Evolution equations for truncated moments of the parton distributions

Abstract

We derive evolution equations for the truncated Mellin moments of the parton distributions. We find that the equations have the same form as those for the partons themselves. The modified splitting function for n-th moment $P'(n,x)$ is $x^{n}P(x)$, where $P(x)$ is the well-known splitting function from the DGLAP equation. The obtained equations are exact for each n-th moment and for every truncation point $x_0\in (0;1)$. They can be solved with use of standard methods of solving the DGLAP equations. This approach allows us to avoid the problem of dealing with the unphysical region $x\to 0$. Furthermore, it refers directly to the physical values - moments (rather than to the parton distributions), what enables one to use a wide range of deep-inelastic scattering data in terms of smaller number of parameters. We give an example of an application.