Beauty-full exotic bound states at the LHC

Article: Beauty-full Tetraquarks
Authors: Yang Bai, Sida Lu, and James Osborn

Good Day Nibblers,

As you probably already know, a single quark in isolation has never been observed in Nature. The Quantum Chromo Dynamics (QCD) strong force prevents this from happening by what is called ‘confinement. This refers to the fact that when quarks are produced in a collision for example, instead of flying off alone each to be detected separately, the strong force very quickly forces them to bind into composite states of two or more quarks called hadrons. These multi-quark bound states were first proposed in 1964 by Murray Gell-Mann as a way to explain observations at the time.

The quarks are bound together by QCD via the exchange of gluons (e.g. see Figure 1) and there is an energy associated with how strongly they are bound together. This binding energy between the quarks contributes to the ‘effective mass’ for the composite states and in fact it is what is largely responsible for the mass of ordinary matter (Footnote 1). Most of the theoretical and experimental progress has been in two or three quark bound states, referred to as mesons and baryons respectively. The most familiar examples of quark bound states are the neutron and proton, both of which are baryons composed of three quarks bound together and form the basis for atomic nuclei.

Figure 1: Bound state of four bottom quarks (blue) held together by the QCD strong force which is transmitted via the exchange of gluons (pink).

Of course four and even more quark bound states are possible and some have been observed, but things get much trickier theoretically in these cases. For four quark bound states (called tetra-quarks) the theoretical progress had been largely limited to the case where at least one of the quarks was a light quark, like an up or a down quark.

The paper highlighted here takes a step towards understanding four quark bound states in the case where all four quarks are heavy. These heavy four body systems are extra tricky because they cannot be decomposed into pairs of two body systems which we could solve much more easily. Instead, one must solve the Schrödinger equation for the full four body system for which approximation methods are needed. The example the current authors focus on is the four bottom quark bound state or 4b state for short (see Figure 1). In this paper they use sophisticated numerical methods to solve the non-relativistic Schrödinger equation for a four-body system bound together by QCD. Specifically they solve for the energy of the ground state, or lowest energy state, of the 4b system. This lowest energy state can effectively be interpreted as the mass of the 4b composite state.

In the ground state the four bottom quarks arrange themselves in such a way that the composite system appears as spin-0 particle. So in effect the authors have computed the mass of a composite spin-0 particle which, as opposed to being an elementary scalar like the Standard Model Higgs boson, is made up of four bottom quarks bound together. They find the ground state energy, and thus the mass of the 4b state, to be about 18.7 GeV. This is a bit below the sum of the masses of the four (elementary) bottom quarks which means the binding energy between the quarks actually lowers the effective mass of the composite system.

The interesting thing about this study is that so far no tetra-quark states composed only of heavy quarks (like the bottom and top quarks) have been discovered at colliders. The prediction of the mass of the 4b resonance is exciting because it means we know where we should look at the LHC and can optimize a search strategy accordingly. This of course increases the prospects of observing a new state of matter when the 4b state decays, which it can potentially do in a number of ways.

For instance it can decay as a spin-0 particle (depicted as \varphi in Figure 2) into two bound states of pairs of b quarks, which themselves are referred to as \Upsilon mesons. These in turn can be observed in their decays to light Standard Model particles giving many possible signatures at the LHC. As the authors point out, one such signature is the four lepton final state which, as I’ve discussed before, is a very precisely measured channel with small backgrounds. The light mass of the 4b state also allows for it to potentially be produced in large rates at the LHC via the strong force. This sets up the exciting possibility that a new composite state could be discovered at the LHC before long simply by looking at events with four leptons with total energy around 18 – 19 GeV.

Figure 2: Production of a four bottom quark bound state (\varphi) which then decays to two bound states of bottom quark pairs called \Upsilon mesons.

Of course, one could argue this is less exciting than discovering a new elementary particle since if the 4b state is observed it won’t be the discovery of a new particle but instead of yet another manifestation of the QCD strong force. At the end of the day though, it is still an exotic state of nature which has never been observed. Furthermore, these exotic states could be interesting testing grounds for beyond the Standard Model theories which include new forces that communicate with the bottom quark.

We’ll have to wait and see if the QCD strong force can indeed manifest itself as a four bottom quark bound state and if the prediction of its mass made by the authors indeed turns out to be correct. In the meantime, it gives plenty of motivation to experimentalists at the LHC to search for these and other exotic bound states and gives us perhaps some hope for finding physics beyond the Standard Model at the LHC.

Footnote 1: I know what you are thinking, but I thought the Higgs gave mass to matter!? Well yes, but…The Higgs gives mass to the elementary particles of the Standard Model. But most of the matter (that is not dark!) in the universe is not elementary, but instead made up of protons and neutrons which are composed of three quarks bound together. The mass of protons and neutrons is dominated by the binding and kinetic energy of the three quarks systems and therefore it is this that is largely responsible for the mass of normal matter we see in the universe and not the Higgs mechanism.

Other recent studies on heavy quark bound states:




Further reading and video:

1) TASI 2014 has some great introductory lectures and notes on QCD:

The end of the Universe?

