The Jacobsen Relation?

In a previous post, we introduced the mysterious Koide formula in which the masses of the three known leptons satisfy a very simple relation.

Now a new relationship has been discovered and presented by Jacobsen (see the original paper), in which the masses satisfy

m(n) = 3^(n/4) (4 pi)^(1+n) m_e

where m_e is the electon mass, and n is an integer (and ^ represents 'raised to the power of'). Although this formula is not as simple or as beautiful as the Koide formula (and is not even close to having the same accuracy, with mass predictions off by as much as 1% instead of 0.01%), it has one big advantage. This formula expresses the masses in terms of a quantum number n, which provides a strong indication that the heavy leptons are in fact excited quantum states of the electon!