arXiv subjects
Publications and source records attributed to R. S. Thorne.
The first measurements of Delta- xF3 are higher than current theoretical predictions. We investigate the sensitivity of these theoretical predictions upon a variety of factors including: renormalization scheme and scale, quark mass effects, higher twist, isospin violation, and PDF uncertainties.
We use the recent estimates of NNLO splitting functions, made by van Neerven and Vogt, to perform exploratory fits to deep inelastic and related hard scattering data. We investigate the hierarchy of parton distributions obtained at LO, NLO and NNLO, and, more important, the stability of the resulting predictions for physical observables. We use the longitudinal structure function $F_L$ and the cross sections $σ_W, σ_Z$ for $W$ and $Z$ hadroproduction as examples. For $F_L$ we find relatively poor convergence, with increasing order, at small $x$; whereas $σ_{W,Z}$ are much more reliably predicted.
I calculate the anomalous dimension governing the Q^2 evolution of the gluon (and structure functions) coming from the running coupling BFKL equation. This may be expressed in an exact analytic form, up to a small ultraviolet renormalon contribution, and hence the corresponding splitting function may be determined precisely. Rather surprisingly it is most efficient to expand the gluon distribution in powers of alpha_s(Q^2) rather than use the traditional expansion where all orders of alpha_s\ln(1/x) are kept on an equal footing. The anomalous dimension is very different from that obtained from the fixed coupling equation, and leads to a powerlike behaviour for the splitting function as x ->0 which is far weaker, i.e. about x^(-0.2). The NLO corrections to the anomalous dimension are rather small, unlike the fixed coupling case, and a stable perturbative expansion is obtained.
W and Z bosons will be produced copiously at the LHC proton-proton collider. We study the parton distribution dependence of the total production cross sections and rapidity distributions, paying particular attention to the uncertainties arising from uncertainties in the parton distributions themselves. Variations in the gluon, the strong coupling, the sea quarks and the overall normalisation are shown to lead to small but non-negligible variations in the cross section predictions. Ultimately, therefore, the measurement of these cross sections will provide a powerful cross check on our knowledge of parton distributions and their evolution.
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.
We discuss topical issues concerning the MRST parton analysis. We introduce some new parton sets in order to estimate the uncertainty in the cross sections predicted for W and Z production at the Tevatron and the LHC. We compare with CTEQ5 partons.
I examine the solution of the BFKL equation with NLO corrections relevant for deep inelastic scattering. Particular emphasis is placed on the part played by the running of the coupling. It is shown that the solution factorizes into a part describing the evolution in Q^2, and a constant part describing the input distribution. The latter is infrared dominated, being described by a coupling which grows as x decreases, and thus being contaminated by infrared renormalons. Hence, for this part we agree with previous assertions that predictive power breaks down for small enough x at any Q^2. However, the former is ultraviolet dominated, being described by a coupling which falls like 1/(\ln(Q^2/Λ^2) + A(\barα_s(Q^2)\ln(1/x))^1/2)with decreasing x, and thus is perturbatively calculable at all x. Therefore, although the BFKL equation is unable to predict the input for a structure function for small x, it is able to predict its evolution in Q^2, as we would expect from the factorization theory. The evolution at small x has no true powerlike behaviour due to the fall of the coupling, but does have significant differences from that predicted from a standard NLO in alpha_s treatment. Application of the resummed splitting functions with the appropriate coupling constant to an analysis of data, i.e. a global fit, is very successful.
I review the various methods for taking account of finite quark masses in DIS and related processes. I pay particular attention to the so-called variable flavour number schemes (VFNS) which are designed to extrapolate smoothly from the region near threshold of production of heavy quark pairs to the region where the quarks become effectively massless.
This is a summary of the contributions on the next-to-leading order corrections to the BFKL equation which were presented to the `Small-x and Diffraction' working group at the 1998 Durham Workshop on HERA Physics.
We extend a recent global analysis of nucleon parton distributions carried out at next-to-leading order (NLO) in the MSbar scheme to provide distributions in the so-called DIS scheme. We pay particular attention to the translation of the heavy quark distributions in going from the MSbar to the DIS scheme. We repeat the global analysis at leading order (LO) and comment on the major effects produced when going from LO to NLO. Finally we include in the global analysis a freely parameterised form of possible higher twist contributions to make an exploratory study of the size of these effects as a function of x.
I present a method for calculating heavy quark production which extrapolates smoothly from the well understood limits of the fixed-flavour number scheme for Q^2 approx m_H^2 to the zero-mass scheme at Q^2/m_H^2 -> infinity. For all Q^2 > m_H^2 the evolution of the heavy quark distribution is precisely as in the massless MSbar scheme. The method is simple to implement and compares well with data.
