Abstract
In this work, dispersion relations of and have been studied in vacuum in the limit of a weak external magnetic field using a phenomenological pion-nucleon Lagrangian. For our purpose, we have calculated the results up to one loop order in self-energy diagrams with the pseudoscalar and pseudovector pion-nucleon interactions. By assuming a weak external magnetic field, it is seen that the effective mass of the pion gets explicit magnetic field dependence, and it is modified significantly for the case of PS coupling. However, for the PV coupling, only a modest increase in the effective mass is observed. These modified dispersion relations due to the presence of the external field can have substantial influence in the phenomenological aspect of the mesons, both in the context of neutron stars as well as in relativistic heavy ion collisions.
- Received 3 February 2016
DOI:https://doi.org/10.1103/PhysRevD.93.074033
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