How to make a line

I mean a gamma-ray monochromatic line, like the one seen in the Fermi data. Recall the story so far. An independent analysis of publicly available data from the Fermi gamma-ray telescope found a peak in the photon spectrum near 130 GeV. It may be interpreted as a 130 GeV dark matter particle annihilating into a pair of photons with the cross section of about 2*10^-27 cm^3/sec (or a 145 GeV dark matter particle with the cross section twice as large annihilating  into a photon and a Z-boson). Since then the finding was confirmed by other independent groups and there's little doubt that the feature is present in the data. The question however is whether it is indeed a signal of dark matter, or whether it is due to a boring astrophysical process or to an instrumental effect.  Actually, 1 month after the finding, the Fermi collaboration put their own gamma-ray line study on arXiv in which they don't claim any signal but only set upper limits on the production cross section. Inspired by the ostrich tactics, Fermi does not mention Weniger's result at all, nevertheless one can see their limits are in some tension with the annihilation cross section quoted above. 

Anyway, in this post I will brush off the doubt and discuss what sort of dark matter models could explain the monochromatic gamma-ray line in the current Fermi data.  One definitely needs something non-trivial. Dark matter cannot carry an electric charge, therefore, in a generic model,  annihilation into photons is mediated by a loop diagram,  leading to the cross section naively suppressed by 3-4 orders of magnitude  compared to other annihilation channels. This would be problematic for two reasons. Firstly, given the strength of the Fermi line, that total annihilation cross section would by far exceed the thermal cross section 3*10^-26 cm^3/sec, so one would have to invoke some non-thermal mechanism of populating dark matter in the universe. Secondly, Fermi observations of the continuum gamma-ray flux from Milky Way satellite galaxies constrain the allowed annihilation cross sections to about 10^-25 cm^3/sec for a 130 GeV dark matter particle. the precise value depending on the annihilation channel.

For this reason, models fitting the Fermi line have to somehow shut off the tree-level annihilation channels and make the annihilation into photons dominant or nearly dominant. This is tricky and typically requires introducing a turtle standing on an elephant standing upon a giant turtle, as you can see on arXiv every day. Here I pick 3 models on the market that involve imo the smallest number of elephants.

• Chern-Simon portal.In this model the mediator between the dark and visible matter is a Z' vector boson, who is coupled in a funny way to the Standard Model via the Chern-Simons term Z' Z γ (one can consider it an effective coupling after some exotic chiral fermions charged both under the Standard Model and Z' have been integrated out). One assumes dark matter is charged under Z' thus it can annihilate into a pair of Z' as well as (via the Chern-Simons coupling)  into Zγ. Since these two processes depend on two independent adjustable parameters, it is no surprise one can fit both the line (via annihilation into Zγ) and the thermal cross section (via annihilation into Z'Z'). 
• Higgs is space!  Here Z' is also the mediator, however this time on the visible side it couples to the top quark (this can even be motivated in some composite Higgs or Randall-Sundrum constructions). This means dark matter annihilates dominantly into a pair of top quarks, and one can choose the couplings of Z' such that the cross section is the thermal one. But if the dark matter mass is lighter that the top mass the annihilation rate can be suppressed by phase space. On the other hand,  the subleading annihilation channels into Zγ or Hγ proceeding via a loop of the top quark do not suffer from that phase space suppression, therefore their rate can be relatively large, so as to explain the strength of the Fermi line.  
• Box-shaped line. It is hard to annihilate dark matter into photons, but it is much easier to annihilate it into another exotic particle X who, at least part of the time, decays into photons. Of course, this in general does not produce a line, but rather a box-shaped photon spectrum,  as the observed photon energy gets smeared by the motion of the X particle. However, as the mass of X approaches that of dark matter (so that dark matter annihilates into X at rest) the box gets narrower and at some point becomes a line for all practical purpose. So the Fermi line could be explained e.g by a 265 GeV dark matter particle annihilating with the thermal cross section into a 260 GeV particle X, who in turn decays about 10% of the times into a pair of photons.

