Four-loop cusp anomalous dimension in QED

The 4-loop C(F)(3)T(F)n(l) and 5-loop C(F)(4)T(F)n(l) terms in the HQET field anomalous dimension Upsilon h are calculated analytically (the 4-loop one agrees with the recent numerical result [1]). The 4-loopC(F)(3)T(F)n(l) and 5-loop C(F)(4)T(F)n(l) terms in the cusp anomalous dimension (phi) are calculated analytically, exactly in phi (the phi ->infinity asymptotics of the 4-loop one agrees with the recent numerical result [2]). Combining these results with the recent 4-loop d(FF)n(l) contributions to Upsilon h and to the small-phi expansion of Gamma(phi) up to phi(4)[3], we now have the complete analytical 4-loop result for the Bloch-Nordsieck field anomalous dimension in QED, and the small-phi expansion of the 4-loop QED cusp anomalous dimension up to phi(4).