Higgs Discovery: Is it a Higgs?

Matt Strassler [July 10, 2012]

A new particle has been discovered — but is this a Higgs particle or not? And if so, is it an example of the simplest possible Higgs — the Standard Model Higgs particle — or is it not?  

In this article I’ll address the first question; the answer to the second will appear in a sequel.  [You may want to read my articles on how the Standard Model Higgs is produced, decays, and can be studied before you try to make sense of this article.]

Unlike many other articles that I put on this site, this one reflects my own personal view more than the consensus view among my colleagues — mainly because I don’t know what the consensus view is yet. Probably the consensus is still evolving; my own view may as well. I think everyone agrees about what the questions are, but they probably still disagree as to how plausible the different possible answers are.

Also, although I’m thinking for myself here, I believe that all of the points that I’m making here have appeared in various people’s papers (some of them very recent and still in the form of unpublished preprints.)   I’m not making any intentionally original remarks.

Simply put, I am largely convinced this new particle is a Higgs particle of some type. This is a theory bias, not based firmly on evidence from data but on indirect evidence from many years of experience with the theoretical options. And this bias, since it doesn’t come directly from data, is subject to change; if one of my colleagues gives me a good argument as to why I should be less convinced of my viewpoint, I may well change my mind. So no promises are given here.

Things we know or almost know

Before introducing any bias, what do we know from the data? The fact that we observe this particle decaying to two photons as a bump in a plot already tells us, just from basic conservation laws, that the particle

• has a mass of about 125 GeV/c²
• has a lifetime which is long compared to its “heartbeat” (my term), i.e. the period of its natural vibrational frequency [I’ll explain this in a moment]
• is electrically neutral (i.e. has no electric charge)
• is not directly affected by the strong nuclear force (i.e., in technical language, it is chromodynamically neutral, or “color”-neutral for short)
• is a boson (it must have spin that is an integer [a brief discussion of spin follows])
• cannot have spin 1 (a spin 1 particle cannot decay to two photons due to a slightly tricky argument)

Moreover, from the facts that

1. we also observe it decaying to two lepton/anti-lepton pairs at about a rate 20 to 40 times smaller than its decay to two photons, and
2. other production and decay modes, expected to be more difficult to observe, have indeed not yet been solidly confirmed in the data,

we may infer that

• the particle appears to interact much more strongly with Z particles than it does with photons, as would be expected for almost any type of Higgs particle, including the simplest one.

Finally, if we take the claim of the Tevatron experiments CDF and DZero at face value that they also see evidence of the Higgs particle, and we note that certain forms of evidence have not yet been seen at ATLAS and CMS, it must be that

• the particle cannot interact much more weakly with W and Z particles than is expected of a simplest Higgs;
• the particle cannot interact much more strongly with W and Z particles than is expected of a simplest Higgs, unless it decays most of the time in a way that the simplest Higgs is not expected to do and that is hard to observe.

There are a few other statements one can make, but they all come with more complex caveats, so I’ll save them for later.

Explanatory asides

Let me explain two of the remarks made above.

“Heartbeat”, or natural vibrational frequency: a particle is a ripple in a field; specifically, it is the wave of smallest possible intensity. Like any ripple, it is vibrating; at any one location in space, the field becomes larger, then smaller, then larger, then, smaller as time goes by. (Think of sitting on a moored boat as a set of wave troughs and crests go by, you’ll be oscillating up and down in time the wave’s own vibrations.) The time between back-and-forth vibrations of a particle at rest is h / m c² , where m is the mass of the particle, c is the speed of light, and h is Planck’s constant , h = 4.1356675 × 10⁻¹⁵ electron-volt·seconds. Informally, I call this a particle’s “heartbeat”. Notice that a heavy particle has a quicker heartbeat! And we can see from the data that the new particle “lives” (i.e., exists for) many heartbeats (the narrowness of the bump implies at least 50 or so, and possibly many more) before it falls apart.

“Spin”, or intrinsic angular momentum: any spinning object, such as the earth, is said to have angular momentum. Angular momentum is interesting because total angular momentum is conserved, like energy and ordinary momentum. Due to very non-intuitive quantum mechanical effects, it turns out that every type of particle (whether elementary or not) is intrinsically rotating — or at least, it has intrinsic angular momentum, which we call spin. [Whether or not we should picture this as rotation like the Earth’s is a bit in question — I’ve never found having such a picture in my head terribly useful, and most of the time I just treat this little feature of the world using math rather than pictures.][Thanks to quantum mechanics,

• this intrinsic rotation may be oriented in any direction, but it has a magnitude which is fixed for each type of particle
• the spin S is defined to be the angular momentum J divided by h / 2π where h is Planck’s constant (see above).
• it is a theorem that the combination of quantum mechanics and Einstein’s relativity implies that S must either be an integer (for a particle that is a boson) or 1/2 plus an integer (for a particle that is a fermion.) [Read about fermions and bosons here.]

Each type of particle — whether or not it is elementary — has a definite spin. Among the apparently-elementary known and suspected particles, the spins are

• S=0: Higgs particle
• S=1/2: all matter particles known so far — electrons, muons, taus, all neutrinos, all quarks, (and all of their anti-particles)
• S=1: the carriers of the three known non-gravitational forces: photons, gluons, W and Z particles (which are their own anti-particles, except the W+ and W- which are anti-particles of each other)
• S=2: the graviton (the carrier of gravity)

There are various theoretical reasons to expect lightweight elementary particles to have spin no greater than 2, and for the only particle of spin 2 to be the graviton.