Hello nibblers,

Don’t worry, my title doesn’t refer to the recent US election. Only to the end of the Universe due to the Higgs boson. Let me explain…

Last time I wrote, I discussed new methods for determining whether the Higgs boson interacts with itself. As you will recall, establishing whether this is the case is crucial for determining the precise form of the Higgs scalar potential which is responsible for breaking electroweak symmetry and generating masses for the W and Z bosons via the Higgs mechanism. You might also remember that I briefly mentioned that these Higgs self interactions might have deep implications for the stability of our universe. Since I think this topic is interesting enough for its own post I wanted to go into a little more. Its a fascinating topic, but the details can get hairy pretty quickly so ill keep it as simple as possible and just try and give a flavor before going into more detail in future posts.

In the Standard Model, the Higgs potential determines the ‘vacuum’ of our universe, which by definition is the lowest energy state and presumably the one in which we live in today. We can think of the Higgs potential as a ‘background, along with spacetime, in which the various processes which occur in the Universe are acted out. In the Standard Model the Higgs potential before electroweak symmetry can be written as a very simple polynomial in H (after requiring gauge invariance and renormalizability),

V(H) = \mu^2 H^2 + \lambda H^4.

Assuming \mu^2 > 0 and \lambda > 0, this looks like the function drawn in Figure 1. Visually it is easy to see that H = 0 is a minimum of V(H). We call this a stable minimum because if you imagine a ball sitting at the bottom of the ‘bowl’ and moving it to the left or right it will simply role back down to H = 0. Since at this point the energy is a minimum, we call it the vacuum. In order for our universe to be stable we must live in a minimum such as this, i.e. a stable vacuum.

Figure 1: The Higgs potential for $latex \mu^2 > 0$ and $latex \lambda > 0$. This potential has a stable minimum at $latex H = 0$.
Figure 1: The Higgs potential for \mu^2 > 0 and \lambda > 0. This potential has a stable minimum at H = 0.

If on the other hand we have \mu^2 > 0 and \lambda < 0, the potential now looks like that in Figure 2. Clearly now H=0 is no longer a stable point as can be understood by again considering a ball sitting at H = 0 and moving it to the left or right. As we see in Figure 2, instead of rolling back to H = 0 as before, it will simply keep rolling down to the left or right to arbitrarily large values of H, never to return to H = 0. We say this potential is unstable and something like it would be disastrous for our universe. So we see in this very simple example already how the sign of \lambda is crucial for determining whether the vacuum, and as a consequence our universe, is stable.


Figure 2: The Higgs potential for $latex \mu^2 > 0$ and $latex \lambda < 0$. This potential is not stable.
Figure 2: The Higgs potential for \mu^2 > 0 and \lambda < 0. This potential is not stable.

Once electroweak symmetry breaking occurs the potential becomes a little more complicated, but more interesting. Still, the stability of our vacuum will depend on the sign of \lambda. We can see this by considering the case \mu^2 < 0 and \lambda > 0 for which the Higgs develops a vacuum expectation value (VEV) and breaks electroweak symmetry. The Higgs potential looks like what we see in Figure 3. Now the minimum is not at H = 0, but at H = \pm v where v is the value of the Higgs’ VEV and we can think of the two minima as equivalent due to symmetry.

Figure 3: The Higgs potential for $latex \mu^2 0$. This potential breaks electroweak symmetry and has a stable minimum at $latex H = v$.
Figure 3: The Higgs potential for \mu^2 < 0 and \lambda > 0. This potential breaks electroweak symmetry and has a stable minimum at H = v.

The subtlety comes when we consider what happens at very large H. In Figure 3 the potential appears to increase forever as H gets larger and thus H = v would an absolute minimum of V(H). But is it possible that at large enough values of H we’ll find another even deeper minimum which would thus be the `true’ vacuum? This is possible if \lambda < 0 which could generate a potential of the form shown in Figure 4.

Figure 4: The Higgs potential for $latex \mu^2 0$. This potential breaks electroweak symmetry and has a 'false' vacuum at $latex H = v$ with the 'true' deeper vacuum at much larger $latex H$.
Figure 4: The Higgs potential for \mu^2 < 0 and \lambda < 0. This potential breaks electroweak symmetry and has a ‘false’ vacuum at H = v with the ‘true’ deeper vacuum at much larger H.

In this case there can be a deeper ‘well’ than the one where we currently live near H = v. Naively we would need enough energy to get over the large humps and fall to the deeper minimum. Thus there is no worry that our Universe will suddenly decay away to some other lowest energy state which probably would not include people and we can rest easy….buuut…this is only what would happen in a classical world.

Here the magic of quantum mechanics (or should I say terror?) comes into play. Due to quantum fluctuations even though the Higgs lives the vast majority of the time in the minimum around H = v there is a tiny probability that the Higgs boson can suddenly fluctuate to very large values of H. If there is a deeper minimum at these large values as shown in Figure 4, then we could quantum mechanically ‘tunnel’ from our current vacuum, to the deeper ‘true’ vacuum.

Needless to say this sounds bad. So what happens in the Standard Model, is the Universe stable? The answer turns out to be closely related to the Higgs boson and top quark masses and takes us into the deep waters of renormalization, but i’ll save this interesting connection to a future post. For now we can just appreciate the importance of determining \lambda by measuring the Higgs self interactions at the LHC or future colliders.

