# QCD Mass Versus Higgs Mass

1. Apr 24, 2010

### inflector

I'm trying my best to learn particle physics and cosmology for the last year or so. One of the concepts I'm trying to understand is how the 95% figure humanino quotes above is arrived at. I've seen this figure (or something close to it) a few times here.

I read the paper http://arxiv.org/abs/0906.3599" [Broken], and it indicates that they were able to compute the masses of all hadrons using Lattice QCD. It seems that they (S.Durr et al.) were able to develop a table of mass ratios and then by plugging in one experimental value, they were able to compute the masses for the other particles. This implies that physicists must understand a lot about how the glue mechanism contributes to mass if they can compute mass using QCD theory. Or am I missing something?

How do scientists know that 95% of the mass is attributable to glue while 5% is attributable to the Higgs mechanism?

What it is about the glue that gives particles mass? I've seen descriptions of how the Higgs field is supposed to do this but I haven't seen a discussion of how the glue does this, at least not in terms I could understand. Does anyone know of an accessible text or article on this?

I've also seen some posts from some of the forums better posters (from my personal observation) that say we don't really know what mass is? Is this a widely held opinion? How can we compute it if we don't know what it is?

Last edited by a moderator: May 4, 2017
2. Apr 24, 2010

### ansgar

We can calculate the mass of the proton, neutron with assumption that quarks are massless :) And yes, we know "a lot" about QCD, or rather, we know how to calculate things in QCD and we know that all observables we have calculated so far is in agreement with the experiments testing those observables. So what do you think? did you think scientists GUESS? No, we calculate things.

The issue is that E = m in special relativity, binding energy influences the mass of a bound system!

This is also applicable to non-quantum systems.

For instance the mass of the sun + earth is larger than the mass of the sun + mass of the earth due to the binding energy between the sun and the earth!

Another famous example is of course the atomic nucleus, there the binding energy is of the same order as the mass of the constituents themselves!

Finally in the proton and neutron themselves, the binding energy of the gluons is MUCH larger then the masses of the (valence)quarks!! In fact, one can show and calculate (PCAC-theorem etc.) that the protons and neutrons have mass even though the quarks are massless.

But to mathematically PROVE that (calculations are not proofs) is difficult, in fact you'll get 1 000 000 \$ from claymath instutite if you can prove that the ground state in Yang Mills theory is not massless ;)

We know what math IS, but we don't know WHY the particles in the standard models HAVE mass. According to the symmetries of the Standard Model, the elementary particles should be massless! So it depends on what one MEANS with "we don't know what mass is".

This is where the Higgs field comes in, the Higgs field BREAKS the symmetry which forbids the elementary fermions and bosons in the standard model for having mass. Now they can have mass, by coupling to this higgs field.

So there are 3 ways a particle can have mass:

1) by binding energy (applies to composite particles)

2) simply by "having" a mass, it just HAS mass in the same way it has charge, spin etc. (this would be true in the REAL world if the standard model were not Chiral, i.e. distinguish between left and right handed particles).

If there is a symmetry such that the particles CAN'T have mass, then they will be massless, and - opposite - if there us a symmetry which FORBIDS the particles to have mass (as the symmetry in the standard model) then they MUST have mass - everything that is allowed can happen in quantum mechanics.

3) by "interacting" with the field which breaks the symmetry which forbids the particles to have mass (see #2 above)

Let me know if you need material to study which is suitable for your academic background.

3. Apr 24, 2010

### the_house

Just a couple of quick corrections. Because of the binding energy, the mass of a nucleus is less than the sum of the masses of the individual protons and neutrons. Also, the binding energy is only around 1% of the total mass. Similarly with bound systems such as your example of the earth/sun system, at least in principle (although in contrast this is not a measurable effect.) Even though the sign is different, it's similar in that the main point is the equivalence between energy and mass.

The quick answer to the original question is that we can easily imagine a hypothetical standard model with all massless fundamental particles (quarks). If we calculate the mass of a proton or neutron in this hypothetical theory, it turns out to be around 95% of the actual mass of the real particle in the real world with massive quarks. In turn, protons and neutrons account for essentially all of the mass of the world around us (neglecting dark matter, which we don't really know much about). Thus, it can be argued as somewhat misleading to talk about the bare masses of the fundamental particles in the standard model (Higgs mechanism, etc.) as the source of mass in the universe, since even without these fundamental mass terms, there would still be plenty of mass in the (highly relativistic) bound state systems of the massless constituent particles.

