QCD sum rule analysis of Bottomonium ground states

The in-medium masses of the bottomonium ground states [$1S$ ($\Upsilon (1S), \eta_b$) and $1P$ ($\chi_{b0},\chi_{b1}$)] are investigated in the magnetized vacuum (nuclear medium), using the QCD sum rule framework. In QCD sum rule approach, the mass modifications are calculated in terms of the medium modifications of the scalar and twist-2 gluon condensates, which are obtained in the nuclear medium, from the medium change of a scalar dilaton field, $\chi$ within a chiral effective model. The in-medium masses of the bottomonium ground states are observed to decrease with increasing density. P-wave states are observed to have more appreciable mass-shifts than the S-wave states. In the present investigation, the effects of spin-mixing between 1S bottomonium states, $\Upsilon(1S)$ and $\eta_b$ are taking into account in presence of an external magnetic field. The contribution of magnetic fields are seen to be dominant via spin-magnetic field interaction effects, which leads to an appreciable rise and drop in the in-medium masses of the longitudinal component of vector $1S$ state ($\Upsilon$) and pseudoscalar state ($\eta_b$) respectively. For zero magnetic field, the effects of baryon density on the bottomonium ground states in isospin asymmetric nuclear medium are observed to be quite appreciable. These should have observable consequences for the production of the open and hidden bottom meson states resulting from high energy asymmetric nuclear collisions in facilities which probe high density baryonic matter. There is observed to be large contributions to the masses of the longitudinal component of the vector bottomonium state, $\Upsilon (1S)$ and pesudoscalar state $\eta_b$ in strong magnetic fields.