Abstract
We analyze the radiative pion decay π+→e+νeγ within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors FV and FA at q2=0 — where q2 is the e+νe squared invariant mass — and the slope a of FV(q2) at q2→0. The calculations are carried out considering different nonlocal form factors, in particular those taken from lattice QCD evaluations, showing a reasonable agreement with the corresponding experimental data. The comparison of our results with those obtained in the (local) NJL model and the relation of FV and a with the form factor in π0→γ⁎γ decays are discussed.
Highlights
We analyze the radiative pion decay π + → e+νeγ within nonlocal chiral quark models that include wave function renormalization
According to the standard description, the corresponding decay amplitude consists of the inner bremsstrahlung (IB) and structure-dependent (SD) terms
Since π + → e+νe is helicity suppressed, same happens to the IB terms that contribute to its radiative counterpart, and, π + → e+νeγ turns out to be an appropriate channel to uncover the nonperturbative SD amplitude
Summary
We analyze the radiative pion decay π + → e+νeγ within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors F V and. Gómez Dumm et al / Physics Letters B 698 (2011) 236–242 nonlocality arises naturally in several well-established approaches to low energy quark dynamics This is e.g. the case of the instanton liquid model [13] and the Schwinger–Dyson resummation techniques [14], and lattice QCD calculations [15,16,17] indicate that quark interactions should act over a certain range in momentum space. Replacing in the bosonized effective action and expanding in powers of meson fluctuations we get
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