4. Apr 24, 2010

### ansgar

yeah, the binding energy of a proton RAISES the energy. Do this comparison then, Imagine that you have a box with walls which are 100% opaque and massless, in that box you put a lot of photons. Now put this box on a scale, it will have mass due to the energy content of the photons...

5. Apr 24, 2010

### tom.stoer

Have a look at ordinary matter. Approx 2/3 of the particles are nucleons, 1/3 are electrons. As electrons are rather light (511 keV) let's forget about them; protons and neutrons are much heavier: 938 and 940 MeV respectively.

Now we have to compare the mass ratios of the nucleons a) from the Yukawa coupling to the Higgs and b) from the strong interaction. According to the particle data group the masses of "free" u- and d-quarks (as measured in the asymptotic limit of deep inelastic scattering) are ~ 2-3 MeV and 3-6 MeV, respectively. So the contribution of the quark masses to the nucleon mass is below 2%.

6. Apr 24, 2010

### diggy

I'm a little confused on the binding energy argument. Typically binding energies lower the composite objects mass, the argument above implies that they raise the quarks mass to the much larger say proton mass.

Also in the paper above (I didn't carefully read through it, running on short time here), but I think they used pions and kaons as parameters with O(200) MeV masses, compared to bare quark masses that are O(5) MeV. So there is a missing factor of ~40 for the u/d -> proton left unexplained (for strange its only an order 5). -- I could be wrong on this last paragraph -- I will try and give the paper a read later.

7. Apr 24, 2010

### ansgar

What do you mean by "typically"?

8. Apr 24, 2010

### the_house

Intuitively one expects that the bound state should have a lower energy than the individual free constituents, otherwise it will be unstable and decay. In that sense you could say it's more "typical".

Nucleons are a bit special because the individual quarks and gluons are not valid asymptotic states--a proton has nothing to decay into. (A free neutron will eventually decay into a slightly lower mass proton, but not nearly as fast as you would expect if it could decay into a few ~5 MeV free quarks.) They are highly energetic, relativistic systems, and all this localized energy translates into a mass.

This can be contrasted with what you're calling a "typical" bound state, such as the earth-sun gravitational system, where the kinetic energy involved is smaller than the negative potential energy (otherwise it wouldn't be a bound system at all and the earth would go flying off into space.)

9. Apr 24, 2010

### tom.stoer

You must not think about a quantum state as a collection of massive classical particles minus the binding energy.

Think about QCD with massless quarks: the nucleon energy (three quarks in the naive picture) would change only slightly, whereas the pion (one quark, one antiquark) would be exactly massless; this is due to the fact that the pion is the Goldstone boson of the (broken) chiral symmetry. Naively one expects

$$m_\pi = \frac{2}{3}m_{p,n}$$

but in reality one finds (with massless quarks)

$$m_\pi = 0$$

That means that the mass of the nucleon is due to quantum effects and is not (nearly) related to "bare" and unobservable masses of "free" quarks.

10. Apr 24, 2010

### ansgar

I would not draw an equivalence between intuition and classical mechanics though

11. Apr 24, 2010

### humanino

I should comment on my wording "fraud". It has a twofold meaning.

First, least importantly, it is wrong to say that the Higgs accounts for our mass. As was described above, most of our mass is in the glue and/or virtual sea of partons of our protons and neutrons.

Second, and most importantly, there is in this claim a denial of importance in this phenomenon. I do agree that the Higgs sector(s) of the standard model is quite important and potentially underlies news physics, such as supersymmetry. But I refuse to compare this importance to the one I think the QCD strong sector deserves.

The confinement of quark and dynamical chiral symmetry breaking are cornerstones of the standard model. They should be logically studied first before embarking on the speculations of new physics beyond the SM in the electroweak sector. Among the many reasons :
• Quantum corrections down to the nuclear structure are small. Starting from the nucleon structure (light quarks cannot be non-relativistic), they become essential. At this scale, our intuition fails altogether, much more badly than anywhere else we can access experimentally (including heavy quark physics). This observation is at the heart of all the difficulties.
• The standard treatment in Feynman diagrams is a perturbation around the vacuum. We do not know the vacuum of QCD. There are many different QCD-inspired models, and it is not always clear how they manage to predict comparable observables with different underlying physics ingredients.
• This non-perturbative sector requires the concept of effective field theory, which is mandatory to go beyond the standard model (indeed, beyond the SM, the SM itself becomes effective). That is beautifully described by Weinberg.
• QCD is today the only unbroken non-abelian gauge theory we have to study experimentally. Possibly, there are other ones (dynamical electroweak symmetry breaking, compositeness, extra-dimensions, and modern technicolor).

12. Apr 24, 2010

### tom.stoer

Thanks to humanino for mentioning the most relevant topics like "light quarks cannot be non-relativistic", "The standard treatment in Feynman diagrams is a perturbation around the vacuum", ...

The difficulty with QCD is that vacuum and bound states (nucleons) are both "non - non-relativistic" due to the light quarks and non-perturbative due to the complex vacuum structure. This is to be contrasted with the Higgs effect which can be understood based on purely classical reasoning w/o any quantum effect.

13. Apr 24, 2010

### diggy

I just meant any "classical-quantum-relativistic" decay where a heavier nucleus (for example) decays into lighter nucleons plus energy. I'd consider that the typical interpretation.

Is the basic argument that the proton mass is larger than its constituent parts on account of the effective energy/mass of the QCD field or some such?

Just for the record I don't have a preference for the outcome of this -- its just news to me (that the Higgs only accounts for 5% of nuclear matter), and I'd like to understand the skeleton of the argument.

14. Apr 24, 2010

### inflector

So, it seems to me that the case of quarks binding energy and the nucleon binding energy is different and opposite in nature.

Something about putting protons and neutrons together into a nucleus lowers the masses of the combination. That's why He has a much lower mass-per-nucleon than H, or D. In this case, the nucleons want to be together because they get lower energy by the combination.

In the case of the nucleons themselves, being composed of quarks, their constituents have less mass, so the combination is higher energy. This is, I suppose, what makes them so counter-intuitive. It doesn't seem to our intuition that the quarks should stay together since they'd have less energy apart. But then quarks don't exist apart so that's not a meaningful comparison. Also, I don't see how they can measure the mass of a quark since it doesn't exist as a separate particle (but that's a topic for another thread).

In the case of a nucleus, since most of the mass of the nucleons comes from the glue, and not the quarks, it seems that there must be something about the combination of nucleons in close proximity that reduces the effect of the mass generation from the glue in protons and neutrons that makes the overall combination in a nucleus have less energy when combined than when together.

So, for quarks combining you need more energy to keep them together, but you can't separate them. While for protons and neutrons combining, you need less energy to keep them together.

It's a very strange world indeed inside the atom.

15. Apr 24, 2010

### inflector

Thanks everyone for the answers so far. It's helped my understanding.

16. Apr 25, 2010

### ansgar

Well the colour force is a very "special" force so it should have very special results assigned to it :)

Like massless mediators but still finite range due to asymptotic freedom, that's why I think the analogy with the massless box filled with photons is quite good one actually!

17. Apr 25, 2010

### ansgar

The forces between nucleons are short ranged and mediated by colourless- massive particles (pions, rho meson etc.)

Now, to measure the mass of quarks, there are three ways:

1) invariant mass method. Assume you produce a b bbar pair, this you can be sure of due to something called "b-tagging". Measure the invariant mass of it's hadronization and decay products -> "mass" of the b-quark

2) Model tuning. MS-bar Masses of quarks comes in many formulas for models describing observables. Make predictions for such observables and compare with experiment. So now one can have "model-mass" of quarks, which in general will differ from model to model, but one can get a feeling for it atleast.

3) low energy QCD, Chiral Perturbation Theory - also one of those "models" but on a more solid physics ground than those.

What is important to take with you I think is that there are different kinds of masses in QFT, mass is always equivalent to "gravitational inertia" as it is in classical mechanics :)

18. Apr 25, 2010

### tom.stoer

Good point.

In low energy effective models the constituent quarks masses are approx. 1/3 of the nucleon mass. But here the constituent quark is an effective degree of freedom. If you look closer (as you do in deep inelastic scattering) you see the stream quarks masses with the very small masses I mentioned before.

As you are interested in the origin of the nucleon masses I would use the "model quarks mass" of lattice QCD.

19. Apr 25, 2010

### genneth

A good "classical model" is that you can't get free quarks, so they exist only as 2 or 3 particles connected by elastic bands. (Effectively, renormalising out the possibility of pair creation.) They are also constrained by Heisenberg uncertainty, so are in a state of constant agitation. This stretches the elastic bands, and also gives the quarks kinetic energy, which all contribute to the mass.

As Wilczek fancifully puts it: "quark are born free, but everywhere in chains".

20. Jul 31, 2010

### cbd1

Is this serious? Adding photons into a container adds no gravitational weight to the container; the photons have no weight and no inertia. Sure, there will be more mass equivalence in the box, box it will never gain mass of the kind that you can weigh on a scale.