Anthropic Estimates of the Charge and Mass of the Proton

By combining a renormalization group argument relating the charge e and mass mp of the proton by e 2 lnmp ≈ − 0.1π (in Planck units) with the Carter-Carr-Rees anthropic argument that gives an independent approximate relation mp ∼ e between these two constants, both can be crudely estimated. Using the rough relations with known discrete parameters (e.g., the number of generations), but with unknown numerical factors set equal to unity, one gets the charge of the proton correct to within about 8%, though the mass estimate is off by a factor of about 1000 (16% error on a logarithmic scale). When one adds a fudge factor of 10 previously given by Carr and Rees, the agreement for the charge is within about 2%, and the mass is off by a factor of about 3 (2.4% error on a logarithmic scale). Alberta-Thy-03-04, hep-th/0203051 Internet address: [email protected]