The most stringent bounds on the anomalous magnetic and electric dipole
moments of the tau lepton was derived by Escribano and Mass\'{o}[6] from the Z
width at LEP in an effective lagrangian approach to the new physics. In this
paper we point out that the higher dimensional operators introduced by
Escribano and Mass\'{o} not only modify the neutral currents of the tau lepton
to Z gauge boson and the photon, but also induce lepton flavor violation (LFV).
The size of the LFV effect depends crucially on the dynamics of the lepton mass
generation. Assuming the lepton mass matrices in the form of an Fritzsch
ansatz, we point out that the experimental limit on $\mu \to e \gamma$ will
push the anomalous magnetic and electric dipole moments of the tau lepton down
to $10^{-11}$ and $10^{-25} e cm$ respectively.Comment: 6 pages, latex, no figure

Caso

Escribano

Fritzsch

Tao Huang

Xinmin Zhang

Zhi-Hai Lin

Physics Letters B

English

arXiv

Crossref

Bounds on anomalous magnetic and electric moments of tau lepton from LEP and lepton flavor violation

The most stringent bounds on the anomalous magnetic and electric dipole moments of the tau lepton was derived by Escribano and Massó[6] from the Z width at LEP in an effective lagrangian approach to the new physics. In this paper we point out that the higher dimensional operators introduced by Escribano and Massó not only modify the neutral currents of the tau lepton to Z gauge boson and the photon, but also induce lepton flavor violation (LFV). The size of the LFV effect depends crucially on the dynamics of the lepton mass generation. Assuming the lepton mass matrices in the form of an Fritzsch ansatz, we point out that the experimental limit on $\mu \to e \gamma$ will push the anomalous magnetic and electric dipole moments of the tau lepton down to $10^{-11}$ and $10^{-25} e cm$ respectively

