From Constituent Quark to Hadron Structure in the Next-to-Leading Order: Nucleon and Pion

Abstract

We calculate the partonic structure of constituent quark in the Next-to-Leading Order for the first time. The structure of any hadron can be obtained thereafter using a convolution method. Such a procedure is used to generate the structure function of proton and pion in NLO. It is shown that while the constituent quark structure is generated purely perturbatively and accounts to most part of the hadronic structure, there is a few percent contributions coming from the nonperturbative sector in the hadronic structure. This contribution plays the key role in explaining the SU(2) symmetry breaking of the nucleon sea and the observed violation of Gottfried sum rule. These effects are calculated. Excellent agreement with data in a wide range of $x=[10^{-6}, 1]$ and $Q^{2}=[0.5, 5000]$ $GeV^{2}$ is reached for proton structure function. We have also calculated Pion structure and compared it with the existing data. Again nice agreement is achieved.