoscalar target constitute an impressive data set of more than 400 points in π and 400 in K, covering a large kinematical domain in (x, z, Q2 ), which will be used in future NLO QCD fits to extract quark fragmentation functions into π and K. A LO fit is performed to extract the favoured and unfavoured quark fragmentation functions into pions.

Results on longitudinal spin physics at COMPASS

The COMPASS experiment at the CERN SPS has taken data on deep inelastic scattering of polarised muons on a polarised NH3 target in 2007 and 2011 and on a polarised LiD target in 2002–2004 and 2006. The new results on the longitudinal double spin asymmetry A 1 p and the spin-dependent structure function g 1 p obtained from the 2011 data set are presented. These results are used in a NLO QCD fit to the world data to obtain the polarised parton distributions. Also an update of the results on the Bjorken sum rule, connecting the integral of the non-singlet spin-dependent structure function with the ratio of the weak coupling constants, will be given.Direct access to the gluon polarisation is possible via the photon gluon fusion process in semi-inclusive deep inelastic scattering. This process is studied using the p T dependence of charged hadron asymmetries. The latest results indicate a positive gluon polarisation in the kinematic region of COMPASS

Compass Measurement of g1 and QCD Fits

We present the latest COMPASS results on the proton spin structure function g[Formula: see text](x) at 200[Formula: see text]GeV. The data improve the statistical precision by a factor of [Formula: see text]2 at low x. A reevaluation of the Bjorken sum rule based on COMPASS proton and deuteron data confirms its validation to a 9% accuracy. Finally, results from a global NLO QCD fit of g1 world data are shown. The extracted spin singlet distribution leads to an integrated value of [Formula: see text] at Q[Formula: see text] (GeV/c)2. The large uncertainty is mainly driven by the unknown shape of the distribution.

Results on longitudinal spin physics at COMPASS

The COMPASS experiment at the CERN SPS has taken data for deep inelastic scattering of polarised muons off a polarised NH3 target in 2007 and 2011 and off a polarised 6LiD target in 2002–2004 and 2006.We present our new results on the longitudinal double spin asymmetry A1p and the spin-dependent structure function g1p obtained from the 2011 data set. These results are used in a NLO QCD fit to the world data to obtain the polarised parton distributions. Also an update on our results on the Bjorken sum rule, connecting the integral of the non-singlet spin-dependent structure function with the ratio of the weak coupling constants, is given.The gluon polarisation can be accessed directly via the photon gluon fusion process in semi-inclusive deep inelastic scattering. This process is studied using the pT dependence of charged hadron asymmetries. The latest results indicate a positive gluon polarisation in the kinematic region of COMPASS.

New COMPASS results on [formula omitted] and [formula omitted] and QCD fit

During its 2011 data taking campaign, the COMPASS experiment at CERN has collected data of 200 GeV polarised muons scattering off a target with polarised protons. These data allow the extension of the phase-space coverage of the COMPASS data obtained in 2007 with a beam of 160 GeV polarised muons, namely to access lower values of x for any given value of Q2.The data in the DIS region were used to extract the longitudinal double spin asymmetry A1p and the spin dependent structure function g1p. Thereafter, our world data NLO QCD fits of polarised parton distributions were updated. It was also possible to improve our test on the Bjorken sum rule.The asymmetries A1p and the structure function g1p were likewise extracted from the two beam energy data sets for Q2<1(GeV/c)2, thus complementing our extraction of similar quantities in the non-perturbative region for the deuteron.

