In-medium modification and decay asymmetry of ω mesons in cold nuclear matter

We discuss an asymmetry of the decay $\omega \to e^{+}{e}^{-}$ in nuclear matter with respect to the electron and positron energies. This asymmetry is sensitive to the properties of the ω meson self-energy and, in particular, it has a nontrivial dependence on the ω energy and momentum. Therefore, this asymmetry may serve as a powerful tool in studying the properties of the ω meson in the nuclear medium.

Figure 1

Geometry of the $\omega \to e^{+}{e}^{-}$ decay. (a) and (b) correspond to cases where $\alpha =\pi /2$ (i.e., $\xi =0$) and $\alpha =0$ ($\mathrm{i}.\mathrm{e}.,\hspace{1em}\xi =1$), respectively, while (c) depicts an intermediate case $0<\alpha <\pi /2$ (i.e., $0<|\xi ⩽1$).

Figure 2

(a) Tree-level diagram for the Compton $\omega N$ scattering through nucleon resonance excitations. (b) Schematic presentation of the imaginary part of the amplitude evaluated by cutting the intermediate baryon ($B$) and meson ($M$) lines.

Figure 3

The imaginary part of the ω meson self-energy at $\mathbf{q}=0$ (a) and 0.75 GeV/$c$ (b). The thin solid and dashed curves in (b) correspond to the transverse and longitudinal components, respectively. The thick solid curves correspond to the total contributions. The vacuum contribution is depicted by dot-dashed curves.

Figure 4

The real part of the ω meson self-energy. Notation as in Fig. 3.

Figure 5

The functions $W^{T,L}$ for different values $\left|\mathbf{q}\right|$. The solid (dashed) curve depicts $W^T$ ($W^L$). The vacuum case is shown by dot-dashed curve.

Figure 6

(a) The ω meson decay asymmetry for different values $\left|\mathbf{q}\right|$. (b) The same as in (a) but at $M~M_{\omega }$.

Figure 7

Results for the resonance model dominated by the $P_{11}(1710)$ resonance. (a) and (b) are for the imaginary and real parts of the ω meson self-energy, respectively, while (c) exhibits the decay asymmetry.

Figure 8

The ω meson decay asymmetry for models A and B depicted by solid and dashed curves. (a) dependence on $M$ at $\left|\mathbf{q}\right|=0.75$ GeV/$c$, (b) dependence on $\left|\mathbf{q}\right|$ at $M=0.7$ GeV.

Figure 9

The ω meson self-energy in vacuum.