750 ways to leave your lover

A new paper last week straightens out the story of the diphoton background in ATLAS. Some confusion was created because theorists misinterpreted the procedures described in the ATLAS conference note, which could lead to a different estimate of the significance of the 750 GeV excess. However, once the correct phenomenological and statistical approach is adopted, the significance quoted by ATLAS can be reproduced, up to small differences due to incomplete information available in public documents. Anyway, now that this is all behind, we can safely continue being excited at least until summer.  Today I want to discuss different interpretations of the diphoton bump observed by ATLAS. I will take a purely phenomenological point of view, leaving for the next time  the question of a bigger picture that the resonance may fit into.

Phenomenologically, the most straightforward interpretation is the so-called everyone's model: a 750 GeV singlet scalar particle produced in gluon fusion and decaying to photons via loops of new vector-like quarks. This simple construction perfectly explains all publicly available data, and can be easily embedded in more sophisticated models. Nevertheless, many more possibilities were pointed out in the 750 papers so far, and here I review a few that I find most interesting.

Spin Zero or More?  
For a particle decaying to two photons, there is not that many possibilities: the resonance has to be a boson and, according to young Landau's theorem, it cannot have spin 1. This leaves at the table spin 0, 2, or higher. Spin-2 is an interesting hypothesis, as this kind of excitations is predicted in popular models like the Randall-Sundrum one. Higher-than-two spins are disfavored theoretically. When more data is collected, the spin of the 750 GeV resonance can be tested by looking at the angular distribution of the photons. The rumor is that the data so far somewhat favor spin-2 over spin-0, although the statistics is certainly insufficient for any serious conclusions.  Concerning the parity, it is practically impossible to determine it by studying the diphoton final state, and both the scalar and the pseudoscalar option are equally viable at present. Discrimination may be possible in the future, but  only if multi-body decay modes of the resonance are discovered. If the true final state is more complicated than two photons (see below), then the 750 GeV resonance may have  any spin, including spin-1 and spin-1/2.

Narrow or Wide? 
The total width is an inverse of particle's lifetime (in our funny units). From the experimental point of view, the width larger than detector's  energy resolution  will show up as a smearing of the resonance due to the uncertainty principle. Currently, the ATLAS run-2 data prefer the width 10 times larger than the experimental resolution  (which is about 5 GeV in this energy ballpark), although the preference is not very strong in the statistical sense. On the other hand, from the theoretical point of view, it is much easier to construct models where the 750 GeV resonance is a narrow particle. Therefore, confirmation of the large width would have profound consequences, as it would significantly narrow down the scope of viable models.  The most exciting interpretation would then be that the resonance is a portal to a dark sector containing new light particles very weakly coupled to ordinary matter.    

How many resonances?  
One resonance is enough, but a family of resonances tightly packed around 750 GeV may also explain the data. As a bonus, this could explain the seemingly large width without opening new dangerous decay channels. It is quite natural for particles to come in multiplets with similar masses: our pion is an example where the small mass splitting π± and π0 arises due to electromagnetic quantum corrections. For Higgs-like multiplets the small splitting may naturally arise after electroweak symmetry breaking, and  the familiar 2-Higgs doublet model offers a simple realization. If the mass splitting of the multiplet is larger than the experimental resolution, this possibility can tested by precisely measuring the profile of the resonance and searching for a departure from the Breit-Wigner shape. On the other side of the spectrum is the idea is that there is no resonance at all at 750 GeV, but rather at another mass, and the bump at 750 GeV appears due to some kinematical accidents.
   
Who made it? 

