Anomaly-Free Flavor Symmetry and Neutrino Anarchy

We show that one can describe the quark and lepton masses with a single anomaly-free U(1) flavor symmetry provided a single order one parameter is enhanced by roughly 4-5. The flavor symmetry can be seen to arise from inside the $E_6$ symmetry group in such a way that it commutes with the SU(5) grand unified gauge group. The scenario does not distinguish between the left-handed lepton doublets and hence is a model of neutrino anarchy. It can therefore account for the large mixing observed in atmospheric neutrino experiments and predicts that the solar neutrino oscillation data is consistent with the large mixing angle solution of matter-enhanced oscillations.Comment: 5 pages, 1 figur

Four-neutrino analysis of 1.5km-baseline reactor antineutrino oscillations

The masses of sterile neutrinos are not yet known, and depending on the orders of magnitudes, their existence may explain reactor anomalies or the spectral shape of reactor neutrino events at 1.5km-baseline detector. Here, we present four-neutrino analysis of the results announced by RENO and Daya Bay, which performed the definitive measurements of $\theta_{13}$ based on the disappearance of reactor antineutrinos at km-order baselines. Our results using 3+1 scheme include the exclusion curve of $\Delta m^2_{41}$ vs. $\theta_{14}$ and the adjustment of $\theta_{13}$ due to correlation with $\theta_{14}$. The value of $\theta_{13}$ obtained by RENO and Daya Bay with a three-neutrino oscillation analysis is included in the $1\sigma$ interval of $\theta_{13}$ allowed by our four-neutrino analysis.Comment: 14 pages, 7 figures. arXiv admin note: text overlap with arXiv:1303.617

Light sterile neutrino and leptogenesis

We studied models of leptogenesis where three right-handed Majorana neutrinos are involved and the minimal-extended seesaw mechanism including an additional singlet field produces four light neutrinos. This study shows that the type of mass ordering and heavy Majorana scales can be determined by inputting the simplest orthogonal matrix into the Casas-Ibarra(CI) representation of seesaw. The CP asymmetry produced from the decays of heavy neutrinos and the dilution mass are predicted in terms of the mass and mixing elements of the fourth neutrino. Upon the choice of CI matrix, the existence of a light sterile neutrino is required to explain the high-energy lepton asymmetry in light of phenomenological measurements. Although there are several free parