Sources Of CP Violation Research Articles

Predictions for the leptonic Dirac CP-violating phase

In this paper, we explore the theoretical constraints on the observable parameters of neutrino mixing on predictions for the leptonic Dirac CP-violating phase within a well-studied class of simple theoretical models that includes a single source of CP violation due to charged lepton corrections. The approach guarantees that a physically meaningful prediction for the most likely values for the leptonic Dirac CP-violating phase is obtained.

Filtered asymmetric dark matter during the Peccei-Quinn phase transition

In this paper, we propose a bubble filtering-out mechanism for an asymmetric dark matter scenario during the Peccei-Quinn (PQ) phase transition. Based on a QCD axion model, extended by extra chiral neutrinos, we show that the PQ phase transition can be first order in the parameter space of the model and regarding the PQ symmetry breaking scale, the mechanism can generate PeV-scale heavy neutrinos as a dark matter candidate. Considering a CP-violating source, during the phase transition, discriminating between the neutrino and antineutrino number density, we find the observed dark matter relic abundance, such that the setup can be applied to the first order phase transition with different strengths. We then calculate effective couplings of the QCD axion addressing the strong CP problem within the model. We also study the energy density spectrum of gravitational waves generated from the first order phase transition and show that the signals can be detected by future ground-based detectors such as Einstein Telescope. In particular, for a visible heavy axion case of the model, it is shown that gravitational waves can be probed by DECIGO and BBO interferometers. Furthermore, we discuss the dark matter-standard model neutrino annihilation process as a source for the creation of PeV-scale neutrinos.

Uncovering an axion mechanism with the EDM portfolio

Effective field theory arguments suggest that if BSM sectors contain new sources of CP-violation that couple to QCD, these sources will renormalize the $\theta$ term and frustrate ultraviolet solutions to the strong CP problem. Simultaneously, they will generate distinctive patterns of low-energy electric dipole moments in hadronic, nuclear, atomic, and molecular systems. Observing such patterns thus provides evidence that strong CP is solved by an infrared relaxation mechanism. We illustrate the renormalization of $\theta$ and the collections of EDMs generated in a several models of BSM physics, confirming effective field theory expectations, and demonstrate that measurements of ratios of electric dipole moments at planned experiments can provide valuable input on the resolution of the strong CP problem.

Leptogenesis and low-energy CP violation in a type-II-dominated left-right seesaw model

We consider leptogenesis in a left-right-symmetric seesaw scenario in which neutrino mass generation and leptogenesis are dominated by the type-II seesaw term. Motivated by grand unification, we assume that the neutrino Dirac mass matrix is dominated by a single entry of the order of the top-quark mass, which leaves the low-energy phases of the lepton mixing matrix as the only sources of CP violation. Working in a regime where the triplet scalar predominantly decays into leptons, this results in a predictive scenario based on a minimal number of parameters. We perform a detailed analysis of the flavored Boltzmann equations within a revised density matrix framework and demonstrate that the observed baryon asymmetry can be successfully generated in this simple model. We point out that the significance of flavor effects is limited, and we discuss the implications for low-energy observables such as the Dirac CP phase and neutrinoless double beta decay.

The search for the neutron electric dipole moment at PSI

The existence of a nonzero permanent electric dipole moment (EDM) of the neutron would reveal a new source of CP violation and shed light on the origin of the matter–antimatter asymmetry of the Universe. The sensitivity of current experiments using stored ultracold neutrons (UCN) probe new physics beyond the TeV scale. Using the UCN source at the Paul Scherrer Institut, the nEDM collaboration has performed the most sensitive measurement of the neutron EDM to date, still compatible with zero (|d_n|<1.8\times 10^{-26} \, e {cm}|dn|<1.8×10−26ecm, C.L.,90%). A new experiment designed to improve the sensitivity by an order of magnitude, n2EDM, is currently under construction.

