Recent Progress in Parton Distributions and Implications for LHC Physics
I outline some of the most recent developments on the global fit to parton distributions performed by the MRST collaboration.
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arXiv subjects
R. S. Thorne
Publications and source records attributed to R. S. Thorne.
A Variable Flavour Number Scheme at NNLO
I present a formulation of a Variable Flavour Number Scheme for heavy quarks that is implemented up to NNLO in the strong coupling constant and may be used in NNLO global fits for parton distributions.
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Gluon Distributions and Fits using Dipole Cross-Sections
I investigate the relationship between the gluon distribution obtained using a dipole model fit to low-x data on F_2(x,Q^2) and standard gluons obtained from global fits with the collinear factorization theorem at fixed order. I stress the necessity to do fits of this type carefully, and in particular to include the contribution from heavy flavours to the inclusive structure function. I find that the dipole cross-section must be rather steeper than the gluon distribution, which at least partially explains why dipole model fits produce dipole cross-sections growing quite strongly at small x, while DGLAP based fits have valence-like, or even negative, small-x gluons as inputs. However, I also find that the gluon distributions obtained from the dipole fits are much too small to match onto the conventional DGLAP gluons at high Q^2, i.e. approx 50 GeV^2, where the two approaches should coincide. The main reason for this discrepancy is found to be the large approximations made in converting the dipole cross-sections into structure functions using formulae which are designed only for asymptotically small x. The shortcomings in this step affect the accuracy of the extracted dipole cross-sections in terms of size and shape, and hence also in terms of interpretation, at all scales.
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Parton distributions incorporating QED contributions
We perform a global parton analysis of deep inelastic and related hard-scattering data, including ${\cal O}(α_{\rm QED})$ corrections to the parton evolution. Although the quality of the fit is essentially unchanged, there are two important physical consequences. First, the different DGLAP evolution of u and d type quarks introduces isospin violation, i.e. $u^p \neq d^n$, which is found to be unambiguously in the direction to reduce the NuTeV $\sin^2θ_W$ anomaly. A second consequence is the appearance of photon parton distributions $γ(x,Q^2)$ of the proton and the neutron. In principle these can be measured at HERA via the deep inelastic scattering processes $e N \to eγX$; our predictions are in agreement with the present data.
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Physical Gluons and High $E_T$ Jets
We propose a more physical parameterization of the gluon distribution for global parton analyses of deep inelastic and related hard scattering data. In the new parameterization the gluon distribution at large x in the MSbar-scheme is driven by the valence quarks, which naturally produces a shoulder-like form at high x, and hence produces a better description of the Tevatron inclusive jet data. We perform the new analysis at both NLO and NNLO. The improvement is found to be even better at NNLO than at NLO. We make available the new sets of NLO and NNLO partons, which we denote by MRST2004.
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Update of MRST Parton Distributions
I present a brief summary of the most important updates in the MRST determinations of the NLO and NNLO parton distributions. I concentrate on uncertainties due to input assumptions and possible theoretical corrections, particularly isospin violation, QED corrections, NNLO and corrections at low Q^2 and small x.
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Parton Distributions
I discuss our current understanding of parton distributions. I begin with the underlying theoretical framework, and the way in which different data sets constrain different partons, highlighting recent developments. The methods of examining the uncertainties on the distributions and those physical quantities dependent on them is analysed. Finally I look at the evidence that additional theoretical corrections beyond NLO perturbative QCD may be necessary, what type of corrections are indicated and the impact these may have on the uncertainties.
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Uncertainties of predictions from parton distributions. I: Theoretical errors
We study the uncertainties in parton distributions, determined in global fits to deep inelastic and related hard scattering data, due to so-called theoretical errors. Amongst these, we include potential errors due to the change of perturbative order (NLO to NNLO), ln(1/x) and ln(1-x) effects, absorptive corrections and higher-twist contributions. We investigate these uncertainties both by including explicit corrections to our standard global analysis and by examining the sensitivity to changes of the x,Q^2,W^2 cuts on the data that are fitted. In this way we expose those kinematic regions where the conventional DGLAP description is inadequate. As a consequence we obtain a set of NLO, and of NNLO, conservative partons where the data are fully consistent with DGLAP evolution, but over a restricted kinematic domain. We also examine the potential effects of such issues as the choice of input parameterization, heavy target corrections, assumptions about the strange quark sea and isospin violation. Hence we are able to compare the theoretical errors with those uncertainties due to errors on the experimental measurements, which we studied previously. We use W and Higgs boson production at the Tevatron and the LHC as explicit examples of the uncertainties arising from parton distributions. For many observables the theoretical error is dominant, but for the cross section for W production at the Tevatron both the theoretical and experimental uncertainties are small, and hence the NNLO prediction may serve as a valuable luminosity monitor.
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MRST partons and uncertainties
We discuss uncertainties in the extraction of parton distributions from global analyses of DIS and related data. We present conservative sets of partons, at both NLO and NNLO, which are stable to x,Q^2,W^2 cuts on the data. We give the corresponding values of alpha(M_Z^2) and the cross sections for W production at the Tevatron.
