Convergence and gauge dependence properties of the resummed one-loop quark-quark scattering amplitude in perturbative QCD

The one-loop QCD effective charge α _s ^eff for quark-quark scattering is derived by diagrammatic resummation of the one-loop amplitude using an arbitrary covariant gauge. Except for the particular choice of gauge parameter ξ = −3, α _s ^eff is found to increase with increasing physical scale, Q, as lnQ or ln² Q. For ξ = −3, α _s ^eff decreases with increasing Q and satisfies a renormalization group equation. Also, except for the case ξ = 19/9, convergence radii of geometric series are found to impose upper limits on Q. The text was submitted by the author in English.     

A comparison of high statistics measurements of the proton and deuteron structure functions

We present a detailed comparison of high statistics measurements of the structure functionF ₂(x, Q ²) from deep inelastic scattering of charged leptons on hydrogen and deuterium targets. It is found that the CERN results from the EMC and BCDMS Collaborations are both compatible with the lowQ ² electron scattering results from SLAC after an adjustment of the relative normalizations. We discuss the residual discrepancy between EMC and BCDMS which persists after this renormalization and find that the SLAC data are in better agreement with the steeperx dependence of the BCDMS results. A phenomenological parametrization ofF ₂(x, Q ²) is given.     

Total and ionization cross-sections of N<Subscript>2</Subscript> and CO by positron impact: Theoretical investigations

In this paper we report our calculations on several important total cross-sections (TCSs) of positron impact on isoelectronic N₂ and CO molecules, treated in the complex spherical potential formalism. Basically the total (complete) cross-section Q _T consists of elastic and inelastic contributions. Our total inelastic cross-section (Q _inel) contains ionization and electronic excitations together with positronium formation. Our goal here is to bifurcate Q _inel further to deduce total ionization cross-section, using the ‘complex scattering potential–ionization contribution’ (CSP-ic) method of electron–atom/molecule scattering. The present range of positron energy is 15–2000 eV. All the resulting cross-sections are in a good general accord with the existing data. This work highlights the importance of various scattering channels in e⁺-N₂ and e⁺-CO interactions at intermediate and high energies.     

Measurements of total and positronium-formation cross sections for the scattering of positrons by alkali atoms

We present a review of our recent measurements of total cross sections (Q _T's) for the scattering of positrons by Na, K, and Rb, and positronium-formation cross sections (Q _Ps's) for Na and K. For our total cross section measurements, a beam transmission technique has been used. For ourQ _Ps measurements, our approach involves setting upper and lower limits onQ _Ps using a combination of (1) measuring the transmission of the positron beam with the angular discrimination of the apparatus made as poor as possible, and (2) measuring the 511 keV annihilation gamma rays in coincidence produced by the decay of para-Ps formed in the scattering cell. Comparison with theoretical calculations shows that our measuredQ _T's andQ _Ps's for Na and K agree reasonably well with a close coupling approximation (CCA) calculation which takes into account the formation of Ps in then=1 andn=2 states. In the 3–10 eV energy range, this calculation predicts a peak in theQ _T's andQ _Ps's for K which also appears in our measurements. The absence of such a peak in our measuredQ _T's andQ _Ps's (preliminary) for Na in this energy range is also consistent with the same theory. Comparisons with five-state CCA calculations ofQ _T which do not take Ps-formation into account also show good agreement with our positron-Na, K, and RbQ _T measurements for energies above 20 eV, but show dramatic departures from our measurements below 10 eV for K and Rb.     

Scattering of light by a periodic structure in the presence of randomness VII: Application of statistical detection test

Detection of periodic structures, hidden in random surfaces has been addressed by us for some time and the ‘extended matched filter’ method, developed by us, has been shown to be effective in detecting the hidden periodic part from the light scattering data in circumstances where conventional data analysis methods cannot reveal the successive peaks due to scattering by the periodic part of the surface. It has been shown that if r ₀ is the coherence length of light on scattering from the rough part and Λ is the wavelength of the periodic part of the surface, the extended matched filter method can detect hidden periodic structures for (r ₀/Λ) ≥ 0.11, while conventional methods are limited to much higher values ((r ₀/Λ) ≥ 0.33). In the method developed till now, the detection of periodic structures involves the detection of the central peak, first peak and second peak in the scattered intensity of light, located at scattering wave vectors v _x = 0, Q, 2Q, respectively, where Q = 2Gp/Λ, their distinct identities being obfuscated by the fact that the peaks have width Δv _x = 2Gp/r ₀ ≫ Q. The relative magnitudes of these peaks and the consequent problems associated in identifying them is discussed. The Kolmogorov-Smirnov statistical goodness test is used to justify the identification of the peaks. This test is used to ‘reject’ or ‘not reject’ the null hypothesis which states that the successive peaks do exist. This test is repeated for various values of r ₀/Λ, which leads to the conclusion that there is really a periodic structure hidden behind the random surface.      