Further reading: 

  1. If you want to start learning about the conept of a vacuum here is a good place to start.
  2. Here again is a basic introduction to the physics of the Standard Model Higgs boson.

Does the Higgs talk to itself?

Article: Indirect probes of the trilinear Higgs Coupling
Authors: Martin Gorbahn, Ulrich Haisch
Reference: 1607.03773

Hello particle munchers,

I’m back to further discuss our good friend the Higgs boson.

After its discovery in 2012, there are many properties of the Higgs boson which have since been established. In addition to its spin-0 nature and measuring its mass with high precision (125 GeV), the existence of its couplings to a number of Standard Model particles has also been established.

What has yet to be established is whether the Higgs can “talk to itself”. More precisely, does the Higgs have self interactions involving multiple Higgs bosons (see diagrams in Figure 1) and how strong are these self interactions? Measuring these interactions gives us direct information on the Higgs scalar potential, which is responsible for not only the electroweak symmetry breaking mechanism leading to the generation of mass for the Standard Model particles, but also has implications for the stability of our universe (see Footnote 1) .

The Higgs potential can be written in a very simple form (just a polynomial in the Higgs field H) as shown in Figure 1. The H^2 term represents the Higgs mass while the H^3 and H^4 terms represent the Higgs self interactions we are interested in. In the Standard Model \lambda_3 and \lambda_4 have a precise relation reflecting the underlying symmetries of the SM. By measuring interactions involving 3 and 4 Higgs bosons we can determine these parameters and therefore test directly this prediction of the SM. A deviation from from the Standard Model prediction would signal the presence of new physics which, needless to say, would send theorist into a drunk frenzy not seen since…oh wait, never mind :/.

Figure 1: V(H) represents the Higgs potential. We have also indicated which terms in the potential correspond to interactions between 3 and 4 Higgs bosons.
Figure 1: V(H) represents the Higgs potential. We have also indicated which terms in the potential correspond to interactions between 3 and 4 Higgs bosons.

Typically one attempts to measure \lambda_3 and \lambda_4 using h \to hh and h\to hhh decays respectively (see Footnote 2). The h\to hhh rate is far too small at the LHC to be useful for extracting \lambda_4. Thus, most theoretical and experimental studies (see here and references therein) have focused on measuring \lambda_3 via h\to hh decays.

Since the h\to hh rate is also small, it requires producing many Higgs bosons so that after a long time and massive amounts of data, enough of them will decay off-shell into pairs of Higgs bosons to be seen at colliders. At LHC energies the production rates are not quite large enough to be able see this process if it conforms to the SM prediction. However, if new physics somehow makes the rate much larger than found in the SM, then perhaps it can be seen at the LHC.

The paper highlighted above is interesting because it proposes a new, but indirect, way to measure \lambda_3 at the LHC by looking at gluon fusion Higgs production and h\to \gamma\gamma decays (where \gamma is a photon), which i’ll focus on in todays post. If you recall my earlier post about how we see the Higgs boson in its decays to pairs of photons, you might remember that the interaction between the Higgs and photons is generated through loops of virtual charged particles. At leading one loop order, there can only be charged particles running in the loop and thus no Higgs bosons. This means that at leading order we are not sensitive to \lambda_3. However, if we go to next to leading order at two loops one can have Higgs bosons contribute as shown in Figure 2. In this case we see the Higgs boson can enter in the loops and in particular the \lambda_3 coupling at the vertex with 3 Higgs bosons indicated by the box.

Figure 2: Two loop contributions to Higgs decays to pairs of photons. The box indicates the Higgs self interaction we are interested in.
Figure 2: Two loop contributions to Higgs decays to pairs of photons. The box indicates the Higgs self interaction we are interested in (figure from arxiv: 1607.03773).

Since these two loop processes are next to leading order, they are in general very small. However, the high precision with which h\to \gamma\gamma will eventually be measured at the LHC allows for these tiny effects to be potentially probed. What is interesting is that the authors find that these indirect methods are competitive and complementary to h\to hh decays at the LHC. They find it will be possible to eliminate regions of parameter space in beyond the Standard Model theories which can not be ruled out with the more conventional and direct h\to hh decays.

Though the precision is still not great, due to the importance of establishing the precise form of the Higgs potential, it is crucial to have as many ways as possible of constraining its parameters. Since the LHC will just begin to probe the parameters of the Higgs potential before the end of running, a future collider which could produce far larger numbers of Higgs bosons will be crucial in this endeavor of determining if indeed the Higgs talks to itself.


  1. I’ll discuss this interesting topic of the vacuum stability of the universe more in a future post, but see here for a great discussion or here for a famous paper about it. Or just ask Stephen Hawking.
  2. You might ask how one Higgs boson can decay to multiple Higgs bosons when clearly one Higgs boson has less mass than two or more Higgs bosons. This of course is due to the subtleties of quantum mechanics which leads to the fact that particles can decay `off mass shell’ (more precisely with a 4-momentum squared which is not equal to its physical mass). This means that particles which naively are too light to decay to a particular more massive final state can still do so at the cost of a massive kinematic suppression.

