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.     

Analytical solution of the double-logarithmic integral equation with QCD running coupling

The analytical solution of the double-logarithmic integral equation with QCD running coupling describing small-x behaviour of the non-singlet structure function ? _NS(x,Q ²) has been found for any cut-off parameter μ. Analytical properties of the solution and a position of the right-most singularity in the complex ρ-plane which determines the asymptotics of ? _NS(x,Q ²) at small x have been studied. The asymptotical formula ? _NS(x,Q ²) = C ₁ x ^-λ1{ln^κ1(Q ²/Λ²) —ln^κ1 (μ ²/Λ²) + κ ₁ ln^κ1-1(Q ²/Λ²)[ψ(1) - ψ(λ₁)]} valid if x ? 1 and ln(Q ²/Λ²) ? 1 has been obtained where C ₁, λ₁ are constants, κ ₁ = g/λ₁, λ₁ < g = 8/(33 - 2gh _f), gh _f is a number of active flavours and ψ(ξ) denotes the digamma function.     

Scaling and non-scaling in a rest frame quark-parton model of the proton

Electron-proton deep inelastic scattering is treated as the incoherent scattering of electrons by bound Dirac partons in the proton rest frame. An approximate bound state wave function is used for the initial parton, while the final parton is considered free. A good fit is obtained to the structure function F₁(x,Q²) in the range x > 0.15, Q² > 2 GeV. The subsequent prediction for F₂(x,Q²) is not as good, indicating a small additional contribution by longitudinal photons for W < 2.5 GeV. The parton momentum distribution is found to contain transverse momentum of 400–600 MeV, increasing with x.     

Extraction of the neutron charge form factor G<Superscript>n</Superscript><Subscript>E</Subscript>(Q<Superscript>2</Superscript>) from the charge form factor of deuteron G<Superscript>d</Superscript><Subscript>C</Subscript>(Q<Superscript>2</Superscript>)

We extract the neutron charge form factor G ⁿ _E(Q ²) from the charge form factor of deuteron G ^d _C(Q ²) obtained from T ₂₀(Q ²) data at 0≤Q ²≤ 1.717 (GeV/c)². The extraction is based on the relativistic impulse approximation in the instant form of the relativistic Hamiltonian dynamics. Our results (12 new points) are compatible with existing values of the neutron charge form factor of other authors. We propose a fit for the whole set (36 points) taking into account the data for the slope of the form factor at Q ² = 0. Received: 26 July 2002 / Accepted: 18 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: krutov@ssu.samara.ru RID="b" ID="b"e-mail: troitsky@theory.sinp.msu.ru Communicated by V.V. Anisovich     

On the extraction of elastic neutron electromagnetic form factors from highQ 2 D(e,e′) scattering

The problem of extraction of the neutron magnetic form factor from highQ ² D(e, e′) data is considered. We calculate the inelastic contribution to the cross section using two models of the EMC effect and find that the extracted value ofG _Mn(Q ²) is not sensitive to the deuteron structure forQ ²≦6 GeV². At the same time accurate data atQ ²>10 GeV² and x≧ l would enable to establish presence of the EMC type effect for the deuteron.     

Infrared contribution to the double-logarithmic small-x asymptotics of structure functions

The role playing by the “soft” (κ _T < 1 GeV/c) region in the small-x behaviour ofg ₁(x,Q ²) and the non-singlet structure functionf _{1, NS}(x, Q²) has been studied with the help of the effective QCD Lagrangian which takes into account the lightest degrees of freedom — the constituent quarks and the π-mesons (Goldstone bosons). It has been shown that the quark-quark interaction due to the pion exchange has a negative couplingg for the isovector component (I = 1 in thet-channel) off ₁(x,Q ²) and isosinglet component ofg ₁(x, Q²). Here the pion induced interaction changes mainly the normalization of the quark distribution (it decreasesf _1,NS ^{I = 1} (x,Q ²) two times atx < 3·10^?3) and changes slightly the effective exponents λ (?_1,NS ,g ₁ ～x ^?λ atx → 0). On the other hand due to a positive value of couplingg the value of λ increases by 15% for the isovector part ofg ₁ (x,Q ²) and up to λ ≈ 0.5 (instead of λ ≈ 0.2 without the pion contribution) for the isoscalar non-singlet structure functionf _1,NS ^{I = 0} (x,Q ²).     

Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

We revisit F _π(Q ²) and F _Pγ(Q ²), P = π, η, η′, making use of the local-duality (LD) version of QCD sum rules. We give arguments that the LD sum rule provides reliable predictions for these form factors at Q ² ≥ 5–6 GeV², the accuracy of the method increasing with Q ² in this region. For the pion elastic form factor, the well-measured data at small Q ² give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q ² ≈ 4–8 GeV²; we therefore conclude that large deviations from LD in the region Q ² = 20–50 GeV² seem very unlikely. The data on the (η, η′) → γγ* form factors meet the expectations from the LD model. However, the BaBar results for the π ⁰ → γγ* form factor imply a violation of LD growing with Q ² even at Q ² ≈ 40 GeV², at odds with the η, η′ case and with the general properties expected for the LD sum rule.     

Event-by-event search for charged-neutral fluctuations in Pb-Pb collisions at 158 A⋅GeV

We analyse the proton electromagnetic form factor ratioR(Q ² ) =QF ₂ (Q ² )/F ₁ (Q ² ) as a function of momentum transferQ ² within perturbative QCD. We find that the prediction for (R(Q ² ) at large momentum transferQ depends on the exclusive quark wave functions, which are unknown. For a wide range of wave functions we find thatQF ₂ F ₁ ～ const. at large momentum transfer, which is in agreement with recent JLAB data.     

Hadronic wave functions at short distances and the operator product expansion

The operator product expansion, of appropriate products of quark fields, is used to find the anomalous dimensions which control the short distance behavior of hadronic wave functions. This behavior in turn controls the high-Q² limit of hadronic form factors. In particular, we relate each anomalous dimension of the nonsinglet structure functions to a corresponding logarithmic correction factor to the nominal α_S(Q²)/Q² fall off of meson form factors. Unlike the case of deep inelastic lepton-hadron scattering, the operator product necessary here involves extra terms which do not contribute to forward matrix elements.     

On the polarization of the final nucleon in NC elastic \nu _\mu (\bar \nu _\mu )-N scattering

New short baseline neutrino experiments open new possibilities of high precision study of different neutrino processes. We present here results of the calculation of the polarization of final nucleon in elastic NC $\nu _\mu (\bar \nu _\mu )$ -nucleon scattering. In a numerical analysis the sensitivity to the different choices of the axial and axial strange form factors is examined. Measurements of the polarization of the final proton in elastic e-p scattering drastically changed our knowledge about the electromagnetic form factors of the proton. From measurement of the nucleon polarization in the NC elastic scattering a new additional information about the axial G _A (Q ²) and the strange axial G ^s _A (Q ²) form factors of the nucleon could be inferred.     

Sensitivity of polarization observables in elastic ed scattering to the neutron form factors

The deuteron elastic form factors are calculated within the Bethe-Salpeter approach with separable interaction. The charge, quadrupole, and magnetic form factors [F _C(q ²), F _Q(q ²), and F _M(q ²), respectively]; the structure functions A(q ²) and B(q ²); and the tensor polarization components T ₂₀(q ², T ₂₁(q ²), and T ₂₂(q ²) are investigated up to ?q ²=50 fm^?2. The role of relativistic effects is discussed, and a comparison with nonrelativistic calculations is performed. The effect of the neutron form factors on the deuteron form factors and especially on tensor polarization components is discussed too.     