Recent COMPASS results on the nucleon longitudinal spin structure and QCD fits

The latest measurements of the proton longitudinal spin structure function, ɡ 1 p , in the deep inelastic (DIS) regime are presented. They improve the statistical accuracy of the existing data and extend the kinematic domain to a lower value of x and higher values of Q2 . A global NLO QCD fit of all ɡ 1 world data on the proton, deuteron and neutron has been achieved. The results give a quantification of the quark spin contribution to the nucleon spin, 0.26 )2 in MS scheme. The errors are dominated by the uncertainty on the shape of the functional forms assumed in the fit. A new verification of the fundamental Bjorken sum rule is obtained at a 9% level, using only COMPASS ɡ 1 proton and deuteron measurements. Preliminary results of a reevaluation of the gluon polarization Δɡ /ɡ are presented. The analysis is based on double spin asymmetry of high-p T hadron production cross-sections in the DIS regime. A positive value of 〈Δɡ /ɡ 〉 = 0.113 ± 0.038 ± 0.035 is obtained at leading order at x ~ 0.1. In parallel, the double spin asymmetry in the photoproduction regime is also studied. Finally, preliminary results on quark fragmentation functions into pions extracted from a LO fit of pion multiplicities in semi-inclusive DIS are presented.

Importance of fragmentation functions in determining polarized parton densities

New fragmentation functions (FFs) are extracted from a NLO QCD fit to the preliminary COMPASS data on pion and kaon multiplicities. It is shown that the new kaon FFs are very different from those of De Florian et al. (DSS) and Hirai et al. (HKNS). The sensitivity of the extracted polarized PDFs to the new FFs is discussed.

Measurements of the proton structure at HERA and their impact for LHC

Recent structure function results from H1 and ZEUS are presented. The data have been recorded in e+p and e-p collisions for both Neutral Current and Charged Current reactions, covering a wide kinematic range of squared four-momentum transfers Q2, from 0.2GeV2 to 30000GeV2, and Bjorken x between ~5*10-6 and 0.65. Data from both experiments have been combined, leading to significantly reduced experimental uncertainties. The combined measurements are analysed in a NLO QCD fit, and a set of parton density functions, HERAPDF1.0, is extracted from these data alone. New direct measurements of the structure function FL, making use of dedicated low energy runs of the HERA machine, are also presented. The impact of the HERA data on the parton density functions and predictions for LHC is discussed.

The spin-dependent structure function of the proton [formula omitted] and a test of the Bjorken sum rule

The inclusive double-spin asymmetry, A1p, has been measured at COMPASS in deep-inelastic polarised muon scattering off a large polarised NH3 target. The data, collected in the year 2007, cover the range Q2>1(GeV/c)2, 0.004<x<0.7 and improve the statistical precision of g1p(x) by a factor of two in the region x<0.02. The new proton asymmetries are combined with those previously published for the deuteron to extract the non-singlet spin-dependent structure function g1NS(x,Q2). The isovector quark density, Δq3(x,Q2), is evaluated from a NLO QCD fit of g1NS. The first moment of Δq3 is in good agreement with the value predicted by the Bjorken sum rule and corresponds to a ratio of the axial and vector coupling constants |gA/gV|=1.28±0.07(stat.)±0.10(syst.).

Flavour separation of helicity distributions from deep inelastic muon–deuteron scattering

We present a LO evaluation of helicity densities of valence, Δuv+Δdv, non-strange sea, Δu¯+Δd¯, and strange quarks, Δs (assumed to be equal to Δs¯). They have been obtained from the inclusive asymmetry A1,d and the semi-inclusive asymmetries A1,dπ+, A1,dπ−, A1,dK+, A1,dK− measured in polarised deep inelastic muon–deuteron scattering. The full deuteron statistics of COMPASS (years 2002–2004 and 2006) has been used. The data cover the range Q2>1 (GeV/c)2 and 0.004<x<0.3. Both non-strange densities are found to be in a good agreement with previous measurements. The distribution of Δs(x) is compatible with zero in the whole measured range, in contrast to the shape of the strange quark helicity distribution obtained in most LO and NLO QCD fits. The sensitivity of the values of Δs(x) upon the choice of fragmentation functions used in the derivation is discussed.

Combined HERA deep inelastic scattering data and NLO QCD fits

Previously published data on inclusive neutral and charged current e+p and e-p deep inelastic scattering from HERA have been combined. The new, model-independent method of combining the measured cross sections takes full account of correlated systematics in a coherent way, leading to significantly reduced uncertainties in the combined measurement across the (x, Q^2) plane. The combined cross section data have been used as the sole input for a new next-to-leading order QCD fit to extract the parton distribution functions (PDFs) of the proton. The PDFs extracted have greatly reduced experimental uncertainties, compared to separate QCD analyses on data from H1 and ZEUS. Model uncertainties, including those arising from the parameterisation dependence, have also been carefully considered. The resulting HERA PDFs have impressive precision.

