Working in the basis where the charged-lepton Yukawa matrix is diagonal and making the $τ$-dominance approximations, we analytically derive integral solutions to the one-loop renormalization-group equations (RGEs) for neutrino masses, flavor mixing angles, CP-violating phases and the Jarlskog invariant under the standard parametrization of the PMNS matrix in the standard model or its minimal supersymmetric extension for both Majorana and Dirac neutrinos. With these integral solutions, we carry out numerical calculations to investigate the RGE running of lepton flavor mixing parameters and the Jarlskog invariant, and also compare these integral solutions with the exact results obtained by numerically solving the one-loop RGEs. It is shown that these integral solutions coincide with the exact results and can well describe the evolution of lepton flavor mixing parameters and the Jarlskog invariant in most cases. Some important features of our integral solutions and the evolution behaviors of relevant flavor parameters are also discussed in detail both analytically and numerically.
The essences of the weak CP violation, the quark and lepton Jarlskog invariants, are determined toward future model buildings beyond the Standard Model (SM). The equivalence of two calculations of Jarlskog invariants gives a bound on the CP phase in some parametrization. Satisfying the unitarity condition, we obtain the CKM and MNS matrices from the experimental data, and present the results in matrix forms. The Jarlskog determinant $J^q$ in the quark sector is found to be $\sim 3.11\times 10^{-5}|\sin\delks|$ while $J^\ell$ in the leptonic sector is $\sim 2.96\times 10^{-2}|\sin\delksl|$ in t…
While Jarlskog-like flavor invariants are adequate for estimating CP-violation from closed fermion loops, non-invariant structures arise from rainbow-like processes. For the CKM contributions to the quark electric dipole moments (EDMs), or the PMNS contributions to lepton EDMs, the dominant diagrams have a rainbow topology whose flavor structure does not collapse to flavor invariants. Numerically, they are found typically much larger, and not necessarily correlated with, Jarlskog-like invariants. The flavor structures in the quark and lepton sectors are systematically studied, assuming differe…
The Jarlskog invariant which controls the size of intrinsic CP violation in neutrino oscillation appearance experiments is modified by Wolfenstein matter effects for neutrinos propagating in matter. In this paper we give the exact factorization of Jarlskog invariant in matter into the vacuum Jarlskog invariant times two, two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. We compare the location of the minima of the factorizing resonance factors with the location of the solar and atmospheric resonances, precisely defined. …
In this paper, we show that the ratio of the effective Jarlskog invariant $\widetilde{\cal J}$ for leptonic CP violation in three-flavor neutrino oscillations in matter to its counterpart ${\cal J}$ in vacuum $\widetilde{\cal J}/{\cal J} \approx 1/(\hat{C}^{}_{12} \hat{C}^{}_{13})$ holds as an excellent approximation, where $\hat{C}^{}_{12} \equiv \sqrt{1 - 2 \hat{A}^{}_* \cos 2θ^{}_{12} + \hat{A}^2_*}$ with $\hat{A}^{}_* \equiv a\cos^2 θ^{}_{13}/Δ^{}_{21}$ and $\hat{C}^{}_{13} \equiv \sqrt{1 - 2 A^{}_{\rm c} \cos 2θ^{}_{13} + A^2_{\rm c}}$ with $A^{}_{\rm c} \equiv a/Δ^{}_{\rm c}$. Here $Δ^{}…
The Jarlskog Invariant $J_{ν-map}$ of the neutrino mapping matrix is calculated based on a phenomenological model which relates the smallness of light lepton masses $m_e$ and $m_1$ (of $ν_1$) with the smallness of $T$ violation. For small $T$ violating phase $χ_l$ in the lepton sector, $J_{ν-map}$ is proportional to $χ_l$, but $m_e$ and $m_1$ are proportional to $χ_l^2$. This leads to $ J_{ν-map} \cong {1/6}\sqrt{\frac{m_e}{m_μ}}+O \bigg(\sqrt{\frac{m_em_μ}{m_τ^2}}\bigg)+O \bigg(\sqrt{\frac{m_1m_2}{m_3^2}}\bigg)$. Assuming $\sqrt{\frac{m_1m_2}{m_3^2}}<<\sqrt{\frac{m_e}{m_μ}}$, we find $J_{ν-ma…
We examine the possibility that the form of the lepton mixing matrix can be determined by extremising the Jarlskog flavour invariants associated, eg. with the commutator ($C$) of the lepton mass matrices. Introducing a strictly covariant approach, keeping masses fixed and extremising the determinant (Tr $C^3/3$) leads to maximal CP violation, while extremising the sum of the $2 \times 2$ principal minors ($-{\rm Tr} C^2/2$), leads to a non-trivial mixing with zero CP violation. Extremising, by way of example, a general linear combination of two CP-symmetric invariants together, we show that ou…
