Weekend Plot: axing axions

Assuming the B-modes observed by BICEP2 originate from the metric field fluctuating during inflation, implications are profound. Obviously, inflationary models are now constrained to reproduce the energy scale 10^16 GeV driving the expansion (equivalently, the Hubble scale during inflation 10^14 GeV). But the consequences extend to more general new physics scenarios that a-priori have nothing to do with inflation. One prominent example is high-scale axions. Axions are hypothetical particles that pop up in many theories: as a solution to the strong-CP problem in QCD, as a dark matter candidate, as a prediction of string theory, etc. Here is a snapshot of the axion parameter space after BICEP2:

The plot shows the maximum fraction of dark matter that high-scale axions can account for versus the axion mass. If the axion scale f is larger than 10^14 GeV then the axion field can wildly fluctuate during inflation. Axion fluctuations are uncorrelated with those of the inflaton field, and give rise to the so-called isocurvature perturbations where density fluctuations in radiation and matter add up to zero. The isocurvature perturbations, in turn,  are severely constrained by Planck's CMB measurements: their power has to be less than 4% of the adiabatic perturbations produced by the inflaton field.  Hence the severe constraint on the axion: its initial displacement angle  has to be small enough as to suppress the oscillation amplitude. But the same displacement angle gives rise to the production of axion dark matter. Combining these two inputs, we learn from BICEP2 that high-scale axions alone cannot account for the observed abundance of dark matter in the universe. Moreover, even giving up on axion dark matter, one has to fine-tune the initial displacement of the axion fields to a tiny value (of order 10^-8 for f = 10^16 GeV).      

Of course, like for any model that crashed after the BICEP2 announcement, Microsoft-style patches are already available. In this case, one solution is simply to take f < 10^14 GeV, that is the global symmetry whose breaking gives rise to the axion particle gets broken only after the inflation ends  (although this scenario has problems of its own). Another  possible fix is to ensure the axion acquires a large mass (>10^14 GeV) during inflation, or that the isocurvature modes were diluted by late-time entropy production. Nevertheless, high-scale axions are clearly less motivated than they were a week ago.

Erratum: 
A commenter pointed out that the results in this plot disagree with other literature on the 

subject. The point is that, for the axion scale larger than the Hubble scale during inflation,  the minimum displacement angle is of order H/f. For the relevant scales this always produces too much isocurvature perturbations.  Thus, the conclusions from BICEP2 are stronger than what I wrote above: high scale axions are excluded (up to the caveats in the previous paragraph) irrespectively of any assumptions about the initial displacement angle. The plot on the right visualizes the situation for the QCD axion.   The yellow region is excluded by astrophysical and CMB constraints, while the green  region  corresponds to the BICEP2 measurement of the Hubble scale during inflation. The QCD axion is now constrained to a narrow window of 10^9 ≤ f ≤ 10^11 GeV. At the top of this window it accounts for all dark matter in the universe. 

Curly impressions

Today the BICEP2 experiment announced a significant detection of the primordial B-model in the CMB power spectrum (the excess at lower multipoles in the plot). From that one can infer that the tensor-to-scalar ratio of primordial fluctuations is somewhere between 0.1 and 0.2. Cosmologists are strongly represented in the blogosphere, so for the description of technical aspects of the BICEP results and their impact on the models of inflation better see elsewhere, for example here or here or here.  In this post, let me throw in a few random impressions from a particle physicist.  

• If this holds up, it's huge, comparable in magnitude to the discovery of the Higgs boson. Probably even more exciting because of the surprise element.  
• "If this holds up" is the central question now. This sort of  experiments is subject to pesky instrumental effects and systematic effects due to foreground emission.  It's not impossible that BICEP screwed up;  in fact, experts point out some worrying aspects of the data, for example the excess in the BB spectrum at high multipoles. So I would say at this point it's fifty-fifty.  Fortunately, there are many experiments  out there with similar sensitivity (Planck, ACTPole, SPT, POLARBEAR) that should be able to  confirm or refute the claim in the near future. In particular, the release of Planck polarization data this year should straighten many things out. For the sake of this post I'll drop the conditional, but there really should be "If this holds up" in front of every sentence below. 
• The big thing here is not gravitational waves (we observed them before), and not an evidence for inflation (we've already had a few from the CMB alone:  the temperature isotropy across the sky, the scalar fluctuations, the spectral index). The point is that the amplitude of the primordial tensor modes is directly related to the energy density during inflation. This turns out to be (2*10^16 GeV)^4 -- a whopping energy scale unavailable to particle accelerators in this century. Consequently, the Hubble scale during inflation has also been nailed down, and it's 10^14 GeV. While cosmologist  study the universe when it was being born, particle physicists are getting a glimpse of  physics at a very high-energy scale. 
• The proximity of the inflation scale to the unification scale in minimal supersymmetry is certainly intriguing. It may be a numerical accident.... but I'm sure that there will soon be models on arXiv  "predicting" this coincidence. 
• The plot shows the basic parameters of inflation as of today. 
  
