Proton-neutron mass difference explained

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According to the newly published paper

http://www.sciencemag.org/content/347/6229/1452
Ab initio calculation of the neutron-proton mass difference
Science 27 March 2015:
Vol. 347 no. 6229 pp. 1452-1455
DOI: 10.1126/science.1257050

we owe our existence to an interplay between electromagnetic and mass isospin breaking effects. The preprint can be found at http://arxiv.org/abs/1406.4088

This is one of the problems one of my favourite lecturers as an undergrad said he wanted an answer to before he dies (he is still alive).
 
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Orodruin said:
This is one of the problems one of my favourite lecturers as an undergrad said he wanted an answer to before he dies (he is still alive).
Did you contact him about it? :)
 
He is still around on Tuesdays when he gives a course on the history and epistemology of physics to our grad students. I think he will not be satisfied with this though, he will also want to know why the quark masses have their values and it seems to me they used them as input.
 
They are free parameters in the SM. I don't know where they got the masses from, as using the proton/neutron mass difference looks like a sensible place to evaluate them.
 
Using Lattice gauge theory is nice and of course correct, but it would be nice to have some understanding of this from more analytic methods.