What New Experiments, If Any, Would Help Determine Light Quark Masses?

[ohwilleke]

TL;DR Summary

Given already high precision experimental data about hadrons with light quarks, the main barrier to determining u, d, and s quark masses is doing the QCD calculations. But, are the new experiments that could be done which would advance the measurement of these masses?

The experimentally measured properties of protons and neutrons are known with exquisite detail. Our data is not quite as extremely precise, but still very good more other baryons and mesons with light quarks (u, d, and s) as valence quarks, such as pions and kaons.

Yet, on a percentage basis, the uncertainties in the masses of the u, d, and s quarks are very large, much greater than the masses of c, b, and t quarks, the three charged leptons, the Higgs boson, or the W and Z bosons.

As I understand the matter, the biggest barrier to greater precision in these measurements is taking hadron level experimentally data and turning it into quark mass properties due to the difficulties of the QCD calculations involved. We could make great strides in determining these quantities more precisely simply by getting better at doing QCD calculations (e.g. with quantum computers), without ever collecting another bit of HEP experimental data.

On the other hand, no scientist is ever going to say that less experimental data is better than more experimental data for measuring an experimentally determined physical constant, like the rest mass of a particular kind of quark.

So, my question is:

What new experimentally data, if any, would be most helpful in advancing the cause of more precisely determining the light quark masses?

 

[malawi_glenn]

What mass are you referring to? Polemass?
I think what "we" often talk about when we are referring to quark mass is the current quark-mass or the running quark-masses

https://pdg.lbl.gov/2010/reviews/rpp2010-rev-quark-masses.pdf
https://pdg.lbl.gov/2019/tables/rpp2019-sum-quarks.pdf

Anyway, I know there has been some interest in measuring the η→3π decay since it provides a value for m_d - m_u

 

[Vanadium 50]

What mass are you referring to?

That's the key question. Is it just a parameter of the theory? (pole mass, MSbar mass, etc.) Is it "what the mass would be in some counter-factual universe where quarks weren't confined?"

I believe this question has no good answer because it's not a well-defined question.

 

[Reggid]

That's the key question.

[...] it's not a well-defined question.

If it is your key question that is not well-defined, then you definitely have a problem ;-)

But I don't think that this is the key question in the issue. Usually the masses for the light quarks are quoted in the MSbar scheme, but you could use another scheme if you'd prefer (just the pole mass is particularly not well suited for this purpose). I don't think that the problems of calculating the light quark masses to higher precision have anything to do with not knowing what mass scheme to use, so I would not call that a key question.

 

[Vanadium 50]

If the mass in variouse renormalization schemes were 5, 10 and 15 MeV, what then is the mass?

You tell me the renormalization scheme and I'll tell you the mass.
- or =
You tell me the mass you want, and I'll tell you the renormalization scheme that does it for you.

 

[Reggid]

If the mass in variouse renormalization schemes were 5, 10 and 15 MeV, what then is the mass?

I don't know what you mean with the mass. It seems that for you that is a relevant question, but as you said yourself before, it does not really make sense. The mass is a parameter in the Lagrangian of the QFT, and its numerical value depends on the renormalization scheme that you choose (and maybe also on a renormalization scale). That is just how QFT works.

Also any other coupling has the same issue (and the mass is nothing else than another coupling constant in the Lagrangian). Sure, you quote e.g. the strong coupling at the Z-pole, but also there you have to specify what renormalization scheme you are using for that coupling (by convention we use a running MSbar type scheme with 5 active quark flavors at the Z-pole, for good reasons).

For non-confined objects there is a particular mass scheme that has a simple connection to a more "classical" picture of what the mass of a free particle is, but for objects subject to confinement we don't have this. But what's the problem with that? QFT is not simple, we just have to accept that.

