1. Muon electric dipole moment induced by unparticles

2. VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010 1.Unparticle Physics (UP) overview 2.Moun g-2 3.Unparticle contributions to a f 4.Constraints on UP parameters from muon g-2 5.Fermion electric dipole moment (EDM) 6.Unparticle contributions to EDM 7.Mathematical structure of UP parameters 8.Conclusions

3. SU(2) L U(1) Y BZ G Λ <v Λ =v Λ=ΛuΛ=Λu Λ = Λ planck The standard model does not have the property of scale invariance… But there could be a sector of the theory, as yet unseem, that is exactly scale invariant and very weakly interacting with the rest of the standard model… unparticles. Unparticle Physics ★ ★ H. Georgi, Phys. Rev. Lett. 98, 221601 (2007) E.W. ΛMUΛMU Scheme ΛΛuΛΛu renormalizable couplings  dimensional transmutation nonrenormalizable couplings VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

4. The standard model does not have the property of scale invariance… But there could be a sector of the theory, as yet unseem, that is exactly scale invariant and very weakly interacting with the rest of the standard model… unparticles. Unparticle Physics ★ Scalar-pseudoscalar Vector-Axial Tensor where Kingman Cheung, Wai-Yee Keung and Tzu-Chiang Yuan, Phys. Rev. D.76 055003 (2007) VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

5. The E821 Muon (g-2), Brookhaven National Laboratory, Phys. Rev. Lett. 92 (2004) 161802 The relevant interaction Lagrangian of the fermion Magnetic Dipole Moment al is given by The anomalous magnetic moment of a fermion l is related to the photon-lepton vertex function Γ μ as follows: It is well known that between the experimental value and the SM prediction there is a small discrepancy VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

6. New contributions to a f from unparticles are generated at the one- loop level. The results are Scalar-pseudoscalar Vector-Axial   Andi Hektor, Yuji Kajiyama and Kristjan Kannike, Phys. Rev. D78 053008 (2008) where r fi =m f 2 /m i 2 and the functions F are given by: from the chirality structure, η=+1(-1) for scalar and vector (pseudo scalar and axial) unparticles. VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

7. From the total contributions to a f from unparticles we obtain a constraint on the λ μi k parameters given by a quadric equation of twelve dimensions 207.512 stands for the systematic and experimental errors of Δa μ with 2 standard deviations. Numerical evaluation shows that α μe k i s undefined in the interval where d U guarantees unitarity, Also; We can however project the quadric surface by requiring that λ μe k =0, thus the resulting constraint equation represents an eight dimensional hyperboloid hiper volume with parametric equations (Ω 6 cosh ϑ, Ω 2 sinh ϑ ), where: Ω 6 and Ω 2 represent a six and two dimensional ellipses. VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

8. From the total contributions to a f from unparticles 1 TeV 10 TeV 100 TeV 1000 TeV ✜ Kingman Cheung, Wai-Yee Keung and Tzu-Chiang Yuan, Phys. Rev. D.76 055003 (2007) dudu Λ u (TeV) 2.01.35 1.84 1.623 1.4660 Limit on Λ u with λ μμ v =1 from monophoton production data of σ ( e + e -  γ + X ) ≈0.2 pb at LEP2(95% C.L.) ✜ VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

9. α μμ s α μτ s α μμ v α μτ v α μμ a VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

10. but, what is the allowed interval for the hyperbolic angle ? VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

11. The presence of a non-zero d f would mean that there are both parity and time-reversal violation. In a world with perfect CPT symmetry, a search for d f would also be a direct test of CP symmetry  J. Bailey et al., J. Phys. G 4, 345 (1978) The dipole magnetic moment of a fermion l is related to the T violating form factor F 3 (q 2 ) term of the photon-lepton vertex function Γ μ as follows: The experimental limit on the electric dipole moments [ e-cm ] with 95% C.L. and the theoretical standard model values are: VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

12. The presence of a non-zero d f would therefore signify the existence of both parity and time-reversal violation. In a world with perfect CPT symmetry, a search for d f would also be a direct test of CP symmetry  J. Bailey et al., J. Phys. G 4, 345 (1978) Unparticle contribution to EDM is induced by interference of scalar (vector) and pseudo scalar (axial) operators: where VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

13.  J. Bailey et al., J. Phys. G 4, 345 (1978) we used the parameterization of the hyperboloid (Ω 6 cosh ϑ, Ω 2 sinh ϑ ) to correctly use the phenomenological bound of effective parameters discussed above, and we found: our prediction is well above the experimental bound! VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

14.  J. Bailey et al., J. Phys. G 4, 345 (1978) ✗ ✗ ✔ we will study another particular case If ? all effective parameters are real numbers VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

15. There are other possibilities for the hyperbolic angle: and λ μi p small and vanishing vector-axial contribution to EDM and λ μi p small and nonvanishing vector-axial contribution to EDM andAll effective parameters about the same order of magnitude VIII Latin American Symposium on High Energy Physics, Valparaíso, Chile, 6-12 December 2010

16. VIII Latin American Symposium on Higth Energy Physics, Valparaíso, Chile, 6-12 December 2010 1.We find phenomenological bounds for some effective parameters ( λ μi k ) on framework of Unparticles Physics Model. 2.The muon electric dipole moment( d μ ) induced by unparticles operators show a complex structure of the coupling parameters. Therefore it reveals an new phases of CP violation. 3.Since the muon electric dipole moment depends very much on the different phases of the effective parameters, it is more sensitive than the standard model approach.