QCD analysis of twist-4 contributions to the g i structure functions

We analyze the twist-4 contributions to Bjorken and Ellis-Jaffe sum rules for spin-dependent structure function g ₁(x, Q ²). We investigate the anomalous dimensions of the twist-4 operators which determine the logarithmic correction to the 1/Q ² behavior of the twist-4 contribution by evaluating off-shell Green’s functions in both flavor non-singlet and singlet case. It is shown that the operators which are proportional to the equation of motion play an important role to extract the anomalous dimensions of physical operators. The calculations to solve the operator mixing of higher-twist operators are given in detail     

Quark mass effects in deeply inelastic scattering

We argue that the difference between the structure functions corresponding to deep inelastic scattering with and without heavy quarks in the current fragmentation region scales at high Q² and fixed (low) x _Bj.     

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.     

The effect of 1Q2 and αs corrections on tests of QCD

We discuss in detail the use of the structure function F₃(x, Q²) of deep-inelastic neutrino scattering for testing quantum chromodynamics. QCD is entirely consistent with all data. However, we show that higher-twist (order $\text{1}\text{Q}{}^2$) contributions, which are commonly neglected, can have a dramatic impact on interpretation of this result. At present the data are not accurate enough to determine the magnitudes of these $\text{1}\text{Q}{}^2$ contributions within the context of QCD. Furthermore, the possible presence of higher-twist terms makes it impossible to unambiguously detect the logarithmic Q² dependence and anomalous dimensions which distinguish QCD from hypothetical alternative theories. As a result, more precise data with higher Q² are needed to provide definitive tests of QCD. The corrections of second-order in α_s introduce fewer complications for testing QCD, and provide a useful context for understanding critical ambiguities in the definitions of α_s and Λ.     

A unified description of the perturbative photon structure function inx space

We give here in detail the derivation of the various contributions to the photon structure function in the perturbative region. The lowx region problem is pointed out and the QCD corrections to the hadronic part are discussed, including the quasi perturbative region of higher twist effects. The transition from highQ ² to lowQ ² is examined and the basis for a realistic and consistent simulation of higher order QCD processes is given.     

Correlation function for topological charge densities within the instanton model in QCD

The QCD sum rule for the correlation of topological charge densities χ(Q ²) and for the longitudinal part of the correlation function for singlet axial currents (the latter is related to the former) is considered within the instanton model. The constant f _η′ of η′-meson coupling to the singlet axial current is determined. Its value appears to be in good agreement with that determined recently from the relation between the proton-spin fraction Σ carried by u, d, and s quarks and the derivative of the QCD topological susceptibility χ′(0). On the basis of the same sum rule, the η-η′ mixing angle θ₈ is found within the model employing two mixing angles. The value of θ₈ coincides with that in effective chiral theory. The correlation function for topological charge densities χ(Q ²) at large Q ² is calculated. It is shown that the Q ² dependence at high Q ² matches well with that at low Q ², the latter being determined by the known values χ′(0) and by the contributions of the π and η mesons.     

Infrared renormalons and the relations between the Gross-Llewellyn Smith and the Bjorken polarized and unpolarized sum rules

It is demonstrated that the infrared renormalon calculus indicates that the QCD theoretical expressions for the Gross-Llewellyn Smith sum rule and for the Bjorken polarized and unpolarized ones contain an identical negative twist-4 1/Q² correction. This observation is supported by the consideration of the results of calculations of the corresponding twist-4 matrix elements. Together with the indication of the similarity of the perturbative QCD contributions to these three sum rules, this observation leads to simple new theoretical relations between the Gross-Llewellyn Smith and Bjorken polarized and unpolarized sum rules in the energy region Q² ≥ 1 GeV². The validity of this relation is checked using concrete experimental data for the Gross-Llewellyn Smith and Bjorken polarized sum rules.     