   If you think that the Planck region is not what you remember, that's right, it's not the one usually shown. The red region in this plot is the Planck constraint when the spectral index ns is allowed to run, that is to say, to depend on the distance scale. It is a challenge for  inflationary models to get the required amount of running. In the more likely scenario with small running the BICEP result is in about 3 sigma tension with the Planck constraints.   
• There's more challenge for inflation model building. In the single-field inflation one can relate how much the inflaton field was displaced during inflation to the value of r and the number of e-folds (the so-called Lyth bound). For r~0.2 one finds that the displacement is larger than the Planck scale. For particle physicists, who generally like effective field theories,  the focus now will be on identifying all exceptions from this rule. But from another (e.g. string-theoretical) point of view this is an opportunity: may be inflation can be our probe of transplanckian physics? In the coming week there will surely  be an arXiv flood on both  of these fronts.  
• Speaking about model building, Higgs inflation is ruled out, at least in the current version. A robust prediction of Higgs inflation is no tensor modes at an observable level. In other words, we have a new evidence for new physics beyond the Standard Model. 
• It is worth remembering that the gravitational waves during inflation is the most plausible but not the unique explanation of BICEP results. For example, an early  phase transition or decay of massive particles during inflation may also  generate tensor perturbations. That's another model building direction worth following in the coming weeks.   
• If you hear a sledgehammer in the corridor of your lab, that may be your local Planck member banging his head on the wall. Yeah,  apart from many noble aspects, science also has this lowly competition side. A billion dollar experiment that misses a Nobel-prize-worth low-hanging fruit... I wouldn't wish  to be in their skin if BICEP is right.  
• One more thing we learned from the BICEP announcement: mankind can study the universe moments after the bing bang, but setting up an internet connection is a totally different story ;)  

The BICEP2 paper is here, for more material see this page.  

Weekend Plot: flexing biceps

All of us will spend this weekend waiting for it to pass. To kill time, you may stare at the plot of the parameter space of inflation. This is the current status after the measurements of the Cosmic Microwave Background temperature fluctuations by the Planck satellite:

Take a good look as it won't be the same on Monday.  COBE was first to measure the amplitude As of the primordial scalar  fluctuations  in the CMB. More recently, WMAP and Planck and other experiments pinned down the so-called spectral index ns (x-axis in the plot),   which measures the departure of the scalar  fluctuation spectrum from scale invariance.  In the vanilla model of inflation, these two parameters are related to three parameters of the inflationary potential: the absolute value, and  the first and second derivatives during inflation. To connect all dots we need another observable -  the amplitude At of the primordial tensor perturbation spectrum, or equivalently, the tensor-to-scalar ratio r=At/As (the y-axis of the plot). This observable is directly related to the absolute value of the potential during inflation. To measure the tensor amplitude, one needs to see a special pattern in the CMB polarization spectrum - the so-called  B-mode (more precisely, the primordial B-mode; the non-primordial B-mode, induced by gravitational lensing effects on the CMB, was observed  by the  SPT and  POLARBEAR experiments). The rumor is that BICEP2 - a small-scale experiment down at the South Pole measuring the polarization of the CMB - pinned down the primordial B-mode. Various rumors quote the measured value of the tensor-to-scalar ratio between 0.06 and 0.2. For the former value, it is hard to understand how BICEP2 could obtain a statistically significant discovery, while the latter value is in tension with the results from WMAP and Planck.  We'll see on Monday, when the press conference of BICEP2 is scheduled. If this is true, we learn that the energy scale where inflation happened is around 2*10^16 GeV. This would be the first direct evidence for a new particle physics scale between the electroweak and the Planck scales.

