arXiv subjects
Publications and source records attributed to A. I. Veselov.
An additional $Z_6$ symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently. It has a singular nature and is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In this paper we report our results on the numerical simulation of its Electroweak sector.
By cooling of equilibrium lattice fields at finite temperature in SU(2) gauge theory it has been shown that topological objects (calorons) observed on the lattice in the confined phase possess a dyonic substructure which becomes visible under certain circumstances. Here we show that, with decreasing temperature of the equilibrium ensemble, the distribution in the caloron parameter space is modified such that the calorons appear non-dissociated into constituent dyons. Still the calorons have nontrivial holonomy which is demonstrated by the Polyakov line behaviour for these configurations. At vanishing temperature (on a symmetric lattice) topological lumps obtained by cooling possess rotational symmetry in 4D and a characteristic double peak structure of Polyakov lines (defined with respect to temporal and spatial directions) with non-trivial asymptotics.
Finite temperature Euclidean SU(2) lattice gauge fields close to the deconfinement phase transition are subjected to cooling. We find relatively stable or absolutely stable configurations with an action below the one-instanton action $S_{inst}=2π^2$ both in the deconfinement and the confinement phases. In this paper we attempt an interpretation of these lowest action configurations. Their action is purely magnetic and amounts to $S/S_{inst} \approx N_t/N_s$, where $N_t$ ($N_s$) is the timelike (spacelike) lattice size, while the topological charge vanishes. In the confined phase part of the corresponding lattice configurations turns out to be absolutely stable with respect to the cooling process in which case Abelian projection reveals a homogeneous, purely Abelian magnetic field closed over the "boundary" in one of the spatial directions. Referring to the dyonic structure established for the confinement phase near $T_c$ and based on the observation made for this phase that such events below the instanton action $S_{inst}$ emerge from dyon-antidyon annihilation, the question of stability (metastability) is discussed for both phases. The hypothetically different dyonic structure of the deconfinement phase, inaccessible by cooling, could explain the metastability.
We investigate numerically 10 - dimensional Euclidean quantum gravity (with discretized Einstein - Hilbert action) in the framework of the dynamical triangulation approach. For the considered values of the gravitational coupling we observed two phases, the behavior of which is found to be similar to that of the crumpled and elongated phases of 3, 4 and 5 dimensional models. Surprisingly, (for the observed lattice sizes) the natural state of the 10 D system (when the Einstein - Hilbert action is turned off) is found to resemble branched polymer while in the low dimensional systems the natural state belongs to the crumpled phase.
The $b\bar b$ spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings $Δ_1= Υ({\rm 1D})-χ_b({\rm 1P})$ and other splittings are very sensitive to the QCD constant $Λ_V(n_f)$ which occurs in the Vector scheme, and good agreement with the experimental data is obtained for $Λ_V(2$-loop, $n_f=5)= 325\pm 10$ MeV which corresponds to the conventional $Λ_{\bar{MS}} (2-$loop, $n_f=5)= 238\pm 7$ MeV, $α_s(2-$loop, $M_Z)=0.1189\pm 0.0005,$ and a large freezing value of the background coupling: $α_{\rm crit} (2$-loop, $q^2=0)=α_{\rm crit} (2$-loop, $r\to \infty)=0.58\pm 0.02$. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling $α_{\rm static}=const$ is introduced, as in the Cornell potential, then precise agreement with $Δ_1({\rm exp})$ and $Δ_2({\rm exp})$ can be reached for the rather large value $α_{\rm static} =0.43\pm 0.02$. We predict a value for the mass M(2D) = 10451\pm2 MeV.
We study QCD with two flavors of non-perturbatively improved Wilson fermions at finite temperature on the $16^3 8$ lattice. We determine the transition temperature at lattice spacings as small as $a \sim 0.12$ fm, and study string breaking below the finite temperature transition. We find that the static potential can be fitted by a two-state ansatz, including a string state and a two-meson state. We investigate the role of Abelian monopoles at finite temperature.
10 D Euclidean quantum gravity is investigated numerically using the dynamical triangulation approach. It has been found that the behavior of the model is similar to that of the lower dimensional models. However, it turns out that there are a few features that are not present in the lower dimensional models.
We found an additional symmetry hidden in the fermion and Higgs sectors of the Standard Model. It is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the whole Standard Model is constructed that possesses this symmetry.
The masses of $uudd\bar s $ and $uudd\bar d$ pentaquarks are evaluated in a framework of the Effective Hamiltonian approach to QCD using the Jaffe-Wilczek $[ud]^2\bar q$ approximation. The mass of the $[ud]^2\bar s$ state is found to be $\sim 300-500$ MeV higher than the observed $Θ^+(1540)$ mass.
