Motivated by LHC results, we modify the usual criterion for naturalness by
ignoring the uncomputable power divergences. The Standard Model satisfies the
modified criterion ('finite naturalness') for the measured values of its
parameters. Extensions of the SM motivated by observations (Dark Matter,
neutrino masses, the strong CP problem, vacuum instability, inflation) satisfy
finite naturalness in special ranges of their parameter spaces which often
imply new particles below a few TeV. Finite naturalness bounds are weaker than
usual naturalness bounds because any new particle with SM gauge interactions
gives a finite contribution to the Higgs mass at two loop order.Comment: 17 pages, 3 figures. v3: final version uploaded, references added,
numerical error in the last column of table 1 fixe