In this paper, the flavor structure of quark and lepton EDMs in the SM and beyond is investigated using tools inspired from Minimal Flavor Violation. While Jarlskog-like flavor invariants are adequate for estimating CP-violation from closed fermion loops, non-invariant structures arise from rainbow-like processes. Our goal is to systematically construct these latter flavor structures in the quark and lepton sectors, assuming different mechanisms for generating neutrino masses. Numerically, they are found typically much larger, and not necessarily correlated with, Jarlskog-like invariants. Fina…
The renormalization-group equation (RGE) approach to neutrino matter effects is further developed in this work. We derive a complete set of differential equations for effective mixing elements, masses and Jarlskog-like invariants in presence of a light sterile neutrino. The evolutions of mixing elements as well as Jarlskog-like invariants are obtained by numerically solving these differential equations. We calculate terrestrial matter effects in long-baseline (LBL) experiments, taking NOvA, T2K and DUNE as examples. In both three-flavor and four-flavor frameworks, electron-neutrino survival pr…
As SMEFT is a framework of growing importance to analyze high-energy data, understanding its parameter space is crucial. The latter is commonly split into CP-even and CP-odd parts, but this classification is obscured by the fact that CP violation is actually a collective effect that is best captured by considering flavor-invariant combinations of Lagrangian parameters. First we show that fermion rephasing invariance imposes that several coefficients associated to dimension-six operators can never interfere with operators of dimension $\leq4$ and thus cannot appear in any physical observable at…
For neutrino propagation in matter, we show that the Jarlskog invariant, which controls the size of true CP violation in neutrino oscillation appearance experiments, factorizes into three pieces: the vacuum Jarlskog invariant times two simple two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. If the solar effective matter potential and the atmospheric effective $Δm^2$ are chosen carefully for these two resonance factors, then the fractional corrections to this factorization are an impressive 0.04\% or smaller. We also sho…
Parametrization of the quark and lepton mixing matrices is the first attempt to understand the mixing of fermions. In this work, we parameterize the quark and lepton matrices with the help of quark-lepton complementarity (QLC) in a tri-bimaximal pattern of lepton mixing matrix. In this way, we combine the parametrization of the two matrices with each other. We apply this new parametrization to several physical quantities, and show its simplicity in the expression of, e.g., the Jarlskog parameter of CP violation.
A preliminary determination of the Dirac phase in the PMNS matrix is $\dell\approx -\fracπ{2}$. A rather accurately determined Jarlskog invariant $J$ in the CKM matrix is close to the maximum. Since the phases in the CKM and PMNS matrices will be accurately determined in the future, it is an interesting problem to relate these two phases. This can be achieved in a families-unified grand unification if the weak CP violation is introduced spontaneously {\it à la} Froggatt and Nielsen at a high energy scale, where only one meaningful Dirac CP phase appears.
Terrestrial matter effects in neutrino propagation are T-invariant, so that any observed T violation when neutrinos pass through the Earth, such as an asymmetry between the transition probabilities P(nu_mu -> nu_e) and P(nu_e -> nu_mu), would be a direct indication of T violation at the fundamental level. Matter effects do however modify the magnitudes of T-violating asymmetries, and it has long been known that resonant enhancement can lead to large effects for a range of plausible values of the relevant parameters. We note that the determinant of the commutator of the lepton mass matrices is …
The observation of a charged-lepton flavor violating process would be a definite sign for physics beyond the Standard Model, but would actually only prove that one particular linear combination of lepton numbers is violated. We categorize lepton-flavor-violating processes by their quantum numbers and show how their discovery can be interpreted model independently, studying in particular which processes are required to establish that the entire flavor group is broken. We also comment on total lepton number, seeing as lepton number violation practically implies lepton flavor violation as well.