We present results for QCD with $N_f=2$ flavors of dynamical quarks using nonperturbatively improved Wilson fermions at finite temperature on $16^3 \times 8$ and $24^3 \times 10$ lattices. We determine the transition temperature in the range of quark masses $0.6 \lesssim m_π/m_ρ\leq 0.8$. After fixing the Maximal Abelian gauge we investigate the contribution of Abelian monopoles to the Polyakov loop, Polyakov loop susceptibility and confirm Abelian and monopole dominance in full QCD.
We discuss the validity of replacing the complicated three-body confinement operator of the Y string junction type by three kinds of approximation which are numerically much simpler to handle: a one-body operator with the junction point at the centre of mass, a two-body operator corresponding to half the perimeter of the triangle formed by the three particles, and the average of both. Two different approaches for testing the quality of the approximations are proposed: a geometrical treatment based on the comparison of the potential energy strengths for the various inter quark distances, and a dynamical treatment based on the comparison of the corresponding effective string tensions using a hyperspherical approach. Both procedures give very similar results. It is shown how to simulate the genuine string junction operator by the approximations proposed above. Exact three-body calculations are presented in order to compare quantitatively the various approximations and to confirm our analysis.
We report the observation of calorons with nontrivial holonomy and fractional topological charge objects in cooled lattice samples derived from SU(2) equilibrium ensembles at $T<T_c$.
We have studied the three quark systems in an Effective Hamiltonian approach in QCD. With only two parameters: the string tension sigma and the strong coupling constant alpha_s we obtain a good description of the ground state light and heavy baryons. The prediction of masses of the doubly heavy baryons not discovered yet are also given. In particular, a mass of 3620 MeV for the lightest (ccu) baryon is found by employing the hyperspherical formalism to the three quark confining potential with the string junction.
We perform the careful study of the Gribov copies problem in SU(2) lattice gauge theory for maximal direct and maximal indirect center projections. We find that this problem is much more severe than it was thought before. The projected string tension is not in agreement with the physical string tension. We also show that the particle--like objects, nexuses, might be important for the confinement dynamics.
With the help of the cooling method applied to SU(2) lattice gauge theory at non-zero $T \le T_c$ we present numerical evidence for the existence of superpositions of Kraan-van Baal caloron (or BPS monopole pair) solutions with non-trivial holonomy, which might constitute an important contribution to the semi-classical approximation of the partition function.
We study the Abelian and non-Abelian action densitynear the monopole in the maximal Abelian gauge of SU(2) lattice gauge theory. We find that the non-Abelian action density near the monopoles belonging to the percolating cluster decreases when we approach the monopole center. Our estimate of the monopole radius is R_mon ~ 0.04 fm.
We consider the SU(2) lattice gauge model and investigate numerically the continuum limit of the simple center vortices which are singular configurations of the gauge fields. We found that the vortices remain alive in the continuum theory. Also we investigate the Creutz ratio and found that for all $β$ it vanishes for those field configurations which do not contain the simple center vortices inside the considered Wilson loop. It leads us to the conclusion that these singular field configurations play a real role in the continuum theory.
Finite temperature Euclidean SU(2) lattice gauge fields generated in the confinement phase close to the deconfinement phase transition are subjected to cooling. The aim is to identify long-living, almost-classical local excitations which carry (generically non-integer) topological charge. Two kinds of spatial boundary conditions (fixed holonomy and standard periodic boundary conditions) are applied. For the lowest-action almost-classical configurations we find that their relative probability semi-quantitatively agrees for both types of boundary conditions. We find calorons with unit topological charge as well as (anti-)selfdual lumps (BPS-monopoles or dyons) combined in pairs of non-integer (equal or opposite sign) topological charge. For calorons and separated pairs of equal-sign dyons obtained by cooling we have found that (i) the gluon field is well-described by Kraan-van Baal solutions of the Euclidean Yang-Mills field equations and (ii) the lowest Wilson-fermion modes are well-described by analytic solutions of the corresponding Dirac equation. For metastable configurations found at higher action, the multi-center structure can be interpreted in terms of dyons and antidyons, using the gluonic and fermionic indicators as in the dyon-pair case. Additionally, the Abelian monopole structure and field strength correlators between the centers are useful to analyse the configurations in terms of dyonic constituents. We argue that a semi-classical approximation of the non-zero temperature path integral should be built on superpositions of solutions with non-trivial holonomy.