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Global Fits of Parton distributions
I discuss recent developments in the determination of parton distributions from global fits. I concentrate on the errors associated with these parton distributions and with the physical quantities which are determined in terms of them. I outline the various techniques used to quantify the uncertainties due to errors on experimental data used in the fits, and provide a number of examples of predictions with their uncertainties. However, I demonstrate that this source of errors may, in some circumstances, be less important than errors due to underlying assumptions in the fitting procedure and due to the incomplete nature of the theoretical framework currently employed.
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Update of MRST Parton Distributions
We discuss the latest update of the MRST parton distributions in response to the most recent data. We discuss the areas where there are hints of difficulties in the global fit, and compare to some other updated sets of parton distributions, particularly CTEQ6. We briefly discuss the issue of uncertainties associated with partons.
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Uncertainties on Parton Related Quantities
I discuss the issue of uncertainties in parton distributions and in the physical quantities which are determined in terms of them. While there has been significant progress on the uncertainties associated with errors on experimental data, there are still outstanding questions. Also, I demonstrate that in many circumstances this source of errors may be less important than errors due to underlying assumptions in the fitting procedure and due to the incomplete nature of the theoretical calculations.
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Questions on Uncertainties in Parton Distributions
A discussion is presented of the manner in which uncertainties in parton distributions and related quantities are determined. One of the central problems is the criteria used to judge what variation of the parameters describing a set of partons is acceptable within the context of a global fit. Various ways of addressing this question are outlined.
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NNLO global parton analysis
We perform a NNLO (and a LO) global parton analysis in which we include the new precise data for deep inelastic scattering from HERA and for inclusive jet production at the Tevatron, together with the improved knowledge of the three-loop splitting functions. The results are compared with our recent NLO analyses. The LO fit produces significantly worse results in general, but gives a surprisingly good fit to the Tevatron high-E_T jet data. For the approximate NNLO analysis we notice a slight improvement in the quality of the global fit, and find that the partons are changed by up to 10% at Q^2=10 GeV^2$, in particular in the x<0.01 regime.
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MRST2001: partons and alpha_S from precise deep inelastic scattering and Tevatron jet data
We use all the available new precise data for deep inelastic and related hard scattering processes to perform NLO global parton analyses. These new data allow an improved determination of partons and, in particular, the inclusion of the recent measurements of the structure functions at HERA and of the inclusive jets at the Tevatron help to determine the gluon distribution and alpha_S better than ever before. We find a somewhat smaller gluon at low x than previous determinations and that alpha_S(M_Z^2) = 0.119 +/- 0.002 (expt.) +/- 0.003 (theory).
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The Running Coupling BFKL Anomalous Dimensions and Splitting Functions
I explicitly calculate the anomalous dimensions and splitting functions governing the Q^2 evolution of the parton densities and structure functions which result from the running coupling BFKL equation at LO, i.e. I perform a resummation in powers of ln(1/x) and in powers of beta_0 simultaneously. This is extended as far as possible to NLO. These are expressed in an exact, perturbatively calculable analytic form, up to small power-suppressed contributions which may also be modelled to very good accuracy by analytic expressions. Infrared renormalons, while in principle present in a solution in terms of powers in alpha_s(Q^2), are ultimately avoided. The few higher twist contributions which are directly calculable are extremely small. The splitting functions are very different from those obtained from the fixed coupling equation, with weaker power-like growth ~x^(-0.25), which does not set in until extremely small x indeed. The NLO BFKL corrections to the splitting functions are moderate, both for the form of the asymptotic power-like behaviour and more importantly for the range of x relevant for collider physics. Hence, a stable perturbative expansion and predictive power at small x are obtained.
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MRST Global Fit Update
We discuss the impact of the most recent data on the MRST global analysis - in particular the new high-E_T jet data and their implications for the gluon and the new small x structure function data. In the light of these new data we also consider the uncertainty in predictions for physical quantities depending on parton distributions, concentrating on the W cross-section at hadron colliders.
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A Variable Flavour Number Scheme for Charged Current Heavy Flavour Structure Functions
The Thorne-Roberts variable flavour number scheme (VFNS) for heavy quarks is presented in detail for the specific case of charged current DIS. As in neutral current DIS this provides a smooth extrapolation from the fixed flavour number scheme (FFNS) appropriate at low $Q^2$ to the zero-mass variable flavour number scheme (ZM-VFNS) appropriate as $Q^2 \to \infty$, and differs from alternative versions of a VFNS by the definition of the coefficient functions at each order, and the strict ordering of the expansion in $α_S$. However, there are subtle differences from the neutral current case which are addressed here. We discuss both the LO and NLO expressions, the latter unfortunately requiring some (minimal) modelling due to the current lack of some necessary ${\cal O}(α^2_S)$ FFNS coefficient functions.
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