arXiv subjects

G. Tavares-Velasco

Publications and source records attributed to G. Tavares-Velasco.

At least 19 recordsLinked to original sources

arXiv2026

Forward--backward asymmetry in the $H\to Zγ\to\overline{f}{f}γ$ decay

We study the forward--backward asymmetry in the three-body decay process $H\to Zγ\to\overline{f}fγ$, induced by complex form factors in the $HZγ$ vertex. To estimate its magnitude, we derive constraints on the real and imaginary parts of the $CP$-violating form factor $h_3^{Zγ}$ using current LHC measurements, obtaining upper limits of about $0.9$ GeV. These bounds are of the same order of magnitude as those derived from electric dipole moments (EDM). We find that the asymmetry can reach values of order $10^{-1}$ and may be accessible at the HL-LHC.

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arXiv2026

$CP$-odd form factor in the $HWW$ vertex

We revisit the $CP$-odd form factor in the $HWW$ vertex within the Standard Model (SM), which is induced only at the one-loop level when one of the $W$ bosons is off-shell. To the best of our knowledge, the numerical evaluation of this form factor is presented for the first time. The relevant contributions from quark loops are of order $10^{-5}$, well below the current experimental sensitivity. The phenomenological implications are studied through asymmetries in unpolarized and polarized observables in three-body decays.

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arXiv2025

Non-diagonal contributions to $ZγV^\ast$ vertex, polarizations and bounds on $Z\overline{t}q$ couplings

We study the flavor-changing neutral current contributions to the trilinear neutral gauge boson couplings $ZγV^\ast$ ($V=Z$, $γ$) at the one-loop level. Only the $CP$-conserving form factor $h_3^Z$ is induced, with the relevant contributions arising from top quark couplings. To our numerical analysis, constraints on the $Z\overline{t}q$ ($q=c$, $u$) couplings are obtained from current LHC data, leading to bounds of $|g_{\text{V}}^{tu}|\text{,}|g_{\text{A}}^{tu}|\leqslant 0.007$ and $|g_{\text{V}}^{tc}|\text{,}|g_{\text{A}}^{tc}|\leqslant 0.0095$ for the vector and axial couplings. The new contributions to the $h_3^Z$ form factor are of order $10^{-7}$. Furthermore, we analyze the polarized partial decay widths of the $V^\ast\rightarrow Zγ$ process, and a new type of left-right asymmetry is also discussed. We find that in the presence of new physics, the polarized $Γ(V^\ast\rightarrow Zγ)$ exhibits significant deviations from the SM prediction, resulting in a non-zero asymmetry.

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arXiv2024

Polarized and unpolarized off-shell $H^\ast\to ZZ\rightarrow 4\ell$ decay above the $2m_Z$ threshold

An analysis of the off-shell $H^\ast\rightarrow ZZ \rightarrow \overline{\ell}_1\ell_1\overline{\ell}_2\ell_2$ decay width is presented for both unpolarized and polarized $Z$ gauge bosons in the scenario with the most general $H^*ZZ$ vertex function, which is given in terms of two $CP$-even ($\hat b_Z$ and $\hat c_Z$) and one $CP$-odd ($\tilde b_Z$) anomalous couplings. The SM contributions to the $H^*ZZ$ coupling up to the one-loop level are also included. Explicit analytic results for the unpolarized and polarized $H^\ast\rightarrow ZZ \rightarrow \overline{\ell}_1\ell_1\overline{\ell}_2\ell_2$ square amplitudes and the four-body phase space are presented, out of which several observable quantities can be obtained straightforwardly. As far as the numerical analysis is concerned, a cross-check is performed via \texttt{MadGraph5\_aMC@NLO}, where our model was implemented with the aid of FeynRules. We then consider the most stringent bounds on anomalous complex $H^*ZZ$ couplings and analyze the effects of the polarizations of the $Z$ gauge bosons through the polarized $H^\ast\rightarrow ZZ \rightarrow \overline{\ell}_1\ell_1\overline{\ell}_2\ell_2$ decay width as well as left-right and forward-backward asymmetries, which are found to be sensitive to new-physics effects. Particular focus is put on the effects of the absorptive parts of the anomalous $H^*ZZ$ couplings, which have been largely overlooked up to now in LHC analyses. It is found that the studied observable quantities, particularly the left-right asymmetries, can be helpful to look for effects of $CP$-violation in the $H^*ZZ$ coupling and set bounds on the absorptive parts. For completeness, we also analyze the case of unpolarized $Z$ gauge bosons.