Broken scaling neutrino mass matrix and leptogenesis based on A4 modular invariance

In this work, we have proposed a modular A4 symmetric model of neutrino mass which, simultaneously, explains observed baryon asymmetry of the Universe (BAU). In minimal extension of the standard model (SM) with two right-handed neutrinos we work in a supersymmetric framework. At Type-I seesaw level, the model predicts scaling in the neutrino mass matrix. In order to have correct low energy phenomenology, we propose two possible scenarios of scale-breaking in the neutrino mass matrix emanating from Type-I seesaw. Scenario-1 is based on the dimension-5 Weinberg operator whereas scenario-2 implements Type-II seesaw via scalar triplet Higgs superfields (∆, overline{Delta } ). Interestingly, the breaking patterns in both, otherwise dynamically different scenarios, are similar which can be attributed to the same charge assignments of superfields (∆, overline{Delta } ) and the Higgs superfield Hu under modular A4 symmetry. The breaking is found to be proportional to the Yukawa coupling of modular weight 10 ( {Y}_{1,1prime}^{10} ). We, further, investigates the predictions of the model under scenario-2 (Type-I+II) for neutrino mass, mixings and matter-antimatter asymmetry of the Universe. The model predicts normal hierarchical neutrino masses and provide a robust range (0.05 − 0.08)eV for sum of neutrino masses (Σmi). Lepton number violating 0νββ decay amplitude (Mee) is obtained to lie in the range (0.04 − 0.06)eV. Future 0νββ decay experiments such as NEXT and nEXO shall pose crucial test for the model. Both CP conserving and CP violating solutions are allowed in the model. Interesting correlations are obtained, specially, between Yukawa couplings of modular weight 2 and complex modulus τ. Contrary to {Y}_2^2 and {Y}_3^2 , the Yukawa coupling {Y}_1^2 is found to be insensitive to τ and thus to CP violation because complex modulus τ is the only source of CP violation in the model. We, also, investigate the prediction of the model for BAU. The model exhibit consistent explanation of BAU for right-handed Majorana neutrino mass scale in the range ((1 − 5) × 1013) GeV.

Flavour mixing transport theory and resonant leptogenesis

We derive non-equilibrium quantum transport equations for flavour-mixing fermions. We develop the formalism mostly in the context of resonant leptogenesis with two mixing Majorana fermions and one lepton flavour, but our master equations are valid more generally in homogeneous and isotropic systems. We give a hierarchy of quantum kinetic equations, valid at different approximations, that can accommodate helicity and arbitrary mass differences. In the mass-degenerate limit the equations take the familiar form of density matrix equations. We also derive the semiclassical Boltzmann limit of our equations, including the CP-violating source, whose regulator corresponds to the flavour coherence damping rate. Boltzmann equations are accurate and insensitive to the particular form of the regulator in the weakly resonant case ∆m » Γ, but for ∆m ≲ Γ they are qualitatively correct at best, and their accuracy crucially depends on the form of the CP-violating source.

Flavor dependent U(1) symmetric Zee model with a vector-like lepton

We extend the Zee model by introducing a vector-like lepton doublet and a flavor dependent global U(1) symmetry. Flavor changing neutral currents in the quark sector can be naturally forbidden at tree level due to the U(1) symmetry, while sufficient amount of lepton flavor violation is provided to explain current neutrino oscillation data. In our model, additional sources of CP-violation appear in the lepton sector, but their contribution to electric dipole moments is much smaller than current experimental bounds due to the Yukawa structure constrained by the U(1) symmetry. We find that there is a parameter region where the strongly first order electroweak phase transition can be realized, which is necessary for the successful scenario of the electroweak baryogenesis in addition to new CP-violating phases. In the benchmark points satisfying neutrino data, lepton flavor violation data and the strongly first order phase transition, we show that an additional CP-even Higgs boson H mainly decays into a lighter CP-odd Higgs boson A, i.e., H→AZ or H→AA with a characteristic pattern of lepton flavor violating decays of A.

