Search NASA⌕ Search

SEARCH · Search NASA

Results for “Tau leptons”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Search for the Lepton Flavor Violating Decays B + → K + τ ± ℓ ∓ ( ℓ = e , μ ) at Belle

We present a search for the lepton flavor violating decays B + → K + ⁢$\tau$ ±⁢ ℓ ∓ , with ℓ = (e,μ), using the full data sample of 772×10 6 B$\overline{B}$ pairs recorded by the Belle detector at the KEKB asymmetric-energy e + ⁢e - collider. We use events in which one B meson is fully reconstructed in a hadronic decay mode. We find no evidence for B ± → K ±⁢ $\tau$⁢ℓ decays and set upper limits on their branching fractions at the 90% confidence level in the (1 - 3) × 10 -5 range. The obtained limits are the world’s best results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Search for flavour-changing neutral-current couplings between the top quark and the Higgs boson in multi-lepton final states in 13 TeV pp collisions with the ATLAS detector

A search is presented for flavour-changing neutral-current interactions involving the top quark, the Higgs boson and an up-type quark (q = u, c ) with the ATLAS detector at the Large Hadron Collider. The analysis considers leptonic decays of the top quark along with Higgs boson decays into two W bosons, two Z bosons or a τ + τ - pair. It focuses on final states containing either two leptons (electrons or muons) of the same charge or three leptons. The considered processes are $t\bar{t}$ and Ht production. For the $t\bar{t}$ production, one top quark decays via $t\rightarrow Hq$. The proton–proton collision data set analysed amounts to (140 fb -1 ) at $(\sqrt{s}={13}\,\hbox {TeV})$. No significant excess beyond Standard Model expectations is observed and upper limits are set on the $t\rightarrow Hq$ branching ratios at 95 % confidence level, amounting to observed (expected) limits of $\mathcal {B}(t\rightarrow Hu)<2.8\,(3.0) \times 10^{-4}$ and $\mathcal {B}(t\rightarrow Hc)<3.3\,(3.8) \times 10^{-4}$. Combining this search with other searches for tHq flavour-changing neutral-current interactions previously conducted by ATLAS, considering $H\rightarrow b\bar{b}$ and $H\rightarrow \gamma \gamma$ decays, as well as $H\rightarrow \tau ^{+}\tau ^{-}$ decays with one or two hadronically decaying τ-leptons, yields observed (expected) upper limits on the branching ratios of $\mathcal {B}(t\rightarrow Hu)<2.6\,(1.8) \times 10^{-4}$ and $\mathcal {B}(t\rightarrow Hc)<3.4\,(2.3) \times 10^{-4}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Long-lived axionlike particles from tau decays

Axionlike particles (ALPs) are well-motivated examples of light, weakly coupled particles in theories beyond the Standard Model. In this work, we study long-lived ALPs coupled exclusively to leptons in the mass range between 2⁢𝑚 𝑒 and 𝑚 𝜏 − 𝑚 𝑒 . For anarchic flavor structure the leptophilic ALP production in tau decays or from ALP-tau bremsstrahlung is enhanced thanks to derivative couplings of the ALP and can surpass production from electron and muon channels, especially for ALPs heavier than 𝑚 𝜇 . Using past data from high-energy fixed-target experiments such as CHARM and BEBC we place new constraints on the ALP decay constant 𝑓 𝑎 , reaching scales as high as 𝒪⁡(10 8 ) GeV in lepton-flavor-violating channels and 𝑓 𝑎 ∼ 𝒪⁡(10 2 ) GeV in lepton-flavor-conserving ones. We also present projections for the event-rate sensitivity of current and future detectors to ALPs produced at the Fermilab Main Injector, the CERN SPS, and in the forward direction of the LHC. We show that SHiP will be sensitive to 𝑓 𝑎 values that are over an order of magnitude above the existing constraints.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

