arXiv subjects
Publications and source records attributed to J. Smith.
We discuss how the operator product expansion (OPE) can be used to derive asymptotic expressions for certain integrals. This yields operator matrix elements (OME's) which determine the matching conditions for $\bar{\rm MS}$ parton densities across heavy flavour thresholds. Then we construct four and five-flavour densities from a three-flavour set via the AP equation using LO and NLO splitting functions.
We compare variable number schemes for heavy quark electroproduction
Where appropriate, the abbreviation 'VFNS' is replaced by 'CSN' to indicate the scheme using massive heavy quark coefficient functions proposed in this paper. The text below Eq. (2.13) and between Eqs. (2.33) and (2.36) has been considerably changed.
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 $α_s^2$ the two sets are discontinuous at $μ=m_b$ 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 $Q^2$.
A study is made of charm and bottom flavor matching conditions on parton densities. Starting from an $\bar{\rm MS}$ three-flavor density set, where the scale $μ< m_c$, and using the recently derived two-loop matching conditions, we provide a new set of four-flavor parton densities where $ m_c \le μ< m_b$ and five-flavor densities where $μ\ge m_b$. The effect of the next-to-next-to-leading order matching conditions on the evolution equations is important for scales just above the transition regions. This includes the small $x$ and small $Q^2$ domain studied by the H1 and ZEUS experiments at HERA. At small $x$ the effects of the matching conditions never die away even for large $μ^2$.
We discuss two topics in the production of heavy quarks in deep-inelastic scattering: the next-to-leading order Monte-Carlo HVQDIS and the next-to-leading logarithmic resummation of soft gluon effects, including estimates of next-to-next-to-leading order corrections therefrom.
We present the two-loop corrected operator matrix elements contributing to the scale evolution of the longitudinal spin structure function $g_1(x,Q^2)$ calculated up to finite terms which survive in the limit $ε= N - 4 \to 0$. These terms are needed to renormalize the local operators up to third order in the strong coupling constant $α_s$. Further the expressions for the two-loop corrected operator matrix elements can be inserted into one loop graphs to obtain a part of the third order contributions to these matrix elements. This work is a first step in obtaining the third order anomalous dimensions so that a complete next-to-next-to-leading order (NNLO) analysis of the above mentioned structure function can be carried out. In our calculation particular attention is paid to the renormalization constant which is needed to restore the Ward-identities violated by the HVBM prescription for the $γ_5$-matrix in $N$-dimensional regularization.
A next-to-leading order Monte Carlo program for the calculation of heavy quark cross sections in deeply inelastic scattering is described. Concentrating on charm quark and D^*(2010) production at HERA, several distributions are presented and their variation with respect to charm quark mass, parton distribution set, and renormalization-factorization scale is studied.
We present the two-loop corrected operator matrix elements calculated in N-dimensional regularization up to the finite terms which survive in the limit $ε= N - 4 \to 0 $. The anomalous dimensions of the local operators have been previously extracted from the pole terms and determine the scale evolution of the deep inelastic structure functions measured in unpolarized lepton hadron scattering. The finite $ε$-independent terms in the two-loop expressions are needed to renormalize the local operators up to third order in the strong coupling constant $α_s$. Further the unrenormalized expressions for the two-loop corrected operator matrix elements can be inserted into specific one loop graphs to obtain a part of the third order contributions to these matrix elements. This work is a first step in obtaining the anomalous dimensions up to third order so that a complete next-to-next-to-leading order (NNLO) analysis can be carried out for deep inelastic electroproduction.
We discuss three theoretical schemes to describe charm quark electroproduction.
We examine the charm component F_{2,c}(x,Q^2,m^2) of the proton structure function F_2(x,Q^2) in three different schemes and compare the results with the data in the x and Q^2 region explored by the HERA experiments. Studied are (1) the three flavour number scheme (TFNS) where the production mechanisms are given by the photon-gluon fusion process and the higher order reactions with three light-flavour parton densities as input (2) the four flavour number scheme (FFNS) where F_{2,c} is expressed in four light flavour densities including one for the charm quark and (3) a variable-flavour number scheme (VFNS) which interpolates between the latter two. Both the VFNS and the TFNS give good descriptions of the experimental data. However one cannot use the FFNS for the description of the data at small Q^2.
We study how next-to-leading logarithms modify predictions from leading logarithmic soft-gluon resummation in the heavy quark production cross section near threshold. Numerical results are presented for top quark production at the Fermilab Tevatron and bottom quark production at fixed-target energies.
Starting from fixed-order perturbation theory (FOPT) we derive expressions for the heavy-flavour components of the deep-inelastic structure functions FL and F2 in the variable-flavour number scheme (VFNS). These expressions are valid in all orders of perturbation theory. This derivation establishes a relation between the parton densities parametrized at N and N light flavours. The consequences for the existing parametrizations of the parton densities are discussed. Further we show that in charm electroproduction the exact and asymptotic expressions for the heavy-quark coefficient functions yield identical results for F2 when Q^2>20 (GeV/c)^2. We also study the differences between the FOPT and the VFNS descriptions for F2. It turns out that the charm structure function in the VFNS is larger than the one obtained in FOPT over the whole Q^2-range. Furthermore inspection of the perturbation series reveals that the higher order corrections in the VFNS are smaller than those present in FOPT for Q^2>10 (GeV/c)^2. Therefore the VFNS gives a better prediction for the charm structure function at large Q^2-values than FOPT.
We present theoretical and experimental considerations pertaining to deeply inelastic heavy-flavour production at HERA. The various theoretical uncertainties in the cross section calculation are discussed. Cuts are imposed to determine the fraction of charm production accessible to the detectors. The production of charm at asymptotic $Q^2$ and bottom production are also covered. Experimental aspects include current charm production data analysis and prospects for future analyses including anticipated high precision and distinguishing photon-gluon fusion charm events from excitation from the charm parton density. The feasibility of measuring $F_2^{b\overline b}(x,Q^2)$ is investigated.
The cross sections for charm and bottom quark production in the threshold region are discussed. We consider the effects of an all order resummation of initial state soft-plus-virtual gluon radiation on the total cross sections compared to the order $α_s^3$ results.
Deep-inelastic production of heavy quarks at HERA, especially charm, is an excellent signal to measure the gluon distribution in the proton at small $x$ values. By measuring various differential distributions of the heavy quarks this reaction permits additional more incisive QCD analyses due to the many scales present. Furthermore, the relatively small mass of the charm quark, compared to the typical momentum transfer $Q$, allows one to study whether and when to treat this quark as a parton. This reaction therefore sheds light on some of the most fundamental aspects of perturbative QCD. We discuss the above issues and review the feasibility of their experimental investigation in the light of a large integrated luminosity.
We present analytic formulae for the heavy flavour coefficient functions for polarized deep inelastic lepton-hadron scattering. The expressions are valid in the kinematical regime $Q^2\gg m^2$ where $Q^2$ and $m^2$ stand for the masses squared of the virtual photon and heavy quark respectively. Using these coefficient functions we have computed the next-to-leading order $α_s$ corrections to polarized charm production at HERA collider energies, where both the electron and proton beams are polarized. We also give an estimate of these corrections at fixed target experiments where the typical $Q^2$ values are much smaller than at HERA.