New Sources of Leptonic CP Violation at the DUNE Neutrino Experiment

We check the capability of the DUNE neutrino experiment to detect new sources of leptonic CP violation beside the single phase expected in the Standard Model. We illustrate our strategy based on the measurement of CP asymmetries in the case that new physics will show up as nonstandard neutrino interactions and sterile neutrino states and show that the most promising one, once the experimental errors are taken into account in both scenarios, is the one related to the νμ→νe transition.

Finger printing the presence of extra scalars in the h \u2192 Vff\u2032 forward-backward asymmetry

In this work we analyse the forward-backward asymmetry of the h → V f f′ decay in the Aligned two-Higgs Doublet Model. The Standard Model prediction for this asymmetry for V = W is small, as it suffers from Yukawa suppression and is absent for V = Z. This does not necessarily have to hold true in the Aligned model where these contributions can in principle be re-enhanced through the independent alignment factors ςf. In this analysis we conclude that, due to the additional contributions corresponding to the Aligned two-Higgs Doublet Model together with extra sources of CP-violation for the V = Z channel, the Standard Model predictions can be significantly modified in a great region of the parameter space. These deviations, that could be potentially measured at the High Luminosity LHC or future Higgs factories, would be a clear signal of new physics, and would shed new light on the possible extensions of the Standard Model and new sources of CP-violation.

Global fits in the Aligned Two-Higgs-Doublet model

We present the results of a global fit to the Aligned Two-Higgs Doublet Model, assuming that there are no new sources of CP violation beyond the quark mixing matrix. We use the most constraining flavour observables, electroweak precision measurements and the available data on Higgs signal strengths and collider searches for heavy scalars, together with the theoretical requirements of perturbativity and positivity of the scalar potential. The combination of all these constraints restricts the values of the scalar masses, the couplings of the scalar potential and the flavour-alignment parameters. The numerical fits have been performed using the open-source HEPfit package.

Electric dipole moments in the extended scotogenic models

Electric dipole moments (EDMs) of charged leptons arise from a new source of CP violation in the lepton sector. In this paper, we calculate the EDMs of the charged leptons in the minimal scotogenic model with two singlet fermions, and the models extended with one or two triplet fermions instead of the singlet fermions, taking into account the constraints of the neutrino oscillation data, the charged lepton flavor violation and perturbative unitarity bound for the Yukawa couplings. We show that the hybrid model with one singlet and one triplet fermions predicts an electron EDM larger than the other models in both normal and inverted neutrino mass hierarchy. We find some parameter space has already been ruled out by the current upper bound of the electron EDM and further parameter space can be explored by future experiments.

Flavor-diagonal CP violation: the electric dipole moment.

The observed baryon asymmetry in the universe cannot be reconciled with the current form of the Standard Model (SM) of particle physics. The Standard Model breaks charge conjugation parity (CP) symmetry, but not in a sufficient amount to explain the observed matter-antimatter asymmetry. Historically one of the first systems to be studied in the search of symmetry breaking within the Standard Model is the electric dipole moment (EDM) of the neutron. The contribution to the neutron EDM coming from the SM is several order of magnitudes smaller than the current experimental bound, thus providing a unique, background-free window for potential discovery of physics Beyond the Standard Model (BSM). The strong CP-violating theta term can also contribute to the neutron EDM, as can all the CP-violating effective operators describing, at energies below the electro-weak scale, the contributions from BSM. To constrain all these contributions to the neutron EDM we need to precisely determine the hadronic matrix elements of the corresponding renormalized operators. After a brief introduction on baryon asymmetry and baryogenesis, I summarize the current stuatus for experiments in search of a neutron EDM. I then describe in more details the different CP-violating sources, and some results in Chiral Perturbation Theory precede a discussion on the current status of Lattice QCD calculations. I will in particular focus on the 2 main challenges for these type of calculations: the signal-to-noise ratio and the renormalization. I will discuss several improvement techniques trying to improve these two aspects of the calculation and I will conclude with an optimistic view into the future.

