General neutrino mass spectrum and mixing properties in seesaw mechanisms

Neutrinos stand out among elementary particles through their unusually small masses. Various seesaw mechanisms attempt to explain this fact. In this work applying insights from matrix theory we are in a position to treat variants of seesaw mechanisms in a general manner. Specifically, using Weyl's inequalities we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos. We find an estimate on the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos shifted at most by the maximal strength of the coupling to the light neutrino sector. We provide analytical conditions allowing to prescribe that precisely two out of five neutrinos are heavy. For higher-dimensional cases the inverse eigenvalue methods are used. In particular, for the CP invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones, i.e. the respective mass submatrix is positive definite, then large masses are provided by matrices with large elements accumulated on the diagonal. Finally, the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis. This general observation concerning neutrino mixing together with results on the mass spectrum properties opens directions for further neutrino physics studies using matrix analysis.Comment: Improved version after readers remark

Dilations and light-heavy neutrino mixings

A dilation procedure is presented for the interval neutrino mixing matrix in order to explore possible unitary extensions of the three-dimensional neutrino mixings. Limits on light-heavy neutrino mixings are considered

Constraints on neutrino mixing from matrix theory

Jeden z kluczowych problemów współczesnej fizyki cząstek elementarnych dotyczy liczby zapachów neutrin występujących w naturze. Do tej pory udało się ustalić, ze istnieją trzy rodzaje neutrin aktywnych. Istotnym problemem jest ustalenie, czy istnieją inne dodatkowe stany neutrinowe. Neutrina takie nazywamy sterylnymi ze względu na fakt, ze ich oddziaływanie słabe ze znaną materią jest jak do tej pory poniżej eksperymentalnego progu detekcji. Niemniej jednak neutrina sterylne mogą się mieszać z neutrinami aktywnymi pozostawiając tym samym ślady swojego istnienia na poziomie Modelu Standardowego w postaci nieunitarności macierzy mieszania neutrin. Z tego powodu badanie nieunitarności macierzy mieszania jest tak istotne dla pełnego zrozumienia fizyki neutrin. W rozprawie przedstawiamy nową metodę analizy macierzy mieszania neutrin opartą na teorii macierzy. Fundament naszego podejścia do badania macierzy mieszania neutrin stanowią pojęcia wartości osobliwych oraz kontrakcji. Dzięki tym pojęciom zdefiniowaliśmy obszar fizycznie dopuszczalnych macierzy mieszania jako powłokę wypukłą rozpiętą na trójwymiarowych unitarnych macierzach mieszania wyznaczonych na podstawie danych eksperymentalnych. W rozprawie badamy geometryczne własności tego obszaru wyznaczając jego objętość wyrażoną poprzez miarę Haara rozkładu na wartości osobliwe oraz studiując jego strukturę wewnętrzną zależną od minimalnej liczby dodatkowych sterylnych neutrin. Stosując teorię unitarnej dylatacji pokazujemy jak wartości osobliwe pozwalają zidentyfikować nieunitarne macierze mieszania oraz jak tworzyć ich rozszerzenia do pełnej macierzy unitarnej wymiaru większego niż trzy, opisującej kompletną teorię zawierającą neutrina sterylne. Na tej podstawie wyznaczamy nowe ograniczenia w modelach gdzie aktywne neutrina mieszają się z jednym dodatkowym neutrinem sterylnym

New limits on neutrino non-unitary mixings based on prescribed singular values

Singular values are used to construct physically admissible 3-dimensional mix- ing matrices characterized as contractions. Depending on the number of singular values strictly less than one, the space of the 3-dimensional mixing matrices can be split into four disjoint subsets, which accordingly corresponds to the minimal number of additional, non-standard neutrinos. We show in numerical analysis that taking into account present experimental precision and fits to different neutrino mass splitting schemes, it is not pos- sible to distinguish, on the level of 3-dimensional mixing matrices, between two and three extra neutrino states. It means that in 3+2 and 3+3 neutrino mixing scenarios, using the so-called α parametrization, ranges of non-unitary mixings are the same. However, on the level of a complete unitary 3+1 neutrino mixing matrix, using the dilation procedure and the Cosine-Sine decomposition, we were able to shrink bounds for the \light-heavy" mixing matrix elements. For instance, in the so-called seesaw mass scheme, a new upper limit on jUe4j is about two times stringent than before and equals 0.021. For all considered mass schemes the lowest bounds are also obtained for all mixings, i.e. |Ue4|, |Uμ4|, |Uτ4|. New results obtained in this work are based on analysis of neutrino mixing matrices obtained from the global fits at the 95% CL

