We study the CP violation in two-body nonleptonic decays of $B_c$ meson. We concentrate on the decay channels which contain at least one excited heavy meson in the final states. Specifically, the following channels are considered: $B_c\to c\bar c(2S, 2P)+\bar cq(1S, 1P)$, $B_c\to c\bar c(1S)+\bar cq(2S, 2P)$, $B_c\to c\bar c(1P)+\bar cq(2S)$, $B_c\to c\bar c(1D)+\bar cq(1S, 1P)$, and $B_c\to c\bar c(3S)+\bar cq(1S)$. The improved Bethe-Salpeter method is applied to calculate the hadronic transition matrix element. Our results show that some decay modes have large branching ratios, which is of the order of $10^{-3}$. The CP violation effect in $B_c \rightarrow η_c(1S)+D(2S)$, $B_c \rightarrow η_c(1S)+D_0^{*}(2P)$, and $B_c \rightarrow J/ψ+D^{*}(2S)$ are most likely to be found. If the detection precision of the CP asymmetry in such channels can reach the $3σ$ level, at least $10^7$ $B_c$ events are needed.
Within the framework of a $Z'$ model with non-universal leptonic couplings, we analyze possible signatures of leptonic number violation effects at LHC. Results are described for leptonic energy distributions, both from its specific signature and events number, that could allow us to observe this class of models, under reasonable conditions at LHC.
We show that direct CP violation in semi-leptonic and leptonic decays can occur in multi-Higgs doublet extensions of the electroweak standard model with flavor changing neutral currents. For pion and lepton decays these $CP$ violating effects cannot be constrained directly by experimental data since up to now the branching ratio of the decays $π^-$ and $μ^-$ have not been measured in laboratory.
We study the effects induced by excited leptons on the leptonic tau decay at one loop level. Using a general effective lagrangian approach to describe the couplings of the excited leptons, we compute their contributions to the leptonic decays and use the current experimental values of the branching ratios to put limits on the mass of excited states and the substructure scale.
The Minimal Lepton Flavour Violation (MLFV) framework is discussed after the recent indication for CP violation in the leptonic sector. Among the three distinct versions of MLFV, the one with degenerate right-handed neutrinos will be disfavoured, if this indication is confirmed. The predictions for leptonic radiative rare decays and muon conversion in nuclei are analysed, identifying strategies to disentangle the different MLFV scenarios. The claim that the present anomalies in the semi-leptonic $B$-meson decays can be explained within the MLFV context is critically re-examined concluding that…
We consider effective interactions among excited spin-1/2 and spin-3/2 leptons with the usual ones. Assuming that these new leptons are lighter than the Z0 we will study the constraints on their masses and compositeness scale coming from the leptonic Z0 partial width.
Leptonic CP violation is yet to be confirmed as an additional source of CP violation in fundamental interactions. We study the case where leptonic CP violation is spontaneous and is induced by the mixing with a heavy charged vector-like lepton (VLL). We show that the non-decoupling of this VLL is linked with the presence of CP violation and its coupling with the SM leptons are partly fixed from the SM Yukawas. Due to the large leptonic mixing angles, these couplings are typically of the same order and there is no flavor preference. Strong but not definitive constraints come from charged lepton…
We review some recent results on the connection between CP violation at low energies and Leptogenesis in the framework of specific flavour structures for the fundamental leptonic mass matrices with zero textures.
We study leptonic CP violation from a new perspective. For Majorana neutrinos, a new parametrization for leptonic mixing of the form $V=O_{23} O_{12} K_{a}^{i}\cdot O$ reveals interesting aspects that are less clear in the standard parametrization. We identify several important scenario-cases with mixing angles in agreement with experiment and leading to large leptonic CP violation. If neutrinos happen to be quasi-degenerate, this new parametrization might be very useful, e.g., in reducing the number of relevant parameters of models.
Several topics on CP violation in the lepton sector are reviewed. A few theoretical aspects concerning neutrino masses, leptonic mixing, and CP violation will be covered, with special emphasis on seesaw models. A discussion is provided on observable effects which are manifest in the presence of CP violation, particularly, in neutrino oscillations and neutrinoless double beta decay processes, and their possible implications in collider experiments such as the LHC. The role that leptonic CP violation may have played in the generation of the baryon asymmetry of the Universe through the mechanism …
The current status of our knowledge of the 3-neutrino mixing parameters and of the CP violation in the lepton sector is summarised. The discrete symmetry approach to understanding the observed pattern of neutrino mixing and the related predictions for neutrino mixing angles and leptonic Dirac CP violation are reviewed.