One final remark: newspapers are spinning this story as the discovery of gravitational waves. Right, there is a connection: the primordial B-mode amplitude originates from fluctuations of the metric at the time when CMB photons decoupled from matter. So finding the B-mode can be viewed as another (after the Hulse-Taylor binaries) indirect confirmation of the existence of gravitational waves. But the discovery of the primordial B-mode in the CMB is much much bigger than that.

For more rumors and counterrumors see here and here and here. Another rumor is that Guth and Linde will be present at the press conference on Monday. 

Weekend Plot: all of dark matter

To put my recent posts into a bigger perspective, here's a graph summarizing all of dark matter particles discovered so far via direct or indirect detection:

The graph shows the number of years the signal has survived vs. the inferred mass of the dark matter particle. The particle names follow the usual Particle Data Group conventions. The label's size is related to the statistical significance of the signal. The colors correspond to the Bayesian likelihood that the signal originates from dark matter, from uncertain (red) to very unlikely (blue). The masses of the discovered particles span impressive 11 orders of magnitude, although the largest concentration is near the weak scale (this is called the WIMP miracle). If I forgot any particle for which a compelling evidence exists, let me know, and I will add it to the graph.

Here are the original references for the Bulbulon, Boehmot, Collaron, CDMeson, Daemon, Cresston, Hooperon, Wenigon, Pamelon, and the mother of Bert and Ernie. 

Signal of WIMP dark matter

You may have  heard about the excess of gamma-ray emission from the center of the Milky Way measured by the Fermi telescope. This excess can be interpreted as a signal of a 30-40 GeV dark matter particle - the so-called hooperon -  annihilating into a pair of b-quarks. The inferred annihilation cross section is of order 1 picobarn, perfectly fitting the thermal dark matter paradigm.  The story is not exactly new; the anomaly and its dark matter interpretation was first claimed 4 years ago. Since then there has been a steady trickle of papers by different groups arguing that the signal is robust and proposing dark matter or astrophysical explanations. Last week the story hit several news outlets, see for example here for a nice write up. What has changed that the anomaly was upgraded from a tantalizing hint to a compelling evidence of WIMP dark matter?


First, here is a bit more detailed description of the signal.  The Fermi satellite measures gamma rays from all sky with a good angular and energy resolution. Many boring astrophysical processes produce gamma rays, for example cosmic rays scattering on the interstellar medium, or violent events happening around black holes and pulsars. However, known point sources, galactic and extragalactic diffuse emission, and the emission from the Fermi Bubbles do not seem to be enough to explain what's going on in the center of our galaxy. A better fit is obtained if one adds a new component with a spatial distribution sharply peaked around the galactic center and the energy spectrum with a broad peak near 2 GeV, see the plot. How much better fit?  This paper quotes 40 sigma preference for this new component in the inner galaxy region. That's hell of a significance, even after translating the astrophysical sigmas to the ones used in conventional statistics ;)

Now, WIMP dark matter can easily reproduce the new component.  Cold dark matter is expected to be sharply peaked near the galactic center, with the 1/r or similar profile. Furthermore, when dark matter annihilates into charged particles, the latter can radiate a part of their energy producing photons via the final state radiation, Compton scattering, and bremsstrahlung. This leads to emission of gamma rays with the energy spectrum depending on the dark matter mass and the identity of particles it annihilates into.   Annihilation into leptons (electron, muons, taus) would produce a sharper peak than what is observed. As the plot shows, annihilation into quarks, whether the bottom or lighter one, fits the signal much better. All in all, the excess can be explained by a 15-40 GeV dark matter particle annihilating into quarks with the cross section in the  0.1-1 pb range.

This was known before, more or less. As far as I understand, the recent paper by Daylan et al. adds the following. They repeat the analysis using a subset of the Fermi data where the photon direction  is more reliably reconstructed.  This allows them to better study the morphology of the signal. They show that the excess is steeply falling (approximately as 1/r^1.4) all the way to about 2 kiloparsecs from the galactic center. Moreover, they demonstrate that  the excess is to a good degree spherically symmetric. This can be regarded as an argument against conventional astrophysical explanations. For example, a school of several thousand milisecond pulsars could produce a similar energy spectrum as the excess, but would not be expected to be distributed this way.