Electric quadrupole and magnetic dipole moments of the first excited 2+ states of186Os and188Os

The spectroscopic quadrupole moments and the magnetic dipole moments of the lowest 2⁺ states in¹⁸⁶Os (137 keV) and¹⁸⁸Os (155 keV) have been determined by Mößbauer transmission experiments. The electric quadrupole momentsQ ₂₊(Os 186)=? (1.80±0.22) b andQ ₂₊(Os 188)=?(1.81±0.24) b as well as their ratioQ ₂₊(Os 188)/Q ₂₊(Os 186)=1.00±0.07 within the limits of error agree withB(E2) data, if a comparison on the basis of the rotational model is made. For the g-factors and their ratio g₂₊(Os 186)=0.281±0.008, g₂₊(Os 188)=0.305±0.015 andg ₂₊(Os 188)/g ₂₊(Os 186)=1.08±0.05 was obtained. All results are compared with recent model calculations.     

Possible parametrization of parton distributions incorporating singular smallx behaviour implied by QCD and its phenomenological implications for HERA

The gluon and quark distributions of the nucleon are evaluated using the Altarelli-Parisi equations with the input distributions atQ ₀ ² =5 GeV² for seaquarks and gluons modified by the factor (ax ^?0.5+b). The new parametrization is constrained to satisfy the momentum sum rule and after backward evolution (fromQ ₀ ² =5 GeV² toQ ²=1 GeV²) it is also constrained to give approximately 1/x behaviour of the sea-quark and gluon distributions in the limited region of smallx (10^?3<x<10^?2 or so). The theoretical predictions relevant for HERA for structure functionsF ₂(x, Q ²) andF _L (x, Q ²) in the region of very smallx(10^?4<x<10^?2) and largeQ ² and for the cross-sectionσ(γ^* p→ΨX) are presented. Distributions of heavy quarks (c,b,t) are also discussed.     

Analysis ofx F 3: QCD and higher twist

We have analysed all available data on the non-singlet neutrino structure functionxF ₃ taking into account systematic errors and EMC corrections. A good fit to all data withQ ²≧5 (GeV/c)²,W ²≧10 (GeV/c)² is obtained neglecting higher twist contributions, with Λ=0.18±0.07 GeV, corresponding toα _s (Q ²=25(GeV/c)²)=0.18±0.02. On lowering the cuts toQ ²≧3 (GeV/c)²,W ²≧3 (GeV/c)², we find evidence for a small negative higher-twist term. Incorporating such a term in a simple parametrisation yields an increased Λ value of 0.27±0.05 GeV, corresponding toα _s (Q ²=25(GeV/c)²)=0.20±0.01.     

Mössbauer studies and nuclear quadrupole moments of186, 188, 189, 190 Os

Mössbauer transmission experiments with the 137, 155, 69 and 187 keV gamma rays of^{186, 188, 189, 190}Os, respectively, yielded the electric quadrupole splitting of these gamma resonance lines in OsO₂ and OsP₂. From the results the following ratios of quadrupole moments were derived:Q ₂ ⁺(¹⁸⁶Os, 137 keV):Q ₂ ⁺(¹⁸⁸Os, 155keV):Q ₂ ⁺(¹⁹⁰Os, 187 keV):Q _3/2 ^?(¹⁸⁹Os, g.s.)=(+1.100±0.020): 1.0:(+0.863±0.051): (?0.586±0.011) andQ _5/2 ^?(¹⁸⁹Os, 69 keV)/Q _3/2 ^?(¹⁸⁹Os, g.s.)=?0.735 ±0.012. The ratios for^{180, 188, 190}Os are, within their limits of error, in agreement with the expectation of the rotational model, indicating that the pairing-plusquadrupole model calculations of Kumar and Baranger predict too rapid a transition form rotational to vibrational nuclei. Applying this argument to¹⁸⁶Os in particular and using the measured ratios, one obtains a set of values for the quadrupole moments themselves, namelyQ ₂ ⁺ (¹⁸⁶Os)=?(1.50 ± 0.10)b,Q ₂ ⁺(¹⁸⁸Os)=?(1.36± 0.09) b,Q ₂ ⁺ (¹⁹⁰Os)=?(1.18 ± 0.08) b,Q _3/2 ^?(¹⁸⁹Os)=+ (0.80 ± 0.06) b, andQ _5/2 ^? (¹⁸⁹Os)=? (0.59 ± 0.05) b. For the electric field gradient at Os nuclei in Re metal a value ofV _zz=?(3.3 ± 0.6) · 10¹⁷ V/cm² was found. A measurement with a magnetically split source yielded δ=+ 0.685 ± 0.025 for theE2/M1 mixing parameter of the 69 keV transition of¹⁸⁹Os,g _5/2 ^?/g _3/2 ^?=0.895 ± 0.006 for the ratio of theg-factors of the 69 keV state and the groundstate, andH _i=?(1135 ± 20) kOe for the hyperfine field at Os nuclei in an iron matrix.     

