Monday, 25 February 2008

The Lenin of the Week


Other famous sayings of Lenin:

Sometimes theory needs a push.
Asymptotic freedom will not satisfy the hungry masses.
One man with a grant can control 100 without one.
A paper cited often enough becomes the truth.
Every cook should be able to run Monte Carlo.

Saturday, 23 February 2008


At the last Cosmo Coffee, Celine Boehm was discussing the current status of the 511 keV gamma-ray line from the Milky Way center, in light of the recent results from the INTEGRAL satellite. Photons carrying 511 keV energy arise from annihilation of positrons and electrons that are more less at rest. It is not clear which mechanism is responsible for injecting enough positrons into the interstellar medium of the galactic bulge. One hypothesis is that the positrons are scattered remnants of the ILC (Interplanetary Linear Collider) - an unfinished project of a technologically advanced civilization from that region. More contrived explanations involve black holes, radioactive nuclei from supernovae, pulsars and other fluffy toys.

Yet another, quite exciting possibility is that the positrons come from annihilation of dark matter. At first sight this seems quite natural. We are pretty confident that a lot of dark matter is present in the galactic center and its distribution should be roughly spherical, something which agreed quite well with the earlier INTEGRAL observations. Furthermore, it is likely that dark matter can annihilate into ordinary matter so that its present abundance is a thermal relic. But a dark matter particle that could explain the INTEGRAL signal must be quite peculiar. In particular, it cannot be a WIMP: its mass should be in the MeV range. If it were heavier, annihilation would yield too energetic positrons and the 511 keV line would not stand so prominently over the continuum gamma-ray radiation.

On the microscopic level, MeV dark matter can be realized as a scalar particle (so as to avoid the Lee-Weinberg bound) annihilating via an exotic heavy fermion exchange, or via an exotic heavy gauge boson. See the artist's view above. In fact, both diagrams are needed to explain the INTEGRAL signal and, at the same time, derive the correct dark matter abundance from the thermal relic density computation. The first diagram leads to the cross section that goes to a constant at small velocities and this one is relevant for the annihilation of dark matter today. The second leads to the cross section that goes like $\sigma \sim b v^2$, and it's supposed to dominate in the early hot universe.

Recently, the INTEGRAL satellite announced new results which show an asymmetry of emission (by a factor of two) with respect to the central axis of the galaxy. Morevover, the asymmetry seems to be correlated with the distribution of low mass X-ray binaries (LMXB) - systems including a neutron star or a black hole that accretes matter from its companion. LMXBs have long been one of the suspects in the positron case. The general feeling is that the new results make the dark matter explanation unlikely; Julianne on CV readily flushed MeV dark matter down her toilet. Celine, on the other hand, is more reluctant to push the button (she is, in fact, responsible for much of the stuff being thrown into the toilet). She argued that: 1) We still don't know a conventional astrophysical explanation that could account for enough positron emission, 2) While part of the gamma-ray emission maybe due to boring astrophysics, there's still a large, roughly spherical component that could be due to MeV dark matter. In fact, if only a part of the emission is assigned to dark matter, the microscopic models can more readily satisfy constraints from other experiments, for example, from measurements of the electron anomalous magnetic moment.

I guess it's fair to say that, at the moment, a conventional astrophysical explanation seems far more likely. My faith in that signal is further diminished by the fact that astrophysics provides us with too many excesses (EGRET, for example), each one having its dark matter particle that's supposed to explain it. Finally, MeV dark matter is hard to accommodate in our favourite Beyond the Standard Model schemes. But this last argument should always be taken with a grain of salt, since all existing BSM models suck. It's better to keep our eyes open...

Monday, 18 February 2008

Non-Gaussianity Again

I wrote not so long ago about a possible observation non-Gaussianity in the CMB spectrum. Last Wednesday Tony Riotto gave an overwiew seminar explaining what that non-Gaussianity really is. I used to think that the issue was complicated. Tony explained very clearly and pedagogically that it is bloody damn complicated.

Unfortunately, it is also important. There is an overabundance of inflationary models and several mechanisms in which these models could produce the primordial density perturbations. The number of observables to discriminate between the models is less outgrown. What we've got so far is the amplitude and the spectral index of density perturbations. Applied to the minimal slow-roll scenario, these two provide useful constraints, but at the moment they do not clearly favour a particular class of models. One way to improve the situation is to measure the spectral index with greater precision. Detecting tensor perturbations would be fantastic, but many models (and most of those sensible from the effective field theory point of view) predict tensor perturbations well below the sensitivity of near-future experiments. Non-Gaussianity of the primordial perturbation spectrum provides another complementary handle on inflationary models. A mere detection of large primordial non-Gaussianity would flush many models down the drain, including the single field slow-roll inflation.

Gaussianity of the primordial perturbation spectrum arises when the inflaton behaves approximately as a free field in a curved background. This is never quite true: the inflaton potential introduces non-linear self-interactions and, more importantly, the inflaton is coupled to gravity which is itself non-linear. In simplest inflationary scenarios, however, these non-linear effects are negligible. In such a case, the equation governing the inflaton perturbations is just the harmonic oscillator equation with a time-varying frequency. Different oscillator frequencies are decoupled and they oscillate independently, seeding the universe with Gaussian perturbations. This means that the power spectrum of the two-point correlation function (that funny thing with peaks that CMB people show) carries all the statistical information about density fluctuations. In the presence of non-Gaussianity, the three- and higher-point correlation functions are independent from the two-point one. The only way to learn about non-Gaussianity is to perform statical tests on these higher-point functions.

