Sensitivity on the electromagnetic dipole moments of the tau-lepton at the CLIC

In this paper we established model independent bounds on the anomalous magnetic and electric dipole moments of the tau-lepton using the process γγ→ τ+τ−. We use data collected with the future e+e− linear collider such as the CLIC at p s = 380, 1500, 3000 GeV, and we consider systematic uncertainties of δsys = 0%, 3%, 5%. The theory predictions are a very good prospect for probing the dipole moments of the tau-lepton at the future e+e− linear collider at the γγ mode. Copyright M. A. Hernández-Ruíz et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 19-11-2018 Accepted 10-01-2019 Published 22-02-2019 Check for updates doi:10.21468/SciPostPhysProc.1.045


Introduction
In this work, using γγ → τ + τ − reaction we establish model independent sensitivity estimates on the dipole moments a τ and d τ of the tau-lepton. The high center-of-mass energies what has been proposed for the Compact Linear Collider (CLIC) make it an appropriate machine to probe the anomalous magnetic (MM) and electric dipole (EDM) moments which are more sensitive to the high energy and high luminosity of the collider. The CLIC is a proposed future e + e − collider, designed to fulfill e + e − collision at center-of-mass energies of 0.35 TeV, 1.4 TeV and 3 TeV planned to be constructed with a three main stage research region. This enables the investigation of de γγ and eγ interactions by converting the original e − or e + beam into a photon beam through the Compton back-scattering mechanism.
This paper is organized as follows: In Section 2, we present the total cross section and the electromagnetic dipole moments of the tau-lepton for the γγ → τ + τ − reaction. In section 3, the results. In section 4, we give our conclusion.
2 The process γγ → τ + τ − To calculate the γγ → τ + τ − total cross section, the corresponding Feynman diagrams are given in Fig. 1. We determine sensitivity estimates on the electromagnetic dipole moments of the tau-lepton a τ and d τ via the two-photon process [6]. The future Collider CLIC can produce very hard photons at high luminosity in Compton backscattering of laser light off high energy e + e − beams. The electromagnetic current between on-shell tau-lepton and the photon is given by [7,8,9,10] where the q 2 -dependent form factors F 1,2,3,4 (q 2 ) have interpretations for q 2 = 0: F 1 (0) = Q τ is the electric charge; F 2 (0) = a τ is anomalous MM and F 3 (0) = 2mτ e d τ with d τ the EDM. F 4 (q 2 ) is the anapole form factor. Here, e is the charge of the electron, m τ is the mass of the tau-lepton, σ αµ = i 2 [γ α , γ µ ] represents the spin 1/2 angular momentum tensor, and q = p ′ − p is the momentum transfer.
The spectrum of Compton backscattered photons to the process γγ → τ + τ − is given by where and E 0 is energy of the incoming laser photon while for E e is initial energy of the electron beam before Compton backscattering, and E γ is the energy of the backscattered photon.
The total cross section can be written as, where E 1 and E 2 is the energy of the particles of the final state. Now, we present the total cross section as a polynomial in powers of F 2 and F 3 for the process γγ → τ + τ − . The formulas have been obtained with the help of the package CALCHEP [11], which can computate the Feynman diagrams, integrate over multiparticle face space and event simulation.
3 Bounds on the a τ and d τ through γγ → τ + τ − at the CLIC We now proceed with our numerical analysis of the total cross section σ N P (γγ → τ + τ − ) = σ N P ( √ s, F 2 , F 3 ), as well as of the electromagnetic dipole moments of the tau-lepton, here the free parameters are √ s, L, F 2 and F 3 . For this purpose, we use the usual formula for the χ 2 function [12,13,14,15]: σ N P ( √ s, F 2 , F 3 ) is the total cross section which includes contributions to the SM and new physics, is the statistical error, δ sys is the systematic error and N SM is the number of signal expected events N SM = L int × BR × σ SM , L int is the integrated CLIC luminosity.

Results
In this section we presented a set of figures, which illustrate our results. The total cross sections σ γγ→τ + τ − ( √ s, F 2 , F 3 ) are calculated as a function of the anomalous couplings F 2 and F 3 with the center-of-mass energies of √ s = 380 GeV, √ s = 1500 GeV and √ s = 3000 GeV. The total cross section shows a strong dependence on the anomalous paramaters F 2 ,  Figure 6; while, Figure 7, and systematic uncertainties of δ sys = 0%, 3%, 5% [1,16].
These results that we get for the process γγ → τ + τ − at the CLIC indicate the improved sensitivity on anomalous electromagnetic dipole moments of tau-lepton with respect to the existing experimental bounds by two orders of magnitude. The best sensitivities obtained on a τ and d τ are −0.00012 ≤ a τ ≤ 0.00014 and |d τ (ecm)| = 7.445 × 10 −19 [6].

Conclusion
In conclusion, we have shown that the γγ → τ + τ − process at the CLIC leads to an improvement in the existing sensitivity estimates on the a τ and d τ . We present an optimistic scenario regarding the potencial precision, energy, and luminosity that may be achievable at the future e + e − colliders. Our results for the process γγ → τ + τ − at the CLIC could improve the sensitivity on anomalous electromagnetic dipole moments of τ -lepton with respect to the existing experimental bounds (see Table I in Ref. [6]) by 2 orders of magnitude. The best sensitivities obtained onã τ andd τ were −0.00015 ≤ã τ ≤ 0.00017 and |d τ | = 9.040 × 10 −19 , respectively, as shown in Tables III-V in Ref. [6]. These are compared with experimental results of earlier studies for a linear collider as published by the DELPHI and BELLE Collaborations [1,4].