Further reading: 

  1. Very similar study proposing additional indirect probes of \lambda_3
  2. A basic introduction to the physics of the Standard Model Higgs boson

Inspecting the Higgs with a golden probe

Hello particle nibblers,

After recovering from a dead-diphoton-excess induced depression (see here, here, and here for summaries) I am back to tell you a little more about something that actually does exist, our old friend Monsieur Higgs boson. All of the fuss over the past few months over a potential new particle at 750 GeV has perhaps made us forget just how special and interesting the Higgs boson really is, but as more data is collected at the LHC, we will surely be reminded of this fact once again (see Fig.1).

Figure 1: Monsieur Higgs boson struggles to understand the Higgs mechanism.

Previously I discussed how one of the best and most precise ways to study the Higgs boson is just by `shining light on it’, or more specifically via its decays to pairs of photons. Today I want to expand on another fantastic and precise way to study the Higgs which I briefly mentioned previously; Higgs decays to four charged leptons (specifically electrons and muons) shown in Fig.2. This is a channel near and dear to my heart and has a long history because it was realized, way before the Higgs was actually discovered at 125 GeV, to be among the best ways to find a Higgs boson over a large range of potential masses above around 100 GeV. This led to it being dubbed the “gold plated” Higgs discovery mode, or “golden channel”, and in fact was one of the first channels (along with the diphoton channel) in which the 125 GeV Higgs boson was discovered at the LHC.

Figure 2: Higgs decays to four leptons are mediated by the various physics effects which can enter in the grey blob. Could new physics be hiding in there?
Figure 2: Higgs decays to four leptons are mediated by the various physics effects which can enter in the grey blob. Could new physics be hiding in there?

One of the characteristics that makes the golden channel so valuable as a probe of the Higgs is that it is very precisely measured by the ATLAS and CMS experiments and has a very good signal to background ratio. Furthermore, it is very well understood theoretically since most of the dominant contributions can be calculated explicitly for both the signal and background. The final feature of the golden channel that makes it valuable, and the one that I will focus on today, is that it contains a wealth of information in each event due to the large number of observables associated with the four final state leptons.

Since there are four charged leptons which are measured and each has an associated four momentum, there are in principle 16 separate numbers which can be measured in each event. However, the masses of the charged leptons are tiny in comparison to the Higgs mass so we can consider them as massless (see Footnote 1) to a very good approximation. This then reduces (using energy-momentum conservation) the number of observables to 12 which, in the lab frame, are given by the transverse momentum, rapidity, and azimuthal angle of each lepton. Now, Lorentz invariance tells us that physics doesnt care which frame of reference we pick to analyze the four lepton system. This allows us to perform a Lorentz transformation from the lab frame where the leptons are measured, but where the underlying physics can be obscured, to the much more convenient and intuitive center of mass frame of the four lepton system. Due to energy-momentum conservation, this is also the center of mass frame of the Higgs boson. In this frame the Higgs boson is at rest and the \emph{pairs} of leptons come out back to back (see Footnote 2) .

In this frame the 12 observables can be divided into 4 production and 8 decay (see Footnote 3). The 4 production variables are characterized by the transverse momentum (which has two components), the rapidity, and the azimuthal angle of the four lepton system. The differential spectra for these four variables (especially the transverse momentum and rapidity) depend very much on how the Higgs is produced and are also affected by parton distribution functions at hadron colliders like the LHC. Thus the differential spectra for these variables can not in general be computed explicitly for Higgs production at the LHC.

The 8 decay observables are characterized by the center of mass energy of the four lepton system, which in this case is equal to the Higgs mass, as well as two invariant masses associated with each pair of leptons (how one picks the pairs is arbitrary). There are also five angles (\Theta, \theta_1, \theta_2, Φ, Φ1) shown in Fig. 3 for a particular choice of lepton pairings. The angle \Theta is defined as the angle between the beam axis (labeled by p or z) and the axis defined to be in the direction of the momentum of one of the lepton pair systems (labeled by Z1 or z’). This angle also defines the ‘production plane’. The angles \theta_1, \theta_2 are the polar angles defined in the lepton pair rest frames. The angle Φ1 is the azimuthal angle between the production plane and the plane formed from the four vectors of one of the lepton pairs (in this case the muon pair). Finally Φ is defined as the azimuthal angle between the decay planes formed out of the two lepton pairs.

Figure 3: Angular center of mass observables ($latex \Theta, \theta_1, \theta_2, Φ, Φ_1$) in Higgs to four lepton decays.
Figure 3: Angular center of mass observables in Higgs to four lepton decays.

To a good approximation these decay observables are independent of how the Higgs boson is produced. Furthermore, unlike the production variables, the fully differential spectra for the decay observables can be computed explicitly and even analytically. Each of them contains information about the properties of the Higgs boson as do the correlations between them. We see an example of this in Fig. 4 where we show the one dimensional (1D) spectrum for the Φ variable under various assumptions about the CP properties of the Higgs boson.

Figure 4: Here I show various examples for the Φ differential spectrum assuming different possibilities for the CP properties of the Higgs boson.
Figure 4: Here I show various examples for the Φ differential spectrum assuming different possibilities for the CP properties of the Higgs boson.

