Upsilon states in magnetized nuclear matter

Abstract: The mass modifications of the bottomonium states ($\Upsilon (NS)$,$N=1,2,3,4$ and $\Upsilon (1D)$) in magnetized nuclear matter are studied using chiral effective model. The in-medium masses are calculated from the medium modification of the scalar dilaton field in the chiral effective model, which simulates the gluon condensates of QCD. The strengths of the wave functions (assumed to be harmonic oscillator wave functions) denoted by the parameter, $\beta$, of the $\Upsilon (NS)$, $N=1,2,3,4$, are fitted from their observed decay widths to $e^+e^-$. The decay width for the channel, $\Upsilon (1D) \rightarrow e^+ e^-$ %, which has not yet been observed experimentally, has been predicted in the present work, by using the value of the parameter, $\beta$ for $\Upsilon(1D)$, interpolated from the $\beta$ versus mass relation, for the upsilon states. The effects of the isospin asymmetry of the nuclear medium on the masses of the upsilon states are investigated and are observed to be large for high densities. This should have observable consequences at the asymmetric heavy ion collisions at the Compressed baryonic matter (CBM) experiments at FAIR, GSI as well as at SPS, CERN. The study of the bottomonium states at CBM will however require access to higher energies than the energy regime planned at present. The effects of magnetic field on the masses of bottomonium states in nuclear matter are studied in the present work. These masses are investigated including the anomalous magnetic moments (AMM) of the nucleons, and compared to the results when the AMMs of nucleons are not taken into account. The effects of magnetic field as well as isospin asymmetry on the upsilon masses are obserevd to be large at high densities.