We construct three different sum rules from the two-point correlation function with pion, i fd4xeiq'x(O[TJN(X)JN(O)l~r(p)), beyond the soft-pion limit. The PS and PV coupling schemes in the construction of the phenomenological side are carefully considered in each sum rule. We discuss the dependence of the result on the specific Dirac structure and identify the source of the dependence by making specific models for higher resonances.
Within QCD sum rules, the rNN coupling constant, gTrN, is often calculated [1,2], for example, from the correlation function,
/ d4xe~q'~(O[TJp(x)Jn(O)lrc+(p)) ,
(1) i where Jp is the proton interpolating field [3] and Jn is the neutron interpolating field. Shiomi and Hatsuda [1] considered i~/5 Dirac structure from this correlation function in the soft-pion limit (p, -+ 0). Later, Birse and Krippa [2] pointed out that the use of soft-pion limit does not constitute an independent sum rule from the nucleon chiral-odd sum rule, and proposed to look at the Dirac structure, i75 ~, beyond the soft-pion limit.
Recently [4], we have pointed out that the previous calculations of this sort have dependence on how one models the phenomenological side; either using the pseudoscalar (PS) or the pseudovector (PV) coupling scheme. Beyond the soft-pion limit, we presented a new sum rule for the 75a~,q~'p " structure. This sum rule is independent of the coupling schemes and provides g,N relatively close to its empirical value.
Then we ask, can we get similar results from the other Dirac structures, i3, 5 and i3'5 ~, constructed beyond the soft-pion limit ? If not, what are the reasons for the differences ? In this work, we will try to answer these questions by studying all three sum rules and investigating the reliability of each sum rule.
In calculating the OPE of Eq. ( 1), we only keep the quark-antiquark component of the pion wave function, D,~ -(Olu~(x)d ~, (0)Ir+(p)) , (2) *JSPS Fellow. tAvH Fellow.