I present a calculation of structure functions at leading order which includes an unambiguous inclusion of the leading ln(1/x) terms for each power of alpha_s, and also the correct effects due to the mass of the charm and bottom quarks. I compare the results of fits to data to those obtained using conventional NLO in alpha_s calculations, noting a clear preference for my approach, especially at small x. The predictions for both the charm structure function and F_L(x,Q^2) using the two approaches are compared, the latter being much more discriminating.
We present a new analysis of parton distributions of the proton. This incorporates a wide range of new data, an improved treatment of heavy flavours and a re-examination of prompt photon production. The new set (MRST) shows systematic differences from previous sets of partons which can be identified with particular features of the new data and with improvements in the analysis. We also investigate the sensitivities of the results to (i) the uncertainty in the determination of the gluon at large x, (ii) the value of alpha_S(M_Z^2) and (iii) the minimum Q^2 cut on the data that are included in the global fit.
The transition from the low $Q^2$ region in deep inelastic scattering where charm production is described by photon-gluon fusion to a region where the charm structure function $F_2^c$ is largely generated by a charm quark density should be a smooth passage. The all orders prescription for matching between the two schemes does not uniquely determine all the relevant coefficient functions (CF's) or guarantee the correct threshold behaviour at fixed order in $α_s$. The constraints of matching not only the value but also the evolution of $F_2^c$ order by order allows all CF's to be determined at any order, each of which reduces to the appropriate massless $\msb$ expression as $Q^2 \to \infty$, and leads to a smooth transition in the threshold region. This procedure gives an excellent description of the $F_2^c$ data for all $Q^2$.
We present consistently ordered calculations of the structure functions F_2(x,Q^2) and F_L(x,Q^2), in different expansion schemes. After discussing the standard expansion in powers of alpha_s(Q^2) we consider a leading-order expansion in ln(1/x) and finally an expansion which is leading order in both ln(1/x) and alpha_s(Q^2), and which is the only really correct expansion scheme. Ordering the calculation in a renormalization-scheme-consistent manner, there is no factorization scheme dependence, and the calculational method naturally includes to the ``physical anomalous dimensions'' of Catani. However, it imposes stronger constraints than just the use of these effective anomalous dimensions. A relationship between the small-x forms of the inputs F_2(x,Q_I^2) and F_L(x,Q_I^2) is predicted. Analysis of a wide range of data for F_2(x,Q^2) is performed, and a very good global fit obtained, particularly for data at small x. The fit allows a prediction for F_L(x,Q^2) to be produced, which is smaller than those produced by the usual NLO-in-alpha_s(Q^2) fits to F_2(x,Q^2) and different in shape.
At low Q^2, charm production in deep-inelastic scattering is adequately described by assuming generation in electroweak boson-light parton scattering (dominantly boson-gluon fusion) which naturally incorporates the correct threshold behaviour. At high Q^2 this description is inadequate, since it does not sum logs in Q^2/m_c^2, and is replaced by the treatment of the charm quark as a light parton. We show how the problem of going from one description to the other can be solved in a satisfactory manner to all orders. The key ingredient is the constraint of matching the evolution of the physical structure function F_2 order by order in alpha_s(Q^2) in addition to the matching of the value of F_2 itself. This leads to new expressions for the coefficient functions associated with the charm parton which are unique in incorporating both the correct threshold and asymptotic behaviours at each order in perturbation theory. The use of these improved coefficients lead to an improvement in global fits and an excellent description of the observed F_2,charm.
We present calculations of the structure functions F_2(x,Q^2) and F_L(x,Q^2), concentrating on small x. After discussing the standard expansion of the structure functions in powers of α_s(Q^2) we consider a leading-order expansion in ln(1/x) and finally an expansion which is leading order in both ln(1/x) and α_s(Q^2), and which we argue is the only really correct expansion scheme. Ordering the calculation in a renormalization-scheme- consistent manner, there is no factorization scheme dependence, as there should not be in calculations of physical quantities. The calculational method naturally leads to the ``physical anomalous dimensions'' of Catani, but imposes stronger constraints than just the use of these effective anomalous dimensions. In particular, a relationship between the small-x forms of the inputs F_2(x,Q_0^2) and F_L(x,Q_0^2) is predicted. Analysis of a wide range of data for F_2(x,Q^2) is performed, and a very good global fit obtained, particularly for data at small x. The fit allows a prediction for F_L(x,Q^2) to be produced, which is smaller than those produced by the usual NLO-in-α_s(Q^2) fits to F_2(x,Q^2) and different in shape.