STRUCTURE FUNCTIONS

Recent progress in the understanding of the nucleon is presented. The unpolarized structure functions are obtained with unprecedented precision from the combined H1 and ZEUS data and are used to extract proton parton distribution functions via NLO QCD fits. The obtained parametrization displays an improved precision, in particular at low Bjorken x, and leads to precise predictions of cross-sections for LHC phenomena. Recent data from proton–antiproton collisions at Tevatron indicate further precise constraints at large Bjorken x. The flavor content of the proton is further studied using final states with charm and beauty in DIS ep and [Formula: see text] collisions. Data from polarized DIS or proton–proton collisions are used to test the spin structure of the proton and to constrain the polarized parton distributions.

The approximation method for calculation of the exponents of the gluon distribution, λ g , and the structure function, λ S ,at low x

We present a set of formulae using the solution of the QCD Dokshitzer-Gribov-Lipatov-Altarelli-parisi (DGLAP) evolution equation to the extract of the exponent $\lambda_g$ gluon distribution and $\lambda_S$ structure function from the Regge- like behavior at low $x$. The exponents are found to be independent of $x$ and to increase linearly with ln$Q^{2}$ and compared with the most data from H1 Collaboration. We also calculated the structure function $F_{2}(x,Q^{2})$ and the gluon distribution $G(x,Q^{2})$ at low $x$ assuming the Regge- like behavior of the gluon distribution function at this limit and compared with NLO QCD fit to the H$1$ data, two Pomeron fit, multipole Pomeron exchange fit and MRST (A.D.Martin, R.G.Roberts, W.J.Stirling and R.S.Thorne), DL(A.Donnachie and P.V.Landshoff), NLO-GRV(M.Gluk, E.Reya and A.Vogt) fit results, respectively.

Higher twists in polarized DIS and the size of the constituent quark

The spontaneous breaking of chiral symmetry implies the presence of a short-distance scale in the QCD vacuum, which phenomenologically may be associated with the size of the constituent quark, $\ensuremath{\rho}\ensuremath{\approx}0.3\text{ }\text{ }\mathrm{fm}$. We discuss the role of this scale in the matrix elements of the twist-4 and 3 quark-gluon operators determining the leading power ($1/{Q}^{2}$)-corrections to the moments of the nucleon spin structure functions. We argue that the flavor-nonsinglet twist-4 matrix element, ${f}_{2}^{u\ensuremath{-}d}$, has a sizable negative value of the order ${\ensuremath{\rho}}^{\ensuremath{-}2}$, due to the presence of sea quarks with virtualities $\ensuremath{\sim}{\ensuremath{\rho}}^{\ensuremath{-}2}$ in the proton wave function. The twist-3 matrix element, ${d}_{2}$, is not related to the scale ${\ensuremath{\rho}}^{\ensuremath{-}2}$. Our arguments support the results of previous calculations of the matrix elements in the instanton vacuum model. We show that this qualitative picture is in agreement with the phenomenological higher-twist correction extracted from an NLO QCD fit to the world data on ${g}_{1}^{p}$ and ${g}_{1}^{n}$, which include recent data from the Jefferson Lab Hall A and COMPASS experiments. We comment on the implications of the short-distance scale $\ensuremath{\rho}$ for quark-hadron duality and the $x$-dependence of higher-twist contributions.

Extraction of Structure Function and Gluon DistributionFunction at Low-x from Cross Section Derivative by Regge Behavior

An approximation method based on Regge behavior is presented.This new method relates the reduced cross section derivative andthe structure function Regge behavior at low x. With theuse of this approximation method, the C and λ parametersare calculated from the HERA reduced cross section data taken atlow-x. Also, we calculate the structure functionsF2(x,Q2) even for low-x values, which have not beeninvestigated. To test the validity of calculated structurefunctions, we find the gluon distribution function in the Leadingorder approximation based on Regge behaviour of structure functionand compare to the NLO QCD fit to H1 data and NLO partondistribution function.

