Cross sections for semihard interactions in hardronic collisions beyond the leading order of perturbative QCD

An estimate of cross sections which correspond to semihard interactions such as gluon (mini) jet production is presented. It takes into account recent results concerning gluon distributions in the small x region beyond the leading log Q² approximation and rescattering corrections in the hadron-hadron channel. The estimated cross sections are at very high energies significantly smaller in their magnitude than a simple integration of the two-jet inclusive cross section might imply yet they are still expected to constitute a substantial part or σ_tot in the TeV energy regime.     

Radiative corrections to high-energy neutrino scattering

Motivated by precise neutrino experiments, we reconsider the electromagnetic radiative corrections to the data. We investigate the usefulness and demonstrate the simplicity of the “leading log” approximation: the calculation to order α ln (Q/μ), α ln (Q/m_q). Here Q is an energy scale of the overall process, μ is the lepton mass and m_q is a hadronic mass, the effective quark mass in a parton model. We identify those questions the answers to which do not depend on unknown hadron parameters like quark masses. The leading log radiative corrections to dδ/dy distributions and to suitably interpreted dδ/dx distributions are quark-mass independent. We improve upon the conventional leading log approximation and compute explicitly the largest terms that lie beyond the leading log level. In practice this means that our model-independent formulae, though approximate, are likely to be excellent estimates everywhere except at low energy or very large y. We point out that radiative corrections to measurements of deviations from the Callan-Gross relation and to measurements of the “sea” constituency of nucleons are gigantic. The QCD inspired study of deviations from scaling is of particular interest. We compute, beyond the leading log level, the radiative corrections to the QCD predictions.     

Ionic conductivity of silver chalcogenide glasses

The dynamic response by electrical spectroscopy of ionically conducting chalcogenide glasses (Ag₂S)_x(GeS₂)_1–x has been studied. The activation energies E_d.c deduced from the Arrhenius plots are temperature dependent. Fitting the curves to log(σ_a.c)=f(log ω) leads to values of characteristic parameters that are dependent both on temperature and frequency. The obtained experimental results are compared with a theoretical model based on the concept of “free volume” fluctuations. A new approch is proposed leading to acceptable hopping distances. Paper presented at the 1st Euroconference on Solid State Ionics, Zakynthos, Greece, 11–18 Sept. 1994.     

On the energy loss of high energy quarks in a finite-size quark-gluon plasma

The induced gluon emission from a fast quark passing through a finite-size QCD plasma is studied within the light-cone path integral approach. It is shown that the leading log approximation used in previous studies fails when the gluon formation length becomes on the order of the length of the medium traversed by the quark. Calculation of the energy loss beyond the leading log approximation gives the energy loss which grows logarithmically with quark energy, contrary to the energy-independent prediction of the leading log approximation.     

Leading log radiative corrections to deep inelastic neutral and charged current scattering at HERA

TheO(α) radiative corrections for neutral and charged current deep inelastic scattering are calculated in the leading log approximation. The numerical results are found to agree within a few per cent with the results of a completeO(α) calculation by Bardin et al. It is demonstrated that both for the leading log and completeO(α) calculation all light quark mass terms can be eliminated from the cross section.     

Relating hard QCD processes through universality of mass singularities

Hard QCD processes involving final jets are studied and compared by means of a simple approach to mass singularities. This is based on the Lee-Nauenberg-Kinoshita theorem and on a rather subtle use of gauge invariance in hard collinear gluon bremsstrahlung. One-loop results are easily derived for processes involving any number of initial quarks and/or currents. The method greatly simplifies the computation of higher-order loops at the leading log level and our preliminary results allow us to conclude that the crucial features encountered at the one-loop level will persist. We are thus able to relate different hard processes and to show that suitable ratios of cross sections, being free from mass singularities, can be computed perturbatively, as usually assumed in QCD-inspired parton models. We are also able to relate our universal leading mass singularities to leading scaling violations and to extend therefore the results of the operator product expansion method to processes outside the range of the light-cone analysis. Some delicate points caused by confinement-related singularities (e.g., narrow resonance poles) are also discussed.     

Quark-antiquark-gluon jets in dis diffractive dissociation

We study the diffractive production of jets with large transverse momenta in the region of large diffractive masses (small ). Cross sections for transverse and longitudinal photons are obtained in the leading log and log approximation, keeping all powers in log . We perform a numerical study and illustrate the angular distribution of the three jets. We also estimate the integrated diffractive three jet cross section and compare with the dijet cross section obtained before. Received: 11 March 1999 / Published online: 14 October 1999     

Modified Breit–Wigner formula for mesonic resonances describing OZI decays of confined q\bar{q} states and the light scalar mesons

Evolution equations for multiplicities in QCD cascades can, both in the parton and dipole picture, be used to estimate corrections beyond the formal accuracy of the modified leading log approximation (MLLA). The differences between the two pictures, and other uncertainties beyond first order MLLA corrections, are here investigated in some detail. For example, I discuss how some colour suppressed corrections, which cannot be determined without better knowledge of non-perturbative QCD, are related to the question of colour reconnection. A generalized evolution equation for the dipole cascade is also presented. Received: 19 October 2000 / Revised version: 26 January 2001 / Published online: 15 March 2001     

Structural interpretation of endurance of polymeric fibers

Endurance results in cyclic tension of several polymeric fibers are reviewed and analyzed in terms of Prevorsek-Lyons theory. It is shown that the plots of log (cycles to failure) against strain amplitude can be divided into regions of short and long term endurance. An expression is derived correlating the inflection point on the S-N curve with the structural parameters: fracture surface energy p, tensile modulus E, activation energy associated with the process of crack growth F*, and stress concentration factor, q. Manson-Coffin endurance plots expressed in terms of log (strain amplitude), log (stress amplitude), and log (strain energy amplitude) are examined. From the log Nf—log (strain energy amplitude) are derived the relative values of fracture surface energy of these fibers. Experimental data are shown which reflect the structural changes which occur in fibers during endurance experiments and an analysis is carried out leading to an estimate of the corresponding changes in p, E, and q.     

