Unparticle physics at the photon collider

Recently, a conceptually new physics beyond the standard model (SM), unparticle, has been proposed, where a hidden conformal sector is coupled to the SM sector through higher dimensional operators. In this setup, we investigate unparticle physics at the photon collider, in particular, unparticle effects on the $\gamma \gamma \to \gamma \gamma$ process. Since this process occurs at loop level in the SM, the unparticle effects can be significant even if the cutoff scale is very high. In fact, we find that the unparticle effects cause sizable deviations from the SM results. The scaling dimension of the unparticle $d_{\mathcal{U}}$ reflects the dependence of the cross section on the final state photon invariant mass, so that precision measurements of this dependence may reveal the scaling dimension of the unparticle.

Figure 1

The total cross section of the scattering, $\gamma \gamma \to \gamma \gamma$, for the standard model process, purely unparticle contribution, and the combined result as a function of the photon energy $\sqrt{\widehat{s}}$. Here we have taken the limit $d_{\mathcal{U}}\to 1$ and the cutoff scale to be $\Lambda =5\mathrm{TeV}$. In the integration with respect to the scattering angle, we have imposed a cut as $30°<\theta <150°$. Two possible combinations of the initial photon helicities $({\lambda }_1{\lambda }_2)=(++)$, $(+-)$ are taken into account in this analysis, and the results are shown by the different thickness of each line.

Figure 2

The angular distribution for the $\gamma \gamma \to \gamma \gamma$ process with the initial photon energy $\sqrt{\widehat{s}}=500\mathrm{GeV}$ and the cutoff scale $\Lambda =5\mathrm{TeV}$, in the limit of $d_{\mathcal{U}}\to 1$.

Figure 3

The total cross section of the $\gamma \gamma \to \gamma \gamma$ process for the standard model contribution, the pure unparticle contribution, and the combined result as a function of the scaling dimension, $d_{\mathcal{U}}$, for the initial photon energy $\sqrt{\widehat{s}}=500\mathrm{GeV}$ and $\Lambda =5\mathrm{TeV}$. We have again imposed a cut for the scattering angle as $30°<\theta <150°$ in the integration.

Figure 4

The convoluted cross section of the $\gamma \gamma \to \gamma \gamma$ process in the case of unpolarized beams. The figure shows for the standard model case, pure unparticle case, and the combined result as a function of the incident $e^{+}{e}^{-}$ collider energy $\sqrt{s}$. The top figure shows each contribution for $({\lambda }_1,{\lambda }_2)=(\pm \pm )$ and $(\pm \mp )$. The bottom figure shows the sum of both contributions.

Figure 5

The angular distribution for the process, $\gamma \gamma \to \gamma \gamma$, including the unparticle in the intermediate state. In this figure, we have fixed the incident $e^{+}{e}^{-}$ beam energy as $\sqrt{s}=500\mathrm{GeV}$. The top figure shows each contribution for $({\lambda }_1,{\lambda }_2)=(\pm \pm )$ and $(\pm \mp )$. The bottom figure shows the sum of both contributions.

Figure 6

The total cross section of the $\gamma \gamma \to \gamma \gamma$ process for the standard model contribution, pure unparticle contribution, and the combined result as a function of the scaling dimension, $d_{\mathcal{U}}$. We have fixed the incident $e^{+}{e}^{-}$ beam energy as $\sqrt{s}=500\mathrm{GeV}$ and $\Lambda =5\mathrm{TeV}$. A cut for the scattering angle is taken to be $30°<\theta <150°$. The top figure shows each contribution for $({\lambda }_1,{\lambda }_2)=(\pm \pm )$ and $(\pm \mp )$. The bottom figure shows the sum of both contributions.

Figure 7

The differential cross section $d\sigma /d{M}_{\gamma \gamma }$ for the process $\gamma \gamma \to \gamma \gamma$ ($30°<\theta <150°$) as a function of a final state photon invariant mass $M_{\gamma \gamma }$. The energy is fixed to $\sqrt{s}=500\mathrm{GeV}$ and $\Lambda =5\mathrm{TeV}$. Here we show each contribution from different incident photon beam helicity combinations separately The top figure is for $({\lambda }_1,{\lambda }_2)=(\pm \pm )$ and the bottom is for $(\pm \mp )$. Each curve corresponds to $d_{\mathcal{U}}=1$, 1.05, 1.1, 1.2, 1.3.

Figure 8

The total cross section for the case of unpolarized beams. Figure 8a shows the same figure as Fig. 7 but the initial helicities are summed up to show the unpolarized cross sections. Figure 8b shows the ratio of the signal cross section to the SM cross section (${\sigma }_{\mathcal{U}+\mathrm{SM}}/{\sigma }_{\mathrm{SM}}$) as a function of a lower energy cut on the final state photon invariant mass $M_{\gamma \gamma }^{\mathrm{cut}}$.

Figure 9

The same figure as Fig. 7, but for the case of $\sqrt{s}=1\mathrm{TeV}$.

Figure 10

The same figure as Fig. 8, but for the case of $\sqrt{s}=1\mathrm{TeV}$.

Figure 11

The same figure as Fig. 8, but the beam polarizations are chosen as $(P_e,P_{\ell },P_e^{\prime },P_{\ell }^{\prime })=(\pm \pm \pm \pm )$.

Figure 12

The same figure as Fig. 8, but the beam polarizations are chosen as $(P_e,P_{\ell },P_e^{\prime },P_{\ell }^{\prime })=(\pm \pm \mp \mp )$.

Figure 13

The same figure as Fig. 8, but the beam polarizations are chosen as $(P_e,P_{\ell },P_e^{\prime },P_{\ell }^{\prime })=(\pm \pm \mp \pm )$ or $(\mp \pm \pm \pm )$.

Figure 14

The same figure as Fig. 8, but the beam polarizations are chosen as $(P_e,P_{\ell },P_e^{\prime },P_{\ell }^{\prime })=(\pm \mp \mp \pm )$.

Figure 15

The same figure as Fig. 8, but the beam polarizations are chosen as $(P_e,P_{\ell },P_e^{\prime },P_{\ell }^{\prime })=(\pm \pm \pm \mp )$ or $(\pm \mp \pm \pm )$.

Figure 16

The same figure as Fig. 8, but the beam polarizations are chosen as $(P_e,P_{\ell },P_e^{\prime },P_{\ell }^{\prime })=(\pm \mp \pm \mp )$.