The Second Moment of the Structure Function for Pseudoscalar Mesons in QCD Sum Rules
Y. Nishino · 1994
We calculate the values of the second moment Ms 2 of the flavorsinglet structure function F s 2 for the pion and the kaon in QCD sum rules, and investigate how the results depend on their flavor structure (quark contents). Our calculations give similar values of Ms 2 for these two mesons, because of cancellation among several non-small factors. We emphasize that decay constants, meson masses and quark masses play an essential role in the above cancellation. 1 Structure functions carry information on dynamical distributions of quarks and gluons inside hadrons. Intensive studies of nucleon structure functions have been performed using various lepton induced reactions. In contrast, those of other hadrons are not easy to access. It is not yet clear how the difference in quark contents of hadrons affects the structure functions. In the present paper, we would like to study this problem by calculating the values of the second moment M s 2 of the flavor-singlet structure function F s 2 for the pion and the kaon in QCD sum rules (QSR) The QSR method, developed by Shifman, Vainshtein and Zakharov [1], has been used to study a number of problems in hadron physics [2]. Belyaev and Ioffe studied the Bjorken variable dependence of the structure function F2(ξ, Q 2) of the nucleon based on QSR, and showed that their method is applicable only in the intermediate region of the Bjorken variable ξ [3]. On the other hand, moments of structure functions can be studied by introducing constant external fields into QSR [4]. Using this technique, Belyaev and Blok calculated M s 2 values for the pion and the nucleon [5]. There also exist some applications of this technique to moments of other structure functions [6]. These calculations indicate that QSR is a useful tool in calculating moments of structure functions. Below we adopt this technique to investigate M s 2 values for the pion and the kaon, and study in particular the effects of decay constants, meson masses and quark masses on the momentum fraction carried by quarks. The second moment M s 2 (µ2) of the (unpolarized) flavor-singlet structure function F s 2 is defined as follows: M s 2 (µ2)pµpν = 1