But the limitations of elementary particles do not apply to more complicated composite objects like hadrons (particles made from quarks, anti-quarks and gluons) or atomic nuclei (made from protons and neutrons). Among hadrons there are many, many examples

• S=0: pions, kaons (the lightest mesons)
• S=1/2: protons, neutrons (the lightest baryons)
• S=1: rho mesons, omega mesons, phi mesons
• S=3/2: Delta baryons
• S=2: f₂ mesons
• S>2: nobody remembers the names of the higher-spin hadrons, all of which are very short-lived, but there are lots of them going up to S=6 and beyond.

Atomic nuclei also have many spins.

The interactions with photons and with Z particles

The new particle interacts with Z particles much more strongly than with photons or gluons: How can we see this is true? A simple way is to note that

1. this fact is true of the simplest possible Higgs, and
2. the theory with the simplest Higgs in it predicts the ratio for the production of Higgs particles decaying to two photons to the production of Higgs particles decaying two lepton/anti-lepton pairs (henceforth “four-leptons” for short), and
3. the data about the new particle agrees, to within about a factor of two, with the prediction of the theory of the simplest Higgs; so the new particle too, like the simplest Higgs, must interact more strongly with Z’s than with photons.

The reason why four-lepton events are rare, despite the stronger coupling of the new particle to Z’s, is that

• the new particle is so light that one or both Z’s must be virtual particles (i.e., disturbances in the Z field that aren’t particles at all) and this suppresses the decay probability substantially
• Z particles decay to electron-positron or muon-anti-muon pairs only 6% of the time, so the probability that two pairs are produced is about (0.06)², or about 0.004.

This fact is very important, because it makes it implausible (and in many cases impossible) that this new particle could interact with photons in a way that is similar to how it interacts with W and Z particles. Instead, as is the case for the simplest Higgs, the interaction of the new particle with W and Z particles must be direct, while the interaction of the new particle with photons must be indirect (via virtual particles). This constraint immediately eliminates many types of possible alternative explanations for this particle. [Essentially, since photons and Z particles are mixtures of weak-isospin and hypercharge particles, getting the new particle to interact relatively strongly with Z’s and relatively weakly with photons requires a very delicate balancing act, one which is automatic for a Higgs particle but is in general not going to happen for any particle that isn’t similarly quite tied up with the generation of the W and Z particle masses.]

So we are almost guaranteed that the new particle has something to do with how the W and Z got their masses — maybe in a more complicated way than for a Higgs, but it can’t be completely disconnected from it. If it were, it would treat photons and Z particles too similarly to agree with data.

On top of this, there is a weak but interesting argument that the strength of the new particle’s interaction with W and Z particles tentatively looks as though it is rather close to the right size to be a Higgs particle.  If the interaction were much weaker, then (no matter how you twiddle things) the Tevatron experiments CDF and DZero should see no evidence at all of the Higgs particle in the ways they are looking for it.  [You might choose to disregard their evidence as unconvincing; that’s up to you.] If the interaction were much stronger, then you’d expect much stronger evidence of the new particle in at least one LHC or Tevatron search where little or no evidence is yet seen [except in the one case where all of the new particle’s interactions are uniformly stronger than for a simplest Higgs and yet it has a new exotic way of decaying that is hard to observe and dominates all the others.]

Some Theory Bias — Reasonable but Not Without Holes

Now comes the part that is a little more theoretical and harder to explain. If you take a theory of a new particle of spin 0 or 2, along with massive W and Z particles and massless photons and gluons, and you try to make equations in which this particle interacts directly with the W and Z particles and interacts indirectly with the photons and gluons, the equations, depending on their details, can give a wide range of answers for the production of Higgs particles that decay to photons and leptons, and can give a wide range of possible ratios for the decays to two photons and to four leptons. The equations can also give you whatever you want for the strength of the new particle’s interaction with the W and Z. Uniquely (I think) in the case that this particle is a Higgs particle of some type, and thus is directly associated with the Higgs field that gives the W and Z particles its mass (or one of several such particles and fields) you will automatically get the interactions of the particle with photons, W and Z particles to be of the right size so that you are roughly consistent with the data; and you can easily get the interaction with the gluons with roughly the right size. In all other cases, you can get things to come out right, but not automatically: it’s only as an accident.

[One interesting accident and resulting loophole occurs in the case where the theory above the TeV energy scale becomes scale-invariant. In this case the interaction of the new particle with gluons becomes larger and the interactions with photons and with W and Z particles becomes smaller in just such a way as to remain consistent with present data — as long as you completely discard the evidence of the Higgs from the Tevatron experiments and any of the limited signs of the p p –> q q H process, called “vector boson fusion”.]

[I don’t know of any other interesting accidents like this, but would be interested to learn of other reasonable examples.]

[I am grateful to several colleagues, especially Ben Gripaios, for discussions on this point.]

Summing Up

In the end, however, I must remind you this is all talk.  The question of whether this particle has spin larger than 0 [or, for experts, is spin 0 but is CP-odd instead of CP-even], is something that can be determined experimentally, and this will gradually happen over the next few years. So you won’t have to accept this theory bias in the long run; we’ll know, from data.  For a spin-0 and CP-even particle, it will be trickier to settle the issue, but at some point we’ll gradually be convinced that the alternatives don’t make sense. All I’m telling you today is that I’d personally be very surprised if this were not a Higgs particle of some type. If you accept this point of view (and you shouldn’t do so without thinking it over and remembering the loopholes), then the next question is: is this an example of a simplest Higgs, or is it an example of a more complicated Higgs? That’s the subject of the next article.