We study the relativistic quark-antiquark system embedded in magnetic field (MF). The Hamiltonian containing confinement, one gluon exchange and spin-spin interaction is derived. We analytically follow the evolution of the lowest meson states as a functions of MF strength. Calculating the one gluon exchange interaction energy VOGE and spin-spin contribution aSS we have observed, that these corrections remain finite at large MF, preventing the vanishing of the total ρ meson mass at some Bcrit, as previously thought. We display the ρ masses as functions of MF in comparison with recent lattice data.

Perturbative gluon exchange interaction between quark and antiquark, or in a 3q system, is enhanced in a magnetic field and may cause vanishing of the total qq[over ¯] or 3q mass, and even unlimited decrease of it-recently called the magnetic collapse of QCD. The analysis of the one-loop correction below shows a considerable softening of this phenomenon due to qq[over ¯] loop contribution, similar to the Coulomb case of QED, leading to approximately logarithmic damping of gluon exchange interaction (≈O(1/ln|eB|)) at large magnetic field.

Dynamics of hadro-quarkonium system is formulated, based on the channel coupling of a light hadron (h) and heavy quarkonium (Q\bar{Q}) to intermediate open-flavor heavy-light mesons (Q\bar{q}, \bar{Q}q). The resulting effective interaction is defined by overlap integrals of meson wavefunctions and (hq\bar q) coupling, where h is pi, rho, omega, phi, without fitting parameters. Equations for hadro-quarkonium amplitudes and resonance positions are written explicitly, and numerically calculated for the special case of pi Upsilon(nS) (n=1,2,3). It is also shown, that the recently observed by Belle two peaks Z_b(10610) and Z_b(10650) are in agreement with the proposed theory. It is demonstrated, that theory predicts peaks at the BB*, B*B* thresholds in all available pi Upsilon(nS) channels. Analytic nature of these peaks is investigated, and shown to be due to a common multichannel resonance poles close to the BB*, B*B* thresholds. The general mechanism of these hadro-quarkonium resonances does not assume any molecular or four-quark (tetraquark) dynamics.Comment: 18 pages, 10 figures, minor changes, version to be published in Phys. Rev.

Nonperturbative treatment of quark-hadron transition at nonzero temperature T and chemical potential µ in the framework of Field Correlator Method is generalized to the case of nonzero magnetic field B. A compact form of the quark pressure for arbitrary B, µ, T is derived. As a result the transition temperature is found as a function of B and µ, which depends on only parameters: vacuum gluonic condensate G 2 and the field correlator D E 1 (x), which defines the Polyakov loops and it is known both analytically and on the lattice. A moderate (25%) decrease of T c (µ = 0) for eB changing from zero to 1 GeV 2 is found. A sequence of transition curves in the (µ, T ) plane is obtained for B in the same interval, monotonically decreasing in scale for growing B.

Radiative decays of Xð3872Þ with J PC ¼ 1 þþ are studied in the coupled-channel approach, where the c " c states are described by the relativistic string Hamiltonian, while for the decay channels DD Ã a stringbreaking mechanism is used. Within this method a sharp peak and correct mass shift of the 2 3 P 1 charmonium state just to the D 0 D Ã0 threshold was already obtained for a prescribed channel coupling to the DD Ã decay channels. For the same value of coupling the normalized wave function (w.f.) of Xð3872Þ acquires admixture of the 1 3 P 1 component with the weight c 1 ¼ 0:153 ( ¼ 8:8 ), which increases the transition rate ÀðXð3872Þ ! J=c Þ up to 50-70 keV, making the ratio R ¼ BðXð3872Þ!c 0 Þ BðXð3872Þ!J=c Þ ¼ 0:8 AE 0:2ðthÞ significantly smaller, as compared to R ' 5 for Xð3872Þ as a purely 2 3 P 1 state.