You tell me the renormalization scheme and I'll tell you the mass.
- or =
You tell me the mass you want, and I'll tell you the renormalization scheme that does it for you.

that's in principle equivalent. The more useful way is of course the first: you specify your renormalization scheme (and choose one that is reasonable and well behaved for the situation under consideration), and then you can deduce the mass in that scheme from some experiment. But in principle one could actually do it the other way round, though I doubt anyone - including myself - would see much sense in that.

 

[Vanadium 50]

don't know what you mean with the mass.

That's my point. There is no "the" quark mass, like the OP wants. I can make that number anything I want it to be by suitable choice of calculation/definition.

The closest thing to physics is that this is relatively unimportant because hadrons are mostly glue.

 

[malawi_glenn]

The closest thing to physics is that this is relatively unimportant because hadrons are mostly glue

I have not read anything about lattice qcd in quite a while so I have forgotten most of it - but the calculations of hadron spectrum uses light meson masses as input - not quark masses afaik. But if someone was to use quark masses as input, the error in quark mass would not be that important for the calculation as a whole.

Hadrons with light quarks that is

 

[Reggid]

That's my point. There is no "the" quark mass [...]

Very well, then we fully agree on this point. It seems it was just a misunderstanding on this point:

[...] like the OP wants.

because I do not see where the OP asks for something like "the" quark mass. I can perfectly understand the question about how to make light quark mass measurements more precise without referring to more "philosophical" questions like what "the" mass of a confined particle is. More in the sense of "Whatever it is that people are doing to determine the light quark masses now (i.e. also whatever definition of the mass they are actually using), what can be improved to do that same thing more precisely?". And that question makes absolutely sense to me.

But of course we should not discuss and speculate what was or was not meant, but the thread opener himself/herself can comment on that.

 

[ohwilleke]

What mass are you referring to? Polemass?
I think what "we" often talk about when we are referring to quark mass is the current quark-mass or the running quark-masses

https://pdg.lbl.gov/2010/reviews/rpp2010-rev-quark-masses.pdf
https://pdg.lbl.gov/2019/tables/rpp2019-sum-quarks.pdf

Anyway, I know there has been some interest in measuring the η→3π decay since it provides a value for m_d - m_u

In any well defined scheme such as MS Bar at 1 GeV or 2 GeV which is the standard way of reporting them.

There is a physical reality associated with light quark masses that can be reported in any of several renormalization schemes and my assumption would be that the nature of the experiment which would be most likely to improve the accuracy of a value in the MS Bar scheme would probably also be most likely to improve the accuracy of a value in some other competing scheme (there are some highly technical reasons to view the MS Bar scheme a bit like Microsoft Word format for documents, not necessarily the best on pure merit, but due to overwhelming predominant use, the standard in the field anyway).

I recognize that the pole masses of the light quarks are ill defined in the infrared of perturbative QCD.

 

[ohwilleke]

I do not see where the OP asks for something like "the" quark mass. I can perfectly understand the question about how to make light quark mass measurements more precise without referring to more "philosophical" questions like what "the" mass of a confined particle is. More in the sense of "Whatever it is that people are doing to determine the light quark masses now (i.e. also whatever definition of the mass they are actually using), what can be improved to do that same thing more precisely?". And that question makes absolutely sense to me.

Just so. This is exactly what I was getting at, with the caveat that I'm interested in the experimental side as opposed to the improve QCD calculation methods side.

 

[ohwilleke]

But if someone was to use quark masses as input, the error in quark mass would not be that important for the calculation as a whole.

True.

But, there is intrinsic value in pinning down the values of the fundamental parameters of the Standard Model observationally.

If everything that exists boils down to a couple of dozen or so experimentally observed parameters, the Standard Model Lagrangian, and General Relativity, it is a scientifically obvious goal to pin down those parameters as precisely as possible. And, of course, working on improving our knowledge of one thing doesn't necessarily come at the expense of also wanting to improve our knowledge of other things. Often, for example, one experiment can elucidate more than one question at the same time.

