*Matt Strassler [January 17, 2013]*

**If the New Particle is a Higgs Particle, Might it be Composite?**

The next basic question we should ask is whether the new particle is an **elementary** particle (as an electron appears to be) or a **composite** particle, made from more elementary but as yet unknown particles (and thus more like a proton, made from quarks, antiquarks and gluons.) The simplest type of Higgs particle — a Standard Model Higgs particle — would be elementary. But there have also been many suggestions over the years that the Higgs particle might be composite — an attractive idea, because it could potentially resolve the very disturbing and puzzling hierarchy problem. This possibility was covered in detail by Riccardo Rattazzi at his Higgs Symposium talk. The bottom lines:

- we can’t rule out the possibility completely,
- there’s some amount of circumstantial evidence against this new particle being a composite Higgs
- if it is a composite Higgs, there are some indirect near-term measurements that could well reveal it; completely direct measurements are many years off

If the Higgs is composite, we know from other considerations that it must be very small — with a diameter perhaps 1000 times smaller than that of a proton, or even smaller. We can’t measure its size directly, but we can ask whether any of its properties might indirectly reveal that it is composite. Well, this could have been easy! Most composite Higgs particles that people have imagined over the decades would have had a much larger mass than the 125 GeV/c² mass of the new particle. And some of their properties would have differed widely from those predicted for a Standard Model Higgs by an easily discernible amount. So already we have some evidence that *the new particle is probably not a generic composite Higgs particle; it behaves too much like an elementary Higgs is expected to behave.
*

But the jury is still out, because there are some classes of composite Higgs particles that do specifically resemble elementary ones. In these, the Higgs is even smaller, perhaps 10,000 times smaller in radius than a proton. To rule this possibility out directly requires precise measurements of the new particle’s properties, as Rattazzi described.

However, as Rattazzi also emphasized, any model of this type must also accept that the matter particles of nature — the quarks, the charged leptons and even perhaps the neutrinos *(here you may wish to refer to my figure in this article which shows all the known particles of nature)* — are also composite after all! But this is generally even less evident than for the Higgs, because most of the quarks and leptons would be even smaller than the Higgs* (and — an important but technical point! — because they are mixtures of composite and elementary objects.)*

The problem is that no simple composite model of quarks and charged leptons has ever done a really good job of explaining why certain processes in nature — called “flavor-changing neutral-current processes” — are not observed with large rates. “Flavor” here refers to the various types of matter particles; for instance, particle physicists like to say there are three “flavors” of charged leptons: electrons, muons and taus. An example of a flavor-changing process would be one in which a muon (which is just like an electron in every way, except that it is heavier, and therefore can decay) decays not in its usual way but into an electron plus a photon. The decay of a muon to an electron and a photon has never been observed, despite (ongoing) Herculean efforts. And this suggests that any compositeness model for what nature is up to will have to be very complicated and will not do such a good job of resolving the hierarchy problem — which might indicate this is *not* in fact what nature is really up to.

There’s a more direct way to look for clues. The top quark has a large mass, over 170 GeV/c², which implies it interacts quite strongly with the Higgs field, and therefore with Higgs particles also. But for a composite Higgs particle to interact so strongly with top quarks, the top quark itself *must be comparable in size* to the Higgs particle; it can’t be much smaller. A (non-obvious) consequence of this fact is that we expect to find a heavier version of the top quark (provisionally called the “top-prime” or “t-prime”) with a mass below about 1000 GeV/c² (i.e., 1 TeV/c²). Particle physicists at the LHC experiments ATLAS and CMS are looking for signs of a top-prime-like particle, but so far have seen none. Their measurements exclude the possibility of any top-prime with a mass below 600 GeV/c² or so. *(More precisely, different versions of the top-prime behave differently, so exactly what is excluded depends on which version of the top-prime we’re talking about.)* Other similar particles might also appear, differing from the top quark (which has charge 2/3 [in units where the proton has charge 1 and the electron charge -1]) in having charge 5/3 or -1/3.

