Modification of the B Meson Mass in a Magnetic Field from QCD Sum Rules

Abstract

In this paper we extend the well known QCD sum rules used in the calculation of the mass of heavy mesons to estimate the modification of the charged B meson mass, m_B, in the presence of an external Abelian magnetic field, eB. Two simplifying limits were considered: the weak field limit in which the external field satisfies eB << m^2 (with m being any of the masses involved) and the strong field limit in which the field strength is small in comparison to the bottom quark mass (or the B meson mass) squared but it is large compared to the mass of the light quarks, i.e., m^2_{u,d} << eB << m^2_{b,B}. We found that m_B decreases with the magnetic field in the both of these limits.