Parton distribution functions suitable for Monte-Carlo event generators

In the usual factorization theorems, which give predictions only for inclusive cross sections, there is considerable freedom in the choice of the scheme to define the parton distribution functions. These theorems do not directly apply to Monte-Carlo event generators, and more general factorization theorems which give predictions for fully exclusive cross sections are needed. It has been shown that appropriate parton distribution functions are uniquely defined by the showering algorithm. In this paper, we present results of calculations of the Monte-Carlo parton distribution functions in terms of the commonly used parton distribution functions. At small x the differences are large, which demonstrates the importance of using the correct parton distribution functions in an event generator rather than parton distribution functions. We present some simple approximations that enable an understanding of the sizes of the results to be obtained.