Testing QCD scaling violations in the HERA energy range

High energy electron-proton colliders open new kinematical domains for the investigation of scaling violations in nucleon structure functions. Focussing on HERA as a definite study case we explore the precision which can be expected in determinations of the QCD scale parameter Λ and the running coupling constant α _s (Q ²). Our results provide a quantitative basis for discussions of the possibilities and requirements of QCD tests in inclusive deep inelastic scattering at HERA energies.     

Discriminative deep inelastic tests of strong interaction field theories

It is demonstrated that recent measurements of ∫¹₀F₂(x, Q²)dx eliminate already all strong interaction field theories except QCD. A detailed study of scaling violations of F₂(x, Q²) in QCD shows their insensitivity to the gluon content of the hadron at presently measured values of Q².     

Self-consistent Gaussian model of nonperturbative QCD vacuum

We show that the minimal Gaussian model of nonlocal vacuum quark and quark-gluon condensates in QCD violates the transverse character of the correlator of two vector currents. We suggest the improved Gaussian model of the nonperturbative QCD vacuum, which respects QCD equations of motion and minimizes the revealed gauge-invariance breakdown. We obtain the refined values of pion distribution amplitude (DA) conformal moments 〈ξ^2N 〉_π (N = 1, ..., 5) using the improved QCD vacuum model, including the inverse moment 〈x ^?1〉_π, being inaccessible if one uses the standard QCD SR. We construct the allowed region for Gegenbauer coefficients a ₂ and a ₄ of the pion DA for two values of the QCD vacuum nonlocality parameter, λ _q ² = 0.4 and 0.5 GeV².     

On the Q2 dependence of parton fragmentation functions

The Q² dependences of parton fragmentation functions are calculated using lowest-order quantum chromodynamics (QCD). The resulting scaling deviations have a simple intuitive form when a suitable valence-sea decomposition is employed for the quark fragmentation functions.     

Comparison of moments from the valence structure function with QCD predictions

We present moments (both ordinary and Nachtmann) of the nucleon valence structure function measured in high Q²_νFE scattering, supplemented by data from deep inelastic eD scattering. These data seem to agree with QCD predictions for vector gluons. The QCD parameter Λ is found to be of the order 0.5 GeV.     

B c-meson decays and lifetime within QCD sum rules

On the basis of three-point sum rules, the form factors for the semileptonic decays B _c ⁺ → B _s(B _s ^* )l ⁺ ν _l are calculated with allowance for α _s/v Coulomb corrections for the heavy quarkonium. Generalized relations associated with spin symmetry within the approach combining heavy-quark effective theory and nonrelativistic QCD are derived for form factors in the region of recoil momenta close to zero. The nonleptonic decays of the B _c meson are studied on the basis of the factorization hypothesis. By summing the main exclusive modes of c-quark decays and by using the results of a previous analysis of b-quark decays, the B _c-meson lifetime is estimated within QCD sumrules and within nonrelativistic QCD.     

Theoretical Description and Measurement of the Pion–Photon Transition Form Factor

Detailed predictions for the scaled pion–photon transition form factor are given, derived with the method of light-cone sum rules and using pion distribution amplitudes with two and three Gegenbauer coefficients obtained from QCD sum rules with nonlocal condensates. These predictions agree well with all experimental data that are compatible with QCD scaling (and collinear factorization), but disagree with the high-Q ² data of the BaBar Collaboration that grow with the momentum. A good agreement of our predictions with results obtained from AdS/QCD models and Dyson–Schwinger computations is found.     

Properties of quark matter governed by quantum chromodynamics (II). Renormalization schemes in quark matter

Renormalization schemes are examined (in the Coulomb gauge) for quantum chromodynamics in the presence of quark matter. We demand that the effective coupling constant for all schemes become congruent with the vacuum QCD running coupling constant as the matter chemical potential, μ, goes to zero. Also, to enable us to standardize with the vacuum QCD running coupling constant at some asymptotic momentum transfer, $\text{|}\text{p}{}_0\text{|,}\text{we keep}\text{μ ? ¦}\text{p}{}_0\text{¦}$, to ensure that the matter contribution is negligible at this point. This means all schemes merge with vacuum QCD at $\text{|}\text{p}{}_0\text{|}$ and beyond. Two renormalization group invariants are shown to emerge: (i) the effective or invariant charge, g_inv², which is, however, scheme dependent and (ii) g²(M)/S(M), where S(M)^?1 is the Coulomb propagator, which is scheme independent. The only scheme in which g_inv² is scheme independent and identical to g²(M)/S(M) is the screened charged scheme (previous paper) characterised by the normalization of the entire Green function, S^?1, to unity. We conclude that this is the scheme to be used if one wants to identify with the experimental effective coupling in perturbation theory. However, if we do not restrict to perturbation theory all schemes should be allowed. Although we discuss matter QCD in the Coulomb gauge, the above considerations are quite general to gauge theories in the presence of matter.     