On the Exponentiation of Infrared Logarithms in Massless (φ3)6-theory

We investigate the relation between the coefficients of the perturbative series for the propagator in massless theories and the coefficients of the perturbative series of the renormalization group quantities. This enable us to prove, that the concept of exponentiation in the sense introduced by POGGIO is valid in massless theories to arbitrary high order at the leading log level, but breaks down if nonleading log's are included.     

Linking total cross sections for hard and soft processes through analyticity in Q and sum rules

Using analyticity of the virtual Compton scattering amplitude in Q² sum rules are derived relating meson-nucleon total cross-sections with certain integrals over the large Q² and x0 part of nucleon structure functions. Of preliminary quantitative analysis of the sum rules for both singlet and non-singlet amplitudes is presented. For the singlet amplitude the sum rules relate, in particular, the rise of sea-quark distributions implied by perturbative QCD and the increase of total meson-proton cross sections with energy. Quantitatively, however, nonunitary leading log Q² results for the former give a too rapid increase of the latter.     

The gluon distributions in the smallx region beyond the leading order

The gluon distributions in a proton are calculated in the region of smallx (10^?4?x?10^?2) and largeQ ² taking into account the corrections which correspond to the sum of the leading powers of log 1/x beyond the leading logQ ² approximation. It is shown that they become significant for very small values ofx only provided however that the non-leading terms in the limit of smallx are also consistently included. The leading log 1/x approximation gives the gluon distributions which can differ by a factor of 2 from their leading logQ ² counterpart.     

A consistent next-to-leading-order QCD calculation of hadronic diffractive scattering

We calculate the order _s² and order _s³ QCD contributions to colour-singlet exchange in the leading log s approximation. We implement the resulting amplitude at the hadronic level and thus construct the QCD pomeron and odderon to this order of perturbation theory. We show that the structure of the hadronic form factors provides a natural mechanism through which the odderon gets suppressed at t = 0 whereas it dominates the elastic cross section at large t. We also demonstrate that the inclusion of nonperturbative effects through a modification of the gluon propagator accelerates greatly the convergence of the log s expansion, although not enough to provide agreement with the data.     

Neutralization and excitation in low-energy ion-surface collisions

A model is presented which describes neutralization and excitation occurring in low-energy ion-surface collisions. Important processes that determine experimentally measurable quantities such as the charged fraction ?⁺ and photon yield γ are assumed to be Auger neutralization, electronic excitation and radiationless deexcitation. The model yields ?⁺ and γ in good agreement with experiment data, although log ?⁺ and log γ are found to exhibit nonlinear dependences on the inverse velocity of the incident ion beam.     

QCD corrections to electroweak vector boson scattering at small scattering angles

We investigate the role of a certain class of QCD corrections to electroweak vector boson scattering at small scattering angles and large energies. These are present since, from the perturbative analysis, the vector bosons may dissociate into quark-antiquark pairs giving rise to color dipoles interacting through gluon exchanges. After the computation of the vector boson impact factors, we present expressions for the lowest order QCD scattering amplitude and for the leading logarithmic BFKL amplitude. Particularly we discuss numerical results for the process . The QCD corrections to the cross section resulting from the interference with the electroweak ones are estimated and compared with the leading pure electroweak part. Corrections resulting from the leading log BFKL amplitude are of the order of a few percent already at the 0.5-1 TeV energy range.Received: 21 May 2003, Published online: 29 August 2003     

The jet mass in leading log QCD

The distribution of the jet mass is computed in the leading log approximation. A Sudakov-like damping factor broadens the distribution compared to the first-order result. The leading quark-gluon pair in a jet is seen to have a damped mass spectrum similar to that for color singlet clusters.     

Energy conservation constraints on multiplicity correlations in QCD jets

We compute analytically the effects of energy conservation on the self-similar structure of parton correlations in QCD jets. The calculations are performed both in the constant and running coupling cases. It is shown that the corrections are phenomenologically sizeable. On a theoretical ground, energy conservation constraints preserve the scaling properties of correlations in QCD jets beyond the leading log approximation.     

Relating hard QCD processes through universality of mass singularities (II)

Extending previous techniques we obtain at all orders the factorization of mass singularities for every hard QCD process. These appear in a universal factor that can be reabsorbed into the standard parton density. Thus suitable ratios of cross sections can be computed by a perturbative expansion in the running coupling constant. Moreover, at the leading log level we obtain, after explicit cancellation of infrared divergences, the scaling violation of the operator product expansion.     

The leading two loop divergences of the non-leptonic weak chiral Lagrangian

We calculate the leading divergences at NNLO for the octet part of the non-leptonic weak sector of chiral perturbation theory, using renormalization group methods. The role of counterterms which vanish at the equation of motion and their use to simplify the calculation is shown explicitly. The obtained counterterm Lagrangian can be employed to calculate the chiral double log contributions of quantities in this sector, most notably the amplitude. The double log contribution of the latter is discussed in a separate paper.Received: 21 April 2005, Revised: 24 May 2005, Published online: 27 July 2005     

Vector boson parameters: Scheme dependence and theoretical uncertainties

The renormalization scheme dependence of electroweak parameters shifts is used to estimate uncertainties due to higher order effects. Parameter shifts are calculated from weakly scheme dependent quantities, taking care of a systematic leading log summation. A “non-standard” definition of sin² θ _W is also considered which is to be used if the ρ-parameter is kept as free parameter. Results for the leptonic decay widths of the vector bosons are also given.