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Register a new userPionic dispersion relations in the presence of a weak magnetic field
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In this work, dispersion relations of $pi^0$ and $pi^{pm}$ have been studied in vacuum in the limit of weak external magnetic field using a phenomenological pion-nucleon $(pi N)$ 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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In this work, the self energies of $pi^0$ and $pi^{pm}$ up to one loop order have been calculated in the limit of weak external magnetic field. The effective masses are explicitly dependent on the magnetic field which are modified significantly for the pseudoscalar coupling due to weak field approximation of the external field. On the other hand, for the pseudovector coupling, there is a modest increment in the effective masses of the pions. These theoretical developments are relevant for the study of the phenomenological aspect of mesons in the context of neutron stars as well as heavy ion collisions.
We calculate the momentum dependence of the $rho^0-omega$ mixing amplitude in vacuum with vector nucleon-nucleon interaction in presence of a constant homogeneous weak magnetic field background. The mixing amplitude is generated by the nucleon-nucleon ($NN$) interaction and thus driven by the neutron-proton mass difference along with a constant magnetic field. We find a significant effect of magnetic field on the mixing amplitude. We also calculate the Charge symmetry violating (CSV) $NN$ potential induced by the magnetic field dependent mixing amplitude. The presence of the magnetic field influences the $NN$ potential substantially which can have important consequences in highly magnetized astrophysical compact objects, such as magnetars. The most important observation of this work is that the mixing amplitude is non-zero, leading to positive contribute to the CSV potential if the proton and neutron masses are taken to be equal.
We calculate the rho meson mass in a weak magnetic field using effective $rhopipi$ interaction. It is seen that both $rho^0$ and $rho^pm$ masses decrease with the magnetic field in vacuum. $rho$ meson dispersion relation has been calculated and shown to be different for $rho^0$ and $rho^pm$. We also calculate the $rhopipi$ decay width and spectral functions of $rho^0$ and $rho^pm$. The width is seen to decrease with $eB$ and the spectral functions become narrower.
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