 

[malawi_glenn]

But, there is intrinsic value in pinning down the values of the fundamental parameters of the Standard Model observationally.

We can never measure the bare masses, the fundamental parameters.

I can ask some of my friends who are the hadron physics area if they have any clues regarding your question. Last thing I remember is the measurments of eta meson decays for md-mu limits

 

[ohwilleke]

We can never measure the bare masses, the fundamental parameters.

I can ask some of my friends who are the hadron physics area if they have any clues regarding your question. Last thing I remember is the measurments of eta meson decays for md-mu limits

We can take physical observables to compute the bare masses, which is where our current estimates of these masses come from. In principle, if our calculations were good enough, we could use present data to infer these parameters much more precisely than we do. But, there might also be experiments that would also do the job to improve our data.

For example, it might be possible to use the ratio of quantities measured with respect to different hadrons that are identical except one valence quark on the theory that lots of the calculations cancel out, to get precise relative masses of c, s, d, and u to leverage the more precisely known mass of the c quark.

As another example, as I understand it, the current estimates of the mass difference between the u and d quark come from mostly comparing the masses of the proton and neutron and then calculating the share of that difference which can be attributed to the difference electromagnetic charges of the u and d quark, in order to net out a difference only due to the mass of the u and d quarks respectively, as was done in this 2014 paper.

 

[Vanadium 50]

here is a physical reality associated with light quark masses

There really isn't.

If you go back to F = ma, you cannot move a quark without also moving its surrounding glue field. And determining where you draw the line between a quark and its gluons is scheme dependent.

The closest you can do is either a) a parameter in the theory,or b) what the mass would be in a counterfactual world where quarks are colorless.

 

[ohwilleke]

There really isn't.

If you go back to F = ma, you cannot move a quark without also moving its surrounding glue field. And determining where you draw the line between a quark and its gluons is scheme dependent.

The closest you can do is either a) a parameter in the theory,or b) what the mass would be in a counterfactual world where quarks are colorless.

There is absolutely a physical reality associated with quark masses. See, e.g., here (Section 9.1.2) and here.

A parameter in a theory that defines mass in a particular way arises from a physical reality. The exact numerical value you reach may be definition dependent, and the masses of the five quarks other than the top may have to be backed out of theory.

But ultimately, different quarks have different physical properties that impact the observable properties of things that interact with them that are real observable facts. I can do an experiment in Denver, in Madrid, and in Auckland, or on the Moon, and come up with same result.

Applying any theory consistently, the observational results you will receive are universal. Any sound definition of quark mass can be converted to any other sound definition of quark mass in a one to one correspondence.

To say that it doesn't have physical reality because the line between a quark and its gluons is scheme dependent is a bit like saying that the volume of water in a beaker is scheme dependent because you could define it to be the top or the bottom of the meniscus, or because volume is influenced by temperature. You can get different numbers, but they are perfectly convertible to each other if you know how the definitions differ.

It is true that the exact measured value is scheme dependent and that to state it you need a sufficiently precise definition, but that doesn't mean that the value doesn't correspond to a physical reality that can be discerned in multiple ways.

 

[Vanadium 50]

here is absolutely a physical reality associated with quark masses.

Believe whatever you want.

 

[arivero]

Believe whatever you want.

decay rates I would believe.

 

[Vanadium 50]

Which decay rates?
Can you write down an expresiion like m(q) - f(one or more decay rates).

Note that Sargent's Rule applies to hadrons, not quarks.

 

[vanhees71]

Since quarks can never be observed as asymptotic free states, it's not clear, how to define their "mass". A sign of the trouble is that the section on quark masses in the Review of Particle Physics changes in each new issue ;-)):

https://pdg.lbl.gov/2022/reviews/rpp2022-rev-quark-masses.pdf

 

[ohwilleke]

Since quarks can never be observed as asymptotic free states, it's not clear, how to define their "mass". A sign of the trouble is that the section on quark masses in the Review of Particle Physics changes in each new issue ;-)):

https://pdg.lbl.gov/2022/reviews/rpp2022-rev-quark-masses.pdf

But, for any consistently applied definition, you can improve the precision of the value observed and essentially the same experiments should improve the precision with which you can observe the value for pretty much any of the available definitions.