Non-Gaussianity is conventionally parametrized as
$\zeta(x) = \zeta_{gauss}(x) - 3/5 f_{NL} (\zeta_{gauss}^2(x) - <\zeta_{gauss}^2>)$
Here $\zeta$ is a gauge-invariant characterization of curvature perturbations. The coefficient $f_{NL}$ is not a constant in general but, for simplicity, one often presents just a number corresponding to an overall amplitude of non-Gaussian contributions over the scales of interest. The current constraint for $f_{NL}$ is that it is at most of order 100. It follows that the second non-Gaussian term is a small perturbation (recall that $\zeta \sim 10^{-5}$) and that's what is meant by saying that the primordial perturbation spectrum is approximately Gaussian.

There are several inflationary models that could lead to primordial non-Gaussianity. Tony paused on the curvaton scenario that he seems to like. In the curvaton scenario, density fluctuations are produced by a different field than the inflaton, while perturbations from the inflaton field are negligible (which may well be, for example, when the scale of inflation is low enough). There is another field - the curvaton - who has a negligible impact on the dynamics of inflation, yet it acquires isocurvature perturbations during inflation. As it decays after the end of inflation, it transmits the fluctuation to the hot plasma in the early universe. Non-gaussianity of the primordial spectrum depends on the parameter $r$, which is a ratio of the curvaton energy density to the total energy density just before the curvaton decays. Lyth et al. found $f_{NL} \sim 5/(4r)$.

One thing that makes non-Gaussianity particularly complicated is that detecting it in the CMB does not imply detecting the primordial non-Gaussianity. Many phenomena contaminate the CMB during the evolution of the universe. First of all, gravity is non-linear, so that the second order perturbation theory introduces non-Gaussianity into the CMB at the level of $f_{NL} \sim 1$. This is the minimal amount of non-Gaussianity that we expect in the CMB, if our models of density perturbations evolution are correct. For comparison, the single field slow-roll inflation predicts $f_{NL} \sim (n - 1)$, which is drowned by the gravity contribution because the spectral index n is close to 1. On top of that, there is a whole lot of dirty astrophysics that contributes to non-Gaussianity: secondary anistropies from graviational lensing or Sunyayev-Zeldovich effect, radio point sources, instrument noise etc.

Concerning the possible signal I wrote about, Tony advised not to get excited. Many effects could bias the analysis of Yadav and Wandelt, one thing pointed out was the poorly known distribution of extragalactic radio sources, another was over-substraction of the noise. On the other hand, if the signal is real, Planck will confirm it at 8 sigma confidence level.

A few details or formulas omitted here can be found in this review by Tony et al.

Thursday, 7 February 2008


I have been feeling dizzy all this week and I blame it on the neutrino flux. It happens to be more intense than ever - within 7 days there were 4 neutrino seminars here at CERN. I could not help but learn something about the quest for $\theta_{13}$ from the Thursday seminar by Silvia Pascoli.

Neutrino physics is the only branch of particle physics that can boast of a discovery in the last twenty years (the top quark, some may say, but that was as unexpected as election results in the former Soviet Union). The experimental progress in the last decade has been really impressive. Since the 1998 discovery of neutrino oscillations we have acquired a great deal of data concerning the neutrino masses and mixings. Yet from a theorist's perspective neutrinos are boring. It all amounts to a 3-by-3 unitary matrix that relates flavour eigenstates to mass eigenstates. The matrix is called the MNS matrix and looks like this

As usual, a 3-by-3 unitary matrix has three angles and three phases. Two of these angles were pinpointed by numerous observations of solar and atmospheric neutrino oscillations, as well as by reactor and accelerator experiments. The last angle, the notorious $\theta_{13}$, remains elusive and we only know the upper bound of 12 degrees. The other two angles are much larger than that, which gives hope to the experimenters that the last one is just behind the corner. So, while cosmologists are studying such sexy matters like dark matter or dark energy, the neutrino community is struggling to measure an angle.

One way to measure $\theta_{13}$ is by observing oscillations of muon neutrinos into electron neutrinos. The probability of this process is sensitive $ \sin^2 (2 \theta_{13})$,
$P(\nu_\mu -> \nu_e) = \sin^2 \theta_{23} \sin^2 (2 \theta_{13}) \sin^2 (\Delta m_{13}^2 L/2 E)$.
At the moment, there is an ongoing search for electron neutrino appearance by the Minos experiment that shoots the beam of muon neutrinos from Fermilab to a detector in Soudan mines in Minnesota. This one is however not designed specifically for that search and no great improvement in sensitivity should be expected. In near future (2009-ish) starts another accelerator experiment called T2K (Tokai to Kamioka in Japan, where else) whose sensitivity to $\sin^2 (2 \theta_{13})$ will reach 0.01, (or 3 degrees after some complicated trigonometry). In parallel, there are reactor experiments in preparation, who will play with anti-neutrinos that escape from nuclear reactors and pollute the air. The strategy is to put two detectors close to a reactor and look for disappearance of electron anti-neutrinos on the way between the two. The next reactor experiment to start is Double Chooz, the continuation of the Chooz experiment who already put a bound on $\theta_{13}$ in the past. The Chinese also enter the race with their Daya Bay experiment. These two reactor experiments will have a similar sensitivity to $\theta_{13}$ as T2K.

The measurement of the angle $\theta_{13}$ is very important because it will open the way to measure another angle. More precisely, the CP violating phase $\delta$ in the MNS matrix. The point is that CP violating effects, that is differences in oscillation patterns between neutrinos and antineutrinos, are proportional to $\sin \delta$ but also to $\sin \theta_{13}$. If the latter is large enough, the future superbeams, beta-beams or neutrino factories may discover CP violation in the leptonic sector.

In summary, the future looks bright and gay for neutrinos, as on the picture below

No slides available.