Lam-Tung relation breaking effects and weak dipole moments at lepton colliders

The weak dipole moments of elementary fermions are calculated at the one-loop level in the framework of a renormalizable scalar leptoquark model that forbids baryon number violating processes and so is free from the strong constraints arising from experimental data. In this model there are two scalar leptoquarks accommodated in a $S{U}_{L}(2)\ifmmode\times\else\texttimes\fi{}{U}_{Y}(1)$ doublet: One of these leptoquarks is nonchiral and has electric charge of $5/3e$, whereas the other one is chiral and has electric charge $2/3e$. In particular, a nonchiral leptoquark contributes to the weak properties of an up fermion via a chirality-flipping term proportional to the mass of the virtual fermion, and can also induce a nonzero weak electric dipole moment provided that the leptoquark couplings are complex. The numerical analysis is focused on the weak properties of the $\ensuremath{\tau}$ lepton since they offer good prospects for experimental study. The constraints on leptoquark couplings are briefly discussed for a nonchiral leptoquark with nondiagonal couplings to the second and third fermion generations, a third-generation nonchiral leptoquark, and a third-generation chiral leptoquark. It is found that although the chirality-flipping term can enhance the weak properties of the $\ensuremath{\tau}$ lepton via the top quark contribution, such an enhancement would be offset by the strong constraints on the leptoquark couplings. So, the contribution of scalar leptoquarks to the weak magnetic dipole moment of the $\ensuremath{\tau}$ lepton are smaller than the standard model (SM) contributions but can be of similar size to those arising in some SM extensions. A nonchiral leptoquark can also give contributions to the weak electric dipole moment larger than the SM one but well below the experimental limit. We also discuss the case of the off-shell weak dipole moments and, for completeness, analyze the behavior of the $\ensuremath{\tau}$ electromagnetic properties.

LEP summary on weak dipole moments of the τ lepton

τ weak dipole moments from azimuthal asymmetries

The PRS (perturbed rotational state–rotationally adiabatic state) method is applied to the collision system of an ion and a linear molecule which possesses a strong, weak or vanishing dipole moment. The structure of the intermolecular interaction with a negative quadrupole and a weak dipole moments is characterized by a ridge and two valleys. This structure has a critical importance for the adiabatic state, as is seen in the cases–the two-electron-excited state of atoms and the Rydberg atom in a magnetic field–pointed out by Fano. Consideration of the adiabatic state in the ion-molecule system supplies a classification of polar and weakly-polar molecules.

A calculation of weak dipole moments of charged fermions of the standard model at the one-loop level, in the context of a general effective extended neutral current model with flavor changing vertices, is presented. We give numerical predictions for the anomalous weak magnetic dipole moment , and the weak electric dipole moment (WEDM) , for the τ lepton and t quark. For several Z′ gauge bosons considered, we find that, for the τ lepton, the best prediction for the real part of is of the order of 10−9, while the imaginary part is four orders of magnitude below. The highest value for the WEDM, , corresponds to 10−26 e cm, for its real part, and the imaginary part is three orders of magnitude below. Moreover, we found for the top quark, that the best prediction for the real part of is of the order of 10−7 and its imaginary part is of the order of 10−11. We also found that is of the order of 10−26 e cm for its real part, and its imaginary part can be as high as 10−31 e cm.

We consider renormalizable couplings of neutral $\phi$, singly $\phi^\pm$, and doubly charged $\phi^{\pm\pm}$ scalar bosons to leptons and the $Z$ gauge boson and calculate the one-loop contributions to the anomalous weak magnetic dipole moment (AWMDM) $a_\tau^W$ and the weak electric dipole moment (WEDM) $d_\tau^W$ of a charged lepton in a model independent way. The analytic expressions are presented in terms of both parametric integrals and Passarino-Veltman scalar functions. Among the new contributions, there are those arising from the vertices of the type $\phi^\pm W^\mp Z$ and $Z \phi_i\phi_j$ ($i\ne j$), along with contributions from doubly charged scalar bosons. Both $a_\tau$ and $d_\tau^W$ are evaluated in several scenarios , first in a model independent way and then within some popular models, such as two-Higgs doublet models (THDMs), multiple-Higgs doublet models and Higgs triplet models. As far as $a_\tau^W$ is concerned, its real part reaches values as high as $10^{-10}-10^{-9}$ for masses of the new scalar bosons in the 200 GeV range, whereas the imaginary part is one or two orders of magnitude below. On the other hand, the most promising scenario for a nonvanishing WEDM is offered by a $CP$-violating THDM in a scenario where the heavy neutral scalar bosons are a mixture of $CP$ eigenstates. It is found that the real part of $d_\tau^W$ is of the order of $10^{-24}$ ecm and its imaginary part can reach the $10^{-26}$ ecm level for masses of the new scalar bosons of the order of a few hundred of GeVs. Both the tau AWMDM and WEDM decrease dramatically as the scalar boson masses increase.

