Asymmetry observables ine+e−→π+π−γin theϕregion within a chiral unitar

Abstract

We make a theoretical study of the charge and forward-backward pion asymmetries in the e + e − → π + π − γ process on and off the φ resonance energy. These observables are rather sensitive to the inner details of the theoretical models to describe the reaction. In addition to the standard implementation of the initial state radiation (ISR) and the Bremsstrahlung contribution to the final state radiation (FSR), we use the techniques of the chiral unitary approach to evaluate the contribution from the mechanisms of φ decay into π + π − γ. This contribution involves the implementation of final state interaction from direct chiral loops, the exchange of vector and axial-vector resonances and the final state interaction through the consideration of the meson-meson unitarized amplitudes, which where found important in a previous work describing the φ → ππγ. We find a good reproduction of the experimental data from KLOE for the forward-backward asymmetry, both at the φ peak and away from it. We also make predictions for the angular distributions of the charge asymmetry and show that this observable is very sensitive to the chiral loops involved in φ radiative decay.PACS numbers:

J/ψNinteractions revisited andΛb0→Xiao1 2017Phys. Rev. D15090View full textAdd to dashboardCite

“…[4], Ref. [78] shows that this tree-level contribution is nontrivial which is the same weight as the K − p amplitude as found in Ref. [41].…”

“…4(a), since there would be the contributions from the possible contact term of the tree level in the p wave (see the term of 1) as done in Ref. [78]. Thus, using J ¼ 1=2 sector scattering amplitudes, we obtain the results as shown in Fig.…”

“…Since we do not consider the contributions from the K − p amplitude that was taken into account in Ref. [78] for the Λ 0 b → J=ψK − p decays and in Ref. [38] for the Λ 0 b → J=ψπ − p decays, we emphasize the contributions from the J=ψp amplitude and do not consider this tree-level contribution in the J ¼ 1=2 case.…”

“…But, for the case of J ¼ 3=2, which is different from the one of J ¼ 1=2 above, since J P of Λ 0 b is 1=2 − , the kaon (or pion) should be in the p wave when the J=ψp final state system is J P ¼ 3=2 − in the s wave [79] in the Λ 0 b → J=ψK − ðπ − Þp decays; refer to the appendix of Refs. [78,80] for more details. Therefore, in this case, there is an extra momentum factor for the kaon (or pion) in the p wave in the amplitude of Eq.…”

Axial resonances a 1(1260), b 1(1235) and their decays from the lattice

“…Our result at m π = 266 MeV is close to a ρπ l=0 (m phys π ) ≈ 0.37 fm obtained from Unitarized Effective Field Theory [42], while the corresponding experimental value is not known. However the exact position of the central value for the ground state E 1 in figure 1 with respect to the threshold m ω + m π shows a slight disagreement with the expectation.…”