Studies of Non-standard Particle Mixings Through Singular Values

Singular values provide a method to study mixing matrices in particle physics. The methods of unitary dilations and the cosine–sine matrix decomposition are discussed in the framework of the Standard Model neutrinos mixing with one non-standard neutrino. We show that the mixings are continuous functions of singular values. It implies that the magnitude of non-standard mixing can be estimated from below and above unambiguously from the experimentally determined interval PMNS mixing matrix

New constraints on heavy neutral leptons coming from oscillation data analysis and precision e+e- physics

The current experimental data does not exclude the possibility that additional sterile neutrinos exist. We discuss two methods to determine active-sterile neutrino mixing. Firstly, singular values provide a comprehensive description of the mixing phenomena. By using them, we get the stringent bounds for the active-sterile mixing in the scenario with one additional neutrino. Secondly, we describe a simplified model with a sterile neutrino to show a sensitivity of the invisible Z-boson decay to the sterile neutrino mixings. In the end, we outline the precise analysis of the light-heavy mixings coming from the Z-boson decay taking into account the first-order radiative corrections

General neutrino mass spectrum and mixing properties in seesaw mechanisms

Neutrinos stand out among the elementary particles because of their unusually small masses. Various seesaw mechanisms attempt to explain this fact. In this work, applying insights from matrix theory, we are in a position to treat variants of seesaw mechanisms in a general manner. Specifically, using Weyl's inequalities, we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos. We find an estimate of the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos, shifted at most by the maximal strength of the coupling to the light neutrino sector. We provide analytical conditions allowing one to prescribe that precisely two out of five neutrinos are heavy. For higher-dimensional cases the inverse eigenvalue methods are used. In particular, for the CP-invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones, i.e. if the respective mass submatrix is positive definite, then large masses are provided by matrices with large elements accumulated on the diagonal. Finally, the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis. This general observation concerning neutrino mixing, together with results on the mass spectrum properties, opens directions for further neutrino physics studies using matrix analysis

Coulomb Branch Amplitudes from a Deformed Amplituhedron Geometry

The Amplituhedron provides, via geometric means, the all-loop integrand of scattering amplitudes in maximally supersymmetric Yang-Mills theory. Unfortunately, dimensional regularization, used conventionally for integration, breaks the beautiful geometric picture. This motivates us to propose a 'deformed' Amplituhedron. Focusing on the four-particle amplitude, we introduce two deformation parameters, which can be interpreted as particle masses. We provide evidence that the mass pattern corresponds to a specific choice of vacuum expectation values on the Coulomb branch. The deformed amplitude is infrared finite, making the answer well-defined in four dimensions. Leveraging four-dimensional integration techniques based on differential equations, we compute the amplitude up to two loops. In the limit where the deformation parameters are taken to zero, we recover the known Bern-Dixon-Smirnov amplitude. In the limit where only one deformation parameter is taken to zero, we find a connection to the angle-dependent cusp anomalous dimension.Comment: 6 pages, 2 figure

Phenomenology of Lepton Masses and Mixing with Discrete Flavor Symmetries

The observed pattern of fermion masses and mixing is an outstanding puzzle in particle physics, generally known as the flavor problem. Over the years, guided by precision neutrino oscillation data, discrete flavor symmetries have often been used to explain the neutrino mixing parameters, which look very different from the quark sector. In this review, we discuss the application of non-Abelian finite groups to the theory of neutrino masses and mixing in the light of current and future neutrino oscillation data. We start with an overview of the neutrino mixing parameters, comparing different global fit results and limits on normal and inverted neutrino mass ordering schemes. Then, we discuss a general framework for implementing discrete family symmetries to explain neutrino masses and mixing. We discuss CP violation effects, giving an update of CP predictions for trimaximal models with nonzero reactor mixing angle and models with partial $\mu-\tau$ reflection symmetry, and constraining models with neutrino mass sum rules. The connection between texture zeroes and discrete symmetries is also discussed. We summarize viable higher-order groups, which can explain the observed pattern of lepton mixing where the non-zero $\theta_{13}$ plays an important role. We also review the prospects of embedding finite discrete symmetries in the Grand Unified Theories and with extended Higgs fields. Models based on modular symmetry are also briefly discussed. A major part of the review is dedicated to the phenomenology of flavor symmetries and possible signatures in the current and future experiments at the intensity, energy, and cosmic frontiers. In this context, we discuss flavor symmetry implications for neutrinoless double beta decay, collider signals, leptogenesis, dark matter, as well as gravitational waves.Comment: 55 pages + references, invited review submitted to Progress in Particle and Nuclear Physic