It's All Decay

Contrary to what you might think from the title, this is not about Christmas. This is yet another PAMELA/ATIC related post. If it continues like that I'll have to rename the blog from Resonaances to Bumps.

By now you know the story too well: PAMELA and ATIC have observed an excess of cosmic-ray positrons that may are may not be a manifestation of TeV scale particles that constitute dark matter. Most of the subsequent theoretical activity was focused on explaining the signal via dark matter annihilation. However, there has also been a number of papers pursuing a different scenario in which the dark matter particle is unstable, and the excess positrons are produced while it decays. In fact, there are quite good reasons, both theoretical and phenomenological, to seriously consider this possibility.

On the theoretical side, there are some difficulties with the annihilation scenario. If the dark matter is a thermal relic, the inferred annihilation rate is some 100 times too small to explain the positron excess. In order to boost the annihilation rate today one needs some awkward modeling. One possibility is to assume that the dark matter distribution today is very inhomogeneous, and the average annihilation rate is boosted due to the existence of high-density regions. Another trick is to cook up new forces mediated by some mysterious 1 GeV particles. Of course, one could also drop the assumption of thermal equilibrium and invoke some non-thermal mechanism to explain the present dark matter abundance, in which case the annihilation rate can be high enough.

But who cares about theory? In the end, witty theorists can always find a way out. Indeed, the approach called I-will-fit-PAMELA-to-my-cherished-model-against-all-odds is very popular these days. However, there are purely phenomenological reasons to reserve some skepticism toward the annihilation scenario. That's what can be inferred from the recent paper by Bertone and al.

The observation is that production of 1 TeV electrons and positron inevitably leads to production of high-energy photons via the bremsstrahlung process. Thus, annihilation of dark matter should lead not only to a positron excess but also to a gamma-ray excess. Best limits on the cosmic gamma-ray flux are set by the Namibia-based Cherenkov telescope called HESS (as homage to Rudolf Hess [or maybe another Hess]) who covers the 100 GeV - 100 TeV energy range. It turns out that, assuming the annihilation hypothesis, the parameter space suggested by PAMELA and ATIC (the red region in the plot) is incompatible with HESS. A word of caution is in order here. The results of that analysis depend on the dark matter density profile for which we have only more or less educated guesses. The plot I included here assumes the most popular NFW profile, whereas the bounds are less severe if the density profile is less steep than NFW in the region close to the galactic center. For example, using the Einasto profile (which seems to be preferred by numerical simulations) the bounds are weaker and the PAMELA/ATIC region is only marginally excluded, while for the isothermal profile (less preferred by numerical simulations) the PAMELA/ATIC region is marginally allowed. It is fair to say, however, that there is a tension between the annihilation interpretation of the positron excess and the gamma-ray data. Moreover, observations in radio waves (which should be produced by the synchrotron radiation of the positrons) also seem to be incompatible with the annihilation scenario.


On the other hand, this tension disappears if the PAMELA/ATIC results are explained by an unstable dark matter particle with the life-time of order $10^{26}$ seconds and the mass of order 2 TeV. The plot, taken from this paper, shows that the PAMELA/ATIC region safely satisfies the HESS and radio bounds, even for the NFW profile. The simple reason is that the decay rate depends on the dark matter density as $\rho^1$, unlike the annihilation rate that depends on $\rho^2$. Thus, the growth of the decay rate toward the galactic center is effectively less steep.

Coming back to theory, a very long-lived unstable particle is by no means unusual (I mean in theory, in practice we haven't seen any so far). If the (meta-)stability of the dark matter particle is due to some accidental global symmetry, it is natural that this symmetry is broken at some high-scale. That is to say, the symmetry is broken by higher dimensional non-renormalizable operators suppressed by that high scale, and these operators could be responsible for the slow decay. It was pointed out here that the life-time of $10^{26}$ seconds and the mass of 1 TeV is compatible with dimension-six operators suppressed by the GUT scale. Which is inspiring... Note that, by exactly the same token, we expect that the global baryon symmetry is broken at the GUT scale and that protons are long-lived but eventually decay.

HESS has the potential to improve the bounds, or see the gamma-ray signal if it lurks behind the corner. Unfortunately, astrophysicists are more interested in astrophysical backgrounds. It seems that we need to wait for GLAST-now-FERMI to learn more. Unless...If you're a pirate off the Africa coast reading this blog here's the plan for you: 1) hijack the HESS crew, 2) force them to point the telescope into "nothing", 3) submit the results to ArXiv. The ransom will be paid in Stockholm.