arXiv subjects
Publications and source records attributed to Yu. A. Simonov.
The $η$ production in the $(n,n')$ bottomonium transitions $Υ(n) \to Υ(n') η, $ is studied in the method used before for dipion heavy quarkonia transitions. The widths $Γ_η(n,n')$ are calculated without fitting parameters for $n=2,3,4,5, n'=1$. Resulting $Γ_η(4,1)$ is found to be large in agreement with recent data. Multipole expansion method is shown to be inadequate for large size systems considered.
The spin-dependent interactions in mesons are considered in detail in the framework of the Field Correlator Method. Analytic expressions for the spin-dependent potentials in heavy and light quarkonia are derived with the QCD string moment of inertia taken into account. Recent lattice data are analysed using these formulae and the data are shown to be consistent with very small values of the gluonic correlation length, <0.1 fm. The Field Correlator and the Eichten-Feinberg definitions of the spin-dependent potentials in the lowest, Gaussian approximation for the QCD vacuum are compared to one another and the two approaches are shown to be equivalent in the limit of a vanishing vacuum correlation length, whereas for finite values of the latter the difference between these two approaches can be explained by the contribution of the higher-order field corelators, starting from the quartic one.
In the framework of the coupled channel model the mass shifts of the $P$--wave excitations of $D_s$ and $B_s$ mesons have been calculated. The corresponding coupling to $DK$ and $BK$ channels is provided by the effective chiral Lagrangian which is deduced from QCD and does not contain fitting parameters. The strong mass shifts down for $0^+$ and ${1^+}'$ states have been obtained, while ${1^+}"$ and $2^+$ states remain almost at rest. Two factors are essential for large mass shifts: strong coupling of the $0^+$ and $1^{+'}$ states to the $S$-wave decay channel, containing a Nambu-Goldstone meson, and the chiral flip transitions due to the bispinor structure of both heavy-light mesons. The masses $M(B^*_s(0^+))=5710(15)$ MeV and $M(B_s(1^{+'}))=5730(15)$ MeV are predicted. Experimental limit on the width $Γ(D_{s1}(2536))<2.3$ MeV puts strong restrictions on admittable mixing angle between the $1^+$ and $1^{+'}$ states.
The mass shifts of the $P$-wave $D_s$ and $B_s$ mesons due to coupling to $DK$ and $BK$ channels are calculated in the coupling channel model without fitting parameters. The strong mass shifts down for $0^+$ and ${1^+}'$ states have been obtained, while ${1^+}"$ and $2^+$ states remain almost in situ. The masses of $0^+$ and ${1^+}'$ states of $B_s$ mesons have been predicted.
Dipion transitions of $Υ(nS)$ with $n=5, n'=1,2,3$ are studied using the Field Correlator Method, applied previously to dipion transitions with $n=2,3,4$ The only two parameters of effective Lagrangian were fixed in that earlier study, and total widths $Γ_{ππ} (5, n')$ as well as pionless decay widths $Γ_{BB} (5S), Γ_{BB^*} (5S), Γ_{B^*B^*}(5S)$ and $Γ_{KK} (5, n')$ were calculated and are in a reasonable agreement with experiment. The experimental $ππ$ spectra for $(5,1)$ and (5,2) transitions are well reproduced taking into account FSI in the $ππ$.
The vacuum gluonic correlation length is extracted from recent lattice data on spin-dependent interquark potentials in heavy quarkonia. It is shown that the data are consistent with extremely small values of the correlation length, Tg<0.1 fm.
Spin-dependent interaction in hadrons is considered in the approach of the QCD string. The string moment of inertia, which ensures the correct (inverse) Regge slope 2*pi*sigma, is found to suppress the spin-orbit interaction. For light quarks and moderate angular momenta the suppression constitutes around 25% whereas for large angular momenta the spin-orbit interaction is suppressed by the factor L^(-2/5). For heavy quarks the effect manifests itself as a string correction for the spin-dependent potential.
Dipion transitions of the subthreshold bottomonium levels $Υ(nS)\to Υ(n'S) ππ$ 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 $Υ(n S),B$ 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.
The $η$ production in the $(n,n')$ bottomonium transitions $Υ(n) \to Υ(n') η, $ is studied in the method used before for dipion heavy quarkonia transitions. The widths $Γ_η(n,n')$ are calculated without fitting parameters for $n=2,3,4,5, n'=1$.Resulting $Γ_η(4,1)$ is found to be large in agreement with recent data.
Two- and three-body decays of $Υ(5S)$ into $BB, $$ BB^*, $ $ B^*B^*,$ $ B_sB_s, $ $B_sB_s^*, $ $B_s^* B_s^*$ and $BB^*π, B^*B^*π$ are evaluated using the theory, developed earlier for dipion bottomonium transitions. The theory contains only two parameters, vertex masses $M_{br}$ and $M_ω$, known from dipion spectra and width. Predicted values of $Γ_{tot}(5S)$ and six partial widths $Γ_k(5S), k=BB, BB^*,...$ are in agreement with experiment. The decay widths $Γ_{5S}(πBB^*)$ and $Γ_{5S}(πB^*B^*)$ are also calculated and found to be of the order of 10 keV.
The di-pion spectrum for the $Υ(nS) \to Υ(n'S))$ transition with $n\leq 4$ has the form $\frac{dw}{dq}\sim $ (phase space) $ |η-x|^2$, with $x=\frac{q^2-4m^2_π}{(ΔM)^2 -4 m^2_π}< q^2 \equiv M^2_{ππ}, $ and $ΔM=M(nS) -M(n'S)$. The parameter $η$ is calculated and the spectrum is shown to reproduce the experimental data for all 3 types of decays: $3\to 1, 2\to 1$ and $3\to 2$ with $η\approx 0.5; 0$, and -3, respectively.
