Hawking radiation of unparticles

Unparticle degrees of freedom, no matter how weakly coupled to the standard model particles, must affect the evolution of a black hole, which thermally decays into all available degrees of freedom. We develop a method for calculating the grey-body factors for scalar unparticles for $3+1$ and higher dimensional black holes. We find that the power emitted in unparticles may be quite different from the power emitted in ordinary particles. Depending on the parameters in the model, unparticles may become the dominant channel. This is of special interest for small primordial black holes and also in models with low scale quantum gravity where the experimental signature may significantly be affected. We also discuss the sensitivity of the results on the (currently unknown) unparticle normalization.

Figure 1

The case of the general normalization (many unparticle degrees of freedom). The figure shows the mass distribution $\rho (\mu )$ of unparticles for the fixed normalization scale ${\Lambda }_u$. For convenience, $\rho$ is measured in units of ${\Lambda }_u^{-2}$ while $\mu$ is measured in units of ${\Lambda }_u$. Since the scaling dimension $d_u$ can take the values between 1 and 2, we plot the three characteristic values: $d_u=1.1$ solid line, $d_u=1.5$ dashed line, and $d_u=1.9$ dotted line. As the value of the scaling dimension decreases, the distribution is skewed toward lighter unparticles.

Figure 2

The case of the general normalization (many unparticle degrees of freedom). The figure shows the mass distribution $\rho (\mu )$ of unparticles for the fixed $d_u=1.5$. We plot the distribution for several values of ${\Lambda }_u$: ${\Lambda }_u=1\mathrm{TeV}$ solid line, ${\Lambda }_u=2\mathrm{TeV}$ dashed line, and ${\Lambda }_u=5\mathrm{TeV}$ dotted line. As the value of ${\Lambda }_u$ decreases, there are more unparticle degrees of freedom (for a fixed $d_u$).

Figure 3

The case of the unit normalization (a single unparticle degree of freedom). The figure shows the mass distribution $\rho (\mu )$ for the three characteristic pairs of values: $d_u=1.1$, ${\Lambda }_u=1\mathrm{TeV}$ solid line, $d_u=1.1$, ${\Lambda }_u=2\mathrm{TeV}$ dashed line, and $d_u=1.5$, ${\Lambda }_u=1\mathrm{TeV}$ dotted line. As the value of the scaling dimension decreases, the distribution is skewed toward lighter unparticles. In this case unparticles cannot be heavier than ${\Lambda }_u$, so the distribution stops there.

Figure 4

The Hawking radiation power spectra of unparticles with the fixed value of ${\Lambda }_u$ (general normalization). The mass of the black hole is ${10}^{12}\mathrm{g}$ and the unparticle energy scale is ${\Lambda }_u=1\mathrm{TeV}$. Since the scaling dimension $d_u$ can take the values between 1 and 2, we plot the three characteristic values: $d_u=1.1$ dashed line, $d_u=1.5$ dotted line and $d_u=1.9$ dash-dot line. For comparison, we plot the regular scalar field with the solid line. Scalar unparticle spectrum can clearly be different from the ordinary scalar particle spectrum.

Figure 5

The Hawking radiation power spectra of unparticles for several values of ${\Lambda }_u$ and fixed $d_u=1.5$ (general normalization). The mass of the black hole is ${10}^{12}\mathrm{g}$. We plot ${\Lambda }_u=1\mathrm{TeV}$ dashed line, ${\Lambda }_u=2\mathrm{TeV}$ dotted line, and ${\Lambda }_u=5\mathrm{TeV}$ dash-dot line. The emitted power in unparticles is larger for smaller ${\Lambda }_u$ since then we have more unparticle degrees of freedom at a given energy. For comparison, we plot the regular scalar field with the solid line. Again, scalar unparticle spectrum can clearly be different from the ordinary scalar particle spectrum.

Figure 6

The Hawking radiation power spectra of unparticles with the fixed ${\Lambda }_u$ (unit normalization). The mass of the black hole is ${10}^{12}\mathrm{g}$ and the unparticle energy scale is ${\Lambda }_u=1\mathrm{TeV}$. Since the scaling dimension $d_u$ can take the values between 1 and 2, we plot the three characteristic values: $d_u=1.1$ dashed line, $d_u=1.5$ dotted line, and $d_u=1.9$ dash-dot line. For comparison, we plot the regular scalar field with the dash-dot line. Scalar unparticle spectrum can clearly be different from the ordinary scalar particle spectrum. As $d_u$ is approaching 1, the unparticle spectrum approaches that of a single massless scalar field.

Figure 7

The Hawking radiation power spectra of unparticles for several values of ${\Lambda }_u$ and fixed $d_u=1.5$ (unit normalization). The mass of the black hole is ${10}^{12}\mathrm{g}$. We plot ${\Lambda }_u=1\mathrm{TeV}$ dashed line, ${\Lambda }_u=2\mathrm{TeV}$ dotted line, and ${\Lambda }_u=5\mathrm{TeV}$ dash-dot line. The emitted power in unparticles is larger for smaller ${\Lambda }_u$ since the mass distribution $\rho (\mu )$ gives higher probability for a lighter unparticle. For comparison, we plot the regular massless scalar field with the solid line. Again, scalar unparticle spectrum can clearly be different from the ordinary scalar particle spectrum.

Figure 8

The Hawking radiation power spectrum of unparticles for a higher dimensional black hole. The black hole mass is 5 TeV, the number of extra dimensions is $n=3$, while the higher dimensional Planck mass is 1 TeV. The unparticle energy scale is ${\Lambda }_u=1\mathrm{TeV}$ and we take $d_u=1.1$. The unparticle spectra are represented by the dashed line and dotted line. For comparison we plot the regular massless scalar field with the dashed line. Clearly, unparticles with the general normalization can easily out power ordinary particles by an order of magnitude. Unparticles with the unit normalization can only asymptotically approach the ordinary scalar field in $d_u\to 1$ limit.