This variable has long been known to be sensitive to the CP properties of the Higgs boson. An effect like CP violation would show up as an asymmetry in this Φ distribution which we can see in curve number 5 shown in orange. Keep in mind though that although I show a 1D spectrum for Φ, the Higgs to four lepton decay is a multidimensional differential spectrum of the 8 decay observables and all of their correlations. Thus though we can already see from a 1D projection for Φ how information about the Higgs is contained in these distributions, MUCH more information is contained in the fully differential decay width of Higgs to four lepton decays. This makes the golden channel a powerful probe of the detailed properties of the Higgs boson.

OK nibblers, hopefully I have given you a flavor of the golden channel and why it is valuable as a probe of the Higgs boson. In a future post I will discuss in more detail the various types of physics effects which can enter in the grey blob in Fig. 2. Until then, keep nibbling and don’t let dead diphotons get you down!

Footnote 1: If you are feeling uneasy about the fact that the Higgs can only “talk to” particles with mass and yet can decay to four massless (atleast approximately) leptons, keep in mind they do not interact directly. The Higgs decay to four charged leptons is mediated by intermediate particles which DO talk to the Higgs and charged leptons.

Footnote 2: More precisely, in the Higgs rest frame, the four vector formed out of the sum of the two four vectors of any pair of leptons which are chosen will be back to back with the four vector formed out of the sum of the second pair of leptons.

Footnote 3: This dividing into production and decay variables after transforming to the four lepton system center of mass frame (i.e. Higgs rest frame) is only possible in practice because all four leptons are visible and their four momentum can be reconstructed with very good precision at the LHC. This then allows for the rest frame of the Higgs boson to be reconstructed on an event by event basis. For final states with missing energy or jets which can not be reconstructed with high precision, transforming to the Higgs rest frame is in general not possible.

Discovery of a New Particle or a Sick and Twisted Santa?

Good day particle nibblers,

The last time I was here I wrote about the potentially exciting “bump” which was observed by both the ATLAS and CMS experiments at the LHC.  As you’ll recall, the “bump” I’m referring to here is the excess of events seen at around 750 GeV in data containing pairs of high energy photons, what you may have heard referred to as “the diphoton excess”. The announcement was made by the experimental collaborations just before Christmas last year, ensuring that theorists around the world would not enjoy a Christmas break as instead we plunged head first into model building and speculation of what this “bump” could be. Combined with too much holiday wine, this lead to an explosion of papers in the following weeks and months (see here for a Game of Thrones themed accounting of the papers written).

The excitement was further fueled in March at the Moriond conference when both ATLAS and CMS announced results from re-analyzed data taken at 13 TeV during 2015 (and some 8 TeV data taken in 2012). They found, after optimizing their analysis for both a spin-0 and spin-2 particle, that the statistical significance for the excess increased slightly in both experiments (see Figure 1 for ATLAS results and here for a more in depth discussion).

ATLAS 13 TeV diphoton spectrum with cuts optimized for a spin-0 heavy resonance (left) and for a spin-2 resonance (right).
Figure 1: ATLAS 13 TeV diphoton spectrum with cuts optimized for a spin-0 heavy resonance (left) and for a spin-2 resonance (right).

In the end both experiments reported a (local) statistical significance (see Footnote 1) of more than 3 standard deviations (or 3σ for short). Normally 3σ’s don’t cause such a frenzy, but the fact that two separate experiments observed this made the probability that it was just a statistical fluctuation much lower (something on the order of 1 in a few thousand chance). If this excess really is just a statistical fluctuation it is a pretty nasty one indeed and may suggest a sick and twisted Santa has been messing with the fragile emotional state of particle theorists ever since Christmas (see Figure 2).

Figure 2: Last known photo of the sick and twisted Santa suspected of perpetuating the false hope of a 750 GeV diphoton excess.
Figure 2: Last known photo of the sick and twisted Santa suspected of perpetuating the false hope of a 750 GeV diphoton excess.

Since the update at the Moriand conference in March (based primarily on 2015 data), particle physicists have been eagerly awaiting the first results based on data taken at the LHC in 2016. With the rate at which the LHC has been accumulating data this year, already there is more than enough collected by ATLAS and CMS to definitively pin down whether the excess is real or if we are indeed dealing with a demented Santa. The first official results will be presented later this summer at ICHEP, but we particle physicists are impatient so the rumor chasing is already in full swing.

Sadly, the latest rumors circulating in the twitter/blogosphere (see also here, here, and here for further rumor mongering) seem to indicate that the excess has disappeared with the new data collected in 2016. While we have to wait for the experimental collaborations to make an official public announcement before shedding tears, judging by the sudden slow down of ‘diphoton excess’ papers appearing on the arXiv, it seems much of the theory community is already accepting this pessimistic scenario.

If the diphoton excess is indeed dead it will be a sad day for the particle physics community. The possibilities for what it could have been were vast and mind-boggling. Even more exciting however was the fact that if the diphoton excess were real and associated with a new resonance, the discovery of additional new particles would almost certainly have been just around the corner, thus setting off a new era of experimental particle physics. While a dead diphoton excess would indeed be sad, I urge you young nibblers to not be discouraged. One thing this whole ordeal has taught us is that the LHC is an amazing machine and working fantastically. Second, there are still many interesting theoretical ideas out there to be explored, some of which came to light in attempting to explain the excess. And remember it only takes one discovery to set off a revolution of physics beyond the Standard Model so don’t give up hope yet!