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arXiv2024

Neutrino charge radius and electromagnetic dipole moments via scalar and vector leptoquarks

The one-loop contribution of scalar and vector leptoquarks (LQs) to the electromagnetic properties (NEPs) of massive Dirac neutrinos is presented via an effective Lagrangian approach, with emphasis on the effective neutrino charge radius (NCR), which has never been calculated and is obtained by the background field formalism in a Yang-Mills-like scenario for gauge LQs. Analytical results for nonzero neutrino mass are presented in terms of both Feynman-parameter integrals and Passarino-Veltman scalar functions, which can be useful to obtain the NEPs of heavy neutrinos, out of which approximate expressions are obtained for light neutrinos. For the numerical analysis we concentrate on the only renormalizable scalar and vector LQ representations that do not need extra symmetries to forbid tree-level proton decay. Constraints on the parameter space consistent with current experimental data are then discussed and it is found that the LQ representations $\widetilde{R}_2$ and $U_1$ could yield the largest contributions to the NEPs provided that they have couplings to both left- and right-handed neutrinos of the order of $O(1)$. For a LQ mass of $1.5$ TeV, the magnetic dipole moment (MDM) of the tau neutrino can be of the order of $10^{-9}$ $μ_B$, whereas its neutrino electric dipole moment (EDM) can reach values as high as $10^{-20}$-$10^{-19}$ ecm. On the other hand, the NCR can reach values up to $10^{-35}$ cm$^2$ regardless of the neutrino flavor and even in the absence of right-handed neutrinos. In the latter scenario, the EDM vanishes and the contribution to neutrino MDM would be negligible, of the order of $10^{-14}$ $μ_B$ for the tau neutrino, whereas those for the muon and electron neutrinos would be about two and seven orders of magnitude smaller, respectively. Our estimates could be severely suppressed due to a possible suppression of the LQ coupling constants.

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arXiv2023

A new evaluation of the $HZZ$ coupling: direct bounds on anomalous contributions and $CP$ violating effects via a new asymmetry

The standard model (SM) one-loop contributions to the most general $H^*Z^*Z^*$ coupling are obtained via the background field method in terms of Passarino-Veltman scalar functions, from which the contributions to the $H^*ZZ$ and $HZZ^*$ couplings are obtained in terms of two $CP$-conserving $h_{1,2}^V$ and one $CP$-violating $h_3^V$ form factors ($V=H, Z$). The current CMS constraints on the $HZZ$ coupling ratios are then used to obtain bounds on the real and absorptive parts of the anomalous $HZZ$ couplings. The former are up to two orders of magnitude tighter than previous ones, whereas the latter are the first one of this kind. The effects of the absorptive parts of the $HZZ$ anomalous couplings, which have been overlooked in the past, are analyzed via the partial decay width $Γ_{H^\ast\rightarrow ZZ}$, and a significant deviation from the SM tree-level contribution is observed at low energies, though it becomes negligible at high energies. We also explore the possibility that polarized $Z$ gauge bosons are used for the study of non-SM $HZZ$ contributions via a new left-right asymmetry $\mathcal{A}_{LR}$, which is sensitive to $CP$-violating complex form factors and can be as large as the unity at most, though in a more conservative scenario it is four to five orders of magnitude larger than the SM prediction arising up to the three-loop level. The partial decay widths $Γ_{H^\ast\rightarrow Z_LZ_L}$ and $Γ_{H^\ast\rightarrow Z_RZ_R}$ are also studied in several scenarios and it is observed that the deviations from the SM can be large at high energies and increases as the energy increases. Thus, the use of polarized $Z$ gauge bosons could give hints of $CP$ violation. The Mathematica code for our analytical results and the numerical evaluation is available in our GitLab site.

