Quarkonia decays into two photons induced by space-time noncommutativity

In this article we propose standard model strictly forbidden decay modes, quarkonia ($\overline{Q}{Q}_{1^{--}}=J/\psi ,{\rm Y}$) decays into two photons, as a possible signature of space-time noncommutativity. An experimental discovery of $J/\psi \to \gamma \gamma$ and/or ${\rm Y}\to \gamma \gamma$ processes would certainly indicate a violation of the Landau-Pomeranchuk-Yang theorem and a definitive appearance of new physics.

Figure 1

Contributions to the $\overline{Q}{Q}_{1^{--}}\to \gamma \gamma$ amplitude in the mNCSM, up to the first order in $\theta$.

Figure 2

Additional contributions to the $\overline{Q}{Q}_{1^{--}}\to \gamma \gamma$ amplitude in the nmNCSM, up to the first order in $\theta$.

Figure 3

The allowed region for the $K_{\gamma \gamma \gamma }$ and $K_{Z\gamma \gamma }$ coupling constants [14].

Figure 4

Branching ratio $B{R}^{\mathrm{nmNCSM}}({\rm Y}\to \gamma \gamma )$ as a function of $K_{\gamma \gamma \gamma }$ and $K_{Z\gamma \gamma }$ coupling constants, at the scale of noncommutativity ${\Lambda }_{\mathrm{NC}}=1$ TeV. The horizontal plane at the value of $4.7\times {10}^{-12}$ indicates the $B{R}^{\mathrm{mNCSM}}({\rm Y}\to \gamma \gamma )$, which one obtains by setting $K_{\gamma \gamma \gamma }=K_{Z\gamma \gamma }=0$ in (12).

Figure 5

Branching ratio $B{R}^{\mathrm{nmNCSM}}(J/\psi \to \gamma \gamma )$ as a function of $K_{\gamma \gamma \gamma }$ and $K_{Z\gamma \gamma }$ coupling constants, at the scale of noncommutativity ${\Lambda }_{\mathrm{NC}}=1$ TeV. The horizontal plane at the value of $5.1\times {10}^{-13}$ indicates the $B{R}^{\mathrm{mNCSM}}(J/\psi \to \gamma \gamma )$, which one obtains by setting $K_{\gamma \gamma \gamma }=K_{Z\gamma \gamma }=0$ in (12).