We point out that the determination of the leptonic decay width of radially-excited quarkonia is strongly dependent on the position of the node typical of these excitations. We suggest that this feature could be related with the longstanding rho-pi puzzle.
We introduce a flavor ${\cal U}(1)$ symmetry à la Froggat-Nielsen to explain the magnitude of the CKM mixing angles as well bilarge mixing in the neutrino sector. In the framework of GUTs we also estimate the magnitude of the third leptonic mixing angle $θ_{13}$. Estimates for rare leptonic decays such as $μ\to e \ga $ are also provided. Finally, leptogenesis is exploited for estimating the magnitude of leptonic CP violation.
Future experiments such as SHiP and high-intensity $e^+ e^-$ colliders will have a superb sensitivity to heavy Majorana neutrinos with masses below $M_Z$. We show that the measurement of the mixing to electrons and muons of one such state could imply the discovery of leptonic CP violation in the context of seesaw models. We quantify in the minimal model the CP discovery potential of these future experiments, and demonstrate that a 5$σ$ CL discovery of leptonic CP violation would be possible in a very significant fraction of parameter space.
I review some aspects related with the connections between neutrino physics and the thermal leptogenesis mechanism for the generation of the cosmological baryon asymmetry of the Universe. A special attention is devoted to the problem of establishing a bridge between leptonic CP violation at low and high energies.
We analyze the CP violation in the semileptonic | ΔS|=1 tau-decays in supersymmetric extensions of the standard model (SM) with R parity violating term. We show that the CP asymmetry of tau-decay is enhanced significantly and the current experimental limits obtained by CLEO collaborations can be easily accommodated. We argue that observing CP violation in semi leptonic tau-decay would be a clear evidence for R-parity violating SUSY extension of the SM.
We discuss leptonic mixing and CP violation at low and high energies, emphasizing possible connections between leptogenesis and CP violation at low energies, in the context of lepton flavour models. Furthermore we analyse weak basis invariants relevant for leptogenesis and for CP violation at low energies. These invariants have the advantage of providing a simple test of the CP properties of any lepton flavour model.
We investigate the possibility to find the leptonic CP-violation by combining the reactor experiment with the superbeam experiment without antineutrino superbeam. We show also how much the sensitivity on CP-violating phase delta is affected by the fact that we have not known the sign of Delta m^2_31.
The Daya Bay Collaboration has recently reported the precise measurement of $θ_{13}\simeq 8.8^\circ \pm 0.8^\circ $ or $θ_{13} \neq 0$ at 5.2 σlevel. The observed non-zero $θ_{13}$ can be accommodated by some general modifications to the Democratic mixing matrix. Using such matrices we study the possibility of observing non-zero CP violation in the leptonic sector.
We study hadronic and leptonic flavor physics in a SUSY SO(10) model proposed by Chang, Masiero, and Murayama, which links b -> s transitions to the observed large atmospheric neutrino mixing angle. We find large effects in B_s-B_s-bar mixing and BR(tau -> mu gamma) and comment on B_d -> phi K_S.
The "complementary" Ansatz, Tr$(M_ν)=0$, where $M_ν$ is the prediagonal neutrino mass matrix, seems a plausible approximation for capturing in a self-contained way some of the content of Grand Unification. We study its consequences in the form of relations between the neutrino masses and CP violation phases.
In this talk I discuss CP violation in hyperon decays in Left-Right symmetric models. I show that the asymmetry in polarization in $Λ\to pπ^-$ can be as large as $6\times 10^{-4}$ in these models, which is an order of magnitude larger than the Standard Model prediction.
The spectra and branching ratios of the weak semi-leptonic B meson decays to the first excited D mesons are predicted, taking into account the confined effects of quarks using the covariant oscillator quark model (COQM). In the COQM the same relation between general weak transition form factors as that in HQET is derived, and the concrete form of the Isgur-Wise function is given with no free parameters. Our results are somewhat different from those of other models. The present experimental data are not sufficient for comparison.
