Form factors in the radiative pion decay

Abstract

Abstract. We perform an analysis of the form factors that rule the structure-dependent amplitude in the radiative pion decay. The resonance contributions to π → e νeγ decays are computed through the proper construction of the vector and axial-vector form factors by setting the QCD driven asymptotic properties of the three-point Green functions V V P and V AP , and by demanding the smoothing of the form factors at high transfer of momentum. A comparison between theoretical and experimental determinations of the form factors is also carried out. We also consider and evaluate the role played by a non-standard tensor form factor. We conclude that, at present and due to the hadronic incertitudes, the search for New Physics in this process is not feasible.

Study ofτ−→VP−ντin the framework of resonance chiral theory

“…As pointed in [22], M V can be safely estimated by the mass of ρ(770) meson, while for the axialvector resonance, M A is apparently different from the mass of a 1 (1260) and M A = 0.998(49)GeV is obtained using the experiment value for the axial-vector form factor in [22]. Throughout this paper, we will use M V = M ρ and M A = 0.998GeV to evaluate resonance couplings, but masses appearing in the kinematics will take their values from [1].…”

“…Other parameters related to the heavier vector multiplet d m , d M , d s , will be fit later. Due to the inclusion of the new vector multiplet, some of the well established constraints in [15], such as d 1 + 8d 2 , d 3 , will get corrections [22]. However, since the combination of d 1 + 8d 2 is the coefficient of the mass of pseudoGoldstone mesons, the final results should be rather insensitive to the value of this combination.…”

“…However, including another multiplet, though trivial, may affect the well established relations of the couplings for the lowest multiplet [22].…”

“…where K * ′ corresponds to the physical resonance K * (1410) and we have used the following lagrangian, given in [22], to get Eq. (16):…”

The vector form factor at the next-to-leading order in 1/N C : chiral couplings L9(μ) and C88(μ) − C90(μ)

“…[30] from the study of the π → eν e γ decay, which yields M A = (998 ± 49) MeV. We cannot use the information coming from Γ(ρ → 2π) = (149.4 ± 1.0) MeV [29] in order to determine M A , since G V is constrained by eq.…”