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The nucleons (protons and neutrons) interact with each other via the exchange of pions. Quarks interact with each other via the exchange of gluons which mediate the fundamental strong interaction between the quarks and are governed by QCD. The force at the level of nucleons is a residual of the strong interaction between quarks.

How do we know that the force between nucleons is not another fundamental force but is a "leftover" of the strong force between quarks? Are there theoretical frameworks of QFT that address this question rigorously (say, for example, arrive at the residual strong interaction between nucleons, in the sense of an effective theory) and give an affirmative answer? If yes, can somebody sketch how is this done and what are the insights gained in the process?

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    $\begingroup$ It is all a mater of scales: you envision transitioning from QCD, most tractable at scales much shorter than a fermi, to effective scales larger than a fermi... There is an enduring story that Ken Wilson and Peter Lepage thought about fleshing this on the lattice, decades ago, but the project proved too ambitious. $\endgroup$
    – Cosmas Zachos
    Commented Sep 27 at 16:38

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Let me rephrase your question: "Please explain all of few body nuclear physics from the 1930's to the current program at:

https://www.jlab.org

https://web.mit.edu/lns/research/bates.html

and maybe

https://www.anl.gov

https://lpsc.in2p3.fr/index.php/en/le-lpsc

https://www.psi.ch/en

And two with "meson" in the name:

https://discover.lanl.gov/publications/1663/september-2022/50-years-of-beaming/

https://www.triumf.ca

IDK, I was just listed a few places I've been.

Anyway: mesons and baryons came first. Baryons are fermions, mesons are boson. Fermions exchange bosons in field theories, so that's it.

It's been called "Quantum Hadrodynamics" and is ofc an effective field theory--though I don't see that used much anymore.

One correction: it's not just pion exchange, it's all the mesons that fit. See: http://www.scholarpedia.org/article/Nuclear_Forces

This is not a history site, so I'll keep it short: the quark model and deep inelastic scattering at https://www6.slac.stanford.edu (and other labs) on the experiment side brought it all together.

tl;dr: Your question is too big...you could write a book on it. I don't even know how to give a short answer that does medium energy nuclear physics any justice.

Edit (per comment from OP):

Regarding whether the low energy hadron field theory is derivable from first principles QCD with the known quarks: no. I am not familiar with the state-of-the-art lattice-QCD, but I have never seen say, a deuteron model (that would be cool, tho).

The problem is: QCD is strong, non-abelian, and quantum, for the intractabilty trifecta.

Now Walter Greiner did QED in the strong regime--I'm not sure if it was many-body condensed matter or high $Z$ regions (at $Z=137$, $\alpha Z \approx 1$ and QED is no longer perturbative--irrc), or both. See https://www.semanticscholar.org/paper/Quantum-electrodynamics-of-strong-fields-Reinhardt-Greiner/15fade4903542eb2adaf58ff731ca7cad9898d5d for example. So here you can learn about the challenges of quantum field theory in the strong regime.

Okun has an old and wonderful book (https://www.amazon.com/Books-Introduction-Gauge-Theories/s?rh=n%3A283155%2Cp_28%3AAn+Introduction+to+Gauge+Theories) on the 100 years it took us to take curio of gauge invariance in EM to it being the fundamental symmetry of all the SM forces. In it, he talks about the classical chromodynamic treatment of a flavorless meson, a $q\bar q$ pair...he discusses the what the non-abelian field does, and it is complicated, as it's an 8 dimensional coupled color-"electric" field (and the complimentary 8 dimensions color-"magnetic" fields are not weak in comparison).

(That is a difficulty in just studying excited states of the nucleon, e.g. $N^*$ and $\Delta$...the spin-orbit coupling is not small compared with the charge/anti-charge force).

Regarding both the above examples, I was just an experimentalist, but sat through many theory seminars on such considerations--a long time ago.

So even your restricted question requires research programs to answer in any quantitative manner.

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  • $\begingroup$ In short, I am asking, whether the meson exchange effective theory of the nucleon-level interactions can be obtained from the gluon exchange theory of quarks (or QCD). $\endgroup$
    – Solidification
    Commented Sep 27 at 15:29
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    $\begingroup$ Only the gods of hadronization know. $\endgroup$
    – Cosmas Zachos
    Commented Sep 27 at 16:41
  • $\begingroup$ @Solidification QCD computation is difficult because gluons have color charge, so you get evil divergent series, not nice renormalizable stuff like you get in QED. You have to resort to all sorts of tricks to get stuff to converge to vaguely correct values. When Frank Wilczek did the first elementary computation of the proton mass in QCD, it took several months of CPU time on a Cray supercomputer. And that was only an order of magnitude estimate. We now have somewhat better algorithms and hardware, but QCD is still hard. $\endgroup$
    – PM 2Ring
    Commented Sep 27 at 18:45
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    $\begingroup$ Can you explain the Navier-Stokes equation from QED? $\endgroup$
    – Oбжорoв
    Commented Sep 27 at 18:58
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    $\begingroup$ @Solidification Wilczek has some great popular-level articles on his site. They're several years old now, but still well worth reading to get a feel for QCD & related topics from one of the experts in the field who also happens to be an excellent communicator. frankwilczek.com/core.html $\endgroup$
    – PM 2Ring
    Commented Sep 27 at 18:58

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