Form factors of heavy mesons in QCD

We discuss logarithmic corrections to form factors of mesons built from heavy quarks. The reactions e⁺e^? → η_cγ and H → Jψγ are considered as an example. A novel feature as compared to the well-studied problem of the pion form factor is the existence of transitions between the quark-antiquark state $\text{c}\text{c}$ and the gluonic one. O(α_s) corrections are calculated exactly. An infinite series of the leading logarithmic terms (α_sln[Q²/m_c²])ⁿ is summed up with the help of the operator technique. Apart from ree results already known for quark operators, we use some new results referring to gluon operators and their mixing with those made from quarks. Two alternative derivations of the multiplicatively renormalizable operators are given. The first one reduces to a direct computation of the mixing matrix and its diagonalization, the second is based on conformal symmetry considerations.     

Baryon-number-induced Chern-Simons couplings of vector and axial-vector mesons in holographic QCD

We show that holographic models of QCD predict the presence of a Chern-Simons coupling between vector and axial-vector mesons at finite baryon density. In the Anti de Sitter/Conformal Field Theory dictionary, the coefficient of this coupling is proportional to the baryon number density and is fixed uniquely in the five-dimensional holographic dual by anomalies in the flavor currents. For the lightest mesons, the coupling mixes transverse rho and a1 polarization states. At sufficiently large baryon number densities, it produces an instability, which causes the rho and a1 mesons to condense in a state breaking both rotational and translational invariance.     

Current correlation functions,QCD sum rules and vector mesons in baryonic matter

Based on an effective Lagrangian which combines chiral SU(3) dynamics with vector meson dominance, we have developed a model for the forward vector meson-nucleon scattering amplitudes. We use this as an input to calculate the low energy part of the current-current correlation function in nuclear matter. Its spectrum enters directly in the “left-hand side” of QCD sum rules. For the isovector channel we find a significant enhancement of the in-medium spectral density below the ϱ resonane while the ρ meson mass itself changes only slightly. The situation is different in the isoscalar channel, where the mass and peak position of the ω meson move downward while its width increases less drastically than in the ρ meson case. For the φ meson we find almost no mass shift; the width of the peak broadens moderately. We observe a remarkable degree of consistency with the operator product expansion of QCD sum rules in all three channels. We point out, however, that these results cannot simply be interpreted, as commonly done, in terms of a universal rescaling of vector meson masses in matter.     

Form factors in lattice QCD

Lattice simulations of QCD have produced precise estimates for the masses of the lowest-lying hadrons which show excellent agreement with experiment. By contrast, lattice results for the vector and axial vector form factors of the nucleon show significant deviations from their experimental determination. We present results from our ongoing project to compute a variety of form factors with control over all systematic uncertainties. In the case of the pion electromagnetic form factor we employ partially twisted boundary conditions to extract the pion charge radius directly from the linear slope of the form factor near vanishing momentum transfer. In the nucleon sector we focus specifically on the possible contamination from contributions of higher excited states. We argue that summed correlation functions offer the possibility of eliminating this source of systematic error. As an illustration of the method we discuss our results for the axial charge, g _A , of the nucleon.     

Current propagator: Duality between vector mesons and perturbative QCD

Local duality between vector mesons and perturbative QCD in the current propagator supplies expressions for their leptonic widths in terms of the quark masses, the masses of the lowest vector mesons and their first excitations and the QCD parameter Λ. The experimental data are consistent with this physical principle if ?′(1260 MeV) exists.     

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.     

Hadron wave functions in lattice QCD

Coulomb gauge quark-antiquark wave functions for the pion and the rho are calculated in the valence approximation on a lattice 8³ × 16. We use gauge group SU(2) at β of 2.431 corresponding to an inverse lattice spacing of 1100 ± 100 MeV. The wave functions fall off significantly over the size of the box, are rotationally invariant except at the box's boundary, and are nearly independent of the lagrangian quark mass.     

QCD correction to the leptonic decay rate ofD-wave vector mesons

We show that the first order QCD correction to the leptonic decay rate of heavy quark-antiquark³ D ₁ bound state is identical to that for a³ S ₁ state. Some phenomenological implications of this suppression are also discussed.     

The use of QCD in OZI violating radiative decays of vector mesons

The spin parity (J^P) of the hadronic system produced in OZI violating vector decays V → γ + h is analyzed in the lowest order QCD approach. While the predicted rates for 0^± states agree with the data, theoretically unacceptable anomalies occur for even J ≠ 0, P = +1, channels. Experimental consequences are drawn. We argue that the rate for gluon jet emission in V → γ + 2 gluons is substantially smaller than previously stated.     

QCD sum rules and pion wave functions

We consider light cone sum rules for a vertex function involving a pion state. These incorporate radiative corrections, continuum effects and power corrections; the latter depend on the non-asymptotic form of a higher twist component of the pion wave function. We derive restrictions on this component from sum rules for two-point functions and propose a model wave function for it. Finally we analyse our vertex sum rules in the light of this information and find results for the lowest twist component in good agreement with those already obtained from two-point function sum rules with derivative currents.     

QCD string in mesons and baryons

The distributions of fields generated by static $Q\bar Q$ and QQQ sources are calculated analytically within the bilocal approximation of the method of vacuum correlation functions. At large distances between the quarks, the fields assume a clear-cut stringlike shape. The main contribution to the string comes from the longitudinal component of the chromoelectric field. The contribution of the transverse chromoelectric field is below 3% of the contribution from the longitudinal component. A baryonic string has a Y-like shape with a deep well in the region of the string-junction position. Field distributions are considered for a quark-diquark configuration and in the case of three quarks occurring on a straight line. The interaction potential is calculated for three quarks residing at the vertices of an equilateral triangle.