I also urge you to not pay much attention to the inevitable negative backlash that will occur (and already beginning in the blogosphere) both within the particle physics community and the popular media. There was a legitimate excess in the 2015 diphoton data and that got theorists excited (reasonably so IMO), including yours truly. If the excitement of the excess brought in a few more particle nibblers then even better still! So while we mourn the (potential) loss of this excess let us not give up just yet on the amazing machine that is the LHC possibly discovering new physics. And then we can tell that sick and twisted Santa to go back to the north pole for good!

OK nibblers, thats all the thoughts I wanted to share on the social phenomenon that is (was?) the diphoton excess. While we wait for official announcements, let us in the meantime hope the rumors are wrong and that Santa really is warm and fuzzy and cares about us like they told us as children.

Footnote 1: The global significance was between 1 and 2σ, but I wont get into these details here.

Disclaimer 1: I promise next post I will get back to discussing actual physics instead of just social commentary =).

Disclaimer 2: Since I am way too low on the physics totem pole to have any official information, please take anything written here about rumors of the diphoton excess with a grain of salt. Stay tuned here for more credible sources.

A New Particle at LHC for Christmas??

Hello particle gobblers and happy new year from my new location at the University of Granada.

In between presents and feasting, you may have heard rumblings over the holidays that the LHC could be seeing hints of a new and very massive particle. The rumors began even before the ATLAS and CMS experiments announced results from analyzing the brand new 13 TeV (in particle physics units!) data which was collected in 2015. At 13 TeV we are now probing higher energy scales of nature than ever before. These are truly uncharted waters where high energy physicists basically have no idea what to expect. So there was a lot of anticipation for the first release of new data from the LHC in early December and it appears a tantalizing hint of new physics may have been left there dangling for us, like a just out of reach Christmas cookie.

Since the announcement, a feeding frenzy of theoretical work has ensued as theorists, drunk from the possibilities of new physics and too much holiday food, race to put forth their favorite (or any) explanation (including yours truly I must confess:/). The reason for such excitement is an apparent excess seen by both CMS and ATLAS of events in which two very energetic photons (particles of light) are observed in tandem. By `excess’ I basically mean a `bump‘ on what should be a `smooth‘ background exactly as discussed previously for the Higgs boson at 125 GeV. This can be seen in the CMS (Figure 1) and ATLAS (Figure 2) results for the observed number of events involving pairs of photons versus the sum of their energies.

Figure 1: CMS results for searches of pairs of photons at 13 TeV.
Figure 1: CMS results for searches of pairs of photons at 13 TeV.
Figure 2: ATLAS results for searches of pairs of photons at 13 TeV.
Figure 2: ATLAS results for searches of pairs of photons at 13 TeV.













The bump in the ATLAS plot is easier to see (and not coincidentally has a higher statistical significance) than the CMS bump which is somewhat smaller. What has physicists excited is that these bumps appear to be at the same place at around 750 GeV^1. This means two independent data sets both show (small) excesses in the same location making it less likely to be simply a statistical fluctuation. Conservation of energy and momentum tells us that the bump should correspond to the mass of a new particle decaying to two photons. At 750 GeV this mass would be much higher than the mass of the heaviest known particle in the Standard Model; the top quark, which is around 174 GeV while the Higgs boson you will remember is about 125 GeV.

It is of course statistically very possible (some might say probable) that these are just random fluctuations of the data conspiring to torture us over the holidays. Should the excess persist and grow however, this would be the first clear sign of physics beyond the Standard Model and the implications would be both staggering and overwhelming. Simply put, the number of possibilities of what it could be are countless as evidenced by the downpour of papers which came out just in the past two weeks and still coming out daily.

A simple and generic explanation which has been proposed by many theorists is that the excess indicates the presence of a new, electrically neutral, spin-0 scalar boson (call it \varphi) which is produced from the fusion of two gluons and which then decays to two photons (see Figure 3) very much like our earlier discussion of the Higgs boson. So at first appearance this just looks like a heavy version of the Higgs boson discovered at 125 GeV. Crucially however, the new potential scalar at 750 GeV has nothing (or atleast very little) to do with generating mass for the W and Z bosons of the Standard Model which is the role of the Higgs boson. I will save details about the many possibilities for a future post^2, but essentially the many models put forth attempt to explain what occurs inside the gray `blobs’ in order to generate an interaction between \varphi with gluons and photons.

Figure 3: Production of a new scalar particle via gluon fusion followed by decay into photons.
Figure 3: Production of a new scalar particle via gluon fusion followed by decay into photons.

It will of course take more data to confirm or deny the excess and the possible existence of a new particle. Furthermore, if the excess is real and there is indeed a new scalar particle at 750 GeV, a host of other new signals are expected in the near future. As more data is collected in the next year the answers to these questions will begin to emerge. In the meantime, theorists will daydream of the possibilities hoping that this holiday gift was not just a sick joke perpetrated by Santa.


1. It is a bit difficult to tell by eye because the ATLAS plot axis is linear while that for CMS is logarithmic. A nice discussion of the two bumps and their location can be found here.

2. For those feeling more brave, a great discussion about the excess and its implications can be found here and here.

A New Solution to the Hierarchy Problem?

