Search

Dipion transitions of the subthreshold bottomonium levels $\Upsilon (nS)\to \Upsilon (n'S) \pi\pi$ with $n>n', n=2,3,4, n'=1,2$ are studied in the framework of the chiral decay Lagrangian, derived earlier. The channels $B\bar B, B\bar B^*+ c.c, B^* \bar B^*$ are considered in the intermediate state and realistic wave functions of $\Upsilon (n S),B$ and $B^*$ are used in the overlap matrix elements. Imposing the Adler zero requirement on the transition matrix element, one obtains 2d and 1d dipion spectra in reasonable agreement with experiment., Comment: 34 pages, 18 figures

We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of nonzero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with ${Q}_{\mathrm{index}}=0$. The remaining (ultraviolet) monopoles without vortices and\char22{}to a less extent\char22{}the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble affects the monopoles and vortices only by smoothing, reducing the density only slightly.

Institute for Theoretical and Experimental Physics,B. Cheremushkinskaya 25, Moscow 117259, RussiaIn equilibrium, at finite temperature below and above the deconfining phase transition, we havegenerated lattice SU(2) gauge fields and have exposed them to smearing in order to investigate theemerging clusters of topological charge. Analysing in addition the monopole clusters according tothe maximally Abelian gauge, we have been able to characterize part of the topological clusters tocorrespond either to non-static calorons or static dyons in the context of Kraan-van Baal caloronsolutions with non-trivial holonomy. We show that the relative abundance of these calorons anddyons is changing with temperature and offer an interpretation as dissociation of calorons into dyonswith increasing temperature. The profile of the Polyakov loop inside the topological clusters and the(model-dependent) accumulated topological cluster charges support this interpretation. Above thedeconfining phase transition light dyons (according to Kraan-van Baal caloron solutions with almosttrivial holonomy) become the most abundant topological objects. They are presumably responsiblefor the magnetic confinement in the deconfined phase.

Using smearing of equilibrium lattice fields generated at finite temperature in the confined phase of $SU(2)$ lattice gauge theory, we have investigated the emerging topological objects (clusters of topological charge). Analyzing their monopole content according to the Polyakov gauge and the maximally Abelian gauge, we characterize part of them to correspond to nonstatic calorons or static dyons in the context of Kraan-van Baal caloron solutions with nontrivial holonomy. The behavior of the Polyakov loop inside these clusters and the (model-dependent) topological charges of these objects support this interpretation.

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.