Precise mass-ratio dependence of fourth-order lepton anomalous magnetic moments: Effect of a new measurement of mτ

We consider the fourth-order contribution of the one-bubble diagram to a=(g-2)/2 of the charged leptons for arbitrary mass ratio k=m1/m2. We verify that our recent formulas for a1(k)=a(k), k<1, and a2(k)=a(k), k>1, reduce smoothly to a(k=1)=119/36-π2/3 from both sides, thus verifying the correctness of our formulas for a1 and a2. We also give very accurate results for all combinations of m1, m2=me, mμ, and mτ, where the accuracy is limited only by the present experimental accuracy of the masses me, mμ, and mτ. We consider a new more accurate measurement of the mass of the τ lepton and compute its effect on the QED contribution to aμ and aτ. The results for aτQED and aτ are unchanged. Our result for aμQED is changed by 3.3(5)x10-12, but aμth remains unchanged