arXiv subjects

M. M. Khalifa

Publications and source records attributed to M. M. Khalifa.

4 recordsLinked to original sources

arXiv2020

Gauge-covariant diagonalization of $π$-$a_1$ mixing and the resolution of a low energy theorem

Using a recently proposed gauge covariant diagonalization of $πa_1$-mixing we show that the low energy theorem $F^π=e f_π^2 F^{3π}$ of current algebra, relating the anomalous form factor $F_{γ\to π^+π^0π^-} = F^{3π}$ and the anomalous neutral pion form factor $F_{π^0 \to γγ}=F^π$, is fulfilled in the framework of the Nambu-Jona-Lasinio (NJL) model, solving a long standing problem encountered in the extension including vector and axial-vector mesons. At the heart of the solution is the presence of a $γπ{\bar q} q $ vertex which is absent in the conventional treatment of diagonalization and leads to a deviation from the vector meson dominance (VMD) picture. It contributes to a gauge invariant anomalous tri-axial (AAA) vertex as a pure surface term.

hep-ph↗

arXiv2020

Account for axial vector mesons in the $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays

The rates and spectra of the anomalous $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays are calculated. The approach is based on the effective meson Lagrangian obtained in the Nambu-Jona-Lasinio model with vector and axial-vector mesons by integrating out quark fields. The resulting action is affected by mixing between members of pseudoscalar $J^{PC}=0^{-+}$ and axial-vector $1^{++}$ nonets that violates some low-energy theorems. In this note we point out that a gauge covariant procedure to diagonalize this mixing allows for consistent description of the $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays.

hep-ph↗

arXiv2020

Low-energy theorem for $γ\to 3π$: surface terms against $πa_1$-mixing

We reconsider the contribution due to $πa_1$-mixing to the anomalous $γ\toπ^+π^0π^-$ amplitude from the standpoint of the low-energy theorem $F^π=e f_π^2 F^{3π}$, which relates the electromagnetic form factor $F_{π^0\toγγ}=F^π$ with the form factor $F_{γ\toπ^+π^0π^-}=F^{3π}$ both taken at vanishing momenta of mesons. Our approach is based on a recently proposed covariant diagonalization of $πa_1$-mixing within a standard effective QCD-inspired meson Lagrangian obtained in the framework of the Nambu-Jona-Lasinio model. We show that the two surface terms appearing in the calculation of the anomalous triangle quark diagrams or AVV- and AAA-type amplitudes are uniquely fixed by this theorem. As a result, both form factors $F^π$ and $F^{3π}$ are not affected by the $πa_1$-mixing, but the concept of vector meson dominance (VMD) fails for $γ\toπ^+π^0π^-$.

hep-ph↗

arXiv2018

Electromagnetic interactions of mesons induced by the axial-vector -- pseudoscalar mixings

It is shown that the diagonalization of the axial-vector -- pseudoscalar transitions in the effective meson Lagrangian in presence of electromagnetic interactions leads to a deviation from the vector meson dominance picture which usually arises in the Nambu - Jona-Lasinio model. The essential features of such modification of the theory are studied. Some important examples are considered in detail.

hep-ph↗