Retrodiction of Particle Masses

While researching baryon asymmetry, I came across this article discussing problems with the Standard Model, where it is noted that:

The Standard Model did not and cannot predict the masses of the fundamental particles that make up all of the luminous matter that we can observe. QCD still cannot retrodict the mass of the proton without considerable fudging, and even then it is only good to within 5%. As for retrodicting the mass of the electron, the SM cannot even make an attempt.

I'm not entirely sure I understand what such a retrodiction would look like.

Can someone point me to an example of a formula (including Standard Model) that successfully, accurately retrodicts the mass of a particle and how this is accurately calculated?

EDIT: Sorry, I was really only curious about what retrodiction of a particle's mass looked like and ended up with a response about prediction because of an edit that was not by me. Should I re-ask in a more specific fashion?

• What do you mean by "the formula?" – user4552 Mar 7 '19 at 4:47
• I understand that the Standard Model can be accurately described as a formula. – MacThule Mar 7 '19 at 7:37
• Retrodiction is just prediction of some fact that you already know, without "smuggling" that fact into your prediction. The SM can't retrodict the mass of the electron because that mass is explicitly added into the model by hand, and if you don't explicitly add it, the model has no way to derive it from some more fundamental principles. – PM 2Ring Mar 7 '19 at 8:01
• The Standard Model can be considered a “formula” for calculating a quantity known as action for any possible evolution of quantum fields. (Although physicists don’t use that that terminology.) It isn’t a formula for masses of anything. – G. Smith Mar 7 '19 at 17:45

The article you link is saying that calculating the proton mass is only 5% accurate. This is a retrodiction because of course we already know the proton mass so we're just checking the standard model calculation gives the same result as the observed mass.

The article is correct that the calculation is not exact, but that's because it's a formidably hard calculation. The calculation is done using a method called lattice QCD. This is a hugely complicated numerical calculation. There isn't a simple formula (or even a complicated formula) for calculating hadron masses. The equations involved are just so complicate that there is no way to solve them except to get the biggest computer you can and let it churn for days.

• Thank you! I assume that there is probably a waiting list & cost associated with use of such calculators as could perform a lattice QCD in a reasonable amount of time. That is VERY helpful. The language I found led me to think maybe they were attempting to calculate masses of a particle before observation or something, but from your clarification it sounds more like a method of benchmarking formulae. – MacThule Mar 10 '19 at 18:52

The Standard Model does not predict the masses of fundamental particles such as electrons and quarks. Their masses are determined by interactions with the Higgs field whose couplings are adjustable parameters of the theory.

But the Standard Model can and does predict the masses of composite particles which are bound states of the fundamental ones, such as protons and neutrons. There are many more composite particles than fundamental ones, so getting their masses right is an important test of the model.

Lattice QCD is a computer-based non-analytical computational technique that can predict the masses of a variety of hadrons. It simulates quark and gluon fields on a finite lattice of spacetime points. This paper presents “a full ab-initio calculation of the masses of protons, neutrons and other light hadrons, using lattice quantum chromodynamics.”

• What happened? My question was modified - not by me. It was about retrodiction and became about prediction, which I didn't have a question about. Thank you for the direction - it helps, but I'm confused. – MacThule Mar 7 '19 at 7:36
• @MacThule you can see the edit history of your question here. I edited it to add the quote from the article you linked, but I didn't change retrodiction to prediction. – John Rennie Mar 7 '19 at 8:24
• I see. No, you didn't change the terms I used, it looks like because the inserted quote begins with prediction that's just what the initial respondent seemed to catch on. Thanks for clarifying - I'm not used to this venue and didn't realize posts could be modified by other people. – MacThule Mar 10 '19 at 18:41
• Thank you; following your response I only found further info about prediction and didn't realize that retrodiction is nothing but prediction of a known value (rather than calculation of mass prior to observation or other changes). Your answer actually had a big part of what I needed as well, but I hadn't understood that because the retrodiction language was tripping me up. – MacThule Mar 10 '19 at 18:58