Narrow Results

A non-Abelian extension of electric-magnetic duality implies that dual to confined colour SU(3), there also ought to be a broken threefold symmetry which can play the role of fermion generations. A model constructed on these premises not only gives a raison d'être for 3 and only 3 generations as observed but also offers a natural explanation for the distinctive fermion mass and mixing patterns seen in experiment. A calculation to one-loop order in this model with only 3 fitted parameters already gives correct values, all within present experimental errors, for the following quantities: the mass ratios m_c/m_t, m_s/m_b, m_μ/m_τ, all 9 matrix elements of the CKM mixing matrix |V_rs| for quarks, plus the lepton MNS mixing matrix elements |U_μ3| and |U_e3| studied in neutrino oscillation experiments with respectively atmospheric and reactor neutrinos.

Using an algebraic formulation, we explore two well-known degeneracies involving the mass-squared differences for three-neutrino oscillations assuming CP symmetry is conserved. For vacuum oscillation, we derive the expression for the mixing angles that permit invariance under the interchange of two mass-squared differences. This symmetry is most easily expressed in terms of an ascending mass order. This can be used to reduce the parameter space by one half in the absence of the MSW effect. For oscillations in matter, we derive within our formalism the known approximate degeneracy between the standard and inverted mass hierarchies in the limit of vanishing θ₁₃. This is done with a mass ordering that permits the map Δ₃₁↦-Δ₃₁. Our techniques allow us to translate mixing angles in this mass order convention into their values for the ascending order convention. Using this dictionary, we demonstrate that the vacuum symmetry and the approximate symmetry invoked for oscillations in matter are distinctly different.

We examine the possibility of determining the neutrino mass hierarchy in the limit θ₁₃=0 using atmospheric neutrinos as the source. In this limit, in which θ₁₃ driven matter effects are absent, independent measurements of Δ₃₁ and Δ₃₂ can, in principle, lead to hierarchy determination. Since the difference between these two is Δ₂₁, one needs an experimental arrangement where Δ₂₁ L/E ≳1 can be achieved. This condition can be satisfied by atmospheric neutrinos since they have a large range of energies and baselines. In spite of this, we find that hierarchy determination in the θ₁₃=0 limit with atmospheric neutrinos is not a realistic possibility, even in conjunction with an apparently synergistic beam experiment like T2K or NOνA. We discuss the reasons for this, and also in the process clarify the conditions that must be satisfied in general for hierarchy determination if θ₁₃=0.

We review the current-generation short-baseline reactor neutrino experiments that have firmly established the third neutrino mixing angle θ₁₃ to be nonzero. The relative large value of θ₁₃ (around 9°) has opened many new and exciting opportunities for future neutrino experiments. Daya Bay experiment with the first measurement of is aiming for a precision measurement of this atmospheric mass-squared splitting with a comparable precision as from accelerator muon neutrino experiments. JUNO, a next-generation reactor neutrino experiment, is targeting to determine the neutrino mass hierarchy (MH) with medium baselines (~ 50 km). Beside these opportunities enabled by the large θ₁₃, the current-generation (Daya Bay, Double Chooz, and RENO) and the next-generation (JUNO, RENO-50, and PROSPECT) reactor experiments, with their unprecedented statistics, are also leading the precision era of the three-flavor neutrino oscillation physics as well as constraining new physics beyond the neutrino Standard Model.

Based on the independent measurements on neutrino mass splitting , and recent measurements by the T2K Collaboration, we carry out a simple fitting analysis on and in normal hierarchy and inverted hierarchy respectively, suggesting and in normal hierarchy, or and in inverted hierarchy. The simple analysis indicate that both normal and inverted hierarchies are consistent with current experimental measurements on mass splitting. The p-value for normal hierarchy and that for inverted hierarchy are 62% and 55%, respectively. This reveals a slight favor for the normal hierarchy. It is suggested that further measurements on the mass splitting with higher accuracy are necessary to determine the neutrino mass hierarchy.

One of the remaining undetermined fundamental aspects in neutrino physics is the determination of the neutrino mass hierarchy, i.e. discriminating between the two possible orderings of the mass eigenvalues, known as Normal and Inverted Hierarchies. The Jiangmen Underground Neutrino Observatory (JUNO), a 20 kt Liquid Scintillator Detector currently under construction in the South of China, can determine the neutrino mass hierarchy and improve the precision of three oscillation parameters by one order of magnitude. Moreover, thanks to its large liquid scintillator mass, JUNO will also contribute to study neutrinos from non-reactor sources such as solar neutrinos, atmospheric neutrinos, geoneutrinos, supernova burst and diffuse supernova neutrinos. Furthermore, JUNO will also contribute to nucleon decay studies. In this work, I will describe the status and the perspectives of the JUNO experiment.

