Calculation of electromagnetic ρπ formfactor from QCD sum rules

Electromagnetic ρπ formfactor at intermediate momentum transfer, 0.7 GeV²≦Q ²≦3 GeV², is calculated using QCD sum rules for the vertex function of two vector and one axial vector currents. In this region the results obtained are consistent within 25% accuracy with the vector meson dominance model predictions and can be regarded as its theoretical justification.     

Vertex QCD sum rules,quark model and pion wave function

It is shown that the predictions of the QCD sum rules (SR) and the quark model for the low energy pion wave function can be reconciled within the so-called vertex SR in exclusive kinematics. In contrast to the standard procedure, non-singular terms asx→0 in correlation functions are summed up by means of the conformal symmetry arguments. The soft contribution into the pion form factor is argued to dominate at least up toQ ²～4–6 GeV²     

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.     

DSE Perspective on QCD Modeling,Distribution Amplitudes,and Form Factors

We describe results for the pion distribution amplitude (PDA) at the non-perturbative scale μ = 2 GeV by projecting the Poincaré-covariant Bethe–Salpeter wave-function onto the light-front and use it to investigate the ultraviolet behavior of the electromagnetic form factor, F _π (Q ²), on the entire domain of spacelike Q ². The significant dilation of this PDA compared to the known asymptotic PDA is a signature of dynamical chiral symmetry breaking on the light front. We investigate the transition region of Q ² where non-perturbative behavior of constituent-like quarks gives way to the partonic-like behavior of quantum chromodynamics (QCD). The non-perturbative approach is based on the Dyson–Schwinger equation (DSE) framework for continuum investigations in QCD. The leading-order, leading-twist perturbative QCD result for Q ² F _π (Q ²) underestimates the new DSE computation by just 15 % on \({Q^2\gtrsim 8\,}\) GeV², in stark contrast with the result obtained using the asymptotic PDA.     

QCD analysis of the Bjorken sum rule revisited

We present extended analysis of the polarized Bjorken sum rule using the four-loop expression for the coefficient function C _Bj(α_s) available now and the recent low Q ²-data from the Jefferson Lab and COMPASS experiments. We demonstrate that the perturbative series for the function C _Bj gives a hint to its asymptotic nature manifesting itself in the region Q ² ? 1 GeV². It is confirmed by the considered integral model for the perturbative QCD correction. We analyze values of higher-twist terms extracted from the mentioned data and discuss the interplay between higher orders perturbative and higher-twist contributions. We extend our consideration to the Gross-Llewellyn Smith sum rule and investigate the relation between higher twist coefficients in these two sum rules.     

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.     

QCD corrections at the Z0

All QCD corrections in hadron-initiated lepton-pair production are questionable for Q²?100 GeV² since a perturbative expansion is not justified in this kinematical range. Application of the renormalization group (RG) program at Z₀ energies is meaningful. We exhibit the size of the non-log correction terms, introduce experimental tests, and point to the assumptiona inherent in Drell-Yan (DY) type analyses.     

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.     

Measurement of the proton structure function F 2 at low x and low Q 2 at HERA

We report on a measurement of the proton structure function F ₂ in the range 3.5 × 10^?5 ≤ x ≤ 4 × 10^?3 and 1.5 GeV² ≤ Q ² ≤ 15 GeV² at the ep collider HERA operating at a centre-of-mass energy of ${sqrt s} = 300 {? GeV}$. The rise of F ₂ with decreasing x observed in the previous HERA measurements persists in this lower x and Q ² range. The Q ² evolution of F ₂, even at the lowest Q ² and x measured, is consistent with perturbative QCD.     

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.     

The parton distribution functions of the photon and the structure functionF 2 γ (x,Q 2)

We present new parametrisations of the parton distribution functions of the photon including the first parametrisation in next-to-leading order QCD. We take into account some recent theoretical considerations pertaining to the gluon content of the photon,g ^γ. We argue that if an evolution is started at very lowQ ² and a fit to allF ₂ ^γ data performed with no constraints on the gluon distribution, then physically unreasonable gluon distributions may result. Our results support recent indications thatQ ₀ ² ≤1 GeV² is too low a value from which to start a perturbative evolution. Starting our evolution atQ ₀ ² =5.3 GeV², we evolve up inQ ² using a modified version of Rossi's Ansatz. The limited lever arm inQ ² leads to limited sensitivity to the QCD scale parameter Λ, though there is a preference for low values in the 0.1–0.2 GeV range. We also present new parametrisations of the singular asymptotic quark and gluon distribution functions of the photon which we believe are more accurate than those in current use.     

QCD constraints for the electromagnetic form factor of the pion

Using the modulus representation, we derive constraints for the behaviour of the electromagnetic form factor of the pion in the time like region [1 GeV², +∞], from information given by perturbative QCD in the space like region [?μ ², ?∞]. A phenomenological μ dependent upper bound for the exponent of the first non leading logarithmic correction is deduced. Restrictions and problems of the method are discussed.     

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.     

Model for nucleon gluon and sea quark structure functions at allx and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon gluon and sea quark structure functions at allx, and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =1.25 GeV² andA ²=0.01 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ².     

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.     

NLO predictions for the growth ofF 2 at smallx and comparison with experimental data

We present parametrizations for the proton structure functionF ₂ in the next to leading order in perturbative QCD. We consider that the dominant term toF ₂(x, Q ²) should grow asx ^?ψ _s for smallx values, with the exponentλ _S being essentially independent ofQ ². Comparisons with the most recent H1 and ZEUS data confirm the valueλ _S ～0.35 obtained previously from fits to low energy data.     

Estimate of the screening corrections to gluon distributions in the smallx region

The screening corrections to gluon distributions in a proton corresponding to the triple gluonic ladder diagram are estimated. They are found to be relatively small: their values does not exceed 10% of the leading order QCD gluon distribution forx?10^?4 andQ ² ?100 GeV².     

Measurement of the proton structure function F 2 at low x and low Q 2 at HERA

We report on a measurement of the proton structure functionF ₂ in the range 3.5×10⁻⁵≤x≤4×10⁻³ and 1.5 GeV²≤Q ²≤15GeV² at theep collider HERA operating at a centre-of-mass energy of √s=300GeV. The rise ofF ₂ with decreasingx observed in the previous HERA measurements persists in this lowerx andQ ² range. TheQ ² evolution ofF ₂, even at the lowestQ ² andx measured, is consistent with perturbative QCD. supported by EU HCM contract ERB-CHRX-CT93-0376