We report on the recent results of searches for lepton-flavor-violating tau decays as well as lepton-number-violating B decays with the world-highest data samples accumulated at the Belle.
Implications of a simple model for the mass generation of leptons are studied, in particular for the upcoming long-baseline neutrino experiments. The flavor mixing angles are large (nearly maximal). The probability for the long-baseline ν_μ\leftrightarrow ν_e oscillation is predicted to be about 1%.
We discuss the relation between the CP violation of the quark mixing and that of the lepton mixing by investigating a CP violating observable, the Jarlskog invariant, as well as the CP violating Dirac phase. The down-type quark mass matrix with three zeros is given in terms of the minimal number of parameters, while the up-type quark mass matrix is diagonal. These quark mass matrices leading to the successful CKM mixing angles and CP violation are embedded in both the Pati--Salam and SU(5) models. The leptonic Jarlskog invariant $J_{CP}^l$ (as well as CP violating Dirac phase) is examined for …
Flavor violating processes in the lepton sector have highly suppressed branching ratios in the standard model. Thus, observation of lepton flavor violation (LFV) constitutes a clear indication of physics beyond the standard model (BSM). We review new physics searches in the processes that violate the conservation of lepton (muon) flavor by two units with muonia and muonium--antimuonium oscillations.
We present a model for calculating charged-lepton mixing matrices. These matrices are an essential ingredient for predicting lepton flavor-violating rates in the lepton number nonuniversal models recently proposed to explain anomalies in B-meson decays. The model is based on work on "constrained flavor breaking" by Appelquist, Bai and Piai relating the charged-lepton mass matrix, M_l, to those for the up and down-type quarks, M_{u,d}. We use our recent model of lepton nonuniversality to illustrate the magnitudes of flavor-violating B-decay rates that might be expected. Decays with mu tau final…
We study the lepton flavor violating process, $e+ T \to τ+T'$, at a few GeV. This process can be studied by experiments directing GeV scale electron or positron beams on internal or fixed targets. We study the effects of some low energy lepton flavor violating interactions on this process. We study the sensitivities of this process on these low energy lepton flavor violating interactions and compare them to the sensitivities of lepton flavor violating $τ$ decay processes. Comparing with $τ$ decay processes, this process provides another way to study the lepton flavor violating effects with $e-…
Recent work on F-theory GUTs has shown that the predicted masses, and magnitudes of the mixing matrix elements in the quark and lepton sectors are in close accord with experiment. In this note we estimate the CP violating phase of the mixing matrices by considering the Jarlskog invariant. We find by carefully treating certain cancellations in the computation of the Jarlskog invariant that |J_quark| ~ alpha_GUT^(3) ~ 6*10^(-5), and that the CP violating phase of the quark sector is large, in accord with experiment. Moreover, we predict (up to order one factors) that |J_lepton| ~ alpha_GUT ~ 4*1…
Neutrino masses and mixings have important implications for models of fermion masses, and, most directly, for the charged lepton sector. We consider supersymmetric Abelian flavor models, where neutrino mass parameters are related to those of charged leptons and sleptons. We show that processes such as τto μγ, μto eγand μ-e conversion provide interesting probes. In particular, some existing models are excluded by current bounds, while many others predict rates within reach of proposed near future experiments. We also construct models in which the predicted rates for charged lepton flavor violat…
The simplest realization of the inverse seesaw mechanism in a $SU(3)_C \otimes SU(3)_L \otimes U(1)_X$ gauge theory offers striking flavor correlations between rare charged lepton flavor violating decays and the measured neutrino oscillations parameters. The predictions follow from the gauge structure itself without the need for any flavor symmetry. Such tight complementarity between charged lepton flavor violation and oscillations renders the scenario strictly testable.
