Volume 78B, number 2,3 PHYSICS LETTERS 25 September 1978 FACTORIZATION AND THE PARTON MODEL IN QCD R. Keith ELLIS 1 Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Howard GEORGI 2 and Marie MACHACEK 2 Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02]38, USA and H. David POLITZER 3 and Graham G. ROSS a California Institute of Technology, Pasadena, CA 91125, USA Received 19 Juni 1978 We argue that mass-singularities of inclusive cross sections in QCD factor to all orders in perturbation theory as re- quired for a patton model interpretation. If QCD is the field theory underlying the strong interactions, why does the parton model work? [1] Why is it that the mass singularity logarithms asso- ciated with collinear light-quark and gluon emission do not completely invalidate perturbation theory? The answer must be that the distribution and decay functions of the parton model are "renormalized" quantities which already include the large logarithms of naive perturbative calculations. This explanation reqt/ires that the semi-inclusive parton cross sections computed in perturbation theory must factor (in the sense of the convolution integrals which define the parton model), so that the large logs can be absorbed. [2]. In inclusive lepton-hadron scattering the re- quired factorization does take place to all orders in 1 This work is supported in part through funds provided by the U.S. Department of Energy (DOE) under contract EY- 76-C-02-3069. 2 This work is supported in part by the National Science Foundation under Grant No. PHY-20427 and by the Alfred P. Sloan Foundation. 3 This work is cupported in part by the U.S. Department of Energy (DOE) under contract EY-76-C-03-0068 and by the Alfred P. Sloan Foundation. perturbation theory (as shown by the operator prod- uct expansion). In this note, we summarize an argument to be presented in more detail in a forthcoming paper [3] that the required factorization actually takes place to all orders in perturbation theory for any semi- inclusive process that admits a parton model inter- pretation. We will first define the factorization we want in a theory with massless quarks. To develop an all-orders proof of the factorization property in QCD, we specialize to axial gauge. The key feature of axial gauge is that no large logs from collinear emissions arise from interferance between diagrams in which unobserved partons are emitted from differ- ent legs * 1. Technically speaking, we argue that the contribution to the (off-shell) cross section which is two-particle irreducible in the channel of the leg with momentum pU is finite as p2 _+ 0 * 2. From thereon .1 A special axial gauge, light-cone gauge, has been used to study lowest-order and/or leading log calculations. See ref. [4]. Similar Coulomb gauge calculations have been per- formed in ref. [51. • 2 The importance of the finiteness of the 2PI part for an all-orders proof of factorization was demonstrated by Mueller, ref. [7], for a special case. 281