Calculation of 〈p‖u¯u-d¯d‖p〉 from QCD sum rules and the neutron-proton mass difference

Abstract

The proton matrix element of the isovector-scalar density, p|uu−dd|p /2M p , is calculated by evaluating the nucleon current correlation function in an external isovector-scalar field using the QCD sum-rule method. In addition to the usual chiral and gluon condensates of the QCD vacuum, the response of the chiral condensates to the external isovector field enters the calculation. The latter is determined by two independent methods. One relates it to the difference between the up and down quark chiral condensates and the other uses the chiral perturbation theory. To first order in the quark mass difference δm = m d − m u , the non-electromagnetic part of the neutron-proton mass difference is given by the product δm p|uu − dd|p /2M p ; the resulting value is in reasonable agreement with the experimental value.

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

“…In previous works [3][4][5][6][7][8][9][10][11][12], the phenomenological representation for the correlator is usually obtained by analyzing a double dispersion relation. Here we present an alternative approach to derive the phenomenological representation.…”

“…In the present paper, we shall derive the appropriate phenomenological representation, which includes the piece neglected in Ref. [11]. We use this complete phenomenological representation and a general baryon interpolating field to calculate the matrix element H B for octet baryons.…”

“…In Ref. [11], the proton matrix element p|uu − dd|p /2M p has been calculated in the external field approach. However, one piece of the phenomenological representation has been omitted in the calculation.…”

Chirality and reliability of baryon QCD sum rules

“…As an explicit example, we consider the sum rules for the proton matrix element of H = p|uu − dd|p /2M N , which can be obtained from the linear response of Π to a constant external isovector-scalar field [12,13]. In the formalism suggested in Ref.…”

“…For definiteness, we use β = −1.2 [7] and χ = 2.0 GeV −1 [12,13]. Here, we have put the continuum contributions on the right-hand sides of the sum rules.…”