Radiative corrections to the η(′) Dalitz decays

Abstract

We provide the complete set of radiative corrections to the Dalitz decays η ð0Þ → l þ l − γ beyond the softphoton approximation, i.e., over the whole range of the Dalitz plot and with no restrictions on the energy of a radiative photon. The corrections inevitably depend on the η ð0Þ → γ à γ ðÃÞ transition form factors. For the singly virtual transition form factor appearing, e.g., in the bremsstrahlung correction, recent dispersive calculations are used. For the one-photon-irreducible contribution at the one-loop level (for the doubly virtual form factor), we use a vector-meson-dominance-inspired model while taking into account the η-η 0 mixing.

Radiative corrections to double-Dalitz decays revisited

“…The reason for this is the presence of resonant structures for the electronic modes that require certain care when describing the TFF-especially if dealing with NLO corrections (see Ref. [28] in this respect for the Dalitz decay case). The integrals have been performed numerically using the CUBA library [29] and statistical errors are associated to the MC procedure alone 5 and are in good agreement with Ref.…”

“…30 This produces the following amplitudes appearing in Fig. 9: (26) to (28). At this order, the same counterterm applies to π 0 , η, η 0 and, essentially, to K L as well (see Ref.…”

“…If interested in the operator product expansion (OPE) behavior, one should use a model resembling that of LMD þ V [51] with parameters fixed to the taylor expansion rather than masses. 28 We take the average result from the two parametrizations employed in Ref. [52], the Bergström-Massó-Singer and the D'AmbrosioIsidori-Portolés models, each of them leading to 0.59(2) GeV and 0.62(2) GeV for M K L , respectively.…”

CP violation in η muonic decays

“…As a conclusion, we find that η → µ + µ − decays are the only ones that might show CP -violating signatures for c 2222 edq 10 −2 . 19 We checked that the integral saturates at 2 GeV. The errors for the neutron are shown to illustrate the impact on the scalar form factor model only-dominated by the σπN term.…”

Pseudoscalar pole contribution to the hadronic light-by-light piece of aμ

“…Since some of the parameters could not be constrained by imposing the correct high-energy behavior of the TFF, we fit them to experimental determinations excluding the time-like (q 2 > 0) region of photon four-momenta, since radiative corrections might give large contributions to the TFF in such region [28]. We fitted simultaneously the parameters of our TFF of the π 0 , η and η ′ mesons to the decay widths of the three pseudo-Goldstones given by [7], also to the singly off-shell TFF from CELLO [29] and CELLO [30] for the three pseudo-Goldstones, LEP for η ′ [31], BaBar for π 0 [32], BaBar for η and η ′ [33] and Belle for π 0 [34].…”