Thursday, November 12, 2015

Some Musings About Nomeclature, Mesons And Forces

Almost all of the ordinary matter in the universe (as opposed to "dark matter") is made up of protons and neutrons assembled together into atomic nuclei of atoms with one or more protons and sometimes with sometimes also with some neutrons each.

The atom is completed with one electron per proton in orbit around the nucleus (strictly speaking, "orbit" is a bit misleading as a classical approximation of the actual quantum physics behavior of electrons associated with an atomic nucleus, but it is good enough for the purposes of this post).  If the correspondence between protons and electrons in an "atom" is other than one to one, it is conventional to use the term "ion" rather than "atom" to describe it.

Protons and neutrons are composite particles made up of three quarks each, which are bound together by gluons which are emitted and absorbed by the quarks in the proton or neutron respectively (the generic name that encompasses both protons and neutrons is a "nucleon" often abbreviated "N").

It turns out that protons and neutrons are actually just the two most common examples of a larger class of composite particles made up of three quarks bound together by gluons which are call "baryons".

There is a still more general class of composite particles made up of quarks (not necessarily three) that are bound together by gluons which are called "hadrons" (there is also a hypothetical class of composite particles made up solely of gluons bound together in the absence of quarks often called "glueballs", but I'm not sure if they count as hadrons or not).

Hadrons made up of two quarks (or of blended combinations of two quark pairs) are called "mesons", a term that was coined in the 1930s when the need for a force carrying particle to bind protons in atomic nuclei was hypothesized many years before the first meson was actually observed.

Mesons made up of two different kinds of quarks are usually named based upon the heaviest quark in the mesons.  When that quark is a bottom quark (formerly also known as a beauty quark), the meson is, logically, known as a B meson.  But, most of the lighter mesons were discovered and named before the quark theory of the Standard Model was worked out and the quarks were assigned names.  So, their names are quite arbitrary.

If the heaviest quark in a meson is a charm quark it is usually known as a D meson (but prior to 1986, a meson with a charm quark and a strange quark was known as an F meson). It is also curious that the physics community managed to abolish the historical irregular name for the Ds meson, but not many other of the historical irregular names of other hadrons.

If the heaviest quark in a meson is a strange quark, it is usually known as a "kaon" abbreviated "K".

If we were renaming mesons today, knowing what we do about the Standard Model, they would probably have been called S mesons, C mesons, and B mesons, respectively. But, historical accident and the immense amount of education needed to do the physics that makes knowing these names relevant has allowed the irregular historical monikers to survive.

Different naming conventions apply to "quarkonia", in which a meson and antimeson of the same flavor are both present.

I'd welcome comments from anyone who can explain how it is that Kaons, D mesons, F mesons and any of the other irregular hardon names were assigned (baryon naming, for what it is worth, has fewer irregular hadron names, perhaps because more of them were discovered after the quark model was in place).

As in other areas of language, irregular names for hadrons seem to have persisted more strongly for the most common mesons, than for the rare ones.

We still have arbitrary meson names not precisely tied to quark content for scalar and axial vector mesons, whose quark content is not well understood.

There are several kinds of mesons that contain only up and down quarks (or are at least dominantly comprised of up and down quarks).  The lightest are the pi mesons, also known as pions.  Another kind of meson containing only (or at least dominantly) up and down quarks is the rho meson.

Pions and rhos bring us from the land of history and language in physics to the land of QCD (the physics of the strong force that binds quarks with gluons called "quantum chromodynamics").

It turns out that the force hypothesized back in the 1930s that binds protons and neutrons into atomic nuclei called the "nuclear strong force" is not a fundamental force of nature.  Instead, it is basically a second order effect of the fundamental strong force which is mediated by gluons to hold hadrons together "leaking" out of hadrons to bind them to other nearby hadrons.

The nuclear strong force is mediated not by gluons, which are fundamental in the Standard Model, but by mesons, which are composite particles, although, like gluons, mesons are bosons (a class of particles that has one kind of quantum mechanical behavior) rather than fermions (a class of particles including all baryons and quarks and leptons such as electrons that has another kind of quantum mechanical behavior).

What caught my eye as I was looking into the history of the odd nomenclature of mesons was that while the nuclear strong force is mediated primarily (virtual) pions, it is also mediated in part by other kinds of mesons, especially (virtual) rhos.

This made me think about different kinds of mediator particles for different forces. Electromagnetism is mediated by photons, which are mostly identical, but can differ from each other in frequency, polariziation or helicity.  The strong force is mediated by gluons, which are also mostly identical to each other, but can come in eight different combinations of color charges.

The weak force, in contrast, is mediated by both W bosons (which come in W+ and W- varieties that are antiparticles of each other), and Z bosons which differ in mass and charge from W bosons.  In this respect, the weak force is a bit like the nuclear strong force, which has more than one kind of mediating boson, although the non-fundamental and emergent nuclear strong force, in principle at least within the Standard Model, can have more kinds of potential mediator mesons than the weak force had mediator weak force bosons.

