Continuum-limit isoscalar nucleon form factors at finite momentum transfer

Determine the continuum-limit isoscalar induced-pseudoscalar form factor G^A_{2,0}(Q^2) and pseudoscalar form factor G^P_0(Q^2) over finite Q^2 to enable a complete isoscalar contribution to the pion-coupled four-quark condensate.

Background

The calculation requires isoscalar axial and pseudoscalar nucleon form factors in addition to the isovector form factors. The authors restrict their numerical analysis to the isovector channel because continuum-limit information for the relevant isoscalar form factors at finite momentum transfer is incomplete. Although the forward-limit normalizations permit an estimate of the isoscalar terms, that estimate does not determine the integrated finite-Q2 contribution, particularly in the axial channel, where both GA_{1,0}(Q2) and GA_{2,0}(Q2) enter.

References

Our numerical analysis uses only the isovector form factors, since a complete set of continuum-limit isoscalar form factors is not yet available for a finite-$Q2$ analysis. Recent results from Ref. allow $GA_{1,0}$ to be constructed in the continuum limit, whereas corresponding results for $GA_{2,0}$ and $GP_0$ are still lacking.

— One-nucleon intermediate-state contribution to the pion-coupled four-quark condensate in the $N$--$J/ψ$ interaction  (2610.08260 - Yeo et al., 6 Oct 2026) in Section 2.3.3, “Estimates of isoscalar contributions”