Narrow Results

We investigate a connection between a renormalon ambiguity of heavy quark mass and the gluon condensate contribution into the quark dispersion law related to a virtuality defining a displacement of the heavy quark from the perturbative mass-shell, which happens inside a hadron.

Under assumption of singular behavior of invariant charge α_s(q²) at q²≃0 and of large q² behavior, corresponding to the perturbation theory up to four loops, a procedure is considered of smooth matching the β-function at a boundary of perturbative and nonperturbative regions. The procedure results in a model for α_s for all q²>0 with dimensionless parameters being fixed and dimensional parameters being expressed in terms of only one quantity Λ_QCD. The gluon condensate which is defined by the nonperturbative part of the invariant charge is calculated for two variants of "true perturbative" invariant charge, corresponding to freezing option and to analytic one in nonperturbative region. Dimensional parameters are fixed by varying normalization condition . It is obtained that on the boundary of perturbative region , the procedure results in nonperturbative Coulomb component α_Coulomb≃0.25, the nonperturbative region scale q₀≃1 GeV, the model parameter σ≃(0.42 GeV)² which suits as string tension parameter, the gluon condensate appears to be close for two variants considered, K≃(0.33–0.36 GeV)⁴ (for ).

We present an analytic calculation of Branching Ratio (BR) and Charge-Parity (CP) violating asymmetries of the $B_s^0$ meson decays to $D^{+}{D}^{-}$ by calculating the amplitude and the decay width of the process including the chiral loop and gluon condensate to first-order. We find the BR of $B_s^0\to D_s^{+}{D}_s^{-}=(1.8\pm 0.4)\times 10^{-3}$ which is in agreement with other experimental measurements and theoretical predictions. We also calculate the direct CP violation, CP violation in mixing and CP violation due to interference which are $A_{\mathrm{\text{CP}}}^{\mathrm{\text{dir}}}=0.00348\pm 0.00012$, $(A_{\mathrm{\text{CP}}}^{\mathrm{\text{mix}}})=-0.04395\pm 0.00129$ and $(A_{\mathrm{\Delta }\mathrm{\Gamma }})=-0.99903\pm 0.00122$, respectively.

We apply the Bogoliubov compensation principle to QCD. The nontrivial solution of compensation equations for a spontaneous generation of the anomalous three-gluon interaction leads to the determination of parameters of the theory, including behavior of the gauge coupling α_s(Q²) without the Landau singularity, the gluon condensate V₂ ≃0.01 GeV⁴, mass of the lightest glueball M_G≃1500 MeV in satisfactory agreement with the phenomenological knowledge. The results strongly support the applicability of Bogoliubov compensation approach to gauge theories of the Standard Model.

We make progress towards a derivation of a low energy effective theory for SU(2) Yang–Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov–Taylor identities in the Maximal Abelian Gauge. After that, we perform the Spin-Charge decomposition in a way proposed by Faddeev and Niemi. The resulting action describes a pair of nonlinear O(3) and $\sigma$-models interacting with a scalar field. The potential of the scalar field is a Mexican hat and the location of the minima sets the energy scale of solitonic configurations of the $\sigma$-model fields whose excitations correspond to glueball states.

We discuss the relationship between the large order behavior of the perturbative series for the average plaquette in pure gauge theory and singularities in the complex coupling plane. We discuss simple extrapolations of the large order for this series. We point out that when these extrapolated series are subtracted from the Monte Carlo data, one obtains (naive) estimates of the gluon condensate that are significantly larger than values commonly used in the continuum for phenomelogical purpose. We present numerical results concerning the zeros of the partition function in the complex coupling plane (Fisher's zeros). We report recent attempts to solve this problem using the density of states. We show that weak and strong coupling expansions for the density of states agree surprisingly well for values of the action relevant for the crossover regime.