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arXiv2023

Rare decay $t\to cγγ$ via scalar leptoquark doublets

A calculation of the one-loop contribution to the rare three-body flavor changing neutral current top quark decay $t\to cγγ$ is presented in the framework of models with one or more scalar leptoquark $SU(2)$ doublets with hypercharge $7/6$. Analytical expressions for the invariant amplitude of the generic decay $f_i\to f_jγγ$, with $f_{i,j}$ a lepton or quark, are presented in terms of Passarino-Veltman integral coefficients, from which the amplitudes for the processes $t\to cγγ$ and $\ell_i\to \ell_jγγ$ follow easily. An analysis of the current constraints on the parameter space is presented in the scenario with only one scalar LQ doublet and bounds on the LQ couplings are obtained from the muon $g-2$ anomaly, the lepton flavor violating (LFV) decay $τ\to μγ$ and extra constraints meant to avoid tension between theory predictions and experimental data. For a LQ with a mass in the range of $1$--$1.5$ TeVs, the estimate ${\rm Br}(t\to cγγ)\sim 10^{-11}$--$10^{-12}$ is obtained for the largest allowed values of the LQ coupling constants, which means that this decay would be below the reach of future experimental measurements. We also consider an scenario with three scalar doublets, which was recently proposed to explain the lepton flavor universality violation anomalies in $B$ decays as well as the muon $g-2$ anomaly. Although this scenario allows large LQ couplings to the tau lepton and the $c$ and $t$ quarks, the branching ratio of the $t\to cγγ$ decay is also of the order of $10^{-11}$--$10^{-12}$ for LQ masses of 1.7 TeV.

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arXiv2022

Bounds on the absorptive parts of the chromomagnetic and chromoelectric dipole moments of the top quark from LHC data

Bounds on the absorptive (imaginary) parts of the top quark chromomagnetic $\hatμ_t$ and chromoelectric $\hat{d}_t$ dipole moments are obtained by reinterpreting the most recent LHC data in top quark pair production. It is found that both limits are of the order of $10^{-1}-10^{-2}$, which are consistent with the standard model prediction of ${\rm Im}\big[\hatμ_t\big]$. The effects of the absorptive parts of the top quark dipole moments are also studied via some kinematic distributions of $\bar{t}t$ production, though no significant deviation from the standard model leading order contribution is observed. Our bounds can be useful to constrain the parameter space of standard model extensions.

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arXiv2022

Flavor changing Flavon decay $ϕ\to tc$ ($ϕ=H_F,\,A_F$) at the High Luminosity Large Hadron Collider

We present a study of the flavor changing decays $ϕ\to tc$ ($ϕ=H_F,\,A_F$) of the $CP$-even and $CP$-odd scalar flavons at the large hadron collider and its next stage, the high-luminosity large hadron collider. The theoretical framework is an extension of the standard model that incorporates an extra complex singlet and invokes the Froggatt-Nielsen mechanism with an Abelian flavor symmetry. The projected exclusion and discovery regions in terms of the model parameters are reported. We find that $A_F$ could be detected at the LHC by considering a reasonable scenario of the model parameter space. As far as $H_F$ is concerned, we also found promising results that could be verified experimentally at the high-luminosity LHC.

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arXiv2021

Chromomagnetic and chromoelectric dipole moments of quarks in the reduced 331 model

The one-loop contributions to the chromomagnetic dipole moment $\hatμ_t(q^2)$ and electric dipole moment $\hat d_t(q^2)$ of the top quark are calculated within the reduced 331 model (RM331) in the general case of an off-shell gluon. It is argued that the results are gauge independent for $q^2\ne 0$ and represent valid observable quantities. In the RM331 $\hat μ_t(q^2)$ receives new contributions from two heavy gauge bosons $Z'$ and $V^+$ and a new neutral scalar boson $h_2$, along with a new contribution from the standard model Higgs boson via flavor changing neutral currents. The latter, which are also mediated by the $Z'$ gauge boson and the scalar boson $h_2$, can give a non-vanishing $\hat d_t$ provided that there is a $CP$-violating phase. The analytical results are presented in terms of both Feynman parameter integrals and Passarino-Veltman scalar functions, which are useful to cross-check the numerical results. Both $\hatμ_t(q^2)$ and $\hat d_t$ are numerically evaluated for parameter values still allowed by the constraints from experimental data. It is found that the new one-loop contributions of the RM331 to $\hat μ_t(q^2)$ are of the same order of magnitude or larger than in other standard model extensions, with the dominant contribution arising from the $V^+$ gauge boson for $\|q\|$ in the 30-1000 GeV interval and a mass $m_{V}$ of the order of a few hundreds of GeVs. As for $\hat d_t(q^2)$, it receives the largest contribution from $h_2$ exchange and can reach values of the order of $10^{-20}$, which is smaller than the contributions predicted by other standard model extensions.