Optical behavior of composite carbonaceous aerosols: DDA and EMT approaches

Atmospheric particles may contain a small amount of black carbon (BC) that may affect their optical properties. These optical properties also depend strongly on the particle morphology and internal topology. The efficiency factors for scattering Q_sca, absorption Q_abs, extinction Q_ext, backscattering Q_bk, as well as the asymmetry parameter cos, linear polarization P, and scattering phase functions S₁₁ are analyzed in detail as functions of morphology and internal topology. Backscattering quantities (like Q_bk and P and S₁₁ at large scattering angles) are affected most significantly. The behavior of these quantities depends strongly on the internal mixing of the constituent materials making up the particle. Effective medium theories (EMTs), which assume that the particle is homogeneous and are applied frequently in radiative transfer studies, can underestimate Q_sca and S₁₁ especially when high carbon contents are considered. Contrarily, EMTs also tend to overestimate the values of the asymmetry parameter and Q_abs.     

Electron-impact total cross sections for inelastic processes for furan,tetrahydrofuran and 2,5-dimethylfuran

We report total inelastic, total ionisation and summed total excitation cross sections for electron scattering on furan, tetrahydrofuran (THF) and 2,5-dimethylfuran at energies between the ionisation threshold and 5 keV. We have employed the spherical complex optical potential formalism (SCOP) to calculate the total inelastic cross sections (Q_inel) and have used complex scattering potential-ionisation contribution (CSP-ic) method to derive total ionisation cross sections (Q_ion) and summed total excitation cross sections (∑Q_exc) from the calculated Q_inel. We have also computed Q_ion for these molecules using binary-encounter-Bethe (BEB) approach. We have compared our total cross sections (TCS) with available experimental as well as previous theoretical results and have found good agreement. The results are presented graphically as well as numerically.     

Reactive scattering of alkali dimers: chemi-ionization

Measurements of total cross sections Q_i for chemi-ionization in scattering of a K₂ dimer beam by a range of halogen containing molecules, at translational energies E ～ 7–11 kcal mol^-1, are reported. Substantial cross sections, Q_i ～ 2–10 Ų are exhibited by the halogen molecules Br₂, ICl, IBr, I₂. Distinctly lower values Q_i ～ 0·1–0.2 Ų are exhibited by BrCN and the mercuric and stannic halides, HgX₂, SnX₄. The results show a close correlation with the chemi-ionization exoergicities, particularly for formation of a K⁺,X^- ion pair. These chemi-ionization data and results from previous reactive scattering studies are compared, in order to estimate relative reaction yields for different reaction paths. The reaction dynamics for K₂ with halogen molecules and cyanohalides are rationalized in terms of the electronic structure of the potential surface, where the orientation of the K₂ dimer plays a crucial role.     

Asymptotic bounds on pion form factor

A technique recently developed for inelastic electron proton scattering is applied for inelastic electron pion scattering. It is found that all the derivatives of off-shell form factor of pion nears=m _π ² and for largeQ ² are bounded from above, provided that the dispersion relation for the form factor requires no more than one subtraction. The elastic pion form factor is bounded by [lnQ ²] ^c /Q ², wherec is any positive constant.     

The Q-dependence of the generalised Gerasimov-Drell-Hearn integral for the deuteron,proton and neutron

The Gerasimov-Drell-Hearn (GDH) sum rule connects the anomalous contribution to the magnetic moment of the target nucleus with an energy-weighted integral of the difference of the helicity-dependent photoabsorption cross sections. Originally conceived for real photons, the GDH integral can be generalised to the case of photons with virtuality Q². For spin-1/2 targets such as the nucleon, it then represents the non-perturbative limit of the first moment of the spin structure function g ₁ (x,Q ² ) in deep inelastic scattering (DIS). The data collected by HERMES with a deuterium target are presented together with a re-analysis of previous measurements on the proton. This provides an unprecedented and complete measurement of the generalised GDH integral for photon-virtuality ranging over 1.2&lt;Q ² &lt;12.0 GeV² and for photon-nucleon invariant mass squared W² ranging over 1&lt;W ² &lt;45 GeV², thus covering simultaneously the nucleon-resonance and the deep inelastic scattering regions. These data allow the study of the Q²-dependence of the full GDH integral, which is sensitive to both the Q²-evolution of the resonance form factors and contributions of higher twist. The contribution of the nucleon-resonance region is seen to decrease rapidly with increasing Q². The DIS contribution is sizeable over the full measured range, even down to the lowest measured Q². As expected, at higher Q² the data are found to be in agreement with previous measurements of the first moment of g₁. From data on the deuteron and proton, the GDH integral for the neutron has been derived and the proton-neutron difference evaluated. This difference is found to satisfy the fundamental Bjorken sum rule at Q ² = 5 GeV². Received: 20 October 2002 / Published online: 15 January 2003     

Structure factors for neutron scattering on tunnelling methyl groups in nitromethane

The elastic, quasielastic and inelastic structure factors for neutron scattering on CH₃ groups tunnelling in a sinusoidal hindering potential with threefold symmetry are calculated as a function of the momentum transferQ. A comparison is made with data on methyl groups in nitromethane obtained with high resolution inelastic neutron scattering experiments at high momentum transfer.     