 

[malawi_glenn]

We can not come up with an experiment that directly measure the light quark masses, we can only calculate them "backwards" using models like ChPT and LatticeQCD using hadron masses and decay rates

I did speak with some of my friends who are in the hadron physics business and they basically said that other theoretical issues like axial vector mesons and spin structure are more "urgent". Experimentally, things that can proble BSM physics, like CP-violation and anomalous branching ratios have more attention. Sure, even lower uncertainties on the light quark masses is desirable but it is not a driving "force" at the moment. Isn't the current lattice QCD uncertainty about 1-1,5%? Is that bad? It is pretty remarkable good imo.

You can think it has an intrinsic value and so one. But knowing them with this high centrainty has little pragmatic effect when it comes to understanding other issues like proton spin structure, axial vector mesons, CP-violation and anomalous decay rates (indirect signs of BSM physics), which I already mentioned. And we also have the "exotic" states of quark and gluon particles (which we discussed recently in another thread!)

 

[ohwilleke]

We can not come up with an experiment that directly measure the light quark masses, we can only calculate them "backwards" using models like ChPT and LatticeQCD using hadron masses and decay rates

I did speak with some of my friends who are in the hadron physics business and they basically said that other theoretical issues like axial vector mesons and spin structure are more "urgent". Experimentally, things that can proble BSM physics, like CP-violation and anomalous branching ratios have more attention. Sure, even lower uncertainties on the light quark masses is desirable but it is not a driving "force" at the moment. Isn't the current lattice QCD uncertainty about 1-1,5%? Is that bad? It is pretty remarkable good imo.

You can think it has an intrinsic value and so one. But knowing them with this high centrainty has little pragmatic effect when it comes to understanding other issues like proton spin structure, axial vector mesons, CP-violation and anomalous decay rates (indirect signs of BSM physics), which I already mentioned. And we also have the "exotic" states of quark and gluon particles (which we discussed recently in another thread!)

The questions are interrelated.

A lower priority improvement in experimental data can still make sense if the experimental data is fairly inexpensive to modify existing HEP projects to obtain. But, if the only experiments that would make a difference are very costly, then it doesn't make sense.

The u quark mass uncertainty according to PDF is + 23%/-12% which is not small, although the FLAG group reports a much more precise value based upon different standards for what the two groups consider sufficient to establish a value.

 

[malawi_glenn]

The questions are interrelated.

If it was urgent to know the u & d masses to such high precision to answer those questions which I posted, researchers would pursue it.

A lower priority improvement in experimental data can still make sense if the experimental data is fairly inexpensive to modify existing HEP projects to obtain

I think active researchers are better than you and me to determine what is the most "bang for the buck".

I mean I want to build a huge electron-positron collider to measure the width of the 125 GeV Higgs to surgical precision :)

They closed down the Tevatron! If they would have run it one more year it would have discovered the Higgs! Hadron colliders are discovery machines! They should have run Tevatron more years and instead upgrading LEP, if you ask me. But it is easy to say these things with the outcome at hand...

Science is also politics

 

[ohwilleke]

If it was urgent to know the u & d masses to such high precision to answer those questions which I posted, researchers would pursue it.

Science is also politics

This still doesn't really get to my original question, however, which is what kind of experiments would make a difference. This question goes to understanding what the key physics are that go into making this measurement in addition to the practical desirability of doing it or not.

And, since science is also politics, it is too important to be simply left to scientists when politics are involved. It is also important for non-scientists to understand the issues well enough to make good political decisions.

 

[malawi_glenn]

This still doesn't really get to my original question, however, which is what kind of experiments would make a difference.