We examine the possibility of detecting effects of leptonic CP violation by precise measurement of the solar neutrinos within the framework of standard electroweak theory minimally extended to include neutrino masses and mixing. We prove a ``no-go theorem'' which states that effects of CP violating phase disappear in the nu_e survival probability to the leading order in electroweak interaction. The effects due to the next-to-leading order correction is estimated to be extremely small, effectively closing the door to the possibility we intended to pursue.
We study the leptonic CP violation by employing the complete set of dimension-six pure leptonic effective operators. Connection among the observable at different energy scales can be made by the running of the renormalization group equations. Explicitly, we study the charged lepton electric dipole moment, muon Michel decay, and the triple spin-momentum correlations at the Linear Collider. We found the electron electric dipole moment, which starts at 2-loop level, severely constrains the possibilities to detect the CP violating signatures in muon decay and at the linear colliders.
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 New Physics will show up as Non-Standard 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 $ν_μ\to ν_e$ transition.
We construct extensions of the Standard Model with two Higgs doublets, where there are flavour changing neutral currents both in the quark and leptonic sectors, with their strength fixed by the fermion mixing matrices $V_{CKM}$ and $V_{PMNS}$. These models are an extension to the leptonic sector of the class of models previously considered by Branco, Grimus and Lavoura, for the quark sector. We consider both the cases of Dirac and Majorana neutrinos and identify the minimal discrete symmetry required in order to implement the models in a natural way.
In this talk, we present the physics case for a megaton Water Cerenkov detector in addressing some of the still pending questions in neutrino oscillations physics, particularly the measurement of leptonic CP violation. We compare different future beams that could profit from a water detector and analyse, for the case $θ_{13} \approx 3^\circ$ (the limit that can be reached by under-construction experiments), the signal-to-background rate for a $β$-beam setup with the radioactive ions accelerated to $γ= 350$.
We study leptonic flavor and CP violating observables in supersymmetric (SUSY) models with heavy sfermions, which is motivated by the recent results of the LHC experiments (i.e., the discovery of the Higgs-like boson with the mass of about 126 GeV and the negative searches for the superparticles). Even if the sfermion masses are of O(10-100 TeV), signals may be within the reach of future leptonic flavor- and CP-violation experiments assuming that the off-diagonal elements of the sfermion mass matrices are unsuppressed compared to the diagonal ones. We also consider the SUSY contribution to the…
Using discrete flavour group, $A_5$, combined with generalised CP, we study the mixing parameter correlations which arise from breaking to residual symmetries in the neutrino, $G_ν=\mathbb{Z}_2\times \text{CP}$, and charged lepton sectors, $G_{e}=\mathbb{Z}_2$. By focusing on patterns that agree with current experimental data we demonstrate that non-trivial leptonic phases are predicted and discuss a number of distinctive correlations between mixing parameters.
Flavor effects due to lepton interactions in the early Universe may have played an important role in the generation of the cosmological baryon asymmetry through leptogenesis. If the only source of high-energy CP violation comes from the left-handed leptonic sector, then it is possible to establish a bridge between flavored leptogenesis and low-energy leptonic CP violation. We explore this connection taking into account our present knowledge about low-energy neutrino parameters and the matter-antimatter asymmetry observed in the Universe. In this framework, we find that leptogenesis favors a hi…
Leptogenesis is the most favourable mechanism for generating the observed baryon asymmetry of the Universe (BAU) which implies CP violation in the high energy scale. The low energy leptonic CP violation is expected to be observed in the neutrino oscillations and $0ν2 β$ decay experiments. Generally it is not possible to connect both the CP violations. Here we revisit the issue of connecting the two in flavoured leptogenesis scenario within the Type I seesaw in the light of recent neutrino oscillation and {\it Planck} data. With the recent precise measurements of $θ_{13}$ and BAU we are able to…
We study the correlation between proton lifetime and leptonic CP violation in a class of renormalizable supersymmetric SO(10) grand unified theories (GUTs) with {\bf 10}, {\bf 126} and {\bf 120} Higgs fields, which provides a unified description of all fermion masses and possibly resolution of the strong CP problem. This specific model is unique in that it can readily be compatible with current proton lifetime limits for a supersymmetry (SUSY) breaking scale as low as 5 TeV due to the presence of a specific Yukawa texture. Our investigation here reveals that proton partial lifetimes predicted …
We analyze the capability of the next generation of linear electron--positron colliders to unravel the spin and couplings of excited leptons predicted by composite models. Assuming that these machines will be able to operate both in the $e^+e^-$ and $e^-γ$ modes, we study the effects of the excited electrons of spin $\frac{1}{2}$ and $\frac{3}{2}$ in the reactions $e^-γ\rightarrow e^-γ$ and $e^+e^- \rightarrow γγ$. We show how the use of polarized beams is able not only to increase the reach of these machines, but also to determine the spin and couplings of the excited states.