In summary: a composite Higgs with a size of order 10,000 times smaller than the proton does not seem likely, but if it is true, the LHC experiments should observe heavy top-like particles before too long. Meanwhile, other types of experiments should observe those flavor-changing decays soon — preferably yesterday!

Would a Higgs boson that was a linear combination of the four electroweak bosons be considered composite and is the notion of the Higgs boson as a linear combination of the four electroweak bosons one the makes sense?

Let me explain:

* In electroweak theory, one speaks of the W+, W-, Z and photon as being linear combinations at a particular mixing angle with “more fundamental” bosons. To quote wikipedia on the subject, “The corresponding gauge bosons are the three W bosons of weak isospin from SU(2) (W+, W0, and W−), and the B0 boson of weak hypercharge from U(1), respectively, all of which are massless. In the Standard Model, the W± and Z0 bosons, and the photon, are produced by the spontaneous symmetry breaking of the electroweak symmetry from SU(2) × U(1)Y to U(1)em, caused by the Higgs mechanism (see also Higgs boson). U(1)Y and U(1)em are different copies of U(1); the generator of U(1)em is given by Q = Y/2 + I3, where Y is the generator of U(1)Y (called the weak hypercharge), and I3 is one of the SU(2) generators (a component of weak isospin).The spontaneous symmetry breaking causes the W0 and B0 bosons to coalesce together into two different bosons – the Z0 boson, and the photon (γ)” according to a matrix based on the weak mixing angle.

* There are also several mesons that are described as linear combinations of other mesons (.e.g the neutral pion, the eta meson, the eta prime meson, the K-short meson, the K-long meson, the neutral rho meson, and the Omega meson).

*The Higgs boson mass is very close, to the limit of experimental accuracy to one H mass=(one W+ mass, plus one W- mass, plus one Z mass plus one photon mass)/sqrt(4).

* The four electroweak bosons have a total charge of zero, just as the Higgs boson does.

* The sum of their four spin-1’s, added on a +/- basis as their are in mesons and hadrons, could produce a total spin of zero, observed in the Higgs bosons (one might expect a W+ and W- pair of opposite spin for these purposes, and a Z and a photon of opposite spin for these purposes).

* When mesons form linear combinations, the whole is expressed as the sum of the components that go into the linear combination divided by the square root of the number of linear combination components (usually two or three).

* Of course, multiple bosons, essentially by definition and unlike fermions, can occupy the same space at the same time.

* It seems, however, that even if a Higgs boson was a linear combination of the four electroweak bosons would still be considered “fundamental” rather than “composite” in the sense of the discussion of this post, just as the four electroweak bosons are considered fundamental despite a derivation of a linear combination of massless W+. W-. W0 and B0 bosons via the Higgs mechanism.

If you really mean

linearcombination, the answer is no.A linear combination of spin-1 particles has spin-1. [If I consider A = C + D, then A inherits the quantum numbers shared by C and D.] In fact the spin-1 photon and Z particles are linear combinations of the spin-1 W0 particle and B0 particle (or X0 in some notations). The same is true of all the spin-0 mesons, which are linear combinations of other spin-0 mesons.

Furthermore, the mass of a linear combination of W’s, Z and photon would be ill-defined, because the W’s, Z and photon have definite but different masses, so the linear combination would

nothave a definite mass. Your formula (2m_W + m_Z)/Sqrt[4] would not apply to such a state. The Z has a definite mass and is a linear combination of the W0 and B0 (or X0), but neither the W0 nor the B0 has a definite mass.Similarly, a linear combination of something with charge +1 and something with charge -1 is something with no defined charge at all, not something with charge 0.

The fact that multiple bosons can occupy the same space is irrelevant in a linear combination of particles; since the combination is linear, there is only one boson at a time.

I’m afraid that what’s happening here is that you’re trying to make a linear combination of apples and oranges. This is not the way quantum mechanics works.

correction: “one THAT makes sense”

Wonder what the good professor means when he says that the “charged” leptons are composite and that the electron is elementary?