The most plausible production process is definitely the gluon-gluon fusion. Production in collisions of light quark and antiquarks is also theoretically sound, however it leads to a more acute tension between run-2 and run-1 data. Indeed, even for the gluon fusion, the production cross section of a 750 GeV resonance in 13 TeV proton collisions is only 5 times larger than at 8 TeV. Given the larger amount of data collected in run-1, we would expect a similar excess there, contrary to observations. For a resonance produced from u-ubar or d-dbar the analogous ratio is only 2.5 (see the table), leading to much more  tension. The ratio climbs back to 5 if the initial state contains the heavier quarks: strange, charm, or bottom (which can also be found sometimes inside a proton), however I haven't seen yet a neat model that makes use of that. Another possibility is to produce the resonance via photon-photon collisions. This way one could cook up a truly minimal and very predictive model where the resonance couples only to photons of all the Standard Model particles. However, in this case, the ratio between 13 and 8 TeV cross section is very unfavorable, merely a factor of 2, and the run-1 vs run-2 tension comes back with more force. More options open up when associated production (e.g. with t-tbar, or in vector boson fusion) is considered. The problem with these ideas is that, according to what was revealed during the talk last December, there isn't any additional energetic particles in the diphoton events. Similar problems are facing models where the 750 GeV resonance appears as a decay product of a heavier resonance, although in this case some clever engineering or fine-tuning may help to hide the additional particles from experimentalist's eyes.

Two-body or more?
While a simple two-body decay of the resonance into two photons is a perfectly plausible explanation of all existing data, a number of interesting alternatives have been suggested. For example, the decay could be 3-body, with another soft visible or invisible  particle accompanying two photons. If the masses of all particles involved are chosen appropriately, the invariant mass spectrum of the diphoton remains sharply peaked. At the same time, a broadening of the diphoton energy due to the 3-body kinematics may explain why the resonance appears wide in ATLAS. Another possibility is a cascade decay into 4 photons. If the  intermediate particles are very light, then the pairs of photons from their decay are very collimated and may look like a single photon in the detector.
   
 ♬ The problem is all inside your head ♬  and the possibilities are endless. The situation is completely different than during the process of discovering the  Higgs boson, where one strongly favored hypothesis was tested against more exotic ideas. Of course, the first and foremost question is whether the excess is really new physics, or just a nasty statistical fluctuation. But if that is confirmed, the next crucial task for experimentalists will be to establish the nature of the resonance and get model builders on the right track.  ♬ The answer is easy if you take it logically ♬ 

All ideas discussed above appeared in recent articles by various authors addressing the 750 GeV excess. If I were to include all references the post would be just one giant hyperlink, so you need to browse the literature yourself to find the original references.

Higgs force awakens

The Higgs boson couples to particles that constitute matter around us, such as electrons, protons, and neutrons. Its virtual quanta are constantly being exchanged between these particles.  In other words, it gives rise to a force -  the Higgs force. I'm surprised why this PR-cool aspect is not explored in our outreach efforts. Higgs bosons mediate the Higgs force in the same fashion as gravitons, gluons, photons, W and Z bosons mediate  the gravity, strong, electromagnetic, and  weak forces. Just like gravity, the Higgs force is always attractive and its strength is proportional, in the first approximation, to particle's mass. It is a force in a common sense; for example, if we bombarded long enough a detector with a beam of particles interacting only via the Higgs force, they would eventually knock off atoms in the detector.

There is of course a reason why the Higgs force is less discussed: it has never been detected directly. Indeed, in the absence of midi-chlorians it is extremely weak. First, it shares the feature of the weak interactions of being short-ranged: since the mediator is massive, the interaction strength is exponentially suppressed at distances larger than an attometer (10^-18 m), about 0.1% of the diameter of a proton. Moreover, for ordinary matter, the weak force is more important because of the tiny Higgs couplings to light quarks and electrons. For example, for the proton the Higgs force is thousand times weaker than the weak force, and for the electron it is hundred thousand times weaker. Finally, there are no known particles interacting only via the Higgs force and gravity (though dark matter in some hypothetical models has this property), so in practice the Higgs force is always a tiny correction to more powerful forces that shape the structure of atoms and nuclei. This is again in contrast to the weak force, which is particularly relevant for neutrinos who are immune to strong and electromagnetic forces.

