Strong Coupling Constant from the Photon Structure Function

We extract the value of the strong coupling constant alpha_s from a single-parameter pointlike fit to the photon structure function F_2^gamma at large x and Q^2 and from a first five-parameter full (pointlike and hadronic) fit to the complete F_2^gamma data set taken at PETRA, TRISTAN, and LEP. In next-to-leading order and the MSbar renormalization and factorization schemes, we obtain alpha_s(m_Z)=0.1183 +/- 0.0050(exp.)^+0.0029_-0.0028(theor.) [pointlike] and alpha_s(m_Z)=0.1198 +/- 0.0028(exp.)^+0.0034_-0.0046(theor.) [pointlike and hadronic]. We demonstrate that the data taken at LEP have reduced the experimental error by about a factor of two, so that a competitive determination of alpha_s from F_2^gamma is now possible.