Structural studies of tetrachloride liquids

The differential cross-sections for neutron scattering from liquid carbon tetrachloride have been measured with the TSS instrument at the Harwell Electron Linac. Data were taken at seven different scattering angles for a wavelength range of 0·2–3·5 Å. The observed diffraction patterns at high momentum transfer (> 8–30 Å^-1) have been analysed in terms of the molecular form factor f ₁(Q). It was found that the oscillation amplitudes could be satisfactorily described only by introducing an energy-dependent term into the Debye-Waller factors of the form factor. The f ₁(Q) data were fitted with a four-parameter function for measurements at scattering angles of 150°, 90° and 58°. The carbon-chlorine bond length parameter was accurately defined in all cases and had a mean value of 1·766 ± 0·002 Å. The inclusion of an anharmonicity constant in the form factor gave an improved χ²-fit to the data with an increased value of 1·770 ± 0·002 Å for the bond length. The results are in excellent agreement with other measurements and show the importance of pulsed neutron techniques for molecular structure studies of disordered materials.     

High temperature O2-CARS thermometry

O₂ temperature measurements at T=1910K have been performed by coherent anti-Stokes Raman scattering (CARS) inside a homogeneously heated gas volume of a tube furnace. The oxygen CARS spectrum can now be modeled accurately within the higher vibrational levels of the Q-branch manifold populated at flame temperatures using recently available spectroscopic data and collisional broadening coefficients.     

Strange quarks in the nucleon sea

The HAPPEX Collaboration measured parity-violating electron scattering from ⁴He$(e, e)$and H(e, e) in 2004 and 2005 for Q ²≤0.11GeV^2. Results for the strange-quark contributions to the electromagnetic form factors of the nucleon from the 2004 data will be reviewed. Preliminary results from the 2005 data, which have significantly greater statistical precision, are G _E ^s = 0.004±0.014_stat±0.013_syst for Q ² = 0.0772GeV^2 from the helium data and G _E ^s +0.088G _M ^s = 0.004±0.011_stat±0.005_syst±0.004_FF for Q ² = 0.1089GeV^2 from the hydrogen data.     

Functions of the nucleon structure and determination of the strong coupling constant

The properties of deep inelastic scattering at high energies, as well as results of fitting of experimental data on structure functions, obtained by BCDMS, SLAC, NMC, and BFP collaborations in fixed target experiments, with the aim of determining the strong coupling constant, the shape of parton distributions, and power corrections to F ₂(x, Q ²), are presented.     

Complex scattering potential – ionization contribution (CSP-ic) method for calculating total ionization cross sections on electron impact

In this article, we report calculations of total ionization cross sections, Q _ion , for simple atoms (C, N, O, F) and molecules (NO and NH₃)_{3}) of atmospheric interest on electron impact at energies from threshold to 2000 eV. We have employed the complex scattering potential – ionization contribution (CSP-ic) method for the present study. Attempt has been made to improve the method by computing the parameter that involves the ratio of sum of the total excitation cross sections (Σ Q _exc ) and total inelastic cross section (Q _inel ) at the peak of the inelastic cross section. The present study not only provided a better estimation of the parameter involved in the CSP-ic method but also provided better agreement with the available experimental and theoretical data on the ionization cross sections of the simple atomic and molecular targets studied here.     

Measurements of total cross sections for positron-K and-Rb scattering

A modification of the apparatus that we have been using to measure absolute total cross sections (Q _T′s) for positron and electron scattering by alkali metal atoms has enabled us to more easily obtainQ _T′s at low energies (<10 eV). Our positron-K and-RbQ _T measurements now extend from 1 to 98 eV and we have made the correspondingQ _T measurements for electrons in the same system using the same technique (a beam transmission technique). Our measured positron-K and-RbQ _T values show a peak in the vicinity of 6 eV and decrease substantially as the positron energy is reduced below 6 eV, in sharp contrast to the results obtained in recent 5-state close-coupling approximation calculations. At higher energies (above 10 eV), we have found that the same calculations are in quite good agreement with our measured positron-K and-RbQ _T′s. Our measurements of the correspondingQ _T′s for electrons below 10 eV do not show a peak, but rather continue to increase as the energy is decreased.     

Nuclear effects in deep inelastic scattering of charged-current neutrino off nuclear target

The nuclear effects in the neutrino–nucleus charged-current inelastic scattering process is studied by analyzing the CCFR and NuTeV data. The structure functions F₂(x,Q²) and xF₃(x,Q²) as well as differential cross sections are calculated by using CTEQ parton distribution functions and the EKRS and HKN nuclear parton distribution functions, and these are compared with the CCFR and NuTeV data. It is found that the corrections of the nuclear effect to the differential cross section for the charged-current antineutrino scattering on the nucleus are negligible, the EMC effect exists in the neutrino structure function F₂(x,Q²) in the large x region, the shadowing and anti-shadowing effect occur in the distribution functions of valence quarks in the small and medium x region, respectively. It is also found that shadowing effects on F₂(x,Q²) in the small x region in the neutrino–nucleus and the charged-lepton–nucleus deep inelastic scattering processes are different. It is clear that the neutrino–nucleus deep inelastic scattering data should further be employed in restricting the nuclear parton distributions. PACS 13.15.+g; 24.85.+p; 25.30.-c