Nevertheless, this new paper argues that the situation is not hopeless, and that the current experimental sensitivity is good enough to start probing the Higgs force. The authors propose to do it by means of atom spectroscopy. Frequency measurements of atomic transitions have reached the stunning accuracy of order 10^-18. The Higgs force creates a Yukawa type potential between the nucleus and orbiting electrons, which leads to a shift of the atomic levels. The effect is tiny, in particular it  is always smaller than the analogous shift due to the weak force. This is a serious problem, because calculations of the leading effects may not be accurate enough to extract the subleading Higgs contribution.  Fortunately, there may be tricks to reduce the uncertainties. One is to measure how the isotope shift of transition frequencies for several isotope pairs. The theory says that the leading atomic interactions should give rise to a universal linear relation (the so-called King's relation) between  isotope shifts for different transitions. The Higgs and weak interactions should lead to a violation of King's relation. Given many uncertainties plaguing calculations of atomic levels, it may still be difficult to ever claim a detection of the Higgs force. More realistically, one can try to set limits on the Higgs couplings to light fermions which will be better than the current collider limits.  

Atomic spectroscopy is way above my head, so I cannot judge if the proposal is realistic. There are a few practical issues to resolve before the Higgs force is mastered into a lightsaber. However, it is possible that a new front to study the Higgs boson will be opened in the near future. These studies will provide information about the Higgs couplings to light Standard Model fermions, which is complementary to the information obtained from collider searches.

Gunpowder Plot: foiled

Just a week ago I hailed the new king, and already there was an assassination attempt. A new paper claims that the statistical significance of the 750 GeV diphoton excess is merely 2 sigma local. The  story is being widely discussed in the corridors and comment sections because we all like to watch things die...  The assassins used this plot:

The Standard Model prediction for the diphoton background at the LHC is difficult to calculate from first principles. Therefore,  the ATLAS collaboration assumes a theoretically motivated functional form for this background as a function of the diphoton invariant mass. The ansatz contains a number of free parameters, which are then fitted using the data in the entire analyzed range of invariant masses. This procedure leads to the prediction represented by the dashed line in the plot (but see later). The new paper assumes a slightly more complicated functional form with more free parameters, such that the slope of the background is allowed to change.  The authors argue that their more general  ansatz provides a better fit to the entire diphoton spectrum, and moreover predicts a larger background for the large invariant masses.  As a result, the significance of the 750 GeV excess decreases to an insignificant value of 2 sigma.
     
There are several problems with this claim.  First, I'm confused why the blue line is described as the ATLAS fit, since it is clearly different than the background curve in the money-plot provided by ATLAS (Fig. 1 in ATLAS-CONF-2015-081). The true ATLAS background is above the blue line, and much closer to the black line in the peak region (edit: it seems now that the background curve plotted by ATLAS corresponds to a1=0  and one more free parameter for an overall normalization, while the paper assumes fixed normalization). Second, I cannot reproduce the significance quoted in the paper. Taking the two ATLAS bins around 750 GeV, I find 3.2 sigma excess using the true ATLAS background, and 2.6 sigma using the black line (edit: this is because my  estimate is too simplistic, and the paper also takes into account the uncertainty on the background curve). Third, the postulated change of slope is difficult to justify theoretically. It would mean there is a new background component kicking in at ~500 GeV, but this does not seem to be the case in this analysis.

Finally, the problem with the black line is that it grossly overshoots the high mass tail,  which is visible even to a naked eye.  To be more quantitative, in the range 790-1590 GeV there are 17 diphoton events observed by ATLAS,  the true ATLAS backgrounds predicts 19 events, and the black line predicts 33 events. Therefore, the background shape proposed in the paper is inconsistent with the tail at the 3 sigma level! While the alternative background choice decreases the  significance at the 750 GeV peak, it simply moves (and amplifies) the tension to another place.

So, I think the plot is foiled and the  claim does not stand scrutiny.  The 750 GeV peak may well be just a statistical fluctuation that will go away when more data is collected, but it's unlikely to be a stupid error on the part of ATLAS. The king will live at least until summer.