We review the present understanding of neutrino masses and mixings, discussing what are the unknowns in the three family oscillation scenario. Despite the anticipated success coming from the planned long baseline neutrino experiments in unraveling the leptonic mixing sector, there are two important unknowns which may remain obscure: the mixing angle $θ_{13}$ and the CP-phase $δ$. The measurement of these two parameters has led us to consider the combination of superbeams and neutrino factories as the key to unveil the neutrino oscillation picture.
These proceedings introduce the main techniques and ideas for a systematic effective field theory analysis of CP violation in the charged lepton sector. This study is required because the Standard Model of particle physics predicts a very high degree of CP violation suppression in the lepton sector, and this implies that possible new physics effects can be parameterised in terms of new interactions among the Standard Model fields, in the framework of the so-called Standard Model Effective Field Theory. In analogy with previous investigations of charged lepton flavour violating observables, thi…
We estimate the size of the CP-violating rate asymmetry for the decay Omega^- -> Cascade + pion. Within the standard model we find a value of 2 x 10^(-5), and it could be as much as ten times larger if new physics is responsible for CP violation. Even though our calculation suffers from the usual uncertainty in the estimate of hadronic matrix elements, we find a rate asymmetry that is significantly larger than the corresponding one for octet-hyperon decays.
We show that the simultaneous determination of the leptonic CP-odd phase $δ$ and the angle $θ_{13}$ from the subleading transitions $ν_e\toν_μ$ and ${\barν}_e\to{\barν}_μ$ results generically, at fixed neutrino energy and baseline, in two degenerate solutions. In light of this, we refine a previous analysis of the sensitivity to leptonic CP violation at a neutrino factory, in the LMA-MSW scenario, by exploring the full range of $δ$ and $θ_{13}$. Furthermore, we take into account the expected uncertainties on the solar and atmospheric oscillation parameters and in the average Earth matter densi…
We investigate a general structure of lepton mixing matrix resulting from the SU$_F$(3) gauge family model with an appropriate vacuum structure of SU$_F$(3) symmetry breaking. It is shown that the lepton mixing matrix can be parametrized by using the Wolfenstein parametrization method to characterize its deviation from the tri-bimaximal mixing. A general analysis for the allowed leptonic CP-violating phase $δ_e$ and the leptonic Wolfenstein parameters $λ_e$, $A_e$, $ρ_e$ is carried out based on the observed lepton mixing angles. We demonstrate how the leptonic CP violation correlates to the le…
It was commonly thought that the observation of low energy leptonic CP-violating phases would not automatically imply the existence of a baryon asymmetry in the leptogenesis scenario. This conclusion does not generically hold when the issue of flavour is relevant and properly taken into account in leptogenesis. We illustrate this point with various examples studying the correlation between the baryon asymmetry and the CP-violating asymmetry in neutrino oscillations and the effective Majorana mass in neutrinoless double beta decay.
We study the contribution of the squark flavor mixing from the $LR(RL)$ component of the squark mass matrices to the direct CP violation of the $b\to sγ$ decay and the CP-violating asymmetry in the non-leptonic decays of $B$ mesons. The magnitude of the $LR(RL)$ component is constrained by the branching ratio and the direct CP violation of $b\to sγ$. We predict the correlation of the CP asymmetries among $A_{\text{CP}}^{b \to s γ}$, $\mathcal{S}_{ϕK_S}$ and $\mathcal{S}_{η'K^0}$ of the B decays. The precise data of these CP violations will give us the crucial test for our framework of the squa…
We discuss the usefulness of the CP violating semi-leptonic asymmetry a_{SL} not only as a signal of new physics, but also as a tool in constraining the CKM parameters. We show that this technique could yield useful results in the first years of running at the B factories. We present the analysis graphically in terms of M_{12}, the dispersive part of the B-Bbar mixing amplitude. This is complementary to the usual unitarity triangle representation and often allows a cleaner interpretation of the data.