It is interesting to consider how the Standard Model might be subtly modified to reflect the existence of additional weak force bosons that appear much less frequently the W and Z bosons in much the way that rhos and other mesons mediate the nuclear strong force much less frequently than pions do.

There are hypothetical W' and Z' particles which have been searched for experimentally (and thus far, not discovered).  But, it isn't entirely clear that those models are sufficient to account for the kinds of properties we would predict if the collection of particles that mediate the weak force are analogous to the array of mesons that can mediate the nuclear strong force.

Also, the analogy of the nuclear strong force to the weak force suggests that the W and Z bosons, unlike photons and gluons, might be composite particles, rather than being fundamental. (Electroweak unification involves a concept of blending of more fundamental particles to create the W, the Z and the photon, as opposed to a true composite concept.)  This seems like an interesting line of conjecture to extend to see how far one could take it.

And, of course, we've omitted discussion of the Higgs boson, which shows every indication of being basically a part of the electroweak unification scheme that is not closely related to QCD at all, and gravity, which just plain doesn't play well with the Standard Model, but mostly manages to stay out of the way in circumstances where gravity and the Standard Model might clash with each other.

8 comments:

Unknown said...

Grad student in physics here -- I've appreciated your lucid and intuitive discussions of particle readership for a general audience (particularly the particle lifetimes post). But the analogy between the weak force and meson-mediated low-energy QCD is somewhat off here.

There are three weak force carriers (W^+, W^-, and Z^0) in exactly the same sense as there are 8 gluons: in mathematical terms, the latter are the 8 "generators" of the gauge group SU(3) which describes QCD and the former are the 3 generators of the gauge group SU(2) which describes the weak force. I expect the fact that the weak force gauge bosons are usually discussed as three distinct particles and the gluons are not is largely due to fact that nobody wanted to come up with eight different names for the gluons.

Pions themselves come in the three varieties pi^+, pi^-, and pi^0 (and likewise for the rho mesons). In fact the interactions between up-type and down-type quaks via W^+/W^-/Z bosons are described by exactly the same mathematics as the interactions between protons and neutrons via pions. This is just a coincidence (at least in the standard model, as the symmetry is only approximate in the latter case), but a happy one for the historical development of particle theory: the fact that the model worked so well to describe nucleon interactions led theorists to try to apply variants of it elsewhere.

andrew said...

"Grad student in physics here -- I've appreciated your lucid and intuitive discussions of particle readership for a general audience (particularly the particle lifetimes post)."

Thank you.

"I expect the fact that the weak force gauge bosons are usually discussed as three distinct particles and the gluons are not is largely due to fact that nobody wanted to come up with eight different names for the gluons."

This is surely not the case, because W bosons have an important property (the ability to change quark flavor) that Z bosons do not. In contrast, all eight varieties of gluons do exactly the same thing (i.e. mediate strong force interactions between quarks with particular combinations of color charges).

"But the analogy between the weak force and meson-mediated low-energy QCD is somewhat off here."

Obviously, I know and it is clear that, in the context of the Standard Model, the analogy is wrong. The question is whether it would be possible to imagine a BSM theory that would conform to that analogy (obviously, the answer to that question is yes, because imagination is a powerful thing) and more saliently, whether such a BSM theory could be devised in a manner that does not contradict any current experimental data (an open question, but one that I would expect could be answered in the affirmative).

Moreover, if such a BSM theory existed, my intuition is that the mass ranges for which the hypothetical BSM weak force particles would be excluded would be comparable to the current experimental exclusion of W' and Z' bosons at the LHC.

Now, I understand that electro-weak theory is neat and tidy and seems logically complete which makings the theoretical inclination that there are no other weak force bosons out there very attractive. But, it would be worthwhile for the theoretical physics community to take a moment away from the fool's errand of developing string theory to investigate other possibilities along the lines of this one at a rudimentary level at least, on the off chance that the similarity between the pion mediated interactions between protons and neutrons is more than a coincidence and the symmetry is actually only approximate in the weak force cases as well because BSM physics are true, even if it is very, very good approximation.

I recognize that this is probably a dead end. But, some of the other BSM theories that are routinely tested as benchmarks at the LHC are IMHO far less plausible.

andrew said...

Following the analogy through, the rho and omega mesons are spin-1 vector bosons, while pions are spin-0 pseudo-scalar bosons.

In contrast, the weak force bosons are spin-1 vector bosons. Thus, we would expect in this analogy, either pseduo-scalar spin-0 weak force bosons that have an analogous role to the rho/omega in the nuclear strong force, or perhaps spin-2 tensor bosons that fulfill that role, rather than a spin-1 W' or Z'.

The only known "fundamental" spin-0 boson in the Standard Model is the Higgs boson, and the only widely hypothesized fundamental spin-2 boson is the graviton (there are no fundamental spin-2 bosons in the Standard Model). Given the extent to which the ordinary W and Z boson are sufficient to explain the observed weak force, one would expect that any W' or Z' would be much heavier than the roughly 90 GeV of the Z boson.