Total cross sections and nucleon structure functions in the gargamelle SPS neutrino/antineutrino experiment

Total neutrino and antineutrino cross sections in the energy range 15 to 150 GeV, and the nucleon structure functions, F₂(x, Q²) and xF₃(x, Q²) in the Q² range 0.5 to 50 (GeV/c)² have been measured using a data sample of 3000 neutrino and 3800 antineutrino events. The structure functions show a weak Q² dependence at different x values.     

Structure of Na2O·MO·SiO2·CaF2 (M=Mg,Ca) oxyfluoride glasses

(9−x)CaO·xMgO·15Na₂O·60SiO₂·16CaF₂(x=0, 2, 4, 6, and 9) oxyfluoride glasses were prepared. Utilizing the Raman scattering technique together with ²⁹Si and ¹⁹F MAS NMR, the effect of alkaline metal oxides on the Q species of glass was characterized. Raman results show that as magnesia is added at the expense of calcium oxide, the disproportional reaction Q³→Q⁴+Q² (Qⁿ is a SiO₄ tetrahedron with n bridging oxygens) prompted due to the high ionic field strength of magnesia, magnesium oxide entered into the silicate network as tetrahedral MgO₄, and removed other modifying ions for charge compensation. This reaction was confirmed by ²⁹Si MAS NMR. ¹⁹F MAS NMR results show that fluorine exists in the form of mixed calcium sodium fluoride species in all glasses and no Si–F bonds were formed. As CaO is gradually replaced by MgO (x=6, 9), a proportion of the magnesium ions combines with fluorine to form the MgF⁺ species. Meanwhile, some part of Na⁺ ions complex F⁻ in the form of F–Na(6).     

Measurement of the magnetic formfactor of the deuteron forQ 2=0.5 to 1.3 (GeV/c)2 by a coincidence experiment

Elastic electron deuteron scattering was measured at the Bonn 2.5 GeV Electron-Synchrotron using a two spectrometer coincidence technique. Data were taken at values of the four momentum transfer squaredQ ²=0.50, 0.60, 0.78, 1.00, and 1.3 (GeV/c)² at electron scattering angles θ _e =77.5° to 139.0° in order to separate the magnetic dipole formfactorF _M (Q ²) from the electric formfactorF _E (Q ²). Experimental cross sections are compared to theoretical predictions and to measurements of other laboratories. The results indicate that contributions from meson exchange currents are not negligible in thisQ ² region.     

Electroproduction of η mesons in the region of the resonanceS 11(1535) at momentum transfers of 2 and 3 GeV2

We report on results of η-electroproduction in the resonance region at momentum transfers ofQ ²=2 GeV² and 3 GeV². The differential cross sections obtained in the region of the second nucleon resonance strongly support the dominance of theS ₁₁(1535) in this channel. The total transverse virtual photoproduction cross section of theS ₁₁(1535) shows a flatQ ²-dependence ～e ^?0.39· Q ². Comparison with the total resonant γ _v p cross section in the second resonance region aroundW=1.5 GeV shows that theD ₁₃(1520) production decreases much faster (～e ^?1.6· Q ²). The data are not compatible with the simple harmonic oscillator quark model with spin and orbit excitation of a quark only.