$Q^2$ Dependence of the Bjorken Sum Rule.pdf

a r X i v : h e p - p h / 9 5 1 0 4 1 8 v 1 2 6 O c t 1 9 9 5 Q2 Dependence of the Bjorken Sum Rule1 Lech Mankiewicz?, Eckart Stein??, and Andreas Scha?fer?? ?Institut for Theoretical Physics, TU-Mu?nchen, Germany 2 ??Institut for Theoretical Physics, J.W. Goethe Universita?t Frankfurt, Germany Abstract We discuss various estimates of the magnitude of higher-twist corrections to the Bjorken sum rule in polarized deep inelastic scattering. 1Talk given by L.M. at the ‘Workshop on the prospects of spin physics at HERA’, DESY-Zeuthen, August 28-31, 1995 2On leave of absence from N.Copernicus Astronomical Center, Warsaw, Poland Considerable attention has been paid to measurements of the polarized structure function g1 in deep inelastic scattering. The unexpected EMC [1] results for the first moment of g p 1, the structure function of the proton, invoked tremendous effort to gain more knowledge about polarized scattering. As a result of these intense discussions it became clear that polarization phenomena might offer much better opportunities to test QCD than unpolarized experiments. Meanwhile SMC [2] and SLAC [3] experiments have provided data on gn1 and much improved ones on gp1. Mainly due to this experiments the general interest shifted to related questions most notably to the problem of Q2 dependence. It turned out that an estimate of the magnitude of higher twist contributions is urgently needed in order to compare the experiments of SLAC, SMC and EMC which cover different Q2 regions [4]. This is especially important for the SLAC data which correspond to Q2 around 2 GeV2. The first moment of g1(x,Q 2) at fixed Q2 is given by [5] ∫ 1 0 dx g1(x,Q 2) = 1 2 a(0) + m2N 9Q2 ( a(2) + 4d(2) + 4f (2) ) +O( m4N Q4 ) ≡ 1 2 a(0) + μ GeV 2 Q2 +O( m4N Q4 ) . (1) The above formula does not include perturbative corrections (QCD). Higher order corrections were recently calculated in the leading twist approximation up to O(α3S) for non-singlet quanti- ties, the Bjorken sum rule