Feed LQCD with more precisce hadron masses so that those masses can be computed. Probably the same experiments that have already been performed, but upgraded detectors and higher statistics.

It is also important for non-scientists to understand the issues well enough to make good political decisions.

QFT should be mandatory for everybody to know ;)
These kind of details are way beyond the scope for any ordinary living creature to dwell on. Citizens can not judge if experiment X or Y is better to perform in order to reach goal Z. Should they close the tevatron? Should the build a hadron or electron-positron collider? Should the ATLAS detector use toroidal magnetic field? Ordinary people think the LHC will create black holes that will eat the entire Earth and open portals to other dimensions. Oh well, at least those are in far minority!

 

[arivero]

I am a bit puzzled. We know that the only distinction entre mesons with the same charge composition are the masses of the quarks. Are you telling that one can in principle use a renormalization scheme where say the mass of the top is less that the mass of the up quark, or the bottom smallest than the down, and still get all the correct mesons and their decay rates between them?

 

[Vanadium 50]

The top quark has a variation of maybe a percent due to these factors. The up and down quarks are more like a factor of 2.

If things were as simple as some would have us believe, m(Λ) - m(p) would be the same - absolutely identical - as m(K0) - m(π+). The former is 177 MeV and the latter is 358 MeV.

 

[arivero]

It seems to me that the only objection here is about calling "masses" to some of the parameters of the standard model. Well, we also call "angles" to another set of parameters.

 

[Vanadium 50]

The OP has already rejected the "just a parameter" concept.

 

[fresh_42]

I think that disregard of ...

Since quarks can never be observed as asymptotic free states, it's not clear, how to define their "mass".

For non-confined objects there is a particular mass scheme that has a simple connection to a more "classical" picture of what the mass of a free particle is, but for objects subject to confinement we don't have this.

... is the actual problem with this thread.

 

[arivero]

The OP has already rejected the "just a parameter" concept.

But he is not setting for Newtonian concept of mass neither. I guess all of us could agree in "increasing precision of the parameters of the standard model".

 

[arivero]

... is the actual problem with this thread.

Indeed one would go with more detail here, about renormalisation schemes and how they preserve or transform the measurement errors and the relationships (proportions, absolute max) between parameters. Perhaps too advanced for PF?

 

[Reggid]

While everything being said in this thread about the issues with the definition of quark masses, different renormalizaton schemes, confinement, etc... is true, I still don't see why it was brought up in the first place and what it has to do with the OP question.

The question was simply

What new experimentally data, if any, would be most helpful in advancing the cause of more precisely determining the light quark masses?

so if we make this a bit more precise one could say:

The PDG gives here ( https://pdg.lbl.gov/2022/reviews/rpp2022-rev-quark-masses.pdf ) an estimate for the strange quark mass from lattice QCD in the MSbar scheme at a renormalization scale of $\mu=2\,\rm{GeV}$ in a $N_L = 4$ flavor scheme as

$\bar{m}_s(\mu=2\,\rm{GeV}) = (93.1 \pm 0.6)\,rm{MeV}$ (Eq. 60.5 on page 5)

What can be done not on the theory side, but instead on the experimental side to bring that $\pm 0.6\,\rm{MeV}$ down? (There are other methods than lattice QCD to determine light quark masses, but the equivalent question can be asked for them too)

This seems a well-posed question to me that should be answerable (just not by me, because I simply don't know the answer).

 

[malawi_glenn]

I still don't see why it was brought up in the first place

if we make this a bit more precise one could say

Lack of precision in the question perhaps?

What can be done not on the theory side, but instead on the experimental side to bring that ±0.6MeV down?

Feed LQCD with more precisce hadron masses so that those masses can be computed. Probably the same experiments that have already been performed, but upgraded detectors and higher statistics.

And also

measuring the η→3π decay since it provides a value for md - mu

I forgot to link to this paper, will do it now
https://arxiv.org/pdf/1610.03494.pdf