Is there a renormalizable QFT that can produce a reasonably accurate description of nuclear physics in perturbation theory? Obviously the Standard Model cannot since QCD is strongly coupled at nuclear energies. Even the proton mass cannot be computed from perturbation theory, as far as I understand.
The strong force sector should probably be comprised of a nucleon spinor field Yukawa-coupled to a scalar pion field, the later with quartic self-coupling. The electroweak sector should probably be the Glashow-Weinberg-Salam model with hadrons replacing quarks in some manner.
Some key parameters of what a "reasonably accurate description" should be are:
- Reproducing the entire spectrum of nuclei and predicting which nuclei are stable
- Estimating nuclear masses with precision of ~ 0.1%
- Estimating nuclear decay rates with precision ~ 10%
Assuming this is feasible:
How the precision of the results depends on computation loop order?
It is possible to consider the nonrelativistic limit of the QFT, in which nuclei are described by quantum mechanics of nucleons coupled by a (multibody) interaction potential. The potential can be computed in perturbation theory by considering the nonrelativistic limit of nucleon scattering. Obviously this cannot give the right masses, since mass is additive in non-relativistic physics, but does it give reasonably precise stability criteria and binding energies?
What if we remain with the 2-body potential only?
What happens if we extract the potential from the nonrelativistic limit of the full nonperturbative Standard Model (theoretically, I'm not sure it's manageable in practice)?
- Let me explain my motivation to think such a renormalizable QFT exists. The (sufficiently) fundamental description of nucleons and pions is QCD, but in low energies they can be described by an effective field theory. Such effective field theories are normally nonrenormalizable but the nonrenormalizable interactions are suppressed by powers of E / Lambda, where E is the energy scale of interest and Lambda is the fundamental energy scale: in this case, the QCD scale. Since nuclear binding energies are significantly lower than the QCD scale (highest binding energy per nucleon is about 9 MeV and the QCD scale is about 200 MeV so the ratio is < 5%), it doesn't seem absurd to use renormalizable interactions only
- It is not really possible to compute bound state energies and lifetimes at finite order of perturbation theory. This is because they appear as poles in the S-matrix but these poles don't appear at any finite order. However, maybe it's possible to introduce some meaningul infinite (but not complete) sum which will converge (at least after some resummation technique) and exhibit the required poles? It is certainly possible for bound states in external fields (in this case the infinite sum amounts to including the external field effect in the propagator), maybe there's a way to do it for bound states of dynamic particles as well? Now that I think about it, this issue should have been a separate question... In any case, we can still use perturbation theory to extract the many-body potentials
EDIT: I now realize issue 2 above can be tackled using the Bethe-Salpeter equation. However, I found no good discussion of it so far. Any recommendations? I'd prefer something mathematically-minded
EDIT: Thomas' answer below raised some doubts as to the possibility of describing nuclear physics using a renormalizable QFT. Therefore I wish to expand the question to include nonrenormalizable QFTs. As long as we stick to finite loop order there is a finite number of parameters so the approach makes sense. The question is then: Which QFTs (renormalizable or not) can produce nuclear physics from perturbation theory + Bethe-Salpeter equation? What is the required loop order?
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