Strong first order electroweak phase transition in 2HDM confronting future Z & Higgs factories

The electroweak phase transition can be made first order by extending the Standard Model (SM) Higgs sector with extra scalars. The same new physics can explain the matter-antimatter asymmetry of the universe by supplying an extra source of CP violation and sphaleron processes. In this paper we study the existence of strong first order electroweak phase transition (SFOEWPT) in the type-I and type-II two Higgs doublet models (2HDM). We focus on how the SFOEWPT requirements constraint the spectrum of non-SM Higgs. Through the parameter space scan, we find that SFOEWPT suggests an upper limit on the masses of heavy Higgs {m}_{A/H/{H}^{pm }} , which is around 1 TeV. High temperature expansion and Higgs vacuum uplifting is used for an analytical understanding of our results. After taking into account the probe ability on SFOEWPT from theoretical constraints, Higgs and Z-pole precision measurements up to the one-loop level at future Higgs & Z factories, sizeable loop corrections require {m}_{A/{H}^{pm }}-{m}_H ∈ (100, 250) GeV to meet SFOEWPT condition for Type-II 2HDM, and left|{m}_{A/{H}^{pm }}-{m}_Hright| ∈ (100, 350) GeV or left|{m}_A-{m}_{H/{H}^{pm }}right| ∈ (100, 350) GeV for Type-I 2HDM.

CP violation in mixing and oscillations in a toy model for leptogenesis with quasi-degenerate neutrinos

We study the sources of CP violation for baryogenesis models with quasi-degenerate neutrinos. Our approach is to use the renormalized propagator in a quantum field theory model of neutrino oscillations, paying close attention to unitarity requirements. From the probabilities of lepton number violating processes obtained in this way, we derive a source term for the time evolution of the lepton asymmetry. The source term has contributions that can be identified with CP violation from mixing, oscillations and interference between both. Given that this source term does not involve processes with unstable particles in the initial or final states, neither does it require to calculate number densities of neutrinos, no subtraction of real intermediate states must be performed. In equilibrium the source term is null, as demanded by unitarity and CPT invariance, due to a cancellation between the terms coming from CP violation in mixing and oscillations. The calculations are done in a simple scalar toy model, and the resummed propagator is diagonalized at first order in the decay widths over the mass difference. We also comment on the effect of the interference term, which is mild at the order we work, but seems to become more important with increasing degeneracy.

Electric dipole moments, new forces and dark matter

New sources of CP violation beyond the Standard Model are crucial to explain the baryon asymmetry in the Universe. We discuss the impact of new CP violating interactions in theories where a dark matter candidate is predicted by the cancellation of gauge anomalies. In these theories, the constraint on the dark matter relic density implies an upper bound on the new symmetry breaking scale from which all new states acquire their masses. We investigate in detail the predictions for electric dipole moments and show that if the relevant CP-violating phase is large, experiments such as the ACME collaboration will be able to fully probe the theory.

CP violating effects in 210Fr and prospects for new physics beyond the Standard Model

We report theoretical results of the electric dipole moment (EDM) of 210Fr which arises from the interaction of the EDM of an electron with the internal electric field in an atom and the scalar-pseudoscalar electron-nucleus interaction; the two dominant sources of CP violation in this atom. Employing the relativistic coupled-cluster theory, we evaluate the enhancement factors for these two CP violating interactions to an accuracy of about 3% and analyze the contributions of the many-body effects. These two quantities in combination with the projected sensitivity of the 210Fr EDM experiment provide constraints on new physics beyond the Standard Model. Particularly, we demonstrate that their precise values are necessary to account for the effect of the bottom quark in models in which the Higgs sector is augmented by nonstandard Yukawa interactions such as the two-Higgs doublet model.