Nonperturbative picture of strong interacting quark-gluon plasma is given based on the systematic Field Correlator Method. Equation of state, phase transition in density-temperature plane is derived and compared to lattice data as well as subsequent thermodynamical quantities of QGP.
The mass shifts of the $P$-wave $D_s$ and $B_s$ mesons due to coupling to $DK$, $D^*K$ and $BK$, $B^*K$ channels are studied using the chiral quark-pion Lagrangian without fitting parameters. The strong mass shifts down $\sim 140$ MeV and $\sim 100$ MeV for $D^*_s(0^+)$ and $D_s(1^{+'})$ and $\sim 100$ MeV for $B^*_s(0^+)$ and $B_s(1^{+'})$ are calculated. Two factors are essential for large mass shifts: strong coupling of the $0^+$ and $1^{+'}$ states to the $S$-wave decay channel, containing a Nambu-Goldstone meson, and the chiral flip transitions due to the bispinor structure of both heavy-light mesons. The masses $M(B^*_s(0^+))=5695(10)$ MeV and $M(B_s(1^{+'}))=5730(15)$ MeV,very close to $M(B(0^+))$ and $M(B(1^{+'}))$, are predicted. Experimental limit on the width $Γ(D_{s1}(2536))<2.3$ MeV puts strong restrictions on admittable mixing angle between the $1^+$ and $1^{+'}$ states, $|ϕ|<6^{\circ}$, which corresponds to the mixing angle $θ$ between the $^3P_1$ and $^1P_1$ states, $29^{\circ}<θ< 41^{\circ}$.
Mechanism of di-pion transitions $nS\to n'Sππ(n=3,2; n'=2,1)$ in bottomonium and charmonium is studied with the use of the chiral string-breaking Lagrangian allowing for the emission of any number of $π(K,η),$ and not containing fitting parameters. The transition amplitude contains two terms, $M=a-b$, where first term (a) refers to subsequent one-pion emission: $Υ(nS)\toπB\bar B^*\toπΥ(n'S)π$ and second term (b) refers to two-pion emission: $Υ(nS)\toππB\bar B\toππΥ(n'S)$. The one-parameter formula for the di-pion mass distribution is derived, $\frac{dw}{dq}\sim$(phase space) $|η-x|^2$, where $x=\frac{q^2-4m^2_π}{q^2_{max}-4m^2_π},$ $q^2\equiv M^2_{ππ}$. The parameter $η$ dependent on the process is calculated, using SHO wave functions and imposing PCAC restrictions (Adler zero) on amplitudes a,b. The resulting di-pion mass distributions are in agreement with experimental data.
The vacuum-driven nonperturbative factors $L_i$ for quark and gluon Green's functions are shown to define the nonperturbative dynamics of QGP in the leading approximation. EoS obtained recently in the framework of this approach is compared in detail with known lattice data for $μ=0$ including $P/T^4$, $ε/T^4$, $\frac{ε-3P}{T^4}$. The basic role in the dynamics at $T\la 3T_c$ is played by the factors $L_i$ which are approximately equal to the modulus of Polyakov line for quark $L_{fund}$ and gluon $L_{adj}$. The properties of $L_i$ are derived from field correlators and compared to lattice data, in particular the Casimir scaling property $L_{adj} =(L_{fund})^{\frac{C_2(adj)}{C_2(fund)}}$ follows in the Gaussian approximation valid for small vacuum correlation lengths. Resulting curves for $P/T^4$, $ε/T^4$, $\frac{ε-3P}{T^4}$ are in a reasonable agreement with lattice data, the remaining difference points out to an effective attraction among QGP constituents.
We address the question of the Lorentz nature of the effective interquark interaction in QCD which leads to the formation of the QCD string between colour charges. In particular, we start from a manifestly vectorial fundamental interaction mediated by gluons and demonstrate that, as soon as chiral symmetry is broken spontaneously, the effective interquark interaction acquires a selfconsistently generated scalar part which is eventually responsible for the formation of the QCD string. We demonstrate this explicitly for a heavy-light quarkonium, using the approach of the Schwinger-Dyson-type equation and the quantum-mechanical Hamiltonian method of the QCD string with quarks at the ends.
The Debye mass m_D is computed nonperturbatively in the deconfined phase of QCD, where chromomagnetic confinement is known to be present. The latter defines m_D to be m_D=c_D\sqrt{σ_s}, where c_D \approx 2 and σ_s=σ_s(T) is the spatial string tension. The resulting magnitude of m_D(T) and temperature dependence are in good agreement with lattice calculations.
It is argued that the dominant contribution to the interaction of quark gluon plasma at moderate $T\geq T_c$ is given by the nonperturbative vacuum field correlators. Basing on that nonperturbative equation of state of quark-gluon plasma is computed and in the lowest approximation expressed in terms of absolute values of Polyakov lines for quarks and gluons $L_{fund} (T); L_{adj}(T)=(L_{fund})^{9/4}$known from lattice and analytic calculations. Phase transition at any $μ$ is described as a transition due to vanishing of one of correlators, $ D^E(x)$, which implies the change of gluonic condensate $ΔG_2$. Resulting transition temperature $T_c(μ)$ is calculated in terms of $Δ$$G_2$ and $L_{fund}(T_c)$. The phase curve $T_c(μ)$ is in good agreement with lattice data. In particular $T_c(0)=0.27; 0.19; 0.17$ GeV for $n_f=0,2,3$ and fixed $ΔG_2=0.0035$ GeV$^4$.