In the light of the recent measurement of the leptonic mixing angle $θ_{13}$, implications of the latest mixing data have been investigated for non-minimal textures of lepton mass matrices pertaining to Dirac neutrinos. All these texture specific lepton mass matrices have been examined for their compatibility with the latest data in the cases of normal hierarchy, inverted hierarchy and degenerate scenario of neutrino masses. The implications of all the three lepton mixing angles have been investigated on the lightest neutrino mass as well as the Jarlskog's CP violating parameter in the leptoni…
An analysis of the leptonic texture for the new triangular mass matrices has been carried out. In particular, it is shown that both bimaximal and nearly bimaximal solutions for solar and atmospheric neutrino anomalies can be generated within this pattern. We have also derived exact and compact parametrization of the leptonic mixing matrix in terms of the lepton masses and the parameters $α, β'$ and $δ$. A consistency with the CHOOZ reactor result for $V_m{_{13}}$ and a smallness of the Jarlskog's invariant parameter are obtained.
Lepton Flavor Violating (LFV) processes are clear signals of physics beyond the Standard Model. We investigate the possibility of measuring this kind of processes at present and foreseeable future muon-electron colliders, taking into account present day bounds from existing experiments. As a model of new physics we consider a Z' boson with a $U'(1)$ gauge symmetry and generic couplings. Processes that violate lepton flavor by two units seem to be particularly promising.
We investigate collider signatures of standard model extensions featuring vector-like leptons and a flavorful scalar sector. Such a framework arises naturally within asymptotically safe model building, which tames the UV behavior of the standard model towards the Planck scale and beyond. We focus on values of Yukawa couplings and masses which allow to explain the present data on the muon and electron anomalous magnetic moments. Using a CMS search based on $77.4 \, \rm{fb}^{-1}$ at the $\sqrt{s}=13$ TeV LHC we find that flavorful vector-like leptons are excluded for masses below around $300$ Ge…
In the coming years, experiments underway will increase the sensitivity to charged lepton flavor violation by four orders of magnitude. These experiments will stringently probe weak scale physics. I review the status of global symmetries in the standard model and present several well-motivated models that predict observable lepton flavor violation. Finally, I describe what we might learn from future experimental results, whether positive or null.
Most extensions of the Standard Model lepton sector predict large lepton flavor violating rates. Given the promising experimental perspectives for lepton flavor violation in the next few years, this generic expectation might offer a powerful indirect probe to look for new physics. In this review we will cover several aspects of lepton flavor violation in supersymmetric models beyond the Minimal Supersymmetric Standard Model. In particular, we will concentrate on three different scenarios: high-scale and low-scale seesaw models as well as models with R-parity violation. We will see that in some…
A recent proposal for explaining discrepancies in angular observables in the rare decay B --> K*mu+mu- with a gauged L_mu - L_tau current carried with it the prediction of lepton flavor universality violation in related B-meson decays. This prediction gained empirical support with a subsequent hint for lepton flavor universality violation in the B --> K l+l- decay by LHCb. In this short paper we fully quantify the prediction including the associated uncertainties. We also provide new predictions for a variety of additional observables sensitive to lepton flavor universality violation in B-meso…
Non-Abelian discrete symmetries provide an interesting opportunity to address the flavor puzzle in the lepton sector. However, the number of currently viable models based on such symmetries is rather large. High-precision measurements of the leptonic mixing parameters by future neutrino experiments, including ESSnuSB, T2HK, DUNE, and JUNO, will be crucial to test such models. We show that the complementarity among these experiments offers a powerful tool for narrowing down this broad class of lepton flavor models.
New physics scenarios beyond the Standard Model (SM) for neutrino mass mechanism often necessitate the existence of a neutral scalar $H$ and/or doubly-charged scalar $H^{\pm\pm}$, which couple to the SM charged leptons in a flavor violating way, while evading all existing constraints. Such scalars could be effectively produced at future lepton colliders like CEPC, ILC, FCC-ee and CLIC, either on-shell or off-shell, and induce striking charged lepton flavor violating (LFV) signals. We find that a large parameter space of the scalar masses and the LFV couplings can be probed at lepton colliders,…
We analyze the scalar lepton mass matrices in a supersymmetric SO(10) grand unified model with soft SUSY breaking terms generated at Planck scale and a Georgi-Jarslkog Yukawa texture at GUT scale induced by higher dimensional operators. This model predicts lepton flavor violation. The predictive features of the Georgi-Jarlskog texture are used to estimate branching ratios for the radiative decays $e_{a} \rightarrow e_{b}+γ,$ and we find rates that could provide an experimental test for this kind of model.