To address fermion mass hierarchy and flavor mixings in the quark and lepton sectors, a minimal flavor structure without any redundant parameters beyond phenomenological observables is proposed via decomposition of the Standard Model Yukawa mass matrix into a bi-unitary form. After reviewing the roles and parameterization of the factorized matrix $M_0^f$ and $F_L^f$ in fermion masses and mixings, we generalize the mechanism to up- and down-type fermions to unify them into a universal quark/lepton Yukawa interaction. In the same way, a unified form of the description of the quark and lepton Yukawa interactions is also proposed, which shows a similar picture as the unification of gauge interactions.

We investigate how the data from various future neutrino oscillation experiments will constrain the physics parameters for a three active neutrino mixing model. The investigations properly account for the degeneracies and ambiguities associated with the phenomenology as well as estimates of experimental measurement errors. Combinations of various reactor measurements with the expected J-PARC (T2K) and NuMI offaxis (Nova) data, both with and without the increased flux associated with proton driver upgrades, are considered. The studies show how combinations of reactor and offaxis data can resolve degeneracies (e.g. the θ₂₃ degeneracy) and give more precise information on the oscillation parameters. A primary purpose of this investigation is to establish the parameter space regions where CP violation can be discovered and where the mass hierarchy can be determined. We find that, even with augmented flux from proton drivers, such measurements demand that sin² 2θ₁₃ be fairly large and in the range where it is measurable by reactor experiments.

We first discuss the problem of mass hierarchy and review briefly the main Beyond the Standard Model (BSM) proposals. We then describe the framework of strings, branes and large extra dimensions and give the main experimental predictions in both particle accelerators and microgravity experiments testing gravity at short distances. Finally, we present some models based on intersecting branes and discuss the issue of Standard Model embedding.

The idea of a rank-one rotating mass matrix (R2M2) is reviewed detailing how it leads to ready explanations both for the fermion mass hierarchy and for the distinctive mixing patterns between up and down fermion states, which can be and have been tested against experiment and shown to be fully consistent with existing data. Further, R2M2 is seen to offer, as by-products: (i) a new solution to the strong CP problem in QCD by linking the theta-angle there to the Kobayashi–Maskawa CP-violating phase in the CKM matrix, and (ii) some novel predictions of possible anomalies in Higgs decay observable in principle at the LHC. A special effort is made to answer some questions raised.

Neutrinos are elementary particles in the standard model of particle physics. There are three flavors of neutrinos that oscillate among themselves. Their oscillation can be described by a 3×3 unitary matrix, containing three mixing angles θ₁₂, θ₂₃, θ₁₃, and one CP phase. Both θ₁₂ and θ₂₃ are known from previous experiments. θ₁₃ was unknown just two years ago. The Daya Bay experiment gave the first definitive nonzero value in 2012. An improved measurement of the oscillation amplitude and the first direct measurement of the mass-squared difference were obtained recently. The large value of θ₁₃ boosts the next generation of reactor antineutrino experiments designed to determine the neutrino mass hierarchy, such as JUNO and RENO-50.

I discuss the status of the mass hierarchy problem and prospects for beyond the Standard Model physics in the light of the Higgs scalar discovery at the LHC and the experimental searches for new physics. In particular, I will discuss in this context low energy supersymmetry and large extra dimensions with low string scale.

We consider a toy model with flat thin branes embedded in a five-dimensional Weyl integrable manifold, where the geometric Weyl scalar provides the material that constitute the brane configurations. The brane configuration is similar to the Randall–Sundrum model. However, it is found that the massless graviton is localized on the brane with negative tension. So, in order to solve the gauge hierarchy problem, our world should be confined on the positive tension brane, and this is crucial to reproduce a correct Friedmann-like equation on the brane. The spacings of graviton mass spectrum are very tiny, but these massive gravitons are hidden in low energy experiments because they are weakly coupled with matter on the brane.

Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains:

• the standard Higgs scalar as the framon in the electroweak sector;
• a global $\widetilde{su}(3)$ symmetry dual to colour to play the role of fermion generations.

Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale $\mu$. From previous work, it is known already that a rotating mass matrix will lead automatically to:

• CKM mixing and neutrino oscillations,
• hierarchical masses for quarks and leptons,
• a solution to the strong-CP problem transforming the theta-angle into a Kobayashi–Maskawa phase.

Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter.