We point out the possibility of spontaneous and hard CP-violation in the scalar potential of R-parity broken supersymmetric Standard Model. The existence of spontaneous CP-violation depends crucially on the R-parity breaking terms in the superpotential and, in addition, on the choice of the soft supersymmetry breaking terms. Unlike in theories with R-parity conservation, it is natural, in the context of the present model, for the sneutrinos to acquire (complex) vacuum expectation values. In the context of this model we examine here the global implications, like the strength of the CP-violating…
We uncover an interesting phenomenon that neutrino flavor transformation in slowly varying matter density imitates almost exactly that of vacuum neutrino oscillation under suitably chosen experimental parameters. It allows us to have relatively large CP violating measure ΔP \equiv P(ν_μ \to ν_e) - P(\barν_μ \to \barν_e) which is essentially free from matter effect contamination. We utilize this phenomenon to design a low-energy long-baseline neutrino oscillation experiment to measure the leptonic CP violating phase.
We obtain a phenomenologically acceptable PMNS matrix in a flipped SU(5) model inspired by the compactification of heterotic string $E_8\times E_8'$. To analyze the Jarlskog determinant efficiently, we include the simple Kim-Seo form for the Pontecorbo-Maki-Nakagawa-Sakata matrix. We also noted that $|δ_{\rm PMNS}|\lesssim 64^{\rm o}$ for the normal hierarchy of neutrino masses with the PDG book parametrization.
We present a complete analysis of Lepton Flavor Universality (LFU) violations in leptonic $τ$ decays in motivated models addressing the $B$-physics anomalies, based on the $SU(4)\times SU(3)\times SU(2)\times U(1)$ gauge group. We show that the inclusion of vector-like fermions, required by $B$-physics data, leads to sizable modifications of the leading-log results derived within an Effective Field Theory approach. In the motivated parameter-space region relevant to the $B$-physics anomalies, the models predict a few per-mil decrease of the effective $W$-boson coupling to $τ$, within the reach…
If massive neutrinos are Majorana particles, then the lepton number should be violated in nature and neutrino-antineutrino oscillations $ν^{}_α\leftrightarrow \overlineν^{}_β$ (for $α, β= e, μ, τ$) will definitely take place. In the present paper, we study the properties of CP violation in neutrino-antineutrino oscillations with the non-unitary leptonic flavor mixing matrix, which is actually a natural prediction in the canonical seesaw model due to the mixing between light and heavy Majorana neutrinos. The oscillation probabilities $P(ν^{}_α\to \overlineν^{}_β)$ and $P(\overlineν^{}_α\to ν^{}…
Some theories of new physics accounting for neutrino masses can give rise to a low-energy non-unitary leptonic mixing matrix. It is shown that the CP-asymmetries in the $ν_μ\to ν_τ$ channel are an excellent probe of such new physics. In adition, we clarify the relationship betweeen our framework and the so called "non-standard neutrino interactions" scenarios: the sensitivities explored here apply as well to such constructions, except for extremely fine-tuned cancellations.
We investigate under which circumstances one can show the existence of leptonic CP violation with the help of a positive or negative signal in neutrinoless double beta decay. The possibilities of cancellations are investigated for special mass hierarchies and the different solar solutions. The possibility that the mixing angle connected with the solar neutrino problem is smaller or larger than pi/4 is taken into account. The non-maximality of that angle in case of the LMA solution allows to make several useful statements. The four different CP conserving possibilities are analyzed. It is imple…
Assuming that the axion mechanism of solving the strong CP problem does not exist and the vanishing of theta at tree level is achieved by some model-building means, we study the naturalness of having large CP-violating sources in the leptonic sector. We consider the radiative mechanisms which transfer a possibly large CP-violating phase in the leptonic sector to the theta parameter. It is found that large theta cannot be induced in the models with one Higgs doublet as at least three loops are required in this case. In the models with two or more Higgs doublets the dominant source of theta is t…
The observation of neutrino masses leads to the possibility of leptonic mixing and CP violation. One of the simplest extensions of the Standard Model giving rise to neutrino masses consists of the introduction of one righthanded neutrino field per generation, singlet of SU(2). In the context of the seesaw mechanism this leads to three light and three heavy neutrinos. The charged current interactions couple the charged leptons to both the light and the heavy physical neutrinos and leptonic CP violation may occur at low energies as well as at high energies giving rise to the possibility of lepto…
If the observation by OPERA of apparently superluminal neutrinos is correct, the Lagrangian for second-generation leptons must break Lorentz invariance. We calculate the effects of an energy-independent change in the neutrino speed on another observable, the charged pion decay rate. The rate decreases by an factor [1 - 3/(1 - (m_mu)^2 / (m_pi) ^ 2) (< v_(nu) > - 1)], where < v_(nu) > is the (directionally averaged) neutrino speed in the pion's rest frame. This provides a completely independent experimental observable that is sensitive to the same forms of Lorentz violation as a neutrino time o…
We calculate the CP-violating effects in the top quark semi-leptonic three body decays induced by the supersymmetric CP-odd phase of the top squark trilinear soft breaking term $\arg(A_t)$. The light top squark mass is assumed to be close to the top quark mass $m_{\tilde{t}}\sim m_t$. The CP-conserving phase is provided by the $χ^+$ and $χ^0$ cut. We find that the partial rate asymmetry is in the 0.1% level. In the most favorable parameter region the decay rate asymmetr can reach up to 0.55%.
