Lepton Flavour Violation at the ILC
aa r X i v : . [ h e p - ph ] S e p Lepton Flavour Violation at the ILC ∗ P.M. Ferreira † , R.B. Guedes ‡ and R. Santos , § Centro de F´ısica Te´orica e Computacional, Faculdade de Ciˆencias, Universidadede Lisboa, Avenida Professor Gama Pinto, 2, 1649-003 Lisboa, Portugal Department of Physics, Royal Holloway, University of London, Egham, SurreyTW20 0EX United KingdomWe explore the possibility of detecting lepton flavour violation, now a wellestablished experimental fact, at the International Linear Collider. Usinga model independent approach we conclude that, given all experimentalconstraints available, there is still room to detect lepton flavour violationat the ILC.PACS numbers: 12.60.-i,11.30.Hv,14.60.-z
This work is based on
Lepton flavour violating processes at the InternationalLinear Collider (please see paper for the complete list of references).The effective operator formalism is based on the assumption that the Stan-dard Model (SM) is the low energy limit of a more general theory. Sucha theory would be valid at very high energies but, at a lower energy scaleΛ, we would only perceive its effects through a set of effective operatorsof dimensions higher than four. The effective operators that are importantfor our studies fall into two categories: those that generate lepton flavourviolating (LFV) vertices of the form Z l h l l and γ l h l l , where l h and l l area heavy lepton and a light lepton, respectively, and four-fermion operators,involving only leptonic spinors. The effect of these LFV operators can beseen in two types of decays: a heavy lepton decaying into three light ones, l h → l l l and a Z boson decaying to two different leptons, Z → l h l l . Ex-perimentally, the upper bound on the branching ratio for τ decaying intothree light leptons is of the order of 10 − and of order 10 − for the µ. Thebounds on the Z branching ratios are of the order 10 − for Z → e l h and10 − for Z → τ µ. We concentrate on the most straightforward processeswhere LFV could be detected at the ILC: e + e − → µ − e + , e + e − → τ − e + , ∗ Presented at XXVII PHYSICS IN COLLISION - Annecy, France, 26 - 29 June 2007. † [email protected] ‡ [email protected] § [email protected] P. M. Ferreira, R. B. Guedes and R. Santos, Phys. Rev. D (2007) 055015. (1) and e + e − → τ − µ + , as well as the respective charge conjugates.We computed the cross sections and the decay widths for these LFV pro-cesses and used the experimental constraints to limit the possible range ofthe anomalous couplings. The range of values chosen for each of the cou-pling constants was 10 − ≤ | a/ Λ | ≤ − T eV − , where a stands for ageneric coupling and Λ is in TeV. For a ≈ Z alike), and discard thosecombinations of values for which the several branching ratios we computedearlier are larger than the corresponding experimental upper bounds. Thefollowing figure shows us the example of the number of events occurringat the ILC for the process e + e − → τ − e + in terms of the branching ratio BR ( τ → lll ) . −9 −8 −7 BR( τ → l l l) N u m be r o f e v en t s f o r e + e − → τ − µ + Fig. 1. Number of expected events with a center-of-mass energy of 1 TeV and atotal luminosity of − . We have considered all planed future experiments on LFV. In the foresee-able future, the constraints on the four-fermion τ couplings could decreaseone order of magnitude. Therefore, even in this case, the maximum numberof events at the ILC would be ∼ e + e − → τ + e − → µ + e − ν µ ¯ ν τ we have evaluated the two main backgrounds, e + e − → µ + e − ν µ ¯ ν e and e + e − → τ + τ − → µ + e − ν µ ¯ ν e ν ττ
Lepton flavour violating processes at the InternationalLinear Collider (please see paper for the complete list of references).The effective operator formalism is based on the assumption that the Stan-dard Model (SM) is the low energy limit of a more general theory. Sucha theory would be valid at very high energies but, at a lower energy scaleΛ, we would only perceive its effects through a set of effective operatorsof dimensions higher than four. The effective operators that are importantfor our studies fall into two categories: those that generate lepton flavourviolating (LFV) vertices of the form Z l h l l and γ l h l l , where l h and l l area heavy lepton and a light lepton, respectively, and four-fermion operators,involving only leptonic spinors. The effect of these LFV operators can beseen in two types of decays: a heavy lepton decaying into three light ones, l h → l l l and a Z boson decaying to two different leptons, Z → l h l l . Ex-perimentally, the upper bound on the branching ratio for τ decaying intothree light leptons is of the order of 10 − and of order 10 − for the µ. Thebounds on the Z branching ratios are of the order 10 − for Z → e l h and10 − for Z → τ µ. We concentrate on the most straightforward processeswhere LFV could be detected at the ILC: e + e − → µ − e + , e + e − → τ − e + , ∗ Presented at XXVII PHYSICS IN COLLISION - Annecy, France, 26 - 29 June 2007. † [email protected] ‡ [email protected] § [email protected] P. M. Ferreira, R. B. Guedes and R. Santos, Phys. Rev. D (2007) 055015. (1) and e + e − → τ − µ + , as well as the respective charge conjugates.We computed the cross sections and the decay widths for these LFV pro-cesses and used the experimental constraints to limit the possible range ofthe anomalous couplings. The range of values chosen for each of the cou-pling constants was 10 − ≤ | a/ Λ | ≤ − T eV − , where a stands for ageneric coupling and Λ is in TeV. For a ≈ Z alike), and discard thosecombinations of values for which the several branching ratios we computedearlier are larger than the corresponding experimental upper bounds. Thefollowing figure shows us the example of the number of events occurringat the ILC for the process e + e − → τ − e + in terms of the branching ratio BR ( τ → lll ) . −9 −8 −7 BR( τ → l l l) N u m be r o f e v en t s f o r e + e − → τ − µ + Fig. 1. Number of expected events with a center-of-mass energy of 1 TeV and atotal luminosity of − . We have considered all planed future experiments on LFV. In the foresee-able future, the constraints on the four-fermion τ couplings could decreaseone order of magnitude. Therefore, even in this case, the maximum numberof events at the ILC would be ∼ e + e − → τ + e − → µ + e − ν µ ¯ ν τ we have evaluated the two main backgrounds, e + e − → µ + e − ν µ ¯ ν e and e + e − → τ + τ − → µ + e − ν µ ¯ ν e ν ττ ¯ ν ττ