High Energy Neutrino Physics

Of the twelve subatomic particles that are the building blocks of all the known matter in the universe, three are neutrinos, small neutral particles that interact through the weak interaction with other particles in the Universe. These three neutrinos, paired with the three charged leptons, the familiar electron, the heavier muon, and the still heavier tau, are some of the least well understood particles of these building blocks. Experiments using accelerator beams, like those that are the subject of this grant, can address some of the key questions scientists are posing with respect to the neutrino. Specifically, are there differences between neutrinos and their anti-particles, anti-neutrinos, that could give us some clue to the matter dominated universe, do we understand the spectrum of masses of the three neutrinos, and are there other kinds of neutirnos than the three neutrinos? Coupled with advances in precision neutrino detection, the US is addressing these questions from small scale experiments to the massive DUNE experiment. PI Fleming and her team play critical roles in accelerator based neutrino physics at short and long baseline with participation on MicroBooNE, SBND, and with the group's participation in DUNE. These experiments are at the heart of the US-based high energy physics program.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Stau pairs from natural SUSY at high luminosity LHC

Natural supersymmetry (SUSY) with light Higgsinos is perhaps the most plausible of all weak scale SUSY models while a variety of motivations point to (right) tau sleptons as the lightest of all the sleptons. We examine a SUSY model line with rather light right staus embedded within natural SUSY. For light τ ˜ 1 of a few hundred GeV, the decays τ ˜ 1 → τ χ ˜ 1 , 2 0 and ν τ χ ˜ 1 − occur at comparable rates where the (Higgsino-like) χ ˜ 1 ± and χ ˜ 2 0 release only small visible energy: in this case, the expected τ + τ − + E T signature is diminished from the usual expectations due to the presence of the nearly invisible decay mode τ ˜ 1 → ν τ χ ˜ 1 − . However, once m τ ˜ 1 ≳ m ( b i n o ) , decays to binos such as τ ˜ 1 → τ χ ˜ 3 0 open up where χ ˜ 3 0 decays to Higgsinos plus W ± , Z 0 , and h at comparable rates. For these heavier staus, the stau pair production gives rise to diboson + E T events, which may contain 0, 1, or 2 additional hard τ leptons. From these considerations, we examine the potential for future discovery of tau-slepton pair production at a high-luminosity LHC. While we do not find a 5 σ HL-LHC discovery reach for 3000 fb − 1 , we do find a 95% CL exclusion reach, ranging between m τ ˜ 1 : 100 – 450 GeV for m χ ˜ 1 0 ∼ 100 GeV . This latter reach disappears for m χ ˜ 1 0 ≳ 200 GeV . Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Search for heavy long-lived charged particles with large ionization energy loss in proton-proton collisions at $\sqrt{s}$ = 13 TeV

A search for heavy, long-lived, charged particles with large ionization energy loss within the silicon tracker of the CMS experiment is presented. A data set of proton-proton collisions at a center of mass energy at $\sqrt{s}$ = 13 TeV, collected in 2017 and 2018 at the CERN LHC, corresponding to an integrated luminosity of 101 fb −1 , is used in this analysis. Two different approaches for the search are taken. A new method exploits the independence of the silicon pixel and strips measurements, while the second method improves on previous techniques using ionization to determine a mass selection. No significant excess of events above the background expectation is observed. The results are interpreted in the context of the pair production of supersymmetric particles, namely gluinos, top squarks, and tau sleptons, and of the Drell-Yan pair production of fourth generation (τ′) leptons with an electric charge equal to or twice the absolute value of the electron charge (e). An interpretation of a Z’ boson decaying to two τ′ leptons with an electric charge equal to 2e is presented for the first time. The 95% confidence upper limits on the production cross section are extracted for each of these hypothetical particles.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Semileptonic tau decays beyond the Standard Model

Hadronic τ decays are studied as probe of new physics. We determine the dependence of several inclusive and exclusive τ observables on the Wilson coefficients of the low-energy effective theory describing charged-current interactions between light quarks and leptons. The analysis includes both strange and non-strange decay channels. The main result is the likelihood function for the Wilson coefficients in the tau sector, based on the up-to-date experimental measurements and state-of-the-art theoretical techniques. The likelihood can be readily combined with inputs from other low-energy precision observables. We discuss a combination with nuclear beta, baryon, pion, and kaon decay data. In particular, we provide a comprehensive and model-independent description of the new physics hints in the combined dataset, which are known under the name of the Cabibbo anomaly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

The Belle II Physics Book

The Belle II-Theory interface Platform (B2TiP) was created as a physics prospects working group of the Belle II collaboration in June 2014. It offered a platform where theorists and experimentalists work together to elucidate the potential impacts of the Belle II program, which includes a wide scope of physics topics: B physics, charm, τ, quarkonium physics, electroweak precision measurements and dark sector searches. It is composed of nine working groups (WGs), which are coordinated by teams of theory and experiment conveners: WG1) Semileptonic and leptonic B decays, WG2) Radiative and Electroweak penguins, WG3) φ1 and φ2 (time-dependent CP violation) measurements, WG4) φ3 measurement, WG5) Charmless hadronic B decay, WG6) Charm, WG7) Quarkonium(like), WG8) τ and lowmultiplicity processes, WG9) New Physics. We organised workshops twice a year from 2014 until 2016, which moved from KEK in Japan to Europe and the Americas, gathering experts in the respective fields to discuss with Belle II members. One of the goals for B2TiP was to propose so-called “golden- and silver-channels”: we asked each working group to choose among numerous possible measurements, those that would have the highest potential impact and to focus on them for the writeup. Theorists scrutinised the role of those measurements in terms of understanding the theory behind them, and estimated the theoretical uncertainties, now achievable as well as prospects for the future. For flavour physics, having tight control of hadronic uncertainties is one of the most crucial aspects in the field, and this is considered as an important criteria to determine the golden or silver-channels. Experimentalists, on the other hand, investigated the expected improvements with data from Belle II. For the channels where the errors are dominated by statistical uncertainties, or where systematic errors are reducible, the errors can decrease rapidly as more data becomes available. The impact of the upgraded performance from Belle II is a crucial element for reducing the uncertainties: we therefore include the latest available studies of the detector efficiency using Monte Carlo simulated events. We list the golden(silver)-channel table in this first chapter, as a guide for the chapters that follow. The book is not a collection of reports based on talks given at the workshops. The working group conveners endeavoured to construct a coherent document that can be used by Belle II collaborators, and others in the field of flavour physics, as a reference. There were two books of a similar type written in the past, “The BaBar book” [1] and “The Physics of the B factories” [2]. In order to avoid too much repetition with respect to those references, we refer to them as possible for introductory material. We would like to thank the section editors and contributing authors for the many stimulating discussions and their tremendous effort to bring the book together.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Search for heavy long-lived charged particles with large ionization energy loss in proton-proton collisions at $$ \sqrt{s} $$ = 13 TeV

Abstract A search for heavy, long-lived, charged particles with large ionization energy loss within the silicon tracker of the CMS experiment is presented. A data set of proton-proton collisions at a center of mass energy at $$ \sqrt{s} $$ s = 13 TeV, collected in 2017 and 2018 at the CERN LHC, corresponding to an integrated luminosity of 101 fb −1, is used in this analysis. Two different approaches for the search are taken. A new method exploits the independence of the silicon pixel and strips measurements, while the second method improves on previous techniques using ionization to determine a mass selection. No significant excess of events above the background expectation is observed. The results are interpreted in the context of the pair production of supersymmetric particles, namely gluinos, top squarks, and tau sleptons, and of the Drell-Yan pair production of fourth generation (τ′) leptons with an electric charge equal to or twice the absolute value of the electron charge (e). An interpretation of a Z’ boson decaying to two τ′ leptons with an electric charge equal to 2e is presented for the first time. The 95% confidence upper limits on the production cross section are extracted for each of these hypothetical particles.

Hayrapetyan, A. [Yerevan Physics Institute]↗
DOE OSTI2024

3D-Reconstruction of Tau Neutrinos in LArTPC Detectors

The Deep Underground Neutrino Experiment (DUNE) is a next-generation neutrino experiment currently under construction. DUNE will consist of two high-resolution neutrino interaction imaging detectors exposed to the world’s most intense neutrino beam, with the Near Detector at Fermilab and the Far Detector 1,300 km away in the Sanford Underground Research Facility in South Dakota, US. The high statistics and excellent resolution capabilities of DUNE's $^{40}$Ar detector will allow us to make precision studies of oscillation parameters capable of searching for CP violation in the lepton sector, testing interaction models, and studying phenomena that have until now, seemed too complex to measure, like $\nu_\tau$ detection and therefore, providing the completion of the 3-flavor neutrino paradigm. Knowledge of the $\nu_\tau$ detection can impact a broad spectrum of open questions. These include searching for non-standard neutrino interactions, constraining the unitarity of the PMNS matrix, searching for sterile neutrinos, and studying neutrino interactions. In the case of LArTPC data, the detector hits can be considered nodes in a graph, and the edges represent the spatial and temporal relationships between them. By using graph neural networks, it is possible to exploit these relationships and improve the accuracy of particle identification and reconstruction. During my presentation and specifically for tau neutrino reconstruction, I will show the effectiveness and reliability of our in-house developed graph neural network (GNN), NuGraph. This GNN classifies detector hits based on the particle type responsible for their production, assuring that the system accurately identifies and categorizes information based on its unique characteristics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Parton distribution function uncertainties in theoretical predictions for far-forward tau neutrinos at the Large Hadron Collider

New experiments dealing with neutrinos in the far-forward region at the Large Hadron Collider (LHC) are under design or already in preparation. Two of them, FASERν and SND@LHC, are expected to be active during Run 3 and have the potential to detect the interactions of ν and $\bar {v}$ that come from high-energy collisions in one of the LHC interaction points, extracted along the direction tangent to the beam line. Tau neutrinos and antineutrinos come predominantly from $D^{±}_{s}$ production in pp collisions, followed by the leptonic decay of these mesons. Neutrino pseudorapidities in the range of η > 6.9 and η > 8.9 are relevant to these future experiments. At such pseudorapidities at high energies, QCD theoretical predictions for the flux of ν τ plus $\bar {v}_τ$ rely on parton distribution functions (PDFs) in a combination of very small and large parton–x values. We evaluate PDF un certainties affecting the flux of ν τ + $\bar {v}_τ$ produced by $D^{±}_{s}$ decay in the far forward region at the LHC. Next-to-leading order (NLO) QCD uncertainties are included in the calculation of $D^{±}_{s}$ production and NLO PDF sets are used for consistency. The theoretical uncertainty associated with the 40 PDF sets of the PROSA19 group amounts to ±(20 – 30)% for the (ν τ + $\bar {v}_τ$) number of charged-current (CC) events. Scale uncertainties are much larger, resulting in a range of CC event predictions from ~70% lower to ~90% higher than the central prediction. A comparison of the predictions with those obtained using as input the central PDFs from the 3-flavour NLO PDF sets of the CT14, ABMP16 and NNPDF3.1 collaborations show that far-forward neutrino energy distributions vary by as much as a factor of ~2 – 4 relative to the PROSA19 predictions at TeV neutrino energies. The Forward Physics Facility in the high luminosity LHC era will provide data capable of constraining NLO QCD evaluations with these PDF sets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Optimization Studies for the Long-Baseline Neutrino Facility at Fermilab

The Deep Underground Neutrino Experiment and Long-Baseline Neutrino Facility (DUNE-LBNF) are under development at Fermilab since early 2010s [1]. At present, the work is being performed towards a comprehensive review conducted by US Department of Energy (DOE)-the Critical Decision 2 (CD-2)-that is planned to take place in the middle of 2022. The primary scientific objectives of DUNE are to carry out a comprehensive investigation of neutrino oscillations to test CP violation in the lepton sector, determine the ordering of the neutrino masses, and to test the three-neutrino paradigm (electron, muon and tau neutrino). The LBNF will provide a 120-GeV proton beam on a neutrino production target utilizing a new 800-MeV superconducting Linac which is expected to be completed in 2027 [2]. The neutrino beamline, which utilizes a target and horn systems, decay pipe, hadron absorber and other systems, is a core component of the LBNF. At present-as a result of numerous iterations-there exists an optimized design with a 1.5-m graphite target and focusing system consisting of three horns. Further optimization energy deposition and radiological calculations are performed towards CD-2 and beyond. This paper describes results of the most recent MARS15 [3] optimization studies.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Search for resonant and non-resonant Higgs boson pair production in the $b\overline{b}{\tau}^{+}{\tau}^{-}$ decay channel using 13 TeV $pp$ collision data from the ATLAS detector

A search for Higgs boson pair production in events with two $b$-jets and two $τ$-leptons is presented, using a proton–proton collision dataset with an integrated luminosity of 139 fb -1 collected at $\sqrt{s}$ = 13 TeV by the ATLAS experiment at the LHC. Higgs boson pairs produced non-resonantly or in the decay of a narrow scalar resonance in the mass range from 251 to 1600 GeV are targeted. Events in which at least one $τ$-lepton decays hadronically are considered, and multivariate discriminants are used to reject the backgrounds. No significant excess of events above the expected background is observed in the non-resonant search. The largest excess in the resonant search is observed at a resonance mass of 1 TeV, with a local (global) significance of 3.1$σ$ (2.0$σ$). Observed (expected) 95% confidence-level upper limits are set on the non-resonant Higgs boson pair-production cross-section at 4.7 (3.9) times the Standard Model prediction, assuming Standard Model kinematics, and on the resonant Higgs boson pair-production cross-section at between 21 and 900 fb (12 and 840 fb), depending on the mass of the narrow scalar resonance.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A measurement of the high-mass $\tau \overline{\tau}$ production cross-section at $\sqrt{s}=13$ TeV with the ATLAS detector and constraints on new particles and couplings

The production cross-section of high-mass τ-lepton pairs is measured as a function of the dilepton visible invariant mass, using 140 fb −1 of $\sqrt{s}=13$ TeV proton-proton collision data recorded with the ATLAS detector at the Large Hadron Collider. The measurement agrees with the predictions of the Standard Model. A fit to the invariant mass distribution is performed as a function of b-jet multiplicity, to constrain the non-resonant production of new particles described by an effective field theory or in models containing leptoquarks or Z′ bosons that couple preferentially to third-generation fermions. The constraints on new particles improve on previous results, and the constraints on effective operators include those affecting the anomalous magnetic moment of the τ-lepton.

beyond Standard Model↗
DOE OSTI2023

Measurement of the branching fraction of ${\textrm{D}}_{\textrm{s}}^{+}$ → τ + ν τ via τ + → μ+ν μ $\overline{\nu}$τ

Utilizing 7 . 33 fb - 1 of e + e - collision data taken at the center-of-mass energies of 4.128, 4.157, 4.178, 4.189, 4.199, 4.209, 4.219, and 4.226 GeV with the BESIII detector, the branching fraction of the leptonic decay ${D}_s^{+}$ → τ + ν τ via τ + → μ + ν μ $\overline{\nu}$ τ is measured to be ${\mathcal{B}}_{D_s^{+}\to {\tau}^{+}{\nu}_{\tau }}$ = (5 . 37 ± 0 . 17 stat ± 0 . 15 syst )%. Combining this branching fraction with the world averages of the measurements of the masses of τ + and ${D}_s^{+}$ as well as the lifetime of ${D}_s^{+}$, we extract the product of the decay constant of ${D}_s^{+}$ and the c → s Cabibbo-Kobayashi-Maskawa matrix element to be ${f}_{D_s^{+}}$ |V cs | = (246 . 7 ± 3 . 9 stat ± 3 . 6 syst ) MeV. Taking |V cs | from a global fit in the standard model we obtain ${f}_{D_s^{+}}$ = (253 . 4 ± 4 . 0 stat ± 3 . 7 syst ) MeV. Conversely, taking ${f}_{D_s^{+}}$ from lattice quantum chromodynamics calculations, we obtain |V cs | = 0 . 987 ± 0 . 016 stat ± 0 . 014 syst .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Searching for Sterile Neutrinos In the NOvA Experiment and Measurements of Hadronic Energy Response with NOvA Test Beam Data

The NOvA (NuMI Off-Axis electron neutrino Appearance) experiment is a long-baseline neutrino oscillation experiment composed of two functionally identical detectors: a 300-ton Near Detector and a 14-kton Far Detector, separated by 809 km and placed 14 mrad off the axis of the NuMI neutrino beam created at Fermilab. This configuration enables NOvA’s rich neutrino physics program, which includes measuring neutrino mixing parameters, determining the neutrino mass hierarchy, probing CP violation in the leptonic sector, studying neutrino cross sections, searching for sterile neutrinos, and more.\\ In this thesis I will present two independent analyses developed within the NOvA experiment. The first is a search for light sterile neutrino oscillations in the 3+1 framework using $\nu_\mu$-CC and NC samples from the NOvA Near and Far Detectors. Light sterile neutrinos are hypothetical neutral leptons that do not participate in the weak interactions but can mix with the three known active neutrinos: $\nu_e$, $\nu_\mu$, and $\nu_\tau$. Anomalous results, such as $\nu_e$/$\bar{\nu}e$ appearance in a $\nu_\mu$ ($\bar{\nu}_\mu$) beam observed by the MiniBooNE and LSND experiments, can be explained by the existence of sterile neutrinos. Thus, proving the existence of this type of neutrino is essential. The latest results of these searches in the NOvA experiment, along with contributions to this effort, will be presented.\\ The second is the first measurement of the pion energy response using data from the NOvA Test Beam experiment. The NOvA Test Beam experiment, deployed at Fermilab, uses a scaled-down 30-ton NOvA detector to analyze tagged beamline particles. The beamline can select and identify electrons, muons, pions, kaons, and protons with momenta ranging from 0.4 to 1.4 GeV/c. Pions are an important component of the hadronic system in neutrino interactions, and understanding how the detector responds to these particles is crucial for the validation of the simulation and the reduction of detector calibration uncertainties, which remain one of the largest systematic uncertainties in NOvA analyses.

Dueñas Tonguino, David Francisco [Cincinnati U.] (↗
DOE OSTI2020

New constraints on heavy neutral leptons from Super-Kamiokande data

Abstract Heavy neutral leptons are predicted in many extensions of the Standard Model with massive neutrinos. If kinematically accessible, they can be copiously produced from kaon and pion decays in atmospheric showers, and subsequently decay inside large neutrino detectors. We perform a search for these long-lived particles using Super-Kamiokande multi-GeV neutrino data and derive stringent limits on the mixing with electron, muon and tau neutrinos as a function of the long-lived particle mass. We also present the limits on the branching ratio versus lifetime plane, which are helpful in determining the constraints in non-minimal models where the heavy neutral leptons have new interactions with the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Standard versus non-standard CP phases in neutrino oscillation in matter with non-unitarity

We formulate a perturbative framework for the flavor transformation of the standard active three neutrinos but with a non-unitary flavor mixing matrix, a system which may be relevant for the leptonic unitarity test. We use the $\alpha$ parametrization of the non-unitary matrix and take its elements $\alpha_{\beta \gamma}$ ($\beta,\gamma = e,\mu,\tau$) and the ratio $\epsilon \simeq \Delta m^2_{21} / \Delta m^2_{31}$ as the small expansion parameters. Two qualitatively new features that hold in all the oscillation channels are uncovered in the probability formula obtained to first order in the expansion: (1) The phases of the complex $\alpha$ elements always come into the observable in the particular combination with the $\nu$SM CP phase $\delta$ in the form $[e^{- i \delta } \bar{\alpha}_{\mu e}, ~e^{ - i \delta} \bar{\alpha}_{\tau e}, ~\bar{\alpha}_{\tau \mu}]$ under the Particle Data Group convention of a unitary $\nu$SM mixing matrix. (2) The diagonal $\alpha$ parameters appear in particular combinations $\left( a/b - 1 \right) \alpha_{ee} + \alpha_{\mu \mu}$ and $\alpha_{\mu \mu} - \alpha_{\tau \tau}$, where $a$ and $b$ denote, respectively, the matter potential due to charged current and neutral current reactions. This property holds only in the unitary evolution part of the probability, and there is no such feature in the genuine non-unitary part, while the $\delta$–$\alpha$ parameter phase correlation exists for both. The reason for such remarkable stability of the phase correlation is discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