New Light and Heavy Matter States and Their Role in Astrophysics and Cosmology

Abstract

Many extensions of the Standard Model of particle physics, in particular scenarios based on supergravity or superstrings, predict a hidden sector of new particles interacting only very weakly with Standard Model particles. Such scenarios do not necessarily only contain Weakly Interacting Massive Particles (WIMPs ), new heavy states at the GeV-TeV scale and above some of which are candidates for the dark matter, but often also predict Weakly Interacting Sub-eV (or Slim) Particles (WISPs) that can couple to the photon field $A_\mu$ [926]. The most well-known examples include pseudo-scalar axions and axion-like particles (ALPs) a and hidden photons that mix kinetically with photons. At the high end of the mass spectrum various particle physics models also predict the existence of non-elementary particle states that can be either one-dimensional topological defects such as monopoles or non-topological solitons such as condensations of bosonic states and so-called Q-balls . The particle physics aspects of many of these objects have been introduced in Chap. 2. In the present chapter we discuss them further and review some of their possible astrophysical and cosmological effects.

Problems

15.1

Wave Equation for Photon-ALP Mixing

Derive Eq. (15.27) from the Lagrange densities for the photon, Eq. (2.194), and for the ALP, Eq. (15.2) with Eq. (15.17), using the hints in the text and the general Euler Lagrange equations of motion Eq. (2.60).

15.2

Photon-ALP Transition Probability for Constant Oscillation Frequencies

Derive the photon-ALP transition probability Eqs. (15.37) and (15.38) from Eq. (15.35) for the vacuum oscillations of the transition amplitudes for the case of constant oscillation frequencies. Hint: This problem is very similar to problem 11.1 for vacuum neutrino oscillations and can thus be derived by substituting corresponding quantities.

15.3

Magnetization Induced by Couplings to an ALP Field

Derive the estimate Eq. (15.54) for the magnetization induced perpendicular to an external constant magnetic field $\mathbf{B}_\mathrm{ext}$ by solving Eq. (15.53). Hints: Assume that $\mathbf{B}_\mathrm{ext}$ points in the $z-$direction and write the Bloch equation as an inhomogeneous first order differential equation for the complex variable $m\equiv \varvec{\mu }_m\cdot (\mathbf{e}_x+i\mathbf{e}_y)$ assuming $|m|\ll \varvec{\mu }_m\cdot \mathbf{e}_z$ so that $\varvec{\mu }_m$ is almost parallel to the $z-$axis. Write the solution as a superposition of solutions to the inhomogeneous and homogeneous differential equations and then compute |m| to lowest order in the perturbation $\varDelta E$.

15.4

Forms of the Hidden Photon Lagrange Density

Demonstrate that a suitable linear transformation of the gauge fields $X^\mu$ and $A^\mu$ transforms Eq. (15.21) into Eq. (15.22). To this end, first diagonalize the kinetic term in Eq. (15.21) and then rescale the fields $X^\mu$ and $A^\mu$ such that the kinetic terms have the standard form $-(1/4)(F_{\mu \nu }F^{\mu \nu }+X_{\mu \nu }X^{\mu \nu })$. Then diagonalize the mass terms by a further rotation of $X^\mu$ and $A^\mu$ which does not change the kinetic terms. By using standard trigonometric relations show that the mass eigenvalues are $m_{\gamma ^\prime }$ and 0 and that $j^\mu _\mathrm{em}$ couples to $A_\mu +\tan \chi X_\mu$.

15.5

Madelung Transformation and Fluid Equations

Derive the effective fluid equations (15.79) from the Gross–Pitaevskii equation (15.77) by applying the Madelung transformation Eq. (15.78).