Hello particle Chompers,

Today I want to discuss a slightly more advanced topic which I will not be able to explain in much detail, but goes by the name of the gauge Hierarchy problem or just the `the Hierarchy Problem‘. My main motivation is to simply make you curious enough that you will feel inspired to investigate it further for yourself since it is one of the outstanding problems in particle physics and one of the main motivations for the construction of the LHC. A second motivation is to bring to your attention a recent and exciting paper which proposes a potentially new solution to the hierarchy problem.

The hierarchy problem can roughly be stated as the problem of why the vacuum expectation value (VEV) of the Higgs boson, which determines the masses of the electroweak W and Z bosons, is so small compared to the highest energy scales thought to exist in the Universe. More specifically, the masses of the W and Z bosons (which define the weak scale) are roughly \sim 10^{2} GeV (see Figure 1) in particle physics units (remember in these units mass = energy!).

The W boson as it finds to its astonishment that it has a mass of only about 100 GeV instead of $latex 10^{19}$ GeV as expected.
The W boson as it finds to its astonishment that it has a mass of only about 100 GeV instead of 10^{19} GeV as expected.

On the other hand the highest energy scale thought to exist in the Universe is the planck scale at \sim 10^{19} GeV which is associated with the physics of gravity. Quantum field theory tells us that the Higgs VEV should get contributions from all energy scales (see Figure 2) so the question is why is the Higgs VEV, and thus the W and Z boson masses, a factor of roughly \sim 10^{17} smaller than it should be?

The Higgs vacuum expectation value receives contributions from all energy scales.
The Higgs vacuum expectation value receives contributions from all energy scales.

In the Standard Model (SM) there is no solution to this problem. Instead one must rely on a spectacularly miraculous numerical cancellation among the parameters of the SM Lagrangian. Miraculous numerical `coincidences’ like this make us physicists feel uncomfortable to the point that we give it the special name of `fine tuning’. The hierarchy problem is thus also known as the fine tuning problem.

A search for a solution to this problem has been at the forefront of particle physics for close to 40 years. It is the aversion to fine tuning which leads most physicist to believe there must be new physics beyond the SM whose dynamics are responsible for keeping the Higgs VEV small. Proposals include supersymmetrycomposite Higgs models, extra dimensions, as well as invoking the anthropic principle in the context of a multiverse. In many cases, these solutions require a variety of new particles at energies close to the weak scale (\sim 100-1000 GeV) and thus should be observable at the LHC. However the lack of evidence at the LHC for any physics beyond the SM is already bringing tension to many of these solutions. A solution which does not require new particles at the weak scale would thus be very attractive.

Recently a novel mechanism, which goes by the name of \emph{cosmological relaxation of the electroweak scale}, has been proposed which potentially offers such a solution. The details (which physicists are currently still digesting) are well beyond the scope of this blog. I will just mention that the mechanism incorporates two previously proposed mechanisms known as inflation^1 and the QCD axion^2 which solve other known problems. These are combined with the SM in a novel way such that the weak scale can arise naturally in our universe without any fine tuning and without new particles at the weak scale (or multiple universes)! And as a bonus, the axion in this mechanism (referred to as the `relaxion’) makes a good dark matter candidate!

Whether or not this mechanism turns out to be a solution to the hierarchy problem will of course require experimental tests and further theoretical scrutiny, but its a fascinating idea which combines aspects of quantum field theory and general relativity so I hope it will serve as motivation for you to begin learning more about these subjects!


1. Inflation is a theorized period of exponential accelerated expansion of our Universe in the moments just after the big bang. It was proposed as a solution to the problems of why our Universe is so flat and (mostly) homogenous while also explaining the structure we see throughout the Universe and in the cosmic microwave background.

2. Axions are particles proposed to explain why the amount of CP violation in the QCD sector in the SM is so small, which is known as the `strong CP problem‘.

Uncovering a Higgs Hiding Behind Backgrounds

Hello particle munchers,

Figure 1: Monsieur Higgs boson hiding behind a background.

Last time I discussed the Higgs boson decay into photons, i.e. `shining light on the Higgs boson‘. This is a followup discussing more generally the problem of uncovering a Higgs boson which is hiding buried behind what can often be a large background (see Figure 1).

Perhaps the first question to ask is, what the heck is a background? Well, basically a background is anything that we `already know about’. In this case, this means the well understood Standard Model (SM) processes which do not involve a Higgs boson (which in this case is our `signal’), but can nevertheless mimic one of the possible decays of the Higgs. For most of these processes, we have very precise theoretical predictions in addition to previous experimental data from the LEP and Tevatron experiments (and others) which previously searched for the Higgs boson. So it is in reference to these non-Higgs SM processes when we use the term `background’.

As discussed in my previous post, the Higgs can decay to a variety of combinations of SM particles, which we call `channels’. Each of these channels has its own corresponding background which obscures the presence of a Higgs. For some channels the backgrounds are huge. For instance the background for a Higgs decaying to a pair of bottom quarks is so large (due to QCD) that, despite the fact this is the dominant decay channel (about 60% of Higgs’ decay to bottom quarks at 125 GeV), this channel has yet to be observed.

