Model-independent sensitivity estimates for the electromagnetic dipole moments of the $\tau$-lepton at the CLIC

We establish model-independent sensitivity on the anomalous magnetic and electric dipole moments of the $\tau$-lepton using the two-photon processes $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$ and $\gamma \gamma \to {\tau }^{+}{\tau }^{-}\gamma$. We use $\mathcal{L}=10$, 50, 100, 300, 500, 1000, 1500, 2000, $3000{\mathrm{fb}}^{-1}$ data collected with the future $e^{+}{e}^{-}$ linear collider such as the CLIC at $\sqrt{s}=380$, 1500, 3000 GeV, and we consider systematic uncertainties of ${\delta }_{\mathrm{sys}}=0\%$, 3%, 5%. We obtain sensitivity estimates at 95% C.L. on the anomalous dipole moments to the $\tau$-lepton $-0.00015\le {\tilde{a}}_{\tau }\le 0.00017$ and $|{\tilde{d}}_{\tau }(ecm)|=9.040\times {10}^{-19}$ that may be achievable in future experiments. Our results show that the processes under consideration are very promising for probing the dipole moments of the $\tau$-lepton at the future $e^{+}{e}^{-}$ linear collider at the $\gamma \gamma$ mode.

Figure 1

The Feynman diagrams for the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$.

Figure 2

The Feynman diagrams for the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}\gamma$.

Figure 3

The total cross sections of the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$ as a function of $\kappa$ for center-of-mass energies of $\sqrt{s}=380$, 1500, 3000 GeV.

Figure 4

Same as in Fig. 3, but for $\tilde{\kappa }$.

Figure 5

The total cross sections of the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$ as a function of $\kappa$ and $\tilde{\kappa }$ for center-of-mass energy of $\sqrt{s}=380\mathrm{GeV}$.

Figure 6

Same as in Fig. 5, but for $\sqrt{s}=1500\mathrm{GeV}$.

Figure 7

Same as in Fig. 5, but for $\sqrt{s}=3000\mathrm{GeV}$.

Figure 8

Sensitivity contours at the 95% C.L. in the ($\kappa -\tilde{\kappa }$) plane for the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$ with the $\mathcal{L}=10$, 100, $500{\mathrm{fb}}^{-1}$ and for center-of-mass energy of $\sqrt{s}=380\mathrm{GeV}$.

Figure 9

Same as in Fig. 8, but for $\mathcal{L}=100$, 500, $1500{\mathrm{fb}}^{-1}$ and for center-of-mass energy of $\sqrt{s}=1500\mathrm{GeV}$.

Figure 10

Same as in Fig. 8, but for $\mathcal{L}=100$, 500, $3000{\mathrm{fb}}^{-1}$ and for center-of-mass energy of $\sqrt{s}=3000\mathrm{GeV}$.

Figure 11

Comparison of precisions on ${\tilde{a}}_{\tau }$ in the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$ expected at the CLIC. We assume luminosities as follows: Top panel: $\mathcal{L}=100$, 1000, $3000{\mathrm{fb}}^{-1}$ and $\sqrt{s}=3000\mathrm{GeV}$. Central panel: $\mathcal{L}=100$, 500, $1500{\mathrm{fb}}^{-1}$ and $\sqrt{s}=1500\mathrm{GeV}$. Bottom panel: $\mathcal{L}=10$, 100, $500{\mathrm{fb}}^{-1}$ and $\sqrt{s}=380\mathrm{GeV}$.

Figure 12

Same as in Fig. 11, but as follows: Top panel: ${\delta }_{\mathrm{sys}}=0\%$, 3%, 5% with $\mathcal{L}=3000{\mathrm{fb}}^{-1}$ and $\sqrt{s}=3000\mathrm{GeV}$. Central panel: ${\delta }_{\mathrm{sys}}=0\%$, 3%, 5% with $\mathcal{L}=1500{\mathrm{fb}}^{-1}$ and $\sqrt{s}=1500\mathrm{GeV}$. Bottom panel: ${\delta }_{\mathrm{sys}}=0\%$, 3%, 5% with $\mathcal{L}=500{\mathrm{fb}}^{-1}$ and $\sqrt{s}=380\mathrm{GeV}$.

Figure 13

Same as in Fig. 11, but for ${\tilde{d}}_{\tau }$.

Figure 14

Same as in Fig. 12, but for ${\tilde{d}}_{\tau }$.

Figure 15

The total cross sections of the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}\gamma$ as a function of $\kappa$ for center-of-mass energies of $\sqrt{s}=380$, 1500, 3000 GeV.

Figure 16

Same as in Fig. 15, but for $\tilde{\kappa }$.

Figure 17

The total cross sections of the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}\gamma$ as a function of $\kappa$ and $\tilde{\kappa }$ for center-of-mass energy of $\sqrt{s}=380\mathrm{GeV}$.

Figure 18

Same as in Fig. 17, but for $\sqrt{s}=1500\mathrm{GeV}$.

Figure 19

Same as in Fig. 17, but for $\sqrt{s}=3000\mathrm{GeV}$.

Figure 20

Sensitivity contours at the 95% C.L. in the ($\kappa -\tilde{\kappa }$) plane for the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}\gamma$ with the $\mathcal{L}=10$, 100, $500{\mathrm{fb}}^{-1}$ and for center-of-mass energy of $\sqrt{s}=380\mathrm{GeV}$.

Figure 21

Same as in Fig. 20, but for $\mathcal{L}=100$, 500, $1500{\mathrm{fb}}^{-1}$ and for center-of-mass energy of $\sqrt{s}=1500\mathrm{GeV}$.

Figure 22

Same as in Fig. 20, but for $\mathcal{L}=100$, 500, $3000{\mathrm{fb}}^{-1}$ and for center-of-mass energy of $\sqrt{s}=3000\mathrm{GeV}$.

Figure 23

Comparison of precisions on ${\tilde{a}}_{\tau }$ in the process $\gamma \gamma \to {\tau }^{+}{\tau }^{-}\gamma$ expected at the CLIC. We assume luminosities of the following: Top panel: $\mathcal{L}=100$, 1000, $3000{\mathrm{fb}}^{-1}$ and $\sqrt{s}=3000\mathrm{GeV}$. Central panel: $\mathcal{L}=100$, 500, $1500{\mathrm{fb}}^{-1}$ and $\sqrt{s}=1500\mathrm{GeV}$. Bottom panel: $\mathcal{L}=10$, 100, $500{\mathrm{fb}}^{-1}$ and $\sqrt{s}=380\mathrm{GeV}$.

Figure 24

Same as in Fig. 23, but for the following: Top panel: ${\delta }_{\mathrm{sys}}=0\%$, 3%, 5% with $\mathcal{L}=3000{\mathrm{fb}}^{-1}$ and $\sqrt{s}=3000\mathrm{GeV}$. Central panel: ${\delta }_{\mathrm{sys}}=0\%$, 3%, 5% with $\mathcal{L}=1500{\mathrm{fb}}^{-1}$ and $\sqrt{s}=1500\mathrm{GeV}$. Bottom panel: ${\delta }_{\mathrm{sys}}=0\%$, 3%, 5% with $\mathcal{L}=500{\mathrm{fb}}^{-1}$ and $\sqrt{s}=380\mathrm{GeV}$.

Figure 25

Same as in Fig. 23, but for ${\tilde{d}}_{\tau }$.

Figure 26

Same as in Fig. 24, but for ${\tilde{d}}_{\tau }$.