A constraint on the error of leptonic CP violation, which require the phase $δ_{CP}$ to be less than $π/4$ for it to be distinguishable on a $2π$ cycle, is presented. Under this constraint, the effects of neutrino detector 's distance, beam energy, and energy resolution are discussed with reference to the present values of these parameters in experiments. Although an optimized detector performances can minimize the deviation to yield a larger distinguishable range of the leptonic CP phase on a $2π$ cycle, it is not possible to determine an arbitrary leptonic CP phase in the range of $2π$ with …
We suggest a simple highly predictive ansatz for charged lepton and light neutrino mass matrices, based on the assumption of universality of Yukawa couplings. Using as input the charged lepton masses and light neutrino masses, the six parameters characterizing the leptonic mixing matrix $V_{PMNS}$, are predicted in terms of a single phase $ϕ$, which takes a value around $ϕ={\fracπ{2}}$. Correlations among variuos physical quantities are obtained, in particular $V^{PMNS}_{13}$ is predicted as a function of $Δm^2_{21}$, $Δm^2_{31}$ and $\sin^2(θ_{sol})$, and restricted to the range $0.167<|V^{PM…
Minimal Flavour Violation can be realized in several ways in the lepton sector due to the possibility of Majorana neutrino mass terms. We derive the scalar potential for the fields whose background values are the Yukawa couplings, for the simplest See-Saw model with just two right-handed neutrinos, and explore its minima. The Majorana character plays a distinctive role: the minimum of the potential allows for large mixing angles -in contrast to the simplest quark case- and predicts a maximal Majorana phase. This points in turn to a strong correlation between neutrino mass hierarchy and mixing …
A low-energy non-unitary leptonic mixing matrix is a generic effect of a large class of theories accounting for neutrino masses. It is shown how the extra CP-odd phases of a general non-unitary matrix allow for sizeable CP-asymmetries in channels other than those dominant in the standard unitary case. The $ν_μ\to ν_τ$ channel turns out to be an excellent tool to further constrain moduli and phases. Furthermore, we clarify the relationship between our approach and the so-called "non-standard neutrino interactions" schemes: the sensitivities explored here apply as well to such constructions.
In the light of the recent LHC data, we study precision tests sensitive to the violation of lepton universality, in particular the violation of unitarity in neutrino mixing. Keeping all data we find no satisfatory fit, even allowing for violations of unitarity in neutrino mixing. Leaving out sin$^2 θ_{\scriptsize \mbox{eff}}$ from the hadronic forward-backward asymmetry at LEP, we find a good fit to the data with some evidence of lepton universality violation at the $\mathcal{O}(10^{-3})$ level.
Precision measurement of the neutrino mixing parameters and the determination of mass hierarchy are the primary goals of the present and upcoming neutrino experiments. In this work, we study the sensitivity of T2K,NO$ν$A and LBNE experiments to discover leptonic CP violation and the determination of neutrino mass hierarchy. We obtain the correlation between the CP violating phase $δ_{CP}$ and the mixing angles $θ_{13}$, $θ_{23}$ and the sensitivity to determine the octant of atmospheric mixing angle $θ_{23}$. The entire analysis is done for a total 10 years (5$ν$+ 5$\bar ν$) of running of T2K,…
