Large perturbative corrections to the Drell-Yan process in QCD

The total cross section $\text{d}\text{σ}\text{d}\text{Q}{}^2$ for the production of a muon pair of invariant mass Q²via the Drell-Yan mechanism and the Feynman x_F differential cross section $\text{d}{}^2\text{σ}\text{d}\text{Q}{}^2\text{d}\text{x}{}_{\mathrm{<mtext>F</mtext>}}$ are calculated in QCD retaining all terms up to order α_s(Q². The calculations are performed using dimensional regularisation of the intermediary infrared and collinear singularities, but we present our results in a form independent of such details. The corrections to both these cross sections coming from radiative corrections to the lowest-order $\text{q}\text{q}$ annihilation diagram are found to be large at present values of Q² and S when the cross section is expressed in terms of parton densities derived from leptonproduction, for all Drell-Yan processes of practical interest. Numerical calculations are presented which show, for any reasonable parametrisation of the parton densities, that the neglect of higher-order terms in α_s(Q²) is not justifiable. The quark-gluon diagrams on the other hand give small corrections in this order and are only important for PP scattering.     

Perturbative QCD corrections in Drell-Yan processes

The influence of lowest-order QCD corrections on the Drell-Yan cross section $\text{Q}{}^4\text{(}\text{dσ}\text{dQ}{}^2\text{)(τ, Q}{}^2\text{)}$ is determined and compared with the asymptotic freedom (AF) corrections. The perturbative calculation exhibits the AF-characteristics of a (strongly) rising Q²-dependence for √τ?0.1 (qg-scattering) and falling for √τ?0.2 (qq?-annihilation). Qualitative agreement between the two calculation methods in the entire √τ-range is obtained with α_s = 0.3.     

Two-loop QCD corrections to the longitudinal structure function

We calculate the fourth-order corrections to the longitudinal Wilson coefficient in deep inelastic scattering (for the non-singlet case). We use off-mass-shell states to control collinear singularities. A table of numerical results is presented for different numbers of quark flavours, and from these results we obtain the total next-to-leading order contributions to the moments of the longitudinal structure function.     

NLO QCD corrections to Drell-Yan processes in the SANC framework

NLO QCD corrections to charged and neutral current Drell-Yan processes are computed with help of the computer system SANC. At the partonic level both quark-antiquark and quark-gluon scattering channels are taken into account. Subtraction of collinear singularities in the massive quark scheme is compared with the one in the $ \overline {MS} $ \overline {MS} scheme. Numerical results at the hadronic level are received for the LHC conditions with help of Monte-Carlo integrators and event generator programs based on the standard SANC modules. Comparison with analogous results of the MCFM package is shown.     

Radiative corrections to the helicity asymmetries for the Drell-Yan process in QCD

The next-to-leading-logarthmic corrections to the helicity cross sections for the Drell-Yan process are calculated. While it is well-known that these corrections are large, it is shown here that when considering the helicity asymmetry (initial-initial) these large radiative effects cancel. Thus the leading-order calculation for the asymmetry is a good approximation.     

Uniqueness of the QCD corrections to the Drell-Yan and Deep Inelastic Scattering processes

We present a complete calculation of one loop QCD corrections to the Deep Inelastic Scattering (DIS) and Drell-Yan (DY) processes under various infrared and collinear singularity regularization schemes. We use our final results which have surprisingly simple forms in an analysis of the scheme dependence problem for these singularities. We also comment on some of the other proposals made recently for the resolution of the same problem.     

Beyond leading order QCD perturbative corrections to the pion form factor

The order α_s²(Q²) corrections to the pion form factor, F_π(Q²), are calculated using perturbative quantum chromodynamics and dimensional regularization. In the $\text{MS}$ renormalization scheme these corrections are large. This means that reliable perturbative predictions cannot be made until momentum transfers, Q, of about 300–400 GeV are reached or unless one can sum the large perturbative terms to all orders. Attempts to reorganize the perturbation series so that the first term gives a better approximation of the complete sum indicate that at Q = 10 GeV the pion form factor may be about a factor of two larger than the leading order result.     

Higher order QCD corrections to the energy-energy correlation function

We calculate theO(α _s ² correction to the energy-energy correlation cross section using a Sterman-Weinberg type resolution criterion to account for higher-order/nonperturbative effects. We find that the energy-energy correlation function as well as the asymmetry is sensitive to the choice of resolution parameters.     

