Virtual photons in the pion form factors and the energy–momentum tensor

Abstract

We evaluate the vector and scalar form factor of the pion in the presence of virtual photons at next-to-leading order in two-flavor chiral perturbation theory. We also consider the scalar and tensor pion form factors of the energy-momentum tensor. We find that the intrinsic electromagnetic corrections are of the expected size for the vector form factor and very small for the charged pion scalar form factor. Detector resolution independent photon corrections reduce the vector radius by about one percent. The scalar radius of the neutral pion is reduced by two percent by isospin-breaking contributions. We perform infrared regularization by considering electron-positron annihilation into pions and the decay of a light Higgs boson into a pion pair. We discuss the detector resolution dependent contributions to the various form factors and pion radii.

Mass splittings within heavy baryon isospin multiplets in chiral perturbation theory

“…Our main results are given in Eqs. (19)(20)(21)(22)(23)(24) and in Table 2. To arrive at these results, we constructed both the strong and the em Lagrangians at O(p 2 ) which are responsible for the mass corrections.…”

“…[17]. Chiral Lagrangians with virtual photons have been constructed for the study of isospin symmetry breaking phenomena in mesons and baryons with light up and down quarks (see, e.g., [4,5,18,19,20,21,22,23,24,25,26,27,28,29] for an incomplete list). Recently, this technique was used to study the interaction between Goldstone bosons and heavy-light mesons and the isospin breaking decay width of the D * s0 (2317) [30].…”

Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$

“…We use a simplified version of this result: we only retain the correct thresholds of the two channels (π 0 π 0 and π + π − ), but disregard isospin-violating corrections in the polynomials that describe the effectiverange expansion of the scattering partial wave and the lowenergy form factor expansion. In this way, we retain all the nonanalytic effects due to the pion mass difference that scale like M 2 π − M 2 π 0 near the two-pion thresholds, but neglect regular isospin violation in the form factor of order M 2 π − M 2 π 0 , which can be calculated in chiral perturbation theory [79,80]. In this approximation, the phase of F 0 (s) is given by…”

Isospin Symmetry Breaking within the HLS Model: A Full (rho, omega, phi) Mixing Scheme

“…in most phenomenological studies, by releasing the analyticity assumption ; in 7 We still skip in this Section mixing with the φ meson. 8 We recall that sin iα = i sinh α and cos iα = cosh α.…”

“…This is because the scale is set not by (m u − m d )/(m u + m d ) but (m u − m d )/m s [1]. Interest in the contribution of isospin violation is therefore usually confined to systems where both theoretical (or at least phenomenological) and experimental precision are high; for example a µ [2], CP violation in B → 2P (where P ≡ pseudoscalars) and other CKMmatrix systems [3][4][5][6], the pion form-factor [7,8] and various aspects of charge symmetry violation in the NN system [9].…”