We introduce the program SuSeFLAV for computing supersymmetric mass spectra with flavor violation in various supersymmetric breaking scenarios with/without seesaw mechanism. A short user guide summarizing the compilation, executables and the input files is provided.
We present the correlation of low energy CP phases, both Dirac and Majorana, and the lepton asymmetry for the baryon asymmetry in the universe, with a certain class of Yukawa matrices that consist of two right-handed neutrinos and include one texture zero in themselves. For cases in which the amount of the lepton asymmetry $Y_L$ turns out to be proportional to $θ_{13}^2$, we consider the relation between two types of CP phases and the relation of $Y_L$ versus the Jarlskog invariant or the amplitude of neutrinoless double beta decay as $θ_{13}$ varies.
We consider a parametrization of the lepton mixing matrix in which the deviations from maximal atmospheric mixing and vanishing reactor mixing are obtained in terms of small corrections from the charged lepton sector. Relatively large deviations for the reactor mixing angle from zero as indicated by T2K experiment can be obtained in this parametrization. We are able to further reduce the number of complex phases, thus, simplifying the analysis. In addition, we have obtained the sides of unitarity triangles and the vacuum oscillation probabilities in this parametrization. The Jarlskog rephasing…
In the standard model (SM), lepton flavor violating (LFV) Higgs decay is absent at renormalizable level and thus it is a good probe to new physics. In this article we study a type of new physics that could lead to large LFV Higgs decay, i.e., a lepton-flavored dark matter (DM) model which is specified by a Majorana DM and scalar lepton mediators. Different from other similar models with similar setup, we introduce both left-handed and right-handed scalar leptons. They allow large LFV Higgs decay and thus may explain the tentative Br$(h\raτμ)\sim1\%$ experimental results from the LHC. In partic…
In the minimal supersymmetric standard model, we have studied the evolution of the neutrino flavor mixing by using the renormalization group equation(RGE) with the Georgi-Jarlskog texture for the Yukawa coupling matrices.For the large Yukawa coupling of the charged lepton, i.e.,$\tan\b \gg 1$, the neutrino flavor mixing increases significantly with running down to the electroweak scale by the RGE. If one wishes to get the large neutrino flavor mixing $\sin þ_{23}$ at the electroweak scale, which is suggested by the muon neutrino deficit in the atomospheric neutrino flux, the initial condition …
Even if quark and lepton masses are not uniquely predicted by the fundamental theory, as may be the case in the string theory landscape, nevertheless their pattern may reveal features of the underlying theory. We use statistical techniques to show that the observed masses appear to be representative of a scale invariant distribution, rho(m) ~ 1/m. If we extend this distribution to include all the Yukawa couplings, we show that the resulting CKM matrix elements typically show a hierarchical pattern similar to observations. The Jarlskog invariant measuring the amount of CP violation is also well…
Models of minimal lepton flavor violation where the seesaw scale is higher than the relevant flavor scale predict that all lepton flavor violation is proportional to the charged lepton Yukawa matrix. If extra vector-like leptons are within the reach of the LHC, it will be possible to test the resulting predictions in ATLAS/CMS.
We discuss the impact of fermion mass matrices on some lepton number violating processes, namely baryogenesis via leptogenesis and neutrinoless double beta decay, and on some lepton flavor violating processes, namely radiative lepton decays in supersymmetric seesaw models.
