Running Coupling BFKL Equation and Deep Inelastic Scattering

I examine the form of the solution of the BFKL equation with running coupling relevant for deep inelastic scattering. The evolution of structure functions is precisely determined and well described by an effective coupling of the form 1/(beta_0(ln(Q^2/Lambda^2)+3.6(alpha_s(Q^2)ln(1/x))^1/2)) (until very small x). Corrections to the LO equation are relatively small, and the perturbative expansion is stable. Comparison to data via a global fit is very successful.Comment: Latex file uses epsfig.sty and npb.sty, 4 pages including 1 embedded figure. Contribution to the proceedings of the International Workshop on Deep Inelastic Scattering and QCD (DIS99), Zeuthen, April 199

Uncertainties of predictions from parton distributions I: experimental errors

We determine the uncertainties on observables arising from the errors on the experimental data that are fitted in the global MRST2001 parton analysis. By diagonalizing the error matrix we produce sets of partons suitable for use within the framework of linear propagation of errors, which is the most convenient method for calculating the uncertainties. Despite the potential limitations of this approach we find that it can be made to work well in practice. This is confirmed by our alternative approach of using the more rigorous Lagrange multiplier method to determine the errors on physical quantities directly. As particular examples we determine the uncertainties on the predictions of the charged-current deep-inelastic structure functions, on the cross-sections for W production and for Higgs boson production via gluon-gluon fusion at the Tevatron and the LHC, on the ratio of W- to W+ production at the LHC and on the moments of the non-singlet quark distributions. We discuss the corresponding uncertainties on the parton distributions in the relevant x,Q2 domains. Finally, we briefly look at uncertainties related to the fit procedure, stressing their importance and using sW, sH and extractions of aS(MZ2) as examples. As a by-product of this last point we present a slightly updated set of parton distributions, MRST2002

MRST2001: partons and α <SUB>S</SUB> 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 aS better than ever before. We find a somewhat smaller gluon at low x than previous determinations and that aS (MZ2) = 0.119 ±0.002 (expt.) ±0.003 (theory)

Ad Lucem: QED parton distribution functions in the MMHT framework

We present the MMHT2015qed PDF set, resulting from the inclusion of QED corrections to the existing set of MMHT Parton Distribution Functions (PDFs), and which contain the photon PDF of the proton. Adopting an input distribution from the LUXqed formulation, we discuss our methods of including QED effects for the full, coupled DGLAP evolution of all partons with QED at O(α) , O(ααS) , O(α2) . While we find consistency for the photon PDF of the proton with other recent sets, building on this we also present a set of QED corrected neutron PDFs and provide the photon PDF separated into its elastic and inelastic contributions. The effect of QED corrections on the other partons and the fit quality is investigated, and the sources of uncertainty for the photon are outlined. Finally we explore the phenomenological implications of this set, giving the partonic luminosities for both the elastic and inelastic contributions to the photon and the effect of our photon PDF on fits to high mass Drell–Yan production, including the photon-initiated channel

Charm and beauty quark masses in the MMHT2014 global PDF analysis

We investigate the variation in the MMHT2014 PDFs when we allow the heavy-quark masses mcmc and mbmb to vary away from their default values. We make PDF sets available in steps of Δmc=0.05 GeVΔmc=0.05 GeV and Δmb=0.25 GeVΔmb=0.25 GeV , and present the variation in the PDFs and in the predictions. We examine the comparison to the HERA data on charm and beauty structure functions and note that in each case the heavy-quark data, and the inclusive data, have a slight preference for lower masses than our default values. We provide PDF sets with three and four active quark flavours, as well as the standard value of five flavours. We use the pole mass definition of the quark masses, as in the default MMHT2014 analysis, but briefly comment on the MS¯¯¯¯¯¯¯MS¯ definition

MMHT PDFs: Updates and Outlook

We present the latest results of studies within the MMHT PDF framework. We discuss the impact of the most recent ATLAS 7 TeV jet data, demonstrating that while a good fit can be achieved for individual jet rapidity bins, it is not possible to achieve a good description of the data when all bins are fitted. We examine the role that the experimental correlated systematic uncertainties play in this, and demonstrate that by simply decorrelating no more than two sources of error between rapidity bins, a remarkably improved description of the data can be achieved. We then study the impact of NNLO corrections, showing that a mild decrease in the fit quality is produced. We also present the results of including new LHC W, Z, W + c and tt¯ data on the MMHT14 PDF set, showing that a marked decrease in the s + ¯s uncertainty is in particular achieved. Finally, some discussion of the latest work towards the inclusion of the photon PDF within the MMHT framework is presented

Bottom quark electroproduction in variable flavor number schemes

Two variable flavor number schemes are used to describe bottom quark production in deep inelastic electron-proton scattering. In these schemes the coefficient functions are derived from mass factorization of the heavy quark coefficient functions presented in a fixed flavor number scheme. Also one has to construct a parton density set with five light flavors (u,d,s,c,b) out of a set which only contains four light flavors (u,d,s,c). In order $\alpha_s^2$ the two sets are discontinuous at $\mu=m_b$ which follows from mass factorization of the heavy quark coefficient functions when it is carried out in the ${\bar {\rm MS}}$-scheme. Both variable flavor number schemes give almost identical predictions for the bottom structure functions $F_{2,b}$ and $F_{L,b}$. Also they both agree well with the corresponding results based on fixed order four-flavor perturbation theory over a wide range in $x$ and $Q^2$.Comment: Latex with seventeen PostScript figure

Update of Parton Distributions at NNLO

We present a new set of parton distributions obtained at NNLO. These differ from the previous sets available at NNLO due to improvements in the theoretical treatment. In particular we include a full treatment of heavy flavours in the region near the quark mass. In this way, an essentially complete set of NNLO partons is presented for the first time. The improved treatment leads to a significant change in the gluon and heavy quark distributions, and a larger value of the QCD coupling at NNLO, alpha_S(M_Z^2) = 0.1191 +/- 0.002(expt.) +/- 0.003(theory). Indirectly this also leads to a change in the light partons at small x and modifications of our predictions for W and Z production at the LHC. As well as the best-fit set of partons, we also provide 30 additional sets representing the uncertainties of the partons obtained using the Hessian approach.Comment: 13 pages, 11 figures. Version published. Slight extension and some modification of reference

Cold Plasma Dispersion Relations in the Vicinity of a Schwarzschild Black Hole Horizon

We apply the ADM 3+1 formalism to derive the general relativistic magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild metric. Respective perturbed equations are linearized for non-magnetized and magnetized plasmas both in non-rotating and rotating backgrounds. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed for the existence of waves with positive angular frequency in the region near the horizon. Our results support the fact that no information can be extracted from the Schwarzschild black hole. It is concluded that negative phase velocity propagates in the rotating background whether the black hole is rotating or non-rotating.Comment: 27 pages, 11 figures accepted for publication in Gen. Relat. & Gravi