First-order chiral phase transition in lattice QCD

The chiral phase transition in lattice QCD has been studied for light fermions of mass ma=0.025 on lattices of size 4⁴ and 8³×4 using the hybrid algorithm. We find evidence for a first-order chiral phase transition with a large latent heat. A comparison with 10³×6 data shows violations of asymptotic scaling for T_ch which are similar in magnitude to those observed in the pure gauge sector.     

The axial Ward identity in the presence of a quark-condensing vacuum

Quark-condensate contributions to triangle amplitudes arising from the nonperturbative content of the QCD vacuum are shown to uphold the anomalous axial Ward identity to leading and next-to-leading order in both the expansion parameter [m _quark/momentum]², as well as in the expansion parameter [m _π/m _quark]² appropriate forπ ⁰→ kinematics.     

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.     

A direct method for computing QCD predictions for deep inelastic structure functions

We develop a method for computing QCD predictions for scaling violations in the deep inelastic region. Our technique consists in calculating analytically the convolution products of the probability functions P_ij(x), appearing in the Altarelli-Parisi equations, with the experimentally measured structure functions. We never need to calculate the moments of the latter. As an application we compute the gluon density at Q² = 9 (GeV)² structure functions. A very good agreement with experiment is obtained for Λ = 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.     

Decoupling of heavy quarks in quantum chromodynamics

Decoupling of heavy quarks in quantum chromodynamics (QCD) defined by mass-independent renormalization is investigated. The structure of the relations between the parameters of f flavour QCD and the parameters of the effective f ? 1 flavour QCD below a heavy-quark threshold is discussed to all orders in the loop expansion, and the relations are computed to two-loop approximation for the minimal subtraction schemes (MS) and to one-loop approximation for some Weinberg schemes. These matching relations can be used to systematically determine the renormalization group (RG)-invariant parameters of the effective theory in terms of the RG-invariant parameters of the theory which includes the heavy quark, or vice versa. For the $\text{MS}$ scheme the connection between Λ_{f ? 1} nad Λ_f to two and three loops is given as well as the two-loop connection between the RG-invariant mass parameters of the f ? 1 and f flavour theory. The effect of heavy quarks on the evolution of the QCD coupling is of significance for present QCD phenomenology based on next-to-leading-order perturbation theory. This is illustrated with a few examples within the $\text{MS}$ scheme.     

Decay constants of pseudoscalar and vector mesons with improved holographic wavefunction

We calculate the decay constants of light and heavy-light pseudoscalar and vector mesons with improved soft-wall holographic wavefuntions,which take into account the effects of both quark masses and dynamical spins.We find that the predicted decay constants,especially for the ratio f V/f P,based on light-front holographic QCD,can be significantly improved,once the dynamical spin effects are taken into account by introducing the helicity-dependent wavefunctions.We also perform detailed χ~2 analyses for the holographic parameters(i.e.the mass-scale parameterκ and the quark masses),by confronting our predictions with the data for the charged-meson decay constants and the meson spectra.The fitted values for these parameters are generally in agreement with those obtained by fitting to the Regge trajectories.At the same time,most of our results for the decay constants and their ratios agree with the data as well as the predictions based on lattice QCD and QCD sum rule approaches,with only a few exceptions observed.     

Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wavefunctions and the form factors of mesons

The predictions of quantum chromodynamics for meson form factors at large momentum transfer are given. Evolution equations are derived which determine the structure of hadronic wavefunctions at short distances from their form at large distances. The eigenvalues of the evolution equations appear as exponents in anomalous logarithm corrections to the nominal power law of form factors determined by dimensional counting. The results lead to detailed tests of the spin and scaling structure of QCD at short distances. The predictions for the charged pion, kaon and rho form factors and the γ → π⁰ transition form factor of the photon are absolutely normalized at asymptotic momentum transfer.     

The QCD sum rule approach for the semileptonic decay of the D or B meson into a light meson and leptons

We use the method of QCD sum rules to treat the semileptonic weak decay of the D or B meson into a light meson and leptons. To obtain the transition form factors, we adopt the two-point Green’s function in the presence of an external vector or axial-vector field. We find that this method can be related approximately to the traditional three-point Green’s function in the heavy quark limit (m _Q → ∞). Unlike some existing QCD sum rule calculations, our results indicate that the form factors have simple dipole or monopole behavior. We obtain results on the various form factors of the semileptonic decay of D and B mesons into a light meson and investigate various decay processes such as B?⁰ → π ⁺ τ _^?ν?_τ and B?⁰ → ρ ⁺ τ^～ν?_τ. The method allows us to take into account nonperturbative strong interaction effects, thereby providing a more reliable determination of the Cabibbo-Kobayashi-Maskawa matrix elements from the experimental data.     

Recombination dependence of theO(α s 2 ) three-jet cross section ine + e − annihilation

TheO(α _s ² ) QCD corrections to the thrust distribution for three-jet production ine ⁺ e ^? annihilation are found to depend on the algorithm for recombining four partons into three jets. Several recombination schemes are discussed and results are compared. Results of the recombination approach are compared also to recent direct calculations of three-jet thrust distributions. The importance of terms proportional to jet resolution parameters is stressed.