Apart from the qualitative features described in Paper I (Ref. 1), the renormalization group equation derived for the rotation of the fermion mass matrices are amenable to quantitative study. The equation depends on a coupling and a fudge factor and, on integration, on 3 integration constants. Its application to data analysis, however, requires the input from experiment of the heaviest generation masses $m_t$, $m_b$, $m_{\tau }$, $m_{{\nu }_3}$ all of which are known, except for $m_{{\nu }_3}$. Together then with the theta-angle in the QCD action, there are in all 7 real unknown parameters. Determining these 7 parameters by fitting to the experimental values of the masses $m_c$, $m_{\mu }$, $m_e$, the CKM elements $\left|V_{us}\right|$, $\left|V_{ub}\right|$, and the neutrino oscillation angle ${sin}^2{\theta }_{13}$, one can then calculate and compare with experiment the following 12 other quantities $m_s$, $m_u/m_d$, $\left|V_{ud}\right|$, $\left|V_{cs}\right|$, $\left|V_{tb}\right|$, $\left|V_{cd}\right|$, $\left|V_{cb}\right|$, $\left|V_{ts}\right|$, $\left|V_{td}\right|$, $J$, ${sin}^{2}2{\theta }_{12}$, ${sin}^{2}2{\theta }_{23}$, and the results all agree reasonably well with data, often to within the stringent experimental error now achieved. Counting the predictions not yet measured by experiment, this means that 17 independent parameters of the standard model are now replaced by 7 in the FSM.

The framed standard model (FSM) is obtained from the standard model by incorporating, as field variables, the frame vectors (vielbeins) in internal symmetry space. It gives the standard Higgs boson and 3 generations of quarks and leptons as immediate consequences. It gives moreover a fermion mass matrix of the form: m = m_Tαα^†, where α is a vector in generation space independent of the fermion species and rotating with changing scale, which has already been shown to lead, generically, to up–down mixing, neutrino oscillations and mass hierarchy. In this paper, pushing the FSM further, one first derives to 1-loop order the RGE for the rotation of α, and then applies it to fit mass and mixing data as a first test of the model. With 7 real adjustable parameters, 18 measured quantities are fitted, most (12) to within experimental error or to better than 0.5 percent, and the rest (6) not far off. (A summary of this fit can be found in Table 2 of this paper.) Two notable features, both generic to FSM, not just specific to the fit, are: (i) that a theta-angle of order unity in the instanton term in QCD would translate via rotation into a Kobayashi–Maskawa phase in the CKM matrix of about the observed magnitude (J ~ 10^-5), (ii) that it would come out correctly that m_u < m_d, despite the fact that m_t ≫ m_b, m_c ≫ m_s. Of the 18 quantities fitted, 12 are deemed independent in the usual formulation of the standard model. In fact, the fit gives a total of 17 independent parameters of the standard model, but 5 of these have not been measured by experiment.

We present an overview of our recent investigations regarding the prospects of ongoing neutrino experiments as well as future experiments in determining few of the most important unknowns in the field of neutrino physics, specifically the neutrino mass ordering and leptonic CP-violation phase. The effect of matter oscillations on the neutrino oscillation probabilities has been exploited in resolving the degeneracy between the neutrino mass ordering and the CP violation phase in the leptonic sector. Further, we estimate the extent of extrinsic CP and CPT violation in the experiments with superbeams as well as neutrino factories.

We show that a simultaneous explanation for fermionic mass hierarchy among and within the fermionic families, quark-mixing, can be obtained in an extension of the Standard Model, with real singlet scalar fields, which are UV completed by vector-like fermions and a strongly interacting sector.

The fermion flavor structure is investigated by bilinear decomposition of the mass matrix after EW symmetry breaking, and the roles of factorized matrices in flavor mixing and mass generation are explored. On a new Yukawa basis, the minimal parameterization of flavor mixing is realized containing two relative phases and two free $\mathrm{\text{SO}}{(2)}_L$ rotation angles. It is shown that flavor mixing can be addressed from four independent parameters. The validity of the flavor mixing structure is checked in both the lepton and quark sectors. Under the decomposition of flavor mixing, fermion mass matrices are reconstructed in the hierarchy limit. A flat mass matrix with all elements equal to 1 arises naturally from the requirement that homology exists between up-type and down-type fermion mass matrices. Some hints of a flat matrix and flavor breaking are also discussed.

Neutrinos are elementary particles in the standard model of particle physics. There are three flavors of neutrinos that oscillate among themselves. Their oscillation can be described by a 3×3 unitary matrix, containing three mixing angles θ₁₂, θ₂₃, θ₁₃, and one CP phase. Both θ₁₂ and θ₂₃ are known from previous experiments. θ₁₃ was unknown just two years ago. The Daya Bay experiment gave the first definitive non-zero value in 2012. An improved measurement of the oscillation amplitude and the first direct measurement of the mass-squared difference were obtained recently. The large value of θ₁₃ boosts the next generation of reactor antineutrino experiments designed to determine the neutrino mass hierarchy, such as JUNO and RENO-50.