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arXiv2021

Contributions to $ZZV^\ast$ ($V=γ,Z,Z'$) couplings from $CP$ violating flavor changing couplings

The one-loop contributions to the trilinear neutral gauge boson couplings $ZZV^\ast$ ($V=γ,Z,Z'$), parametrized in terms of one $CP$-conserving $f_5^{V}$ and one $CP$-violating $f_4^{V}$ form factors, are calculated in models with $CP$-violating flavor changing neutral current couplings mediated by the $Z$ gauge boson and an extra neutral gauge boson $Z'$. Analytical results are presented in terms of both Passarino-Veltman scalar functions and closed form functions. Constraints on the vector and axial couplings of the $Z$ gauge boson $\left|g_{VZ}^{tu}\right|< 0.0096$ and $\left|g_{VZ}^{tc}\right|<0.011$ are obtained from the current experimental data on the $t\rightarrow Z q$ decays. It is found that in the case of the $ZZγ^\ast$ vertex the only non-vanishing form factor is $f_5^γ$, which can be of the order of $10^{-3}$, whereas for the $ZZZ^\ast$ vertex both form factors $f_5^{Z}$ and $f_4^{Z}$ are non-vanishing and can be of the order of $10^{-6}$ and $10^{-5}$, respectively. Our estimates for $f_5^γ$ and $f_5^{Z}$ are smaller than those predicted by the standard model, where $f_4^{Z}$ is absent up to the one loop level. We also estimate the $ZZ{Z'}^{*}$ form factors arising from both diagonal and non-diagonal $Z'$ couplings within a few extension models. It is found that in the diagonal case $f_{5}^{Z'}$ is the only non-vanishing form factor and its real and imaginary parts can be of the order of $10^{-1}-10^{-2}$ and $ 10^{-2}-10^{-3}$, respectively, with the dominant contributions arising from the light quarks and leptons. In the non-diagonal case $f_{5}^{Z^\prime}$ can be of the order of $10^{-4}$, whereas $f_4^{Z'}$ can reach values as large as $10^{-7}-10^{-8}$, with the largest contributions arising from the $Z'tq$ couplings.

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arXiv2021

New estimate of the chromomagnetic dipole moment of quarks in the standard model

A new estimate of the one loop contributions of the standard model to the chromomagnetic dipole moment (CMDM) $\hat μ_q(q^2)$ of quarks is presented with the aim to address a few disagreements arising in previous calculations. We consider the most general case with an off-shell gluon with transfer momentum $q^2$ and obtain analytical results in terms of Feynman parameter integrals and Passarino-Veltman scalar functions, which are then expressed in terms of closed form functions when possible. The calculation is done via a renormalizable linear $R_ξ$ gauge and the background field method, which allows one to corroborate that the resulting $\hat μ_q(q^2)$ is gauge independent and thus a valid observable quantity. It is found that the QCD contribution from a three-gluon Feynman diagram has an infrared divergence, which agrees with a previous evaluation and stems from the fact that the static CMDM [$\hatμ(0)$] has no sense in perturbative QCD. For the numerical analysis we consider the region 30 GeV$<\|q\|<$ 1000 GeV and analyze the behavior of $\hat μ_q(q^2)$ for all the standard model quarks. It is found that the CMDM of light quarks is considerably smaller than that of the top quark as it is directly proportional to the quark mass. In the considered energy interval, both the real and imaginary parts of $\hatμ_t(q^2)$ are of the order of $10^{-2}-10^{-3}$, with the largest contribution arising from the QCD induced diagrams, though around the threshold $q^2=4m_t^2$ there are also important contributions from diagrams with $Z$ gauge boson and Higgs boson exchange.