Huang, T

Lin, Z H

Zhang, X

CERN Document Server

BIHEP-TH-98-10Bounds On Anomalous Magnetic And Electric MomentsOf Tau Lepton From LEP And Lepton Flavor ViolationTao Huang, Zhi-Hai Lin, and Xinmin ZhangCCAST(World Laboratory) P.O. Box 8730, Beijing 100080, andInstitute of High Energy Physics, Academia Sinica, P.O.Box 918Beijing 100039, ChinaABSTRACTThe most stringent bounds on the anomalous magnetic and electric dipole moments ofthe tau lepton was derived by Escribano and Masso[6] from the Z width at LEP in an eectivelagrangian approach to the new physics. In this paper we point out that the higher dimensionaloperators introduced by Escribano and Masso not only modify the neutral currents of the taulepton to Z gauge boson and the photon, but also induce lepton flavor violation (LFV). The sizeof the LFV eect depends crucially on the dynamics of the lepton mass generation. Assumingthe lepton mass matrices in the form of an Fritzsch ansatz, we point out that the experimentallimit on  ! eγ will push the anomalous magnetic and electric dipole moments of the taulepton down to 10−11 and 10−25 e cm respectively.PACS: 13.10.+q, 12.60.CnAlthough the Standard Model (SM) has been successful in describing the physics of theelectroweak interaction[1], it is quite possible that the SM is only an eective theory whichbreaks down at higher energies as the structure of the underlying physics emerges. There arereasons to believe that the deviation from the SM might rst appear in the interactions involvingthe third-generation fermions[2]. In the lepton sector, the tau lepton is special in probing newphysics since it is the only lepton which is heavy enough to have hadronic decays and it isgenerally believed that the heavier fermions are more sensitive to the new physics related tomass generation than light fermions. There has been extensive studies on the tau physics in theliterature[3]. In particular, there has been growing interest in the electromagnetic and electricdipole moments of the tau lepton[4][5] in recent years. In general, the anomalous magnetic andthe electric dipole moments of the tau lepton are dened by (which we follow the notation ofRef.[6])a =g − 22= F2(q2 = 0); and d = e ~F2(q2 = 0); (1)where F2 and ~F2 are form factors in the electromagnetic matrix element< p0jJem(0)jp >= eu(p0)(F1γ + [i2mF2 + γ5 ~F2]q)u(p); (2)where q = p0 − p and F1(q2 = 0) = 1.Theoretically the standard model predicts a = 1:1769(4)  10−3 and a very tiny d [4]from CP violation in the quark sector. Experimentally recent analysis of the e+e− ! +−γprocess from L3 and OPAL collaborations give that a = 0:004  0:027  0:023 and d =(0:0 1:5 1:3) 10−16e cm[5]. However the most stringent bounds are that inferred from thewidth Γ(Z ! +−) [6], which are −0:004  a  0:006 and jd j  1:1 10−17e cm. To obtainthese limits, Escribano and Masso took an eective lagrangian approach to new physics,Leff = L0 + 12∑iCiOi; (3)where L0 is the SM Lagrangian,  is the new physics scale and Oi are SUc(3)SUL(2)UY (1)invariant operators. Ci are constants which represent the coupling strengths of Oi. A completelist of CP-violating and CP-conserving operators have been given in Ref.[7]. Regarding the1anomalous magnetic moment of the tau lepton, the authors of Ref.[6] have examined twodimension-six operatorsOB = LRB ; (4)OW = L~R ~W ; (5)where L = ( ; L),  is the Higgs scalar, B and W are eld strengths of UY (1) and SUL(2).When  gets vacuum expectation value, operators OB and OW give rise to anomalousmagnetic moment of the tau lepton and also corrections to the decay width of Z into  .Given that the experimental data on Z width is quite consistent with the prediction of the SM,Escribano and Masso put a strong bound on anomalous magnetic moment of the tau leptonlisted above. In this paper, we extend the work of Ref.[6] by allowing the mixing of the threegenerations and point out that the experimental limits on LFV will put stronger bounds thanRef.[6] on anomalous magnetic and electric dipole moments of the tau lepton.We present our arguments rst with anomalous magnetic moment of the tau lepton. Con-sidering the dimension-six operators, OB and OW , the full eective lagrangian, Leff now canbe written as:Leff = L0 + 12(cBOB + cWOW + h:c:): (6)After the electroweak symmetry is broken and the mass matrices of the fermions and the gaugebosons are diagonalized, the eective neutral current couplings of the leptons to gauge bosonZ and the photon γ areLZ;γeff = egZ;γ eT (γV Z;γ − γγ5AZ;γ)− 12m (ik)SZ;γUl 0 01 U yl e ;(7)where gZ = 1=(4sW cW ); gγ = 1, and V Z;γ = 1−4s2W ; 1, AZ;γ = 1; 0 for Z and photon respectively,andSZ = −8sW cWem2vp2[CW cW − 2CBsW ] ; (8)Sγ =2mep2v2[CWsW2− CBcW]: (9)2The matrix Ul in Eq.(7) is the unitary matrix which diagonalizes the mass matrix of thecharged lepton. In the SM, which corresponds to Leff in the limit of  ! 