# The Family Formula for Leptons and Quarks

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Referee this paper: hal-01967522 by Nikola Perkovic

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requested Aug 22, 2019

paper authored Dec 31, 2018 to hep-ph

## 1 Review

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Some initial comments on this paper... It starts by observing that in the standard model, yukawa couplings are free parameters. Then it goes on to propose formulas for the yukawas of the charged leptons, down-type quarks, and neutrinos.

The yukawa formulas - the prototype of which is equation 8 - are not explained by any physical model, principle, or reasoning that I can see. Until such an explanation is provided, I can only regard them as an exercise in "numerology", i.e. algebraic formulas which, even if they are true for a physical reason and not just by coincidence, ultimately need to be embedded in a physical theory.

The formulas contain a dependency on the fine-structure constant, which is common enough in physics numerology. However, they are unusual (even unique?) in that they employ the running fine-structure constant. Furthermore, the scale employed, is set by the mass of the relevant particle. For example, in equation 13, we see that the muon yukawa depends on the value of the fine-structure constant at the muon mass scale.

This may sound circular; but it also resembles some authentic QFT calculations, in which the value of a quantity is obtained from the constraint of self-consistency. However, as I already said, I don't see how to interpret these formulas as part of a larger coherent theoretical framework, whether that's quantum field theory or something else. In other words, I don't know how to start from a specific quantum field theory, whether defined by a largangian or by some ansatz, and obtain these expressions from it. So it looks like numerology to me; but perhaps the author has explained his theoretical framework in other works.

reviewed Aug 26, 2019 by (1,850 points)

Indeed, it would be interesting to give more details on the (8) construction. However, it is not ad hoc. The author provides the way to get it after a few assumptions. Similar papers ( in the form ) are common from great signatures. More than numerology, it is expressionology that can give ideas to other physicists. Unfortunately, the document covers a heavy domain and requires a lot of time for an useful review.

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