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arXiv2019

Flavor changing neutral current decays $t\to c X$ ($X=γ,\,g,\, Z,\, H$) and $t\to c\bar \ell\ell $ ($\ell=μ,\,τ$) via scalar leptoquarks

The flavor changing neutral current decays $t\to c X$ ($X=γ,\,g,\, Z,\, H$) and $t\to c\bar \ell\ell $ ($\ell=μ,\,τ$) are studied in a renormalizable scalar leptoquark (LQ) model with no proton decay, where a scalar $SU(2)$ doublet with hypercharge $Y=7/6$ is added to the standard model, yielding a non-chiral LQ $Ω_{5/3}$. Analytical results for the one-loop (tree-level) contributions of a scalar LQ to the $f_i\to f_j X$ ($f_i\to f_j \bar f_m f_l$) decays, with $f_a=q_a, \ell_a$, are presented. We consider the scenario where $Ω_{5/3}$ couples to the fermions of the second and third families, with its right- and left-handed couplings obeying $λ_R^{\ell u_i}/λ_L^{\ell u_i}=O(ε)$, where $ε$ parametrizes the relative size between these couplings. The allowed parameter space is then found via the current constraints on the muon $(g-2)$, the $τ\to μγ$ decay, the LHC Higgs boson data, and the direct LQ searches at the LHC. For $m_{Ω_{5/3}}=1$ TeV and $ε=10^{-3}$, we find that the $t\to c X$ branching ratios are of similar size and can be as large as $10^{-8}$ in a tiny area of the parameter space, whereas ${\rm Br}(t\to c\bar ττ)$ [${\rm Br}(t\to c\bar μμ)$] can be up to $10^{-6}$ ($10^{-7}$).

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arXiv2019

Decay $ϕ\to Z γγ$ ($ϕ=h, H,A$) in the minimal supersymmetric standard model

The decays of the CP-even ($h,\,H$) and the CP-odd ($A$) Higgs bosons $h,\,H,\,A\to Zγγ$ are calculated in the context of the minimal supersymmetric standard model (MSSM), where they are induced at the one-loop level via box and reducible Feynman diagrams. For the numerical evaluation of the branching ratios we employ the decoupling limit and consider values for the MSSM parameters still consistent with the current experimental data. We consider a particular scenario for the radiative corrections to the Higgs boson masses, dubbed hMSSM, which leads to only two free parameters, namely $m_A$ and $\tanβ$. We found that the branching ratio of the $CP$-odd Higgs boson decay $A\to Zγγ$ can reach values up to $10^{-8}$ for $m_A=750$ GeV, which is three order of magnitude smaller than that of the $A\toγγ$ channel. On the other hand, the branching ratio of the $H\to Zγγ$ decay is of the order of $10^{-7}$ for large values of $m_H$ and small values of $\tanβ$, which is comparable with the branching ratio of the $H\to Zγ$ channel. As far as the branching ratio of the SM-like Higgs boson decay $h\to Zγγ$ is concerned, it is considerably suppressed, of the order of $10^{-11}$.

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arXiv2018

Chromomagnetic and chromoelectric dipole moments of the top quark in the 4GTHDM

The chromo magnetic dipole moment (CMDM) and chromo electric dipole moment (CEDM) of the top quark are calculated at the one-loop level in the framework of the two-Higgs doublet model with four fermion generations (4GTHDM), which is still consistent with experimental data and apart from new scalar bosons ($H^0$, $A^0$, and $H^\pm$) and quarks ($b'$ and $t'$) predicts new sources of $CP$ violation via the extended $4\times 4$ CKM matrix. Analytical expressions for the CMDM and CEDM of a quark are presented both in terms of Feynman parameter integrals and Passarino-Veltman scalar functions, with the main contributions arising from loops carrying the scalar bosons accompanied by the third- and fourth-generation quarks. The current bounds on the parameter space of the 4GTHDM are discussed and a region still consistent with the LHC data on the 125 GeV Higgs boson is identified. It is found that the top quark CMDM, which is induced by all the scalar bosons, can reach values of the order of $10^{-4}$-$10^{-3}$, with the dominant contributions arising from the fourth generation quarks, though may also be large cancellations for some parameter values, thereby giving a negligible CMDM. As for the top quark CEDM, it only receives contributions from the charged scalar boson and can reach values of the order of $10^{-19}$-$10^{-18}$ ecm for relatively light $m_{H^\pm}$ and large $m_{b'}$, with the dominant contribution arising from the $b'$ quark. The latter would be the most interesting prediction of this model as can be larger than the value predicted by the usual THDMs by one or two orders of magnitude.