Highlights and perspectives of the JLab spin physics program

Nucleon spin structure has been an active, exciting and intriguing subject of interest for the last three decades. Recent precision spin-structure data from Jefferson Lab have significantly advanced our knowledge of nucleon structure in the valence quark (high-x) region and improved our understanding of higher-twist effects, spin sum rules and quark-hadron duality. First, results of spin sum rules and polarizabilities in the low to intermediate Q ² region are presented. Comparison with theoretical calculations, in particular with Chiral Perturbation Theory (ChPT) calculations, are discussed. Surprising disagreements of ChPT calculations with experimental results on the generalized spin polarizability, δ _LT, were found. Then, precision measurements of the spin asymmetry, A ₁, in the high-x region are presented. They provide crucial input for global fits to world data to extract polarized parton distribution functions. The up and down quark spin distributions in the nucleon were extracted. The results for Δd/d disagree with the leading-order pQCD prediction assuming hadron helicity conservation. Results of precision measurements of the g ₂ structure function to study higher-twist effects are presented. The data indicate a significant higher-twist (twist-3 or higher) effect. The second moment of the spin structure functions and the twist-3 matrix element d ₂ results were extracted. The high Q ² result was compared with a Lattice QCD calculation. Results on the resonance spin-structure functions in the intermediate Q ² range are presented, which, in combination with DIS data, enable a detailed study of quark-hadron duality in spin-structure functions. Finally, an experiment to study neutron transversity and transverse spin asymmetries is discussed. A future plan with the 12 GeV energy upgrade at JLab is briefly outlined.     

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.     

Slow and fast quarks in nucleons

Using light-front dynamics, and the notion of the running effective quark mass, we propose a model of the three-quark nucleon wave function, which accounts simultaneously both for the low and the high energy experimental data. Our wave function is a product of a spinor part, inferred from the QCD sum rules, and a gaussian scalar factor, taken for simplicity. Including all three Ioffe currents we get from one wave function both the negative neutron charge radius 〈r²〉_neutron=-0.108 fm² and the decreasing d/u ratio in the proton for x_Bj increasing from 0.5 to 1.     

The applicability of perturbative QCD to the pion form factor and the pionic wavefunction

We reanalyse the pionic form factor by using perturbative QCD theory and contributions from endpoint regions. We find that the perturbative QCD can be applied to the pionic form factor asQ ²>4 GeV² and they become unreliable asQ ²≦4 GeV². Therefore the applicability of perturbative QCD to the form factor is questionable only asQ ²≦4 GeV².     

Small-<Emphasis Type="Italic">x</Emphasis> Behavior of Non-singlet Spin Structure Function and Bjorken Sum Rule with pQCD Correction up to NNLO and Higher Twist Correction

A calculation of the non-singlet part of spin dependent structure function, \(xg_{1}^{NS}(x,Q^{2})\) and associated sum rule, the Bjorken Sum rule up to next-next-to-leading order(NNLO) is presented. We use a unified approach incorporating Regge theory and the theoretical framework of perturbative Quantum Chromodynamics. Using a Regge behaved model with Q ² dependent intercept as the initial input, we have solved the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation up to NNLO at small-x for \(xg_{1}^{NS}(x,Q^{2})\) and the solutions are utilised to calculate the polarised Bjorken sum rule(BSR). We have also extracted the higher twist contribution to BSR based on a simple parametrisation. These results for both of \(xg_{1}^{NS}(x,Q^{2})\) and BSR, along with higher twist corrections are observed to be consistent with the available data taken from SMC, E143, HERMES, COMPASS and JLab experiments. In addition, our results are also compared with that of other theoretical and phenomenological analysis based on different models and a very good agreement is also observed in this regard. Further a very good consistency between our calculated results and theoretical QCD predictions of BSR is also achieved.     