This is in contrast to the Higgs decay to four charged leptons (specifically electrons and muons) channel. This decay (mediated by a pair of virtual Z bosons) was one of the first discovery channels of the Higgs at the LHC despite the fact that roughly only one in every 10,000 Higgs bosons decays to four charge leptons. This is because this channel has a small background and is measured with very high precision. This high precision allows LHC experiments to scan over a range of energies in very small increments or `windows’. Since the background is very small, the probability of observing a background event in any given window is tiny. Thus, if an excess of events is seen in a particular window, this is an indication that there is a non background process occurring at that particular energy.

Figure 2: The energy spectrum of a Higgs decaying to four charged leptons (red) and its associated background (blue).

This is how the Higgs was discovered in the decay to four charged leptons at around 125 GeV. This can be seen in Figure 2 where in the window around the Higgs signal (shown in red) we see the background (shown in blue) is very small. Thus, once about a dozen events were observed at around 125 GeV, this was already enough evidence for experiments at the LHC to be able to claim discovery of the long sought after monsieur Higgs boson.

 Further Reading:

Seeking and Studying the Standard Model Higgs Particle

Decays of the Standard Model Higgs

Shining Light on the Higgs Boson

Figure 1: Here we give a depiction of shining light on monsieur Higgs boson as well as demonstrate the extent of my french.
Figure 1: Here we give a depiction of shining light on monsieur Higgs boson as well as demonstrate the extent of my french.

Hello Particle Nibblers,

This is my first Particlebites entry (and first ever attempt at a blog!) so you will have to bear with me =).

As I am sure you know by now, the Higgs boson has been discovered at the Large Hadron Collider (LHC). As you also may know, `discovering’ a Higgs boson is not so easy since a Higgs doesn’t just `sit there’ in a detector. Once it is produced at the LHC it very quickly decays (in about 1.6 \times 10^{-22} seconds) into other particles of the Standard Model. For us to `see’ it we must detect these particles into which decays. The decay I want to focus on here is the Higgs boson decay to a pair of photons, which are the spin-1 particles which make up light and mediate the electromagnetic force. By studying its decays to photons we are literally shining light on the Higgs boson (see Figure 1)!

The decay to photons is one of the Higgs’ most precisely measured decay channels. Thus, even though the Higgs only decays to photons about 0.2 % of the time, this was nevertheless one of the first channels the Higgs was discovered in at the LHC. Of course other processes (which we call backgrounds) in the Standard Model can mimic the decays of a Higgs boson, so to see the Higgs we have to look for `bumps’ over these backgrounds (see Figure 2). By carefully reconstructing this `bump’, the Higgs decays to photons also allows us to reconstruct the Higgs mass (about 125 GeV in particle physics units or about 2.2 \times 10^{-22} kg in `real world’ units).

Figure 2: Here we show the Higgs `bump' in the invariant mass spectrum of the Higgs decay to a pair of photons.
Figure 2: Here we show the Higgs `bump’ in the invariant mass spectrum of the Higgs decay to a pair of photons.

Furthermore, using arguments based on angular momentum the Higgs decay to photons also allows us to determine that the Higgs boson must be a spin-0 particle which we call a scalar ^1. So we see that just in this one decay channel a great deal of information about the Higgs boson can be inferred.

Now I know what you’re thinking…But photons only `talk to’ particles which carry electric charge and the Higgs is electrically neutral!! And even crazier, the Higgs only `talks to’ particles with mass and photons are massless!!! This is blasphemy!!! What sort of voodoo magic is occurring here which allows the Higgs boson to decay to photons?

The resolution of this puzzle lies in the subtle properties of quantum field theory. More specifically the Higgs can decay to photons via electrically charged `virtual particles ^2. For present purposes its enough to say (with a little hand-waiving) that since the Higgs can talk to the massive electrically charged particles in the Standard Model, like the W boson or top quark, which in turn can `talk to’ photons, this allows the Higgs to indirectly interact with photons despite the fact that they are massless and the Higgs is neutral. In fact any charged and massive particles which exist will in principle contribute to the indirect interaction between the Higgs boson and photons. Crucially this includes even charged particles which may exist beyond the Standard Model and which have yet to be discovered due to their large mass. The sum total of these contributions from all possible charged and massive particles which contribute to the Higgs decay to photons is represented by the `blob’ in Figure 3.

Figure 3: Here we show how the Higgs decays to a pair of photons via `virtual charged particles' or more accurately disturbances in the quantum fields associated with these charge particles.
Figure 3: Here we show how the Higgs decays to a pair of photons via `virtual charged particles’ (or more accurately disturbances in the quantum fields associated with these charge particles)  represented by the grey`blob’.

It is exciting and interesting to think that new exotic charged particles could be hiding in the `blob’ which creates this interaction between the Higgs boson and photons. These particles might be associated with supersymmetry, extra dimensions, or a host of other exciting possibilities. So while it remains to be seen which, if any, of the beyond the Standard Model possibilities (please let there be something!) the LHC will uncover, it is fascinating to think about what can be learned by shining a little light on the Higgs boson!



1. There is a possible exception to this if the Higgs is a spin-2 particle, but various theoretical arguments as well as other Higgs data make this scenario highly unlikely.

2. Note, virtual particle is unfortunately a misleading term since these are not really particles at all (really they are disturbances in their associated quantum fields), but I will avoid going down this rabbit hole for the time being and save it for a later post. See the previous `virtual particles’ link for a great and more in-depth discussion which takes you a little deeper into the rabbit hole.

Further Reading: