We investigate the possibility of unitarity violation in the sequential neutrino mixing matrix in a scenario with extra compact spacelike dimensions. Gauge singlet neutrinos are assumed to propagate in one extra dimension, giving rise to an infinite tower of states in the effective four-dimensional theory. It is shown that this leads to small lepton-number violating entries in the neutrino mass matrix, which can violate unitarity on the order of one per cent.
We show how the tree level unitarity violations of compactified extra dimensional extensions of the Standard Model become much stronger when the scalar sector is included in the bulk. This effect occurs when the couplings are not suppressed for larger Kaluza-Klein levels, and could have relevant consequences for the phenomenology of the next generation of colliders. We also introduce a simple and generic formalism to obtain unitarity bounds for finite energies, taking into account coupled channels including the towers of Kaluza-Klein excitations.
We examine the unitarity constraints in gauge and scalar sectors of non-minimal Universal Extra Dimensional model. We show that some of the tree-level two-body scattering amplitudes in gauge and scalar sectors do not respect partial wave unitarity. Unitarity analysis of this model leads to an upper bound on corresponding boundary-localized (BLT) parameter which depends on the maximum number of Kaluza-Klein (KK) mode considered in the analysis. This upper bound of the relevant BLT parameter decreases with the increasing KK-modes. The results are, in effect, independent of the inverse of compact…
We study the unitarity constraint on the two body Higgs boson elastic scattering in the presence of extra dimensions. The contributions from exchange of spin-2 and spin-0 Kaluza-Klein states can have large effect on the partial wave amplitude. Unitarity condition restrict the maximal allowed value for the ratio $r$ of the center of mass energy to the gravity scale to be less than one. Although the constraint on the standard Higgs boson mass for $r$ of order one is considerably relaxed, for small $r$ the constraint is similar to that in the Standard Model. The resulting bound on the Higgs boson…
Introducing arbitrary number of neutral Higgs bosons in the electroweak symmetry breaking sector, we derive a set of conditions among Higgs couplings which need to be satisfied to maintain the unitarity of the high energy scattering amplitudes of weak gauge bosons at the tree level (unitarity sum rules). It is shown that the unitarity sum rules require the tree level $ρ$ parameter to be 1, without explicitly invoking the custodial symmetry arguments. The one-loop finiteness of the electroweak oblique corrections is automatically guaranteed once these unitarity sum rules are imposed among Higgs…
The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-to…
The conventional method using low energy theorems [3] does not seem to lead to an explicit unitarity limit in the scattering processes of longitudinally polarized gauge bosons for the high energy case in the extra U(1) superstring inspired models, commonly known as eta model, emanating from E6 group of superstring theory. We have made use of an alternative procedure given in [14], which is applicable to SUSY GUT. Explicit unitarity bounds on the Yukawa couplings are obtained from both using unitarity constraints as well as using RGE analysis at one-loop level utilizing critical couplings conce…
There are claims in the literature that in neutrino oscillations and oscillations of neutral kaons and B-mesons the oscillation phase differs from the standard one by a factor of two. We reconsider the arguments leading to this extra factor and investigate, in particular, the non-relativistic regime. We actually find that the very same arguments lead to an ambiguous phase and that the extra factor of two is a special case. We demonstrate that the unitarity triangle (UT) fit in the Standard Model with three families is a suitable means to discriminate between the standard oscillation phase and …
We investigate the impact of extra leptons on observed tensions in the muon $g-2$ and the first-row CKM unitarity. By introducing a new SU(2)$_L$ doublet lepton and a SU(2)$_L$ triplet lepton, we find that both of the tensions can be explained simultaneously under constraints from electroweak precision observables and Higgs-boson decays. Our model could be tested by measurements of $h\toμμ$ at future collider experiments.
The ultrahigh energy cross section for neutrino interactions with nucleons is reviewed, and unitarity constraints are discussed. We argue that existing QCD extrapolations are self-consistent, and do not imply a breakdown of the perturbative expansion in the weak coupling.
A low-energy non-unitary leptonic mixing matrix is a generic effect of some theories of new physics accounting for neutrino masses. We show how the extra CP-phases of a general non-unitary matrix allow for sizeable CP-asymmetries in the $ν_μ\to ν_τ$ channel. This CP-asymmetries turns out to be an excellent probe of such new physics.
The non-unitarity of the effective leptonic mixing matrix at low energies is a generic signal of extensions of the Standard Model (SM) with extra fermionic singlet particles, i.e. sterile or right-handed neutrinos, to account for the observed neutrino masses. The low energy effects of such extensions can be described in a model-independent way by the Minimal Unitarity Violation (MUV) scheme, an effective field theory extension of the SM. We perform a global fit of the MUV scheme parameters to the present experimental data, which yields the up-to-date constraints on leptonic non-unitarity. Furt…
Neutrino masses are one of the most promising open windows to physics beyond the Standard Model (SM). Several extensions of the SM which accommodate neutrino masses require the addition of right-handed neutrinos to its particle content. These extra fermions will either be kinematically accessible (sterile neutrinos) or not (deviations from Unitarity of the PMNS matrix) but at some point they will impact neutrino oscillation searches. We explore the differences and similitudes between the two cases and compare their present bounds with the expected sensitivities of DUNE. We conclude that Non-Un…
The presence of non-unitary neutrino mixing can affect the measurement of the three-neutrino leptonic Dirac CP phase and hamper efforts to probe CP violation due to degeneracies of the extra non-unitary CP phase with the standard CP phase. We study the effect of including non-unitarity on probing CP violation with the long-baseline experiments NO$ν$A, T2K and DUNE. We analyze the effect of non-unitary mixing at the level of oscillation probabilities associated with the relevant baselines, and present the CP violation sensitivity for the individual experiments and their combination. Our results…
We revisit a two right-handed neutrino model with two texture zeros, namely an indirect model based on A4 with the recently proposed new type of constrained sequential dominance (CSD2), involving vacuum alignments along the (0,1,-1)^T and (1,0,2)^T directions in flavour space, which are proportional to the neutrino Dirac mass matrix columns. In this paper we construct a renormalizable and unified indirect A4xSU(5) model along these lines and show that, with spontaneous CP violation and a suitable vacuum alignment of the phases, the charged lepton corrections lead to a reactor angle in good agr…
We propose a minimal extension of the Standard Model where an up-type vector-like quark, denoted $T$, is introduced and provides a simple solution to the CKM unitarity problem. We adopt the Botella-Chau parametrization in order to extract the $4\times 3$ quark mixing matrix which contains the three angles of the $3\times 3$ CKM matrix plus three new angles denoted $θ_{14}$, $θ_{24}$, $θ_{34}$. It is assumed that the mixing of $T$ with standard quarks is dominated by $θ_{14}$. Imposing a recently derived, and much more restrictive, upper-bound on the New Physics contributions to $ε_{K}$, we fin…
We characterize CP violation in the SU(2)xU(1) model due to an extra vector-like quark or sequential family, giving special emphasis to the chiral limit m_{u,d,s}=0. In this limit, CP is conserved in the three generation Standard Model (SM), thus implying that all CP violation is due to the two new CP violating phases whose effects may manifest either at high energy in processes involving the new quark or as deviations from SM unitarity equalities among imaginary parts of invariant quartets (or, equivalently, areas of unitarity triangles). In our analysis we use an invariant formulation, indep…
The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional physical laws), rather than by the four-dimensional one, is explored in order to evade the most awkward problems of higher-dimensional theories with compact extra time-like dimensions: violation of causality and of unitarity.
The precise measurements of the Bd oscillation frequency and the limit on the Bs one one as well as the determination of the Cabibbo-Kobayashi-Maskawa matrix element Vub improve the constraints on the other elements of this matrix. A fit to the experimental data and the theory calculations leads to the determination of the vertex of the unitarity triangle as: rho = 0.160 -0.070 +0.094 eta = 0.381 -0.058 +0.061. The values of its angles, in their customary definition in terms of sines for alpha and beta, are found to be: sin(2 alpha) = 0.06 -0.42 +0.35 sin(2 beta) = 0.75 +/- 0.09 gamma = 68 -12…
The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard scattering well. Extrapolating this observation to the LHC, we conclude that knowledge of many short-distance processes at next-to-leading order may be required to describe the physics of hard scattering. While the field of one-loop computations is quite mature, parton multiplicities in hard LHC events are so high that traditional computational techniques be…
We calculate the contributions of the Kaluza-Klein (KK) modes to the K_L-K_S mass difference ΔM_K, the parameter ε_K, the B^0_{d,s}-\bar B^0_{d,s} mixing mass differences ΔM_{d,s} and rare decays K^+\to π^+ν\barν, K_L\to π^0ν\barν, K_L\toμ\barμ, B\to X_{s,d}ν\barνand B_{s,d}\toμ\barμin the Appelquist, Cheng and Dobrescu (ACD) model with one universal extra dimension. For the compactification scale 1/R= 200 GeV the KK effects in these processes are governed by a 17% enhancement of the ΔF=2 box diagram function S(x_t,1/R) and by a 37% enhancement of the Z^0 penguin diagram function C(x_t/1/R) re…
We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\e$ dimensions to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in $4-2\e$ dimensions can be determined from quadruple, triple and double cuts without the need for independent pentagon contributions using a massive integral basis. The additional mass-dependent integral coefficients may then be extracted from the large mass limit which…
Starting from a (new physics independent) tree level determination of rhobar and etabar, we perform the Unitarity Triangle analysis in general extensions of the Standard Model with arbitrary new physics contributions to loop-mediated processes. Using a simple parameterization, we determine the allowed ranges of non-standard contributions to |Delta F|=2 processes. Remarkably, the recent measurements from B factories allow us to determine with good precision the shape of the Unitarity Triangle even in the presence of new physics, and to derive stringent constraints on non-standard contributions …
In a truly model-independent approach, we reexamine a minimal extension of the Standard Model (SM) through the introduction of an additional $U(1)$ symmetry leading to a new neutral gauge boson ($Z'$), allowing its kinetic mixing with the hypercharge gauge boson. An SM neutral scalar is used to spontaneously break this extra symmetry leading to the mass of the $Z'$. Except for three right-handed neutrinos no other fermions are added. We use the current LHC Drell-Yan data to put model-independent constraints in the parameter space of three quantities, namely, $M_{Z'}$, the $Z$-$Z'$ mixing angle…
We regularize QCD using the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Slavnov. It is known that for pure Yang-Mills theory the Pauli-Villars determinants generate unphysical logarithmic radiative corrections at one loop that modify the beta function. Here we prove that when the gauge fields are coupled to fermions so that one has QCD, these unphysical corrections translate into a violation of unitarity. We provide an understanding of this by seeing that Slavnov's choice for the Pauli-Villars determinants introduces extra propagating degrees of freed…
We consider the scale at which gravity becomes strong in linearized General Relativity coupled to the gauge-Higgs unified(GHU) model. We also discuss the unitarity of S-matrix in the same framework. The Kaluza-Klein(KK) gauge bosons, KK scalars and KK fermions in the GHU models can drastically change the strong gravity scale and the unitarity violation scale. In particular we consider two models GHU_SM and GHU_MSSM which have the zero modes corresponding to the particle content of the Standard Model and the Minimal Supersymmetric Standard Model, respectively. We find that the strong gravity sc…
Tree level unitarity violations of extra dimensional extensions of the Standard Model may become much stronger when the scalar sector is included in the bulk. This effect occurs when the couplings are not suppressed for larger Kaluza-Klein levels, and could have relevant consequences for the phenomenology of the next generation of colliders. We briefly review our formalism to obtain more stringent unitarity bounds when KK modes are present, as well as the generalization to extra dimensions of the Equivalence Theorem between Goldstone bosons and longitudinal gauge bosons
Impact of matter effects on the unitarity test of lepton mixing
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Department of Physics, Faculty of Engineering Science, Yokohama National University（横滨国立大学工学部物理学系）
After the observation of non-zero $θ_{13}$ the goal has shifted to observe $CP$ violation in the leptonic sector. Neutrino oscillation experiments can, directly, probe the Dirac $CP$ phases. Alternatively, one can measure $CP$ violation in the leptonic sector using Leptonic Unitarity Quadrangle(LUQ). The existence of Standard Model (SM) gauge singlets - sterile neutrinos - will provide additional sources of $CP$ violation. We investigate the connection between neutrino survival probability and rephasing invariants of the $4\times4$ neutrino mixing matrix. In general, LUQ contain eight geometri…
We discuss the determination of the CKM parameters from the forthcoming $CP$ violation observables in $B_s \to K^+ K^-$ decays. Combining the information on mixing induced CP violation in $B_s \to K^+ K^-$, with the $B_d \to J/ψK_s$ precision observable $\sin 2β$ and the $B^0_s$--$\bar{B^0_s}$ mixing phase $ϕ_s$, we propose a determination of the unitarity triangle $(\barρ, \barη)$. Computing the penguin parameters $(r, θ)$ within QCD factorization yield precise determination of $(\barρ, \barη)$, reflected by a weak dependence on the $θ$ which is shown as a second order effect. The impact of t…
The strongest constraint on Vtb presently comes from the 3 x 3 unitarity of the CKM matrix, which fixes Vtb to be very close to one. If the unitarity is relaxed, current information from top production at Tevatron still leaves open the possibility that Vtb is sizably smaller than one. In minimal extensions of the standard model with extra heavy quarks, the unitarity constraints are much weaker and the EW precision parameters entail the strongest bounds on Vtb. We discuss the experimental perspectives of discovering and identifying such new physics models at the Tevatron and the LHC, through a …
We calculate the rates of radiative $β^- \to α^- + γ$ decays for $(α, β) = (e, μ)$, $(e, τ)$ and $(μ, τ)$ by taking the {\it unitary} gauge in the $(3+n)$ active-sterile neutrino mixing scheme, and make it clear that constraints on the unitarity of the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix $U$ extracted from $β^- \to α^- + γ$ decays in the {\it minimal unitarity violation} scheme differ from those obtained in the canonical seesaw mechanism with $n$ heavy Majorana neutrinos by a factor $5/3$. In such a natural seesaw case we show that the rates of $β^- \to α^- + γ$ can be us…
The recent measurements of the B_s meson mixing amplitude by CDF and of the leptonic branching fraction BR(B to tau nu) by Belle call for an upgraded analysis of the Unitarity Triangle in the Standard Model. Besides improving the previous constraints on the parameters of the CKM matrix, these new measurements, combined with the recent determinations of the angles alpha, beta and gamma from non-leptonic decays, allow, in the Standard Model, a quite accurate extraction of the values of the hadronic matrix elements relevant for K-Kbar and B_{s,d}-B_{s,d}bar mixing and of the leptonic decay consta…
We present a set of relations between one-loop integral coefficients for dimensionally regulated QCD amplitudes. Within dimensional regularization, the combined use of color-kinematics duality and integrand reduction yields the existence of relations between the integrand residues of partial amplitudes with different orderings of the external particles. These relations can be established for the cut-constructible contributions as well for the ones responsible for rational terms. Starting from the general parametrization of one-loop residues and applying Laurent expansion in order to extract th…
We investigate a flexible method in which we can test the unitarity of the quark flavor mixing matrix step-by-step. Singular-Value-Decomposition (SVD) techniques are used in analyzing the mixing matrix over a broader parameter region than the unitarity region. Unitary constraints make us extract CP violating properties without any specific parametrization when the magnitudes of at least three mixing matrix elements in three generation quark mixing are given. This method can also be applied to the analysis of lepton flavor mixing, in which only a few moduli are presently measured.
We consider extra dimensional gauge theories on an interval. We first review the derivation of the consistent boundary conditions (BC's) from the action principle. These BC's include choices that give rise to breaking of the gauge symmetries. The boundary conditions could be chosen to coincide with those commonly applied in orbifold theories, but there are many more possibilities. To investigate the nature of gauge symmetry breaking via BC's we calculate the elastic scattering amplitudes for longitudinal gauge bosons. We find that using a consistent set of BC's the terms in these amplitudes th…
The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams. To demonstrate these facts we introduce some new techniques for the analysis of conformal field theories. Chief among these is a method for conglomerating local primary operators to extract…
$f_K/f_π$ in iso-symmetric QCD and the CKM matrix unitarity
Helmholtz Institute Mainz, Johannes Gutenberg University（美因茨亥姆霍兹研究所，约翰内斯·古腾堡大学）；GSI Helmholtz Centre for Heavy Ion Research（GSI重离子研究中心）；John von Neumann-Institut für Computing NIC, Deutsches Elektronen-Synchrotron DESY（约翰·冯·诺依曼计算研究所NIC，德国电子同步加速器DESY）；Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València（粒子物理研究所(IFIC)，西班牙科学理事会-瓦伦西亚大学）
We analyze the extraction of weak phases from CP violation in $B\toπ^+π^-$ decays. We propose to determine the unitarity triangle $(\barρ,\barη)$ by combining the information on mixing induced CP violation in $B\toπ^+π^-$, $S$, with the precision observable $\sin 2β$ obtained from the CP asymmetry in $B\toψK_S$. It is then possible to write down exact analytical expressions for $\barρ$ and $\barη$ as simple functions of the observables $S$ and $\sin 2β$, and of the penguin parameters $r$ and $ϕ$. As an application clean lower bounds on $\barη$ and $1-\barρ$ can be derived as functions of $S$ a…
In a recent Letter Martinez et al.2011 have argued that the existence of extra three families is still perfectly in accord with the standard model (SM), as long as an additional Higgs doublet is also present. Here we claim that the mentioned accordance can be obtained with less reliance on BSM physics like additional Higgs doublets, but benefiting from Majorana neutrinos is sufficient.
I point out that $B \to X_q ł^+ ł^-$ decays $(q = s, d)$ are sensitive probes of possible violation of CKM unitarity. I compute the decay rates and asymmetries in a minimal extension of the Standard Model containing an additional isosinglet charge (-1/3) quark, which leads to a deviation from CKM unitarity. It is shown that even for small mixing ratios $|{z_{qb}}/{(V_{tq}^\ast V_{tb})}| \sim O({10}^{-2})$, the contribution of the tree-level $Z-$FCNC appearing in the model should change the rates and asymmetries significantly. Especially the CP asymmetry, $A_{CP} (B \to X_s ł^+ ł^-)$, can be en…
We study the possibility of the existence of extra fermion families and an extra Higgs doublet. We find that requiring the extra Higgs doublet to be inert leaves space for three extra families, allowing for mirror fermion families and a dark matter candidate at the same time. The emerging scenario is very predictive: it consists of a Standard Model Higgs boson, with mass above 400\,\GeV, heavy new quarks between 340 and 500\,\GeV, light extra neutral leptons, and an inert scalar with a mass below $M_Z$.
We compute spin-flip cross section for graviton photoproduction on a spin-1/2 target of finite mass. Using this tree-level result, we find one-loop graviton correction to the spin-flip low-energy forward Compton scattering amplitude by using Gerasimov-Drell-Hearn sum rule. We show that this result agrees with the corresponding perturbative computations, implying the validity of the sum rule at one-loop level, contrary to the previous claims. We discuss possible effects from the black hole production and string Regge trajectory exchange at very high energies. These effects seem to soften the UV…
Unitarity test of lepton mixing via energy dependence of neutrino oscillation
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Department of Physics, Facility of Engineering Science, Yokohama National University（横滨国立大学工学部物理系）
The historical discovery of neutrino oscillations using solar and atmospheric neutrinos, and subsequent accelerator and reactor studies, has brought neutrino physics to the precision era. We note that CP effects in oscillation phenomena could be difficult to extract in the presence of unitarity violation. As a result upcoming dedicated leptonic CP violation studies should take into account the non-unitarity of the lepton mixing matrix. Restricting non-unitarity will shed light on the seesaw scale, and thereby guide us towards the new physics responsible for neutrino mass generation.
Unitarity of the 4d standard model is ensured by the conventional Higgs mechanism with a fundamental spin-0 Higgs boson, responsible for gauge boson mass-generations. On the contrary Kaluza-Klein (KK) compactification of extra spatial dimensions can geometrically realize the gauge boson mass generation without invoking a fundamental Higgs scalar. We reveal that massive gauge boson scattering in the compactified theories is unitary at low energies, and the unitarity violation is {\it delayed} to the intrinsic ultraviolet (UV) scale of the higher dimensional gauge theory. We demonstrate that thi…
Higher-dimensional theories with time-like and space-like extra dimensions are compared both from the conceptual and from the phenomenological points of view. In this context causality and unitarity are discussed. It is shown that additional time-like dimensions allow to recover four-dimensional phenomenology without invoking neither Kaluza-Klein compactification procedure nor brane world construct. It is shown, also, that contrary to scenarios with space-like extra dimensions, in higher-dimensional space-times with additional time-like dimensions the cosmological constant problem can be safel…
Recently, the first ever lattice computation of the $γW$-box radiative correction to the rate of the semileptonic pion decay allowed for a reduction of the theory uncertainty of that rate by a factor of $\sim3$. A recent dispersion evaluation of the $γW$-box correction on the neutron also led to a significant reduction of the theory uncertainty, but shifted the value of $V_{ud}$ extracted from the neutron and superallowed nuclear $β$ decay, resulting in a deficit of the CKM unitarity in the top row. A direct lattice computation of the $γW$-box correction for the neutron decay would provide an …
Models with large extra dimensions offer the possibility of the Planck scale being of order the electroweak scale, thus alleviating the gauge hierarchy problem. We show that these models suffer from a breakdown of unitarity at around three quarters of the low effective Planck scale. An obvious candidate to fix the unitarity problem is string theory. We therefore argue that it is necessary for the string scale to appear below the effective Planck scale and that the first signature of such models would be string resonances. We further translate experimental bounds on the string scale into bounds…
In the background of unparticle-enhanced black hole geometry, we provide the quasinormal modes of scalar, vector, and Dirac particles around it. Ungravity by tensor unparticles contributes positively to the Newtonian gravity and black holes can be formed at the LHC without any extra dimensions. In the ungravity-dominant regime, the gravity looks much like that of the Schwarzschild geometry in fractional number of extra dimensions. We argue in this analysis that quasinormal modes are good fingerprints to distinguish ungravity from extra dimensions, by showing that the unitarity constraints on u…
The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $\vert V_{ub}\vert$ is obtained from exclusive semileptonic $B \to π\ell ν_\ell$ and $B_s \to K \ell ν_\ell$ decays adopting the unitarity-based dispersion matrix approach for the determination of the hadronic form factors (FFs) in the whole kinematical range. We use lattice computations of the relevant susceptibilities and of the FFs in the large-$q^2$ regime in order to derive their behavior in the low-$q^2$ region without assuming any specific momentum dependence and without constraining their shape using experimental data. Then, we address…
The 3X3 Maki-Nakagawa-Sakata-Pontecorvo (MNSP) lepton flavor mixing matrix may be slightly non-unitary if the three active neutrinos are coupled with sterile neutrinos. We show that it is in principle possible to test whether the relation |V_{e1}|^2 + |V_{e2}|^2 + |V_{e3}|^2 = 1 holds or not in a precision reactor antineutrino oscillation experiment, such as the recently proposed Daya Bay II experiment. We explore three categories of non-unitary effects on the 3X3 MNSP matrix: 1) the indirect effect in the (3+ 3) flavor mixing scenario where the three heavy sterile neutrinos do not take part i…