Confirming the existence of the strong CP problem in lattice QCD with the gradient flow

We calculate the electric dipole moment of the nucleon induced by the QCD theta term. We use the gradient flow to define the topological charge and use $N_f = 2+1$ flavors of dynamical quarks corresponding to pion masses of $700$, $570$, and $410$ MeV, and perform an extrapolation to the physical point based on chiral perturbation theory. We perform calculations at $3$ different lattice spacings in the range of $0.07~{\rm fm} < a < 0.11$ fm at a single value of the pion mass, to enable control on discretization effects. We also investigate finite size effects using $2$ different volumes. A novel technique is applied to improve the signal-to-noise ratio in the form factor calculations. The very mild discretization effects observed suggest a continuum-like behavior of the nucleon EDM towards the chiral limit. Under this assumption our results read $d_{n}=-0.00152(71)\ \bar\theta\ e~\text{fm}$ and $d_{p}=0.0011(10)\ \bar\theta\ e~\text{fm}$. Assuming the theta term is the only source of CP violation, the experimental bound on the neutron electric dipole moment limits $\left|\bar\theta\right| < 1.98\times 10^{-10}$ ($90\%$ CL). A first attempt at calculating the nucleon Schiff moment in the continuum resulted in $S_{p} = 0.50(59)\times 10^{-4}\ \bar\theta\ e~\text{fm}^3$ and $S_{n} = -0.10(43)\times 10^{-4}\ \bar\theta\ e~\text{fm}^3$.

Quark level and hadronic contributions to the electric dipole moment of charged leptons in the standard model

We evaluate the electric dipole moment of charged leptons in the standard model, where the complex phase of the Cabibbo-Kobayashi-Maskawa matrix is the only source of CP violation. We first prove that, at the quark-gluon level, it is suppressed by a factor of $m_b^2 m_c^2 m_s^2$ at all orders of perturbation due to the Glashow-Iliopoulos-Maiani mechanism. We then calculate the hadronic long distance contribution generated by vector mesons at one-loop level. The $|\Delta S|=1$ weak hadronic interaction is derived using the factorization, and the strong interaction is modeled by the hidden local symmetry framework. We find that the electric dipole moments of charged leptons obtained from this hadronic mechanism are much larger than the perturbative four-loop level quark-gluon process, by several orders of magnitude.

The \(\varepsilon '/\varepsilon \)-story: 1976–2021

The ratio $\epsilon'/\epsilon$ measures the size of the direct CP violation in $K_L\to\pi\pi$ decays $(\epsilon^\prime)$ relative to the indirect one described by $\epsilon$ and is very sensitive to new sources of CP violation. As such it played a prominent role in particle physics already for 45 years. Due to the smallness of $\epsilon'/\epsilon$ its measurement required heroic efforts in the 1980s and the 1990s on both sides of the Atlantic with final results presented by NA48 and KTeV collaborations 20 years ago. Unfortunately, even 45 years after the first calculation of $\epsilon'/\epsilon$ we do not know to which degree the Standard Model agrees with this data and how large is the room left for new physics contributions to this ratio. This is due to significant non-perturbative (hadronic) uncertainties accompanied by partial cancellation between the QCD penguin contributions and electroweak penguin contributions. While the significant control over the short distance perturbative effects has been achieved already in the early 1990s, with several improvements since then, different views on the non-perturbative contributions to $\epsilon'/\epsilon$ have been expressed by different authors over last thirty years. In fact even today the uncertainty in the room left for NP contributions to $\epsilon'/\epsilon$ is very significant. My own work on $\epsilon'/\epsilon$ started in 1983 and involved both perturbative and non-perturbative calculations. This writing is a non-technical recollection of the steps which led to the present status of $\epsilon'/\epsilon$ including several historical remarks not known to everybody. The present status of the $\Delta I=1/2$ rule is also summarized. This story is dedicated to Jean-Marc Gerard on the occasion of the 35th anniversary of our collaboration and his 64th birthday.