弱磁场中的介子色散关系
Pionic dispersion relations in the presence of a weak magnetic field
摘要：
本文采用唯象的π-核子$(πN)$拉格朗日量，研究了真空中弱外磁场极限下$π^0$和$π^{\pm}$的色散关系。为了达到我们的目的，我们计算了赝标量$(PS)$和赝矢量$(PV)$介子-核子相互作用的自能图中一圈级的结果。通过假设弱的外部磁场，可以看出，π介子的有效质量得到明确的磁场依赖性，它是修改的情况下PS耦合显着。然而，对于PV耦合，仅观察到有效质量的适度增加。由于外场的存在，这些修改后的色散关系可以在中子星以及相对论性重离子碰撞中的介子的唯象方面产生重大影响。
英文摘要：
In this work, dispersion relations of $π^0$ and $π^{\pm}$ have been studied in vacuum in the limit of weak external magnetic field using a phenomenological pion-nucleon $(πN)$ Lagrangian. For our purpose, we have calculated the results up to one loop order in self energy diagrams with the pseudoscalar $(PS)$ and pseudovector $(PV)$ pion-nucleon interactions. By assuming weak external magnetic field it is seen that the effective mass of 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 relativistic heavy ion collisions.
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