Ah, and what does the Fermi collaboration have to say about it? As far as I know, there is no official statement about the excess. In this talk one finds the quote "[In the inner galaxy], diffuse emission and point sources account for most of the emission observed in the region".  So we seem to have two slightly discrepant stories here: 40 sigma vs. nothing to see. If the truth were in the middle that would  be great ;)

In any case, continuous emission from the galactic center will never be regarded as a convincing evidence of dark matter.  To really get excited we would need to find a matching signal in a less messy environment. One possibility is the dwarf galaxies - small galaxies consisting mostly of dark matter that orbit the Milky Way. The Fermi collaboration recently reported the limits on the dark matter annihilation cross section based on observations of 25 dwarf galaxies, see the plot. Intriguingly, there is a small excess (global p-value 0.08) that may be consistent with the dark matter interpretation of the signal from the galactic centre... More data should clarify the situation, but for that we probably need to wait a few more years.

Weekend Plot: wimp race

This weekend's plot encompasses almost the entire field of direct detection of WIMP dark matter:

It shows the existing and projected limits on the scattering cross section of dark matter on nucleons. LUX -- a 370 kg xenon detector -- currently holds the leader position for dar matter masses above 6 GeV and promises to improve the limits by another factor of a few next year. The Xenon collaboration on the other side of the Atlantic is already preparing a nuclear response in the form of a 3 ton detector, to which LUX will retaliate with a 5 ton Led Zeppelin, or maybe LUX-Zeplin. Meanwhile, the SuperCDMS experiment will secure a monopoly in the low-mass region. But the arms race cannot go on forever, as direct detection experiments will inevitably hit the neutrino wall. That is to say, they will reach the sufficient sensitivity to observe nuclear recoils due to elastic scattering of solar and atmospheric neutrinos. That will constitute an irreducible background to dark matter searches  (unless directional detection techniques are developed). And so it'll all come to a bitter end: sometime in the next decade WIMP detection experiments will be downgraded to neutrino observatories.

The plot borrowed from this talk who itself borrowed it from somewhere. 

A 100 TeV question

It is practically decided that the next high-energy collider we build is the ILC - an electron-positron linear collider in Japan starting at the center-of-mass energy starting of 250 GeV. But it's already high time to think of the following step. Two weeks ago a kickoff meeting on future circular colliders took place in Geneva, so it is now officially permitted to dream of a 100 TeV collider.

Particle theorists already started bidding for the most amazing discoveries that await us there. We'll surely find supersymmetry, dark matter, extra dimensions, hairy black holes, a fistful of Higgs bosons, a few bosons more, and the beard of John Ellis. This game seems to ignore the fact that circumstances  have changed after the first run of the LHC. Whatever the  energy of the new machine, 30, 100, 1000 TeV, we currently do not have a no-lose theorem for a discovery of new particles.  

This is an unprecedented situation in collider physics.
For each new collider at the energy frontier in the last 30 years such a firm no-lose theorem existed.
In particular,

• The LHC was certain to discover the Higgs boson,  
• The Tevatron was certain to discover the top quark, 
• LEP was certain to discover supersymmetry,* 
• The SppS was certain to find the W and Z bosons.**  

* There is this apocryphal story of a prominent Italian physicist who vowed to cut off his testicle if superpartners are not found at LEP. It isn't clear whether he had balls to do it. 
** Older readers may remember that the SppS was certain to also discover the top quark and supersymmetry. Just in case, Rubbia initially discovered both of these along with the W boson.

Now it's all different: we have a consistent and experimentally established theory of fundamental interactions that in principle may be valid all the way to the Planck scale. There is no strong case that new particles have to show up at accessible energies, and several precision measurements hint to the contrary. In this situation, banging the drum, like we did before the LHC, is dangerous since we may not have a big discovery to cover for that later. It seems wiser to focus on more certain returns from a 100 TeV collider. That is to say, even if there's no new particles within reach, what shall we learn? Of course, for all of us in the particle community, exploring a new unchartered territory is interesting per se. But we need more to convince others. The argument that we need a 100 TeV collider to prove that electroweak fine-tuning is larger than 0.01% is good. As a joke to relax the atmosphere. Certainly, the case for the new collider is stronger than that. Some ideas that are being bandied around are precision Higgs physics, double Higgs production, rare Higgs and top decays, non-perturbative electroweak physics, or WW scattering. These topics can be made more concrete and several more items can be added to the list.

Or we can study the impact of  the 100 TeV collider on the CMSSM parameter and hope that no one will call the bluff...