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arXiv2018

Searching for LFV Flavon decays at hadron colliders

The search for Flavons with a mass of $\mathcal{O}$(1) TeV at current and future colliders might probe low-scale flavor models. We are interested in the simplest model that invokes the Froggatt-Nielsen (FN) mechanism with an Abelian flavor symmetry, which includes a Higgs doublet and a FN complex singlet. Assuming a CP conserving scalar potential, there are a $CP$-even $H_F$ and a $CP$-odd $A_F$ Flavons with lepton flavor violating (LFV) couplings. The former can mix with the standard-model-like Higgs boson, thereby inducing tree-level LFV Higgs interactions that may be at the reach of the LHC. We study the constraints on the parameter space of the model from low-energy LFV processes, which are then used to evaluate the Flavon decay widths and the $gg\to ϕ\to τμ$ ($ϕ=H_F,\,A_F$) production cross section at hadron colliders. After imposing several kinematic cuts to reduce the SM main background, we find that for $m_{H_F}$ about 200-350 GeV, the decay $H_F \to τμ$ might be at the reach of the LHC for a luminosity in the range 1-3 ab$^{-1}$, however, a luminosity of the order of 10 ab$^{-1}$ would be required to detect the $A_F \to τμ$ decay. On the other hand a future 100 TeV $pp$ collider could probe masses as high as $\mathcal{O}$(10) TeV if it reaches an integrated luminosity of at least 20 ab$^{-1}$. Therefore, the 100 TeV Collider could work as a Flavon factory.

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arXiv2018

Decays $A \to Zγγ$ and $ϕ\to Zγγ$ ($ϕ=h,H$) in two-Higgs doublet models

The one-loop contributions to the decays of the $CP$-odd and $CP$-even scalar bosons $A\to Zγγ$ and $ϕ\to Zγγ$ ($ϕ=h,H$) are calculated within the framework of $CP$-conserving THDMs, where they are induced by box and reducible Feynman diagrams. The behavior of the corresponding branching ratios are then analyzed within the type-II THDM in a region of the parameter space around the alignment limit and still consistent with experimental data. It is found that the $A\to Zγγ$ branching ratio is only relevant when $m_A>m_H+m_Z$, but it is negligible otherwise. For $m_A>600$ GeV and $t_β\simeq O(1)$, $BR(A\to Zγγ)$ can reach values of the order of $10^{-5}-10^{-4}$, but it decreases by about one order of magnitude as $t_β$ increases up to 10. A similar behavior is followed by the $H\to Zγγ$ decay, which only has a non-negligible branching ratio when $m_H>m_A+m_Z$ and can reach the level of $10^{-4}-10^{-3}$ for $m_H>600$ GeV and $t_β\simeq O(1)$. We also estimated the branching ratios of these rare decays in the type-I THDM, where they can be about one order of magnitude larger than in type-II THDM. As far as the $h\to Zγγ$ decay is concerned, since the properties of this scalar boson must be nearly identical to those of the SM Higgs boson, the $h\to Zγγ$ branching ratio does not deviates significantly from the SM prediction, where it is negligibly small, of the order of $10^{-9}$. This result is in agreement with previous calculations.

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arXiv2017

Weak dipole moments of the tau lepton in models with an extended scalar sector

We consider renormalizable couplings of neutral $ϕ$, singly $ϕ^\pm$, and doubly charged $ϕ^{\pm\pm}$ scalar bosons to leptons and the $Z$ gauge boson and calculate the one-loop contributions to the anomalous weak magnetic dipole moment (AWMDM) $a_τ^W$ and the weak electric dipole moment (WEDM) $d_τ^W$ 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 $ϕ^\pm W^\mp Z$ and $Z ϕ_iϕ_j$ ($i\ne j$), along with contributions from doubly charged scalar bosons. Both $a_τ$ and $d_τ^W$ 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 $a_τ^W$ 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 $d_τ^W$ 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.

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