A model of deep inelastic polarized electroproduction

A realistic phenomenological model combining parton/QCD ideas with lower energy SU(6) constraints is proposed for the shape and evolution of the leading spin-dependent structure function G^ep(x, Q²) in polarized electroproduction. Close's broken-SU(6) ansatz is used to relate appropriately defined polarized quark-parton distribution densities to unpolarized ones at the matching momentum scale Q² = Q₀². The differences between spin and helicity distribution densities as well as the complications due to perturbative QCD and parton k_T (with related target-mass) effects are taken into account. Evolution to higher (>10 GeV²) values of Q² (where target-mass effects can be neglected) yields experimentally testable numerical predictions that are presented through various plots. The value of Q₀ is self-consistently determined to be about 0.5 GeV.     

Pion form factor in QCD: How to calculate?

The calculation of the pion form factor F _π(Q ²) in QCD is discussed. The main points of the nonlocal condensate QDC sum rule approach are considered and its results for the pion form factor are shown compared with the predictions of the perturbative and lattice QCD. The local duality (LD) approach for the pion FF in QCD is studied. It is shown that the main parameter of the approach for Q ² ≥ 2 GeV², namely, s ₀^LD(Q ²) should grow with an increase in Q ², rather than remain constant.     

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.     

Sum rules and the pion form factor in QCD

We propose a new approach to the investigation of the pion electromagnetic form factor in QCD based on the systematic use of the QCD sum rule technique. The theoretical curve obtained for F_π(Q²) is in good agreement with existing experimental data.     

QCD analysis of non-singlet neutrino structure functions

We present a systematic analysis of all available neutrinoxF ₃ data, using an analytic parametrisation which incorporates second order QCD predictions forQ ² evolution. We find $$\Lambda _{\overline {MS} } = 0.30 \pm 0.13{\rm{ }}GeV$$ where the error is statistical, and both Fermi andW-boson propagator corrections have been made to the data. Neglect of the former has negligible effects, but neglect of the latter would increase Λ by ～0.1 GeV. We find that higher-twist effects are small and negative, and estimate their effect on the determination of Λ. We are unable to fit the data with higher-twist terms alone.     

Strange quark mass from pseudoscalar sum rule with O(\alpha_s^4) accuracy

We include the new, five-loop, O(α_s⁴) correction into the QCD sum rule used for the s-quark mass determination. The pseudoscalar Borel sum rule is taken as a study case. The OPE for the correlation function with N⁴LO, O(α_s⁴) accuracy in the perturbative part, and with dimension d≤6 operators reveals a good convergence. We observe a significant improvement of stability of the sum rule with respect to the variation of the renormalization scale after including the O(α_s⁴) correction. We obtain the interval m̄_s(2 GeV)=105±6±7 MeV, which exhibits about 2 MeV increase of the central value, if the O(α_s⁴) terms are removed.     

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.     

The infrared spectrum of C3O2: The interaction between ν7 and the ν2 and ν4 vibrations

The 3ν¹₇, 3ν³₇, and 4ν⁰₇ hot bands of the ν₄ fundamental of C₃O₂ in the 1580 cm^?1 region were analyzed from tunable diode laser spectra and the ground state to ν₄ + 2ν⁰₇ band at 1644 cm^?1 from Fourier transform spectra (FTS). The molecular constants for all of the v₄ 1 ← 0 bands as well as the intensity of the ν₀ + 2ν⁰₇ sum band relative to the ν₄ fundamental were in agreement with the predictions of the model of Weber and Ford. FTS spectra at 0.05 cm^?1 resolution were obtained of the sum and difference bands of ν₂ with ν₇ in the 750–900 cm^?1 region. Sharp Q branches occur for each ν₇ state in the sum bands, but only a number of R-branch bandheads and no recognizable Q branches in the difference bands. Assignments of the sum band Q branches through v₇ = 6 were made and molecular constants were determined for the ν₂ + ν¹₇ ← 0 transition at 819.7 cm^?1. The ν₇ potential function in the v₂ = 1 state was found to have a 1.2 cm^?1 barrier with a minimum at α = 4.9°, where 2α is the angular deviation from linearity. The Q-branch positions predicted from the calculated energy levels fit those observed within several cm^?1.