QCD corrections to the Drell-Yan process for the Large Hadron Collider (LHC): Vertex functions and gluon bremsstrahlung

With an eye to future experiments at the Large Hadron Collider (LHC), $ \mathcal{O}\left( {\alpha \alpha _s } \right) $ \mathcal{O}\left( {\alpha \alpha _s } \right) QCD corrections to the Drell-Yan process are calculated for vertex functions and gluon bremsstrahlung. Use is made of fully differential cross sections, so that the result obtained in the present study can readily be applied in analyzing experimental data (in correcting data from future experiments at LHC). It is shown both analytically and numerically that the results are independent of unphysical parameters, including the parameter separating the regions of soft and hard gluons and the quark mass. A numerical analysis of radiative effects was performed by means of the FORTRAN code READY with allowance for the experimental cuts used at the Compact Muon Solenoid (CMS) detector.     

x-space sum rules and the pion wave function in QCD

From two-point correlators of (derivative) axial currents we construct sum rules in Euclidean configuraton space for the moments of the pion wave-function. Analysis of these sum rules gives a value of the second moment \(\left\langle {\xi ^2 } \right\rangle \) compatible with those obtained from conventional sum rules but in disagreement with that obtained in a recent lattice calculation.     

Second order logarithmic corrections to the Drell-Yan cross-section

We present a complete order α _s ² calculation of the large logarithmic terms of the type ln ⁱ (1?x)/(1?x) (x=Q ²/s), which appear in the Wilson coefficient of the total and differential DY cross-sections. These terms are computed using renormalizationgroup methods. It is shown that besides the well known constant part, they constitute the bulk of the radiative correction. This in particular holds for the higher τ-region which is still accessible to experiment. The large logarithmic corrections determine the shape of theK-factor and give a partial explanation of the phenomenon of anomalous scaling.     

QCD sum rules for pion wave function revisited

We analyze new QCD sum rules for the pion wave function (WF) ?_π (x), obtained recently in [1] in the non-local vacuum condensates method for non-diagonal correlators, and suggest a new approach for extracting WF of the π-meson and the mass and WF of the first resonance. As a result, we obtain approximately the same form of the pion WF by two different methods and for two different ansatzes of non-local quark condensates. We predict the mass of the π′-resonance and obtain the form of its WF.     

Radiative corrections to pion nucleus scattering

The radiative corrections to elastic pion-nucleus scattering are evaluated for kinematical conditions pertaining to the pion spectrometer facilities at the newer meson factories, and are found to be experimentally relevant. A reasonably simple, experimentally useful approximation to the exact expression for the radiative correction is given.     

QCD sum rules in exclusive kinematics and pion wave function

We suggest a modification of the QCD sum rules for three-point correlation functions that relates hadron expectation values of an operator of interest to properties of the QCD vacuum in alternating external fields. A new sum rule is obtained for the nucleon magnetic moments. Relations are found between the couplings g_πNN , g_ρωπ and the value of the pion wave function at the point with equal momentum carried by the quark and the antiquark. Our results seem to exclude the possibility of having a pronounced dip in the pion wave function in the middle point, as has been assumed on the evidence of a large value of the second moment.     

Higher-order QCD corrections to exclusive processes: The multiple scattering mechanism

The multiple-scattering diagram, calculated to lowest order in QCD, fits well topp elastic scattering data at larget. It is shown that higherorder QCD corrections seem to spoil this agreement: calculated as far as the insertion of two additional gluons, they give an exponential factor. This factor differs in detail from some previous conjectures. For colour-singlet bound states of quarks, the exponential factor is independent of whether or not the gluon mass is zero, unlike the case of simple quark-quark scatterin. Two régimes are considered:t ands of the same order, andt large but much less thans. Exponentiation seems to occur in both cases, but in a non-abelian theory more diagrams are important for the latter case.     

Contribution of inverse gluon emission to QCD corrections to the Drell-Yan process for experiments at the large hadron collider (LHC)

The contributions of inverse gluon emission to the lowest order QCD corrections to the Drell-Yan process for future experiments at LHC are calculated. The use of fully differential cross sections makes it possible to apply readily the results of these calculations for experimental purposes (in correcting data from future experiments at LHC). It is shown analytically that the present results are independent of the quark mass. A numerical analysis of respective radiative effects is performed by means of the READY FORTRAN code with allowance for the experimental cuts used at the Compact Muon Solenoid (CMS) detector.     

The structure function of the pion

The data on muon-pair production in pion interactions on a nuclear target are reanalysed in the light of what we know about nucleon structure functions in a nuclear environment. A consistent picture of the pion structure function is obtained, which is compatible with the evolution of a hard valence quark distribution atQ ²=2.5 GeV². Vector dominance is used to estimate the hadronic component of the photon structure function atQ ²=2.5 GeV² and it is found to saturate the data there.