Weekend Plot: The king is dead (long live the king)

The new diphoton king has been discussed at length in the blogoshpere, but the late diboson king also deserves a word or two. Recall that last summer ATLAS announced a 3 sigma excess in the dijet invariant mass distribution where each jet resembles a fast moving W or Z boson decaying to a pair of quarks. This excess can be interpreted as a 2 TeV resonance decaying to a pair of W or Z bosons. For example, it could be a heavy cousin of the W boson, W' in short, decaying to a W and a Z boson. Merely a month ago this paper argued that the excess remains statistically significant after combining several different CMS and ATLAS diboson resonance run-1 analyses in hadronic and leptonic channels of W and Z decay. However, the hammer came down seconds before the diphoton excess announced: diboson resonance searches based on the LHC 13 TeV collisions data do not show anything interesting around 2 TeV. This is a serious problem for any new physics interpretation of the excess since, for this mass scale,  the statistical power of the run-2 and run-1 data is comparable.  The tension is summarized in this plot:

The green bars show the 1 and 2 sigma best fit cross section to the diboson excess. The one on the left takes into account  only the hadronic channel in ATLAS, where the excess is most significant; the one on the right is bases on  the combined run-1 data. The red lines are the limits from run-2 searches in ATLAS and CMS, scaled to 8 TeV cross sections assuming W' is produced in quark-antiquark collisions. Clearly, the best fit region for the 8 TeV data is excluded by the new 13 TeV data. I display results for the W' hypothesis, however conclusions are similar (or more pessimistic) for other hypotheses leading to WW and/or ZZ final states. All in all,  the ATLAS diboson excess is not formally buried yet, but at this point any a reversal of fortune would be a miracle.

Do-or-die year

The year 2016 began as any other year... I mean the hangover situation in particle physics. We have a theory of fundamental interactions - the Standard Model - that we know is certainly not the final  theory because it cannot account for dark matter, matter-antimatter asymmetry, and cosmic inflation. At the same time, the Standard Model perfectly describes any experiment we have performed here on Earth (up to a few outliers that can be shrugged off as statistical fluctuations)... If you're having a déjà vu, maybe it's the Monty Python sketch, or maybe because this post begins exactly the same as one written a year ago.   Back then,  I was optimistically  assuming that the 2015 LHC operation would go better than the projections, and that some 15 inverse femtobarn of data would be collected by each experiment. That amount would have clarified our chances for a discovery in the LHC run-2, and determine whether or not we should dust off our No Future t-shirts. Instead, due to machine's hiccups during the summer, only about 4 fb-1 was delivered to each experiment. This added up to the magnet and calorimeters problems in the CMS experiment who managed to collect only 2.4 fb-1 of useful data, against 3.6 fb-1 in ATLAS. With that amount, the discriminating power is improved with respect to run-1 only for particles heavier than ~1 TeV.  As a consequence, the boundaries of our knowledge have changed only slightly compared to the status a year ago. At the end of the day, it's this year, and not the previous one, that is going to be decisive for the field.

So the tension is similar as last year at this time, however the mood is considerably better, see the plot. We have two intriguing hints of new physics that have a non-negligible chance to develop into a strong evidence: one is the B-meson anomalies discussed several times in this blog, and the other is the 750 GeV diphoton excess. Especially the latter stirs theorists' imagination,  even if some experimentalists deplore the fact (theorists writing papers inspired by experimental data? oh horror...).   A significant deviation from the Standard Model seen independently  by 2 different collaborations  in an experimentally clean channel happens for the first time in my life.  In my private poll, the chances for the B-meson anomalies to be new physics are estimated as 1%, while for the diphoton the chances are 10%. This adds up to a whopping 11% chance, the biggest ever, of finding new physics soon. Moreover, if the diphoton excess is really a new particle, we are basically guaranteed to find other phenomena beyond the Standard Model. Indeed, most models accommodating the 750 GeV excess require new colored states with O(1) TeV mass, which are then most naturally embedded in a theory with new strong interactions at a few TeV scale.  Not only would that give a boost to future LHC analyses, but it would also motivate building a higher-energy collider,  e.g.  a 30 TeV collider that could be constructed at a short time scale at CERN.

Anything may happen this year, for good or for worse. Cross your fingers and fasten your seat belts.