






We may try to theoretically estimate the mass. Tommaso Dorigo told us that the newly measured mass basically agrees with the prediction \(3.628\GeV\) by Jonathan Rosner and Marek Karlíner. What about a simple kindergarten estimate of the mass?

Let's try. The proton's mass is about \(0.94\GeV\) or basically \(1\GeV\), much heavier than the sum of the three "almost massless" quarks that are inside. Two of the nearly massless quarks are replaced with the charm quark whose mass is written as \(1.3\GeV\). OK, so if you replace two almost massless quarks by quarks that are some \(1.3\GeV\) heavier, you increase the total mass by some \(2.6\GeV\) and \(1\GeV\) of the proton plus \(2.6\GeV\) of the bonus for the two charm quarks is equal to \(3.6\GeV\), isn't it?

I do acknowledge that much of my self-confidence sketched in the previous paragraph results from my knowledge of the correct answer. But you know, the rough estimate of the mass simply doesn't seem to be a big deal. One combines the individual quark masses – known from some other composite states – with the mass of the "glue" that is inside every baryon and the result seems to be close to the predicted value. Rosner and Karlíner got a little bit more precise answer – some \(6\MeV\) away from the observed value. The reasoning behind their estimate is terribly technical.

The older, single-charged double-charmed xi particle was lighter by \(0.1\GeV\) which is a lot – much more than the mass difference between the up-quark and the down-quark. But because of some mutual interactions between the quarks, the charm quarks must "feel" whether the third, light quark in the baryon is up or down. And this may change the masses by an amount comparable to the QCD scale, i.e. \(0.15\GeV\) or so.

It's great that someone tries to do this difficult and "perfectly scientific" work. Dorigo praises this work with the following comments:

I argue it is this kind of research what makes particle physics the solid, foundational field of science it is - not the exciting promise of new exhilarating exotic states of matter which never concretizes, but rather the painstaking collection of confirmations: you think you understand something, put forth a prediction. Months, years, or decades later, finally somebody goes out and measures the system and comes home with a result that matches it. It is thanks to Karliner and Rosner if we may say we understand the world a little bit more today than we did yesterday. Thanks, Marek.
Right, it's solid. The scientific nature of similar enterprise is unquestionable. But is it important? Is it exciting? Well, whether someone is excited is a subjective thing. But my excitement would be limited. Some rather difficult calculations only produce the particle's mass whose error margin is just 1 order of magnitude finer than the error margin of my two-sentence derivation above. Is it worth it? Wouldn't it be easier or more economic for theorists to simply wait for the experimental measurement of the mass – so that our opinion about the mass goes from \(3.6\GeV\) estimated above to \(3.621.4 \pm 0.0008\GeV\) measured by the LHCb? Without the intermediate \(3.628\GeV\) theoretical estimate? It would surely seem sufficient for practical purposes.

Yes, these estimates are verifying whether QCD is the right theory of hadrons. But could a disagreement between the measured and predicted masses of such hadrons ever convince us that QCD is a wrong theory? I doubt it. The calculations are messy we never really know how big the theoretical error margin is.

People have various psychological biases. For example, some people don't want to theoretically study top-down theories where new effects only appear at very high energy scales – like string theory or at least grand unification – because they think it's right to be focused on the theories that have a chance to be experimentally tested soon. I believe that this bias is marginally a sign of the scientific dishonesty because the truth value of theories about Nature isn't correlated with the ease of their experimental verification and you simply shouldn't train yourself to take some theories seriously just because they're experimentally easy.

But I have some other biases which I consider sensible and morally clean. One of them is that it is normal for people to focus on theoretical calculations of applications that are easier to be made.

The doubly charged baryons are some bound states – not so much different from the helium atom, for example. I still believe that it's a nicer mathematical task to study the helium atom than to theoretically model the xi baryons. For the baryons, we need a harder theory, namely QCD which is a non-Abelian gauge theory, while the helium atom is all about non-relativistic quantum mechanics of particles which may be corrected by some small corrections.

It seems normal when the people prefer to apply theories in situations where the application seems easy enough and there are good reasons to expect that the results are accurate enough. Preferences over "what bound states we want to calculate" are not preferences about our belief how Nature works. They're purely about our strategy to make progress. QCD has worked well enough. The Rosner-Karliner calculation could be improved from a \(6\MeV\) error to a \(2\MeV\) error. But is it sensible to sacrifice thousands of theorists-hours to that task? Wouldn't it be possible that the better accuracy would ultimately be a matter of chance, anyway?

At any rate, we have known that baryons are composed (primarily) of quarks for some 40-50 years. This unavoidably makes the research of bound states of quarks less fundamental according to our best judgement. I believe that the fundamental depth and practical applications are the two main reasons to study something; the third possible motivation are unexpected insights that are useful elsewhere. I would probably apply this principle by concluding that the theoretical and experimental analysis of properties of quarks' bound states isn't terribly exciting and important.

Yes, I agree it still shows why particle physics is the ultimate prototype of a solid science. However, something's being a solid science isn't a sufficient condition for people to be encouraged and paid to spend years on that.

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