Ben said...

Hi Andrew,

Same poster as above. I hope you didn't get the impression that I was disparaging imagination or analogy as a starting point for thinking about BSM physics (or the notion of composite weak force carriers in particular).

My quibble is specifically with the notion that the Standard Model W and Z bosons are fundamentally more different from each other than the different gluons, and the related notion that e.g., up quarks are fundamentally more different from charm quarks than red up quarks are from green up quarks.

The keyword in the above is "fundamentally;" different quark flavors behave very differently at pretty much all accessible energy scales. Nonetheless I'm of the opinion lumping all gluon and quark colors together is pedagogically misleading; I'll try to motivate this briefly below.

You pointed out correctly that the W-bosons participate in flavor-changing processes. The situation is clearer if we avoid flavor (a category which really only makes sense in the context of the historical development of particle physics) and think about quarks coming in two weak isospin varieties ("up-type" and "down-type"), with three generations of each such doublet. For the time being, we can neglect the second and third generations.

At energies far above the electroweak scale, we can consider the interactions of (massless) quarks with (massless) W^+/W^-/Z^0 bosons and with gluons. Each quark is either up or down and either red, green, or blue. In this limit, the QCD <-> Weak force correspondence is clear. An up quark can turn into a down quark by emitting a W^+ in precisely the same way that a red quark can turn into a green quark by emitting the relevant gluon, there's a "neutral" gluon analogous to the Z^0 which can be emitted in the annihilation of a red quark and a red antiquark, and so on.

Two effects spoil this correspondence when we go down to energies relevant to the present-day universe: confinement in QCD and electroweak symmetry breaking. The former ensures that we don't need to think at all about the different quark/gluon colors to understand low-energy phenomena.

The latter enables the up-type and down-type quarks in each generation to have different masses and also makes it possible for the W bosons to mediate generation-mixing interactions (distinct from the more trivial flavor mixing within each generation). It is mathematically completely equivalent to view the generation-changing processes as being mediated by the Higgs rather than W bosons. In one representation the Higgs interactions are nice and flavor-diagonal; in the other, the quark mass terms look ugly but the W couplings are flavor diagonal.

The point of this (extremely long; sorry for the digression) comment is just to clarify that within the Standard Model, interactions of the gluons and weak force bosons are very similar at high energies; effects that make W bosons behave differently than Z bosons and up-type quarks behave differently than down-type quarks are emergent.

Best,
Ben

andrew said...

Thanks for the analysis Ben. I found this part of your discussion particularly intriguing as I've never heard it articulated this way before:

"The latter enables the up-type and down-type quarks in each generation to have different masses and also makes it possible for the W bosons to mediate generation-mixing interactions (distinct from the more trivial flavor mixing within each generation). It is mathematically completely equivalent to view the generation-changing processes as being mediated by the Higgs rather than W bosons. In one representation the Higgs interactions are nice and flavor-diagonal; in the other, the quark mass terms look ugly but the W couplings are flavor diagonal."

Is the reverse true? That is, can Higgs mass be viewed consistently as mediated by W bosons?

andrew said...

The distinction between "trivial flavor mixing within each generation" and "generation mixing" is also an intriguing distinction that I've never heard articulated and don't really see in the ordinary description of the Lagrangian of weak force boson interactions, the quark masses and the CKM matrix.

Ben said...

Hi Andrew,

Apologies for the delay -- the past few weeks have been extremely busy for me. Unfortunately I'm not familiar with any non-technical overviews of the standard model which adopt a non-historical approach. Pgs. 714 and 719-726 in Peskin & Schroeder cover this subject, with a fair amount of formalism that may or may not be familiar, but I found the qualitative descriptions relatively lucid (not something I take for granted with this book or any QFT book for that matter...).

The basic argument is that the quarks that are given mass by the Higgs are arbitrary linear combinations of u, c, t on the one hand and d, s, b on the other. One needs to apply unitary matrices U_u and U_d to the up-type and down-type quark fields to diagonalize Higgs-quark interactions. Doing this causes factors of U_u and U_d to pop up in every other interaction involving quarks in your theory. U_u and its inverse show up in pairs in Z-boson and gluon interactions (and likewise for down-type quarks), so we obtain no flavor-changing effects. However, W bosons in your original basis turn up quarks into down quarks, which implies that in the new basis these interactions can also turn e.g., up quarks into strange quarks. Equivalently, after diagonalizing the quark mass matrix you end up with a factor V = U_u*U_d^-1 in W-boson interactions which you can't get rid of. V is called the CKM matrix.

This all only pertains to the Higgs interactions which give mass to the fermions. The process by which the Higgs vacuum expectation value gives mass to the W and Z bosons is related but conceptually distinct. The Higgs mass on the other hand comes from Higgs self-interactions -- I'm not aware of any way to view it as generated by weak force bosons or fermions.

andrew said...

Thanks for the response.