Dark, chiral fermions carrying lepton flavor quantum numbers are natural candidates for freeze-in. Small couplings with the Standard Model fermions of the order of lepton Yukawas are `automatic' in the limit of Minimal Flavor Violation. In the absence of total lepton number violating interactions, particles with certain representations under the flavor group remain absolutely stable. For masses in the GeV-TeV range, the simplest model with three flavors, leads to signals at future direct detection experiments like DARWIN. Interestingly, freeze-in with a smaller flavor group such as $SU(2)$ is …
The experimental status of charged lepton flavor violation searches is briefly reviewed, with particular emphasis on the three classical searches involving muon transisions: $μ\to e γ$, $μ\to e$ conversion and $μ\to 3e$.
We extend the notion of Minimal Flavor Violation to the lepton sector. We introduce a symmetry principle which allows us to express lepton flavor violation in the charged lepton sector in terms of neutrino masses and mixing angles. We explore the dependence of the rates for flavor changing radiative charged lepton decays (ell(i) -> ell(j) + gamma) and mu-to-e conversion in nuclei on the scales for total lepton number violation, lepton flavor violation and the neutrino masses and mixing angles. Measurable rates are obtained when the scale for total lepton number violation is much larger than th…
We show that non-Hermitian and nearest-neighbor-interacting perturbations to the Fritzsch textures of lepton and quark mass matrices can make both of them fit current experimental data very well. In particular, we obtain θ_{23} \simeq 45^\circ for the atmospheric neutrino mixing angle and predict θ_{13} \simeq 3^\circ to 6^\circ for the smallest neutrino mixing angle when the perturbations in the lepton sector are at the 20% level. The same level of perturbations is required in the quark sector, where the Jarlskog invariant of CP violation is about 3.7 \times 10^{-5}. In comparison, the streng…
In this talk, I will present the status of lepton flavor physics in composite Higgs models with partial compositeness in the light of recent data in the lepton sector. I will consider anarchic flavor setups, scenarios with flavor symmetries, and minimal incarnations of the see-saw mechanism that naturally predict non-negligible lepton compositeness. The focus will be on lepton flavor violating processes, dipole moments, and on probes of lepton flavor universality, all providing stringent tests of partial compositeness. The expected size of effects in the different approaches to lepton flavor a…
We explain the imbalance of the flavor mixing angles between the quark and the lepton sectors in the context of the SU(5) GUT with the see-saw mechanism. The quark masses and the CKM matrix elements are obtained by using, respectively, the Fritzsch and Branco - Silva-Marcos form for the up- and down-quark Yukawa matrices (y^u and y^d) at the GUT scale. The charged-lepton Yukawa matrix (y^e) is the transpose of y^d, modified by the Georgi-Jarlskog factor. We show that the neutrino masses and mixing angles suggested by the recent solar and atmospheric neutrinos are then obtained from a simple te…
We propose two phenomenological scenarios of lepton mass matrices and show that either of them can exactly give rise to \tan^2θ_{13} = m_e/(m_e + 2m_μ), \tan^2θ_{23} = m_μ/(m_e + m_μ) and \tan^2θ_{12} = (m_e m_2 + 2m_μm_1)/(m_e m_1 + 2m_μm_2) in the standard parametrization of lepton flavor mixing. The third relation, together with current experimental data, predicts a normal but weak hierarchy for the neutrino mass spectrum. We also obtain θ_{13} \approx 2.8^\circ for the smallest neutrino mixing angle and J \approx 1.1% for the Jarlskog invariant of leptonic CP violation, which will soon be …
We show that in supersymmetric models with explicit flavor lepton number violation due to soft supersymmetry breaking terms there must be flavor lepton number violation in slepton decays. We propose to look for flavor lepton number violation in righthanded selectron and smuon decays. For selectron and smuon lighter than 80 Gev flavor lepton number violation in slepton decays could be discovered at LEP2 provided the mixing betwen selectron and smuon is not small. We also estimate NLC discovery potential of the lepton flavor number violation in slepton decays.
The observation of charged lepton flavor violation is a clear sign of physics beyond the Standard Model (SM). In this work, we investigate the sensitivity of future lepton colliders to charged lepton flavor violation via on-shell production of bileptons, and compare their sensitivity with current constraints and future sensitivities of low-energy experiments. Bileptons couple to two charged leptons with possibly different flavors and are obtained by expanding the general SM gauge invariant Lagrangians with or without lepton number conservation. We find that future lepton colliders will provide…
