Evolution of Structure Functions with Jacobi Polynomial: Convergence and Reliability

The Jacobi polynomial has been advocated by many authors as a useful tool to evolve non-singlet structure functions to higher Q2. In this work, it is found that the convergence of the polynomial sum is not absolute, as there is always a small fluctuation present. Moreover, the convergence breaks down completely for large N . [PACS : 12.38.-t, 12.38.Bx, 12.90.+b, 13.90.+i ] The structure functions are the necessary tool in our effort to understand the hadronic structure and strong interaction. The study of Q evolution of nucleon structure functions has been an important source of experimental information supporting Quantum Chromodynamics (QCD), which is believed to be the fundamental theory of strong interaction. It has already been shown some time back that [1] QCD is the only theory which can explain the gross features of scaling violations in deep inelastic scattering (DIS). As a result a huge amount of effort is being put, both experimentally as well as theoretically, to understand the nucleon structure functions for different values of x and Q. The evolution of quark distribution with Q is goverened by the Altarelli-Parisi (AP) equation [2]. To leading order in αs, the AP equation is given by, dq(x,Q) dt = αs 2π ∫ x 1dy y q(y,Q)Pqq( x y ) (1) where q is the quark distribution, αs is the strong coupling, t ≡ logQ and Pqq is the quark splitting function which represents the probability of a quark emitting a gluon and so email: [email protected] email: [email protected]