Weekend Plot: Rorschach Test

This weekend you are invited to contemplate a plot which, for obvious reasons, is not available on arXiv. Here is a plot by the PVDIS collaboration recently published, quite suitably, in the Nature magazine:

To understand what is depicted here we need to make a slight detour. The Standard Model of particle physics is being tested not only in high-energy colliders, but also via precision measurements at low energies. One important class of precision experiments  goes under the name parity violating electron scattering, PVES in short.  This enterprise consists in shooting a beam of polarized  electrons at various targets:  hydrogen, deuteron, spiders on the wall, etc. In the language of effective theory, the process can be described by 4-fermion operators with 2 electron and 2 quarks fields. For PVES experiments, the relevant operators are those that violate the parity symmetry, for example

There is nothing exotic here: these 4-fermion operators  are predicted by the Standard Model, as they are effectively induced by the Z boson exchange between electrons and quarks. Their effect is that left- and right-handed polarized electrons interact differently with quarks. Thus, they lead to  different  cross sections for left- and right-hand electron scattering on atoms. The left-right asymmetry  -- the difference of these two cross section normalized to the sum -- is a convenient observable to measure in a experiment. In fact, the asymmetry was experimentally observed already back in 1978 at SLAC, and at the time it was an important confirmation of the Standard Model structure of weak interactions.  Nevertheless, it makes sense to measure the asymmetry (and therefore the parameters Cq) more precisely  so as to test the Standard Model predictions. There are two ways new physics could affect this observable. On one hand, the couplings of the Z boson to electrons and/or quarks could be modified, and then the Z boson exchange diagrams would lead to different coefficients Cq than the ones predicted by the Standard Model. On the other hand, new heavy vector boson with mass M interacting with  electrons and quarks with strength g would induce contact interactions between the two that would effectively shift the parameter Cq by the amount  of order g^2 v^2/M^2.

Now the parameters C1u and C1d have been measured quite precisely, with 3% accuracy, and they agree well with the Standard Model predictions (see here for the most recent update). This can be translated as order 1% constrains on the Z boson couplings  to quarks and leptons. It is worth stressing that for the couplings to quarks these are the most stringent constraints to date (better than the ones from LEP) so these experiments are really exploring new territories.
   
The parameters C2u and C2d are more tricky because, in order to access them in scattering experiments, one needs to resolve the internal structure of the target atom.  Here enters the PVDIS experiment at Jlab. They studied the left-right asymmetry of  deep-inelastic polarized electron scattering on deuterons.  They were able to demonstrate, for the first time, that a particular combination 2 C2u - C2d is non-zero, in agreement with the Standard Model. The resulting constraints on the Z-boson couplings are weaker than those coming from previous experiments. However, since they probe different operators, the provide non-trivial constraints on some new physics, in particular those that  produces only C2q and not C1q. The plot reproduced at the top of this post is a more graphic presentation of their results.  In the plot, the combined constraints from several low-energy experiments  are recast in terms of the scale Λ=Mass/coupling of new physics that contributes to the C1q and C2q coefficients. The yellow and red regions show the new physics reach before and after including the PVDIS results. The exciting thing about the plot is  that it explicitly shows  these experiments probe the mass scales of order 10 TeV, which is well  beyond the reach of the LHC.  

Complementary constraints from ATLAS can be found here.

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.