Revisiting the pion’s scalar form factor in chiral perturbation theory

Abstract

The quark-connected and the quark-disconnected Wick contractions contributing to the pion's scalar form factor are computed in the two and in the three flavour chiral effective theory at next-to-leading order. While the quark-disconnected contribution to the form factor itself turns out to be power-counting suppressed its contribution to the scalar radius is of the same order of magnitude as the one of the quark-connected contribution. This result underlines that neglecting quark-disconnected contributions in simulations of lattice QCD can cause significant systematic effects. The technique used to derive these predictions can be applied to a large class of observables relevant for QCD-phenomenology.

Size of the pion from full lattice QCD with physicalu,d,sandcquarks

“…Our results are in both qualitative agreement and reasonable quantitative agreement with the picture expected from chiral perturbation theory [17]. There the disconnected contribution to the form factor is predicted to be very small at q 2 = 0, becoming negative at negative q 2 values so that the contribution to the radius is substantial (approximately equal to that of the connected contribution) and positive.…”

“…Set a/fm am l,sea ams,sea amc,sea Ls × Lt n cfg T 1 0.1509 0.00235 0.0647 0.831 32×48 1000 9,12,15 2 0.1212 0.00184 0.0507 0.628 48×64 1000 12,15,18 3 0.0879 0.0012 0.0363 0.432 64×96 223 16,21,26 to include quark-line disconnected contributions. The expectation from chiral perturbation theory [17] is for the disconnected contribution to the form factor at q 2 = 0 to be small but for the impact on the radius as defined in eq. (1) to be substantial.…”

Scalar Form Factor of the Pion in the Kroll-Lee-Zumino Field Theory

“…These results for the radius are determined from, for example, chiral extrapolations to the physical pion mass. Our results for the form factor are also in agreement within less than 10% with a CHPT calculation [17] in the range − 2 = 0 − 0.2 GeV 2 .…”

Review of lattice results concerning low-energy particle physics

“…containing the connected and the disconnected piece) scalar pion form factor has been investigated by means of Chiral Perturbation Theory in [240]. It is expected that the technique used can be applied to a large class of observables relevant in QCD-phenomenology.…”