Measurement ofD*±production in deep inelastice±pscattering at DESY HERA

Inclusive production of D*± (2010) mesons in deep inelastic scattering has been measured with the ZEUS detector at DESY HERA using an integrated luminosity of 81.9 pb−1. The decay channel D*+→D0π+ with D0→K−π+ and corresponding antiparticle decay were used to identify D* mesons. Differential D* cross sections with 1.5<Q2<1000GeV2 and 0.02<y<0.7 in the kinematic region 1.5<pT(D*)<15GeV and |η(D*)|<1.5 are compared to different QCD calculations incorporating different parametrizations of the parton densities in the proton. The data show sensitivity to the gluon distribution in the proton and are reasonably well described by next-to-leading-order QCD with the ZEUS NLO QCD fit used as the input parton density in the proton. The observed cross section is extrapolated to the full kinematic region in pT(D*) and η(D*) in order to determine the open-charm contribution, F2cc¯(x,Q2), to the proton structure function, F2. Since, at low Q2, the uncertainties of the data are comparable to those from the QCD fit, the measured differential cross sections in y and Q2 should be used in future fits to constrain the gluon density.Received 1 September 2003DOI:https://doi.org/10.1103/PhysRevD.69.012004©2004 American Physical Society

Structure function results from ZEUS

This contribution presents recent ZEUS results on proton structure functions at HERA. The inclusive φ(1020)-meson cross section was measured, and it was used to determine the s-quark content of the proton. The structure function F 2 was extracted using initial-state radiative events. Neutral and charged current cross sections were used to extract the structure function xF 3 and measure the mass of the W boson, respectively. A NLO QCD fit to ZEUS data and fixed target cross sections was employed to determine the parton density functions of the quarks and of the gluon inside the proton.

Uncertainties on parton distribution functions from the ZEUS NLO QCD fit to data on deep inelastic scattering

An NLO QCD analysis of the ZEUS data on e+p deep inelastic scattering together with fixed-target data has been performed from which the gluon and quark densities of the proton and the value of the strong coupling parameter, αs(M2Z), have been extracted. The study includes a full treatment of the experimental systematic uncertainties, including point-to-point correlations. Different ways of incorporating correlated systematic uncertainties into the fit are discussed and compared.(From the workshop ‘Advanced Statistical Techniques in Particle Physics’, 18–22 March 2002)

Determination of the high-twist contribution to the structure function xFνN3

We extract the high-twist contribution to the neutrino–nucleon structure function xF 3 (ν+ ν ̄ )N from the analysis of the data collected by the IHEP-JINR Neutrino Detector in the runs with the focused neutrino beams at the IHEP 70 GeV proton synchrotron. The analysis is performed within the infrared renormalon (IRR) model of high twists in order to extract the normalization parameter of the model. From the NLO QCD fit to our data we obtain the value of the IRR model normalization parameter Λ 2 3 =0.69±0.37 (exp)±0.16 (theor) GeV 2 . We also obtain Λ 2 3 =0.36±0.22 (exp)±0.12 (theor) GeV 2 from a similar fit to the CCFR data. The average of both results is Λ 2 3 =0.44±0.19 (exp) GeV 2 .

Measurements of the Q2-dependence of the proton and neutron spin structure functions g1p and g1n

The structure functions g 1 p and g 1 n have been measured over the range 0.014< x<0.9 and 1< Q 2<40 GeV 2 using deep-inelastic scattering of 48 GeV longitudinally polarized electrons from polarized protons and deuterons. We find that the Q 2 dependence of g 1 p ( g 1 n ) at fixed x is very similar to that of the spin-averaged structure function F 1 p ( F 1 n ). From an NLO QCD fit to all available data we find Γ 1 p − Γ 1 n =0.176±0.003±0.007 at Q 2=5 GeV 2, in agreement with the Bjorken sum rule prediction of 0.182±0.005.