Magnetized matter effects on dilaton photon mixing

Dilatons [$\varphi (x)$] are a class of bosonic scalar particles associated with scaling symmetry and its compensation (under the violations of the same). They are capable of interacting gravitationally with other massive bodies. As they have coupling to two photons ($\gamma$), they are (also) capable of decaying to the two photons. However, the decay time is long and that makes them a good candidate for dark matter. Furthermore due to two photon coupling, they can produce optical signatures in a magnetic field. In a vacuum or plain matter they couple to one of the transversely polarized states of the photon. But in magnetized matter, they couple to both the transversely polarized state of photons (due to the emergence of a parity violating part of the photon self-energy contribution from magnetized matter). Being spin zero scalar, they could mix with spin zero longitudinal part of photons but they do not. A part of this work is directed towards understanding this issue of mixing the scalar with various polarization states of photons in a medium (magnetized or unmagnetized) due to the constraints from different discrete symmetries, e.g., charge conjugation ($\mathbf{C}$), parity ($\mathbf{P}$) and time reversal ($\mathbf{T}$) associated with the interaction. Based on these symmetry aided arguments, the structure of the mixing matrix is found to be $3\times 3$, as in the case of neutrino flavor mixing matrix. Thus there exists nonzero finite probabilities of oscillation between different polarization states of photon to dilaton. Our analytical and numerical analysis show no existence of periodic oscillation length either in temporal or spatial direction for the most general values of the parameters in the theory. Possible astrophysical consequences of these results can be detected through the discussed observations.

Figure 1

Plot of conversion probability of a parallel polarized photon into a scalar dilaton in magnetic field $\mathrm{B}={10}^{12}$ Gauss (in the left panel) and the same in magnetic field $\mathrm{B}={10}^{11}$ Gauss (in the right panel). The solid line is for conversion probability in presence of magnetized media and the dashed curve is the same in absence of self energy correction ${\mathrm{\Pi }}_{\mu \nu }^p$ from magnetized medium effects. The abscissa [energy of photon ($\omega$) in GeV] is in units of ${10}^{-5}$ and the ordinates are plotted in the units of ${10}^{-4}$. Here, the parameters used are the mass of dilaton (scalar) particle $\varphi$: $(m_{\varphi })=1.0\times {10}^{-12}\mathrm{GeV}$, coupling constant $(g_{\varphi \gamma \gamma })=1.0\times {10}^{-11}\mathrm{GeV}$, photon path length $(z)=1.2\mathrm{km}$, and plasma frequency $({\omega }_p)=1.96\times {10}^{-2}\mathrm{eV}$.

Figure 2

Plot of conversion probability of perpendicularly polarized photon into scalar in magnetic field $\mathrm{B}={10}^{12}$ Gauss (in the left panel) and the same in magnetic field $\mathrm{B}={10}^{11}$ Gauss (in the right panel). The abscissa [energy of photon ($\omega$) in units of ${10}^{-5}\mathrm{GeV}$] and the ordinate are plotted in units of ${10}^{-5}$. Here, the parameters used are mass of dilaton (scalar) particle $\varphi$ $(m_{\varphi })=1.0\times {10}^{-12}\mathrm{GeV}$, coupling constant $(g_{\varphi \gamma \gamma })=1.0\times {10}^{-11}\mathrm{GeV}$, photon path length $(z)=1.2\mathrm{km}$, and plasma frequency $({\omega }_p)=1.96\times {10}^{-2}\mathrm{eV}$.

Figure 3

Left panel: intensity of parallel and perpendicular polarized photons with scalar photon interaction in magnetized media vs energy ($\omega$). The dot curve represents $|A_{\parallel }{|}^2$ and the dashed curve represents $|A_{\perp }{|}^2$. Right panel: difference between ratios of intensity of parallel and perpendicular polarized photons (in absence and in presence of scalar photon interaction) $\mathrm{\Delta }F$. Parameters chosen are $\mathrm{\Gamma }$ (Lorentz boost factor) $=1.0\times {10}^6$, ${\omega }_c\sim 5\times {10}^{-5}\mathrm{GeV}$, $\mathrm{B}\sim {10}^{12}$ Gauss. The abscissa (energy of photon ($\omega$) in GeV) is in units of ${10}^{-5}$.

Figure 4

Evolution of $\mathrm{\Gamma }$ (Lorentz factor) of primary charge particle in the pulsar atmosphere with radiation reaction. The lowest point ($P$) in the curve represents the situation when energy gain by the charge particle is equal to energy loss due to radiation reaction, i.e., when (d2) equals zero.