Former physicist here. Your speculation about path integrals and measure theory isn't quite right.
Lattice QCD methods are definitely proven to be equivalent to the continuum theory when you take the appropriate limits. This isn't some mathematical mystery - Wilson's groundbreaking work in the 70s established this, and it's been rigorously developed since.
The actual g-2 puzzle is much more straightforward: we have competing measurements from different sources:
1. The Fermilab Muon g-2 experiment in Illinois directly measured the muon's anomalous magnetic moment.
2. The "data-driven" prediction used e+e- collision measurements from various experiments (BaBar at SLAC, KLOE in Italy, etc.) to calculate what the Standard Model predicts for g-2. This initially disagreed with Fermilab's measurement.
3. Lattice QCD calculations (like those from the BMW collaboration) produced theoretical predictions that matched Fermilab's experimental result.
4. More recently, new e+e- measurements from the CMD-3 experiment at VEPP-2000 in Russia (2023) are bringing the data-driven approach closer to both the lattice calculations and Fermilab's experimental values.
So it's really just a question of which experimental measurements of e+e- collisions are most accurate/resolve any experimental differences, not some exotic mathematical issue with QFT formulations.
If they've been proven to be equivalent, how is that not a constructive quantum field theory in 4 dimensions? Constructive qft for realistic gauge fields is still referred to as an unsolved problem, so I guess there must be some sort of mismatch.
If I understand idea, this sounds like what physicists might call a 'collective phenomena' effect introducing some type of screening. It's possible -- if true it could independently be tested. I know there are models for this type of stuff in denser matter (and in more extreme conditions), but not sure whats known in situations like the experiment. I assume there is a reason that isnt mentioned, but would love to know from an expert why.
Collective phenomena do show up in high energy/particle physics, albeit rarely, ex: when you collide large enough nuclei together at high enough speeds, you create a highly energy-dense nuclear plasma which effective 'screens' jets of particles that would travel through the center of the collision. If you go to smaller nuclei or lower energy, you can start to see these jets of particles pass through the collision area.
Lattice QCD methods are definitely proven to be equivalent to the continuum theory when you take the appropriate limits. This isn't some mathematical mystery - Wilson's groundbreaking work in the 70s established this, and it's been rigorously developed since.
The actual g-2 puzzle is much more straightforward: we have competing measurements from different sources:
1. The Fermilab Muon g-2 experiment in Illinois directly measured the muon's anomalous magnetic moment.
2. The "data-driven" prediction used e+e- collision measurements from various experiments (BaBar at SLAC, KLOE in Italy, etc.) to calculate what the Standard Model predicts for g-2. This initially disagreed with Fermilab's measurement.
3. Lattice QCD calculations (like those from the BMW collaboration) produced theoretical predictions that matched Fermilab's experimental result.
4. More recently, new e+e- measurements from the CMD-3 experiment at VEPP-2000 in Russia (2023) are bringing the data-driven approach closer to both the lattice calculations and Fermilab's experimental values.
So it's really just a question of which experimental measurements of e+e- collisions are most accurate/resolve any experimental differences, not some exotic mathematical issue with QFT formulations.
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