The anomalous weak dipole moments of the tau lepton are measured in a data sample collected by ALEPHfrom 1990 to 1995 corresponding to an integrated luminosity of 155pb-1. Tau leptons produced in the reaction e+e- -> tau+tau- at energies close to the Z mass are studied using their semileptonic decays to pi, rho, a_1 -> pi 2pi0 or a_1 -> 3 pi. The real and imaginary components of both the anomalous weak magnetic dipole moment and the CP-violating anomalous weak electric dipole moment, Re,mu_tau, Im,mu_tau, Re, d_tau and Im, d_tau, are measured simultaneously by means of a likelihood fit built from the full differential cross section. No evidence of new physics is found. The following bounds are obtained 95% CL: |Re, mu_tau | < 1.14 x 10-3, |Im}, mu_tau | < 2.65 x 10-3, |Re}, d_tau | < 0.91 x 10-3, and |Im, d_tau | < 2.01 x 10-3.

Measurement of the weak dipole moments of the τ lepton

We study the dipole moments, electric dipole moment, weak electric dipole moment, anomalous magnetic moment, anomalous weak magnetic moment, of fermions in the noncommutative extension of the SM. We observe that the noncommutative effects are among the possible candidates to explain the electric and weak electric dipole moment of fermions. Furthermore, the upper bounds for the parameters which carry space-time and space-space noncommutativity can be obtained by using the theoretical and experimental results of the fermion dipole moments.

The spin correlations in the pair of τ leptons produced in high-energy proton-proton collisions are studied. The invariant mass of the τ-lepton pair is chosen close to the Z-boson mass; in these conditions, Z-boson exchange gives the dominant contribution to the Drell-Yan mechanism. The interaction of Z bosons with τ leptons, in addition to the Standard Model couplings, can include weak anomalous magnetic and electric dipole moments (or form factors) of the τ lepton. The dependence of elements of the pp spin-correlation matrix on the weak anomalous moments is determined for various regions of the rapidity of the τ-lepton pair. Based on this calculation, we construct a semirealistic observable built on the momenta of pions in the τ∓→π∓ντ and τ±→ρ±ντ→π±π0ντ decay channels, and we show that this observable can be sensitive to the weak anomalous dipole moments.

Weak electric and magnetic dipole moments of the τ lepton from azimuthal asymmetries

Weak magnetic dipole moments in the MSSM

Using a sample of 4,500 polarized Z decays to τ lepton pairs accumulated with the SLD detector at the SLAC Linear Collider (SLC) in 1993-95, a search has been made for anomalous couplings in the neutral current reaction e+e-→ τ+τ-. A measurement of the CP violating Weak Electric Dipole Moment (WEDM) and the CP conserving Weak Magnetic Dipole Moment (WMDM) of the τ lepton has been performed by considering the transverse spin polarization of τ leptons produced at the Z pole. Using a maximum likelihood technique, the observed τ decay spectra in the e, μ, π, and ρ decay channels are used to infer the net transverse polarization of the underlying tau leptons, and a fit for the anomalous dipole moments is performed. No evidence for these dipole movements is observed, and limits are placed on both the real and imaginary parts of the WEDM and WMDM.

We investigate dimension-five Lorentz-violating (LV) nonminimal interactions in the electroweak sector, in connection with the possible generation of electric dipole moment (EDM), weak electric dipole moment (WEDM), magnetic dipole moment (MDM) and weak magnetic dipole moment (WMDM) for leptons. These couplings are composed of the physical fields in the Standard Model and LV tensors of ranks ranging from 1 to 4. The CPT-odd couplings do not generate EDM behavior nor provide the correct MDM signature, while the CPT-even ones are compatible with EDM and MDM behavior, being subject to improved constraining. Tau lepton experimental data is used to constrain the WEDM and WMDM couplings to the level of 10−4(GeV)−1, whereas electron MDM and EDM data are employed to improve constraints to the level of 10−10(GeV)−1 and 10−16(GeV)−1, respectively.

The pure electroweak mechanism for the $\mathrm{CP}$-odd dipole moments of the quark is studied in the Kobayashi-Maskawa model. We demonstrate the nonvanishing of the weak electric dipole moment at the lowest possible two-loop level. The weak electric dipole moment of the $b$ quark is calculated in the standard model with one additional heavy generation of fermions. It is found to reach ${10}^{\ensuremath{-}25}e$ cm with the most optimistic assumptions about unknown masses and mixing angles. We consider also the electroweak three-loop mechanism for the electric and chromoelectric dipole moments of light quarks and find it to be negligible in the SM case. In the presence of the fourth heavy generation, however, pure electroweak corrections are important and might be several times larger than the corresponding QCD contribution for the masses of the heaviest quarks \ensuremath{\sim} 500-600 GeV. The resulting electric dipole moment of the neutron naturally arises at the level of ${10}^{\ensuremath{-}29}e$ cm.