Sincerely, what do I think?  Well, Nature is a bitch, and that has been especially true with regard to dark matter. So far we've been denied any insight into the identity of the dark matter particle, in spite of tedious efforts in numerous direct and indirect detection or collider experiments. A monochromatic gamma-ray line -- an undeniable smoking gun of dark matter -- just sounds too good to be true. Thus, my best guess is that she's screwing with us again, and the line will be explained away by some instrumental effect.

Which means: hurry up with your gamma-ray line paper, before it's gone ;-)

Dark Matter is Back!

A few weeks ago a paper claiming strong bounds on the local dark matter density made a news, hitting also particle physics blogs. Currently, the most solid evidence of dark matter comes from  analyzing the Cosmic Microwave Background, and from the observed flatness of the galactic rotation curves. It is less known than in our galaxy the support for dark matter comes from studying the rotation curves at distances of 20 kpc or more from the galactic center. In the immediate neighborhood of the Sun (8 kpc from ground zero), the presence of dark matter is more difficult to deduce. The value of the local dark matter typically quoted, ρ = 0.4 GeV/cm^3, is based on extrapolations using particular models of the dark matter halo.

The recent paper by Moni Bidin et al. attempted a direct measurement of the local dark matter density.  Studying the kinematics of a population of stars drifting a few kpc above the galactic plane, they were able to estimate the so-called surface density, that is the integral of the mass density in the vertical (wrt to the galactic plane) direction. If there is only the visible matter concentrated in the disc then the surface density should be constant above the disc. Conversely, if there is dark matter in the form of a spherical halo then the surface density should continue growing above the disc.  The paper finds the data are well fit by a constant surface density for z > 1.5 kpc above the disc, setting the limit ρ < 0.04 GeV/cm^3, that is 10 times smaller than what is usually assumed. 

The authors went as far to saying that  "our results may indicate that any direct DM detection experiment is doomed to fail". This is of course a sheer nonsense, even if their limits were true. The event rate in direct detection experiment depends, among other things, on the product of the  local dark matter density ρ and the scattering cross section of dark matter on protons and neutrons σ.  The latter has no obviously preferred value, and in concrete particle physics models it may span many orders of magnitude. Thus, the constraint on ρ doesn't tell us anything about the subjective chances of detecting dark matter; it only changes the interpretation of direct detection experiments in terms of the limits on σ. A smaller ρ would mean weaker limits on σ, thus weaker limits on the parameter space of dark matter models, which would actually make many of us happy.    

Nevertheless, the claim that there is no indication of the presence of dark matter in the solar neighborhood was somewhat disturbing to these experimentalists who spend entire lives in underground caverns, preparing and running dark matter detection experiments. Those can now utter a sigh of relief. A new paper by Bovy and Tremaine that has just appeared on arXiv says that the paper of Moni Bidin et al is "flawed". The strong limits on the dark matter density were obtained as a consequence of an observationally unsupported assumption about the velocities of the studied population of stars. As can be seen in the plot, correcting the wrong assumption leads to a perfect consistency between the data and the predictions assuming the presence of dark matter. pwned.

One lesson, supported by large statistics, is that papers who come with aggressive press releases are, more often than not, wrong. The present case is however more interesting than that: it seems that although some crucial assumptions were wrong, the proposed method of constraining ρ is promising. Using same data and similar methods, Bovy and Tremaine obtained the best estimate of the local dark matter density to date, ρ = 0.3 ± 0.1 GeV/cm^3; very close to what is usually assumed but with a smaller error. Moreover, the error may be further reduced in the near future when data from other astronomical surveys are analyzed.  This will eliminate one important source of error in interpreting  results of dark matter detection experiments, leading to more reliable constraints on particle physics models. So the second lesson here is that even wrong papers may be for the better...