Testing the Up/Down Susceptibility Profile under Consistent MS̄ Running — and Why ρ = 0.50 ± 0.02 Matters
This paper is a checking paper. It does not try to prove the whole VERSF mechanism. Instead, it asks a simpler but very important question: was one of the most striking patterns in the quark masses real, or was it just an accident caused by comparing numbers quoted in different conventions?
The pattern concerns the way up-type and down-type quarks differ from each other across the three generations. When the differences are written in logarithmic form, the increase from the first generation to the second appears to be roughly twice the increase from the second generation to the third. In plain terms, the pattern seems to “halve” as the generations rise. That matters because VERSF has a possible structural reason why a factor of one-half might appear.
The problem was that the earlier comparison was not clean enough. Some quark masses were being compared at different energy scales, and some could have mixed different mass conventions. That meant the apparent one-half pattern might have been a bookkeeping artefact rather than a real feature of the data.
This paper fixes that by putting all six quark masses into one consistent convention and running them to common scales using standard QCD machinery. The result is that the near-one-half pattern survives. The clean calculation gives a value very close to 0.50, and it remains stable when the common scale is changed. That is the main advance: the programme no longer has to worry that this particular pattern was created by mixing incompatible mass definitions.
The result is encouraging, but it is not a proof. The paper is careful about this. The current uncertainty in the light quark masses, especially the up/down ratio, is still too large to say that the value is exactly one-half. The honest conclusion is that one-half is strongly consistent with the cleaned-up data, but nearby values cannot yet be ruled out.
This moves the VERSF programme forward by clearing an empirical obstacle. Before this audit, the programme first had to ask, “Is one-half even the right target?” After this audit, the answer is: yes, one-half remains a serious and stable empirical target. The burden now shifts back to the theory itself: VERSF must still derive why the one-half structure should appear in the first place.
So the paper strengthens the programme in a bounded but important way. It does not complete the quark-mass explanation, but it removes a major weakness. The near-halving pattern is no longer just a suspicious numerical coincidence produced by inconsistent inputs. It survives a clean test. That means the next papers can focus on the deeper structural question: what in the VERSF architecture forces this pattern?