1, the matrixUl is not measurable because of the zero neutrino masses and furthermore, the universality ofthe gauge interaction guarantees the absence of the flavor changing neutral current, the leptonflavor violation in the lepton sector.The relative size of the Z(γ)  to the flavor changing couplings Z(γ) , etc., in Eq.(7)depends on the rotation matrix Ul. The elements of Ul can be evaluated once the correspondingmass matrix is given. An interesting ansatz in the literature is the one suggested by Fritzschand its variations [8-12]. The latter in Ref.[9] is given byUl = c12c13 s12c13 s13−s12c23 − c12s23s13 c12c23 − s12s23s13 s23c13s12s23 − c12c23s13 −c12s23 − s12c23s13 c23c13 ; (10)where sij  sin ij , cij  cos ij and the three mixing angles are determined by correspondinglepton masses,tan 12 = −1 + 2p3√mem; (11)tan 23 = −p2− 3p2mm; (12)tan 13 = − 2p6√mem: (13)With Ul in Eqs.(10-13), we haveVl = Ul 0 01 U yl = s213 s13s23c13 s13c23c13s13s23c13 s223c213 s23c213c23s13c23c13 s23c213c23 c223c213= 0:0035 −0:049 0:032−0:049 0:701 −0:4550:032 −0:455 0:296 : (14)In the numerical calculation, we take that√me=m  0:0696, and m=m  0:0594.The decay width of l ! l0 + γ is given byΓ(l!l′γ) =ml32(Vll′eSγ mlm)2; (15)3where Vll′ (l 6= l0) are the nondiagonal elements of matrix V dened in Eq. (14). In Eq. (15),We have neglected the mass of the light lepton l0.Given the current experimental upper limits on − ! e−γ, 4:9 10−11 [13], we havejSγj < 1:3 10−10: (16)From Eqs.(7-9), the new physics contribution to the anomalous magnetic moments of thetau lepton is given byj j = jVSγ j : (17)With the bounds on Sγ in (16) and V in (14), we obtain thatj j  3:9 10−11: (18)This limit is much stronger than that in Ref.[6]. The limits from other LFV processes, such as− ! e−γ, are weaker than that in Eq. (18).Similarly, considering operators below which are introduced in Ref.[6],~OB = Liγ5RB ; (19)~OW = Liγ5~R ~W ; (20)and following the procedure above in obtaining the bounds on tau lepton magnetic moment,we put limit on the anomalous electric dipole momentjd j  2:2 10−25 e cm: (21)Again this is stronger than that obtained by Escribano and Masso.In summary, we extend the work by Escribano and Masso to bound the anomalous magneticand electric dipole moments of the tau lepton in the eective lagrangian by allowing the mixingof three generations in the lepton sector. In the standard model, these mixing eects arenot measurable because of vanishing neutrino masses and the universal gauge interactions.With non-universal interaction, the lepton flavor violation happens even with zero neutrino4masses. By taking the lepton mass matrix of Fritzsch ansatz, we have demonstrated that theexperimental limit on ! eγ put stronger limits on the anomalous magnetic and electric dipolemoments of the tau lepton than obtained by Escribano and Masso which is listed in the particledata book[13]. However our results depend on the lepton mass matrix. So future experimentaldata on anomalous magnetic and electric dipole moments of the tau lepton together with leptonflavor violation will provide an experimental test on various lepton mass ansatz.AcknowledgmentsWe thank Z. Z. Xing, J. M. Yang and B.-L. Young for helpful discussions. This work wassupported in part by National Natural Science Foundation of China.References[1] R.D. Peccei, hep-ph/9811309.[2] R.D. Peccei and X. Zhang, Nucl Phys. B337, 269 (1990); R. Peccei, S. Peris and X.Zhang, Nucl. Phys. B349, 305 (1991); X. Zhang and B.-L. Young, Phys. Rev. D51, 6564(1995); H. Georgi, L. Kaplan, D. Morin and A. Shenk, Phys. Rev. D51, 3888 (1995); T.Han, K. Whisnant, B.-L. Young and X. Zhang, Phys. Lett. B385, 311 (1996); D. Carlson,E. Malkawi and C.-P. Yuan, Phys. Lett. B337, 145 (1994), G. Gounaris, M. Kuroda andF. Renard, Phys. Rev. 55, 5786 (12997).[3] For a review, see, A. Pich, hep-ph/9704453.[4] A. Czarnecki and W. Marciano, hep-ph/9810512.[5] L. Taylor, hep-ph/9810463.[6] R. Escribano and E. Masso, Phys. Lett. B395, 369 (1997).[7] T. Huang, J.M. Yang, B.-L. Young and X. Zhang, Phys. Rev. D58, 073007 (1998); T.Huang, Z.-H. Lin and X. Zhang, in preparation.5[8] H. Fritzsch, Nucl. Phys. B 155 (1979) 189.[9] H. Fritzsch and Z. Z. Xing, Phys. Lett. B 372 (1996) 265.[10] H. Fritzsch and J. Plankl, Phys. Lett. B 237 (1990) 451; H. Fritzsch and D .Holt-mannspo¨tter, Phys. Lett. B 338 (1994) 290; H. Fritzsch and Z. Z. Xing, hep-ph/9808272,to be published in Phys. Lett. B; H. Fritzsch and Z. Z. Xing, hep-ph/9807234; M.Fukugita, M. Tanimoto and T. Yanagida, Phys. Rev. D 57, (1998) 4429; M. Tanimoto,hep-ph/9807283.[11] K. Kang, S. K. Kang, C. S. Kim and S. M. Kim, hep-ph/9808419[12] Z. Xing, hep-ph/9804433.[13] C.Caso et al., Particle Data Group, Eur. Phys. J. C 3 (1998) 1.6

Bounds on Anomalous Magnetic and Electric Moments of $\tau$ Lepton from LEP and Lepton Flavor Violation

Bounds On Anomalous Magnetic And Electric Moments Of Tau Lepton From LEP
  And Lepton Flavor Violation

Bounds On Anomalous Magnetic And Electric Moments Of Tau Lepton From LEP And Lepton Flavor Violation

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