# The ratio of the Higgs and QCD condensate contribution to valence quark masses

According to https://en.wikipedia.org/wiki/Quark#Mass, the quarks have the following masses.

I suppose these data in the table shows the valence quark masses, such that the uud valence three quark rest mass is about 9 MeV. This is much smaller than the proton mass 938 MeV. The remained 938 - 9 = 929 MeV much can be attributed to the field energy of the gluons.

1. Now, among the valence quark mass 2.3±0.7 ± 0.5 MeV, how much of it comes from the Higgs condensate? And how much of it comes from the QCD condensate?

2. In general, what is the ratio of the Higgs condensate and QCD condensate contribution to quark masses? For example, Higgs contributes 15%, and QCD condensate contributes 85%? Where can we find those data?

Notice that I am asking the valence quark mass, not the constituent quark mass.

• Higgs condensate just means that the Higgs field $$h$$ gets a vev -- this is a standard way to say it. We do have $$\langle h\rangle \neq 0$$. It is anna v's confusion.

• QCD condensate means that $$\langle \bar q q\rangle \neq 0$$ gets a vev.

I suppose these data in the table shows the valence quark masses, such that the uud valence three quark rest mass is about 9 MeV. This is much smaller than the proton mass 938 MeV. The remained 938 - 9 = 929 MeV much can be attributed to the field energy of the gluons.

This is at least confused, if not wrong:

Firstly, the rest of the hadron mass is not "field energy of the gluons" - see this question and its answers for more discussion on various other contributions to the hadron mass such as the quark binding energy or the trace anomaly.

Secondly, calling these masses "valence quark masses" is pretty pointless precisely because the existence of three identifiable "valence quarks" in the strongly bound QCD state that is a hadron is not that easy - usually we call these quark masses the masses of current (or "bare") quarks; their relationship to the hadron mass is not straightforward. See again the question linked above: There's a "quark condensate" contribution at ~9% of the hadron mass that depends on this current quark mass, which is much larger than what the naive computation in the question supposes.

Finally, these current masses are generally not obtained from direct measurement nor from ab initio simulations that would involve the Higgs mechanism: Instead (see, for instance, the PDG review on quark masses [pdf link]), they are obtained from lattice QCD simulations where the current quark masses are free parameters that are then tuned to result in the correct values for much easier observables (such as hadron masses).

In this sense, the question doesn't really make sense: The current quark masses are precisely the values they need to have to yield the correct hadronic masses; these values are not computed from any distinct contributions, and they are much more just values in the ideal QCD Lagrangian rather than a "real-world mass". In particular, their exact values depend on various renormalization scheme choices of the specific lattice computation and on the renormalization scale they are reported at.

Although I am not entirely certain how "the QCD condensate" is supposed to contribute to the current quark mass anyway, this mass - as the bare mass in the QCD Lagrangian - seems to me to entirely stem from the Higgs mechanism.

• Thanks so much, I vote dup --- what is your comment on anna v's answer? Aug 29, 2022 at 14:55
• What do you think the list of mass here in pdg.lbl.gov/2022/tables/rpp2022-sum-quarks.pdf? Is this current (or "bare") quark or the valence quark mass? thanks! Aug 29, 2022 at 14:56
• I thought (1) Valence quark mass, (2) constituent quark mass, (3) bare or current quark mass are three different concepts. en.wikipedia.org/wiki/Quark#Mass. According to Wikipedia, it indeed says that the 9 MeV out of 938 MeV is from the valence quark mass. Why do you say instead 9 MeV is the bare or current quark mass? Aug 29, 2022 at 15:00
• @annmariecœur "Valence quark mess" is not a distinct concept - it is simply the sum of the three bare/current quark masses of the valence quarks. Aug 29, 2022 at 15:06
• No, they seem to be distinct concepts --- see Wikipedia en.wikipedia.org/wiki/Quark#Mass or check with lattice QCD books: "Two terms are used in referring to a quark's mass: current quark mass refers to the mass of a quark by itself, while constituent quark mass refers to the current quark mass plus the mass of the gluon particle field surrounding the quark." Aug 29, 2022 at 16:50

Now, among the valence quark mass 2.3±0.7 ± 0.5 MeV, how much of it comes from the Higgs condensate? And how much of it comes from the QCD condensate?

There is a basic misunderstanding of the term "mass of quarks" . Quarks are elementary point particles, this means they have no constituents. The mass values in the table you present are attributed uniquely to each of the four quarks , and they are the invariant mass of their four vector ( we are in the special relativity domain too), as measured from the experimental observations, and is identified uniquely to each quark. I do not know what you mean by Higgs condensate, see here on how the present models define the effect of the Higgs field on the masses.

So condensates do not have a role in the mass of quarks shown in your table, only the Higgs mechanism.

In general, what is the ratio of the Higgs condensate and QCD condensate contribution to quark masses? For example, Higgs contributes 15%, and QCD condensate contributes 85%? Where can we find those data?

The Higgs is not a condensate, it is a mechanism .

Maybe you are thinking along the lines of this lecture, which examines zero mass quarks in QCD, and considers the existing masses as corrections to the model.

• Just as a side note, the masses of the quarks are scale and scheme dependent, not even ‘pole mass’ is well defined for any of the quarks due to confinement (renormalon ambiguities). It’s all just book-keeping Aug 16, 2022 at 4:15
• @JoshuaLin The basic premise is that they do have a unique mass, as far as the standard model table goes, now theoretical and experimental variations entering calculations are a different story, Aug 16, 2022 at 7:42
• Higgs condensate just means that the Higgs field $h$ gets a vev -- this is a standard way to say it. We do have $\langle h\rangle \neq 0$. So this is not my confusion, this is your confusion! Aug 17, 2022 at 17:29
• Similarly QCD condensate means that $\langle \bar q q\rangle \neq 0$ gets a vev. Same terminology Aug 17, 2022 at 17:30
• "The numbers you see are attributed uniquely to each of the four quarks , and they are the invariant mass of their four vector" --> This does not make sense to me at all, anna v. Please explain better --- something is weird here. Sorry Aug 17, 2022 at 17:31