Baryon QCD sum rules in an external isovector-scalar field and baryon isospin mass splittings

Abstract

Within the QCD sum-rule approach in an external field, we calculate the baryon matrix element of isovector-scalar current, H B = B|uu− dd|B /2M B , for octet baryons, which appears in the response of the correlator of baryon interpolating fields to a constant isovector-scalar external field. The sum rules are obtained for a general baryon interpolating field with an appropriate form for the phenomenological ansatz of the spectral density. The key phenomenological input is the response of the quark condensates to the external field. To first order in the quark mass difference δm = m d − m u , the non-electromagnetic part of the baryon isospin mass splitting is given by the product of δm and H B . Therefore, QCD sum-rule calculation of H B leads to an estimate of the octet baryon isospin mass splittings. The resulting values are comparable to the experimental values; however, the sum-rule predictions for H B are sensitive to the values of the response of the quark condensates to the external source, which are not well determined.

Second class current in QCD sum rules

“…To obtain f χ , we take C m (GeV 2 ) = (−0.0307) − (−0.0223) which makes the protonneutron mass difference within the interval 1.95GeV ≤ (M n − M p ) ≤ 2.41GeV where the electromagnetic effect are subtracted out [29]. Thus we get χ(0) = (−0.0337) − (−0.0470)…”

Remark on the external-field method in QCD sum rules

“…The isolation of the ground state property relies on that the polynomial (in Borel mass) behavior of the ground state signal is different from those of the transition terms. While this approximation has been used in earlier studies, it has been noticed recently that the parameter representing the transitions, in general, should be dependent on the Borel mass, which can have a sizable impact on the extracted ground state properties [19,17].…”

“…The neglect of such a Borel mass dependence will generate errors in the extracted hadron matrix element (see for example Refs. [19,17]).…”

“…[16] within the traditional external-field QCD sum-rule method (see also Ref. [17]). Here, our purpose is only to compare the new formalism suggested above with the traditional formalism.…”

“…[19]). In particular, a complete form for the phenomenological side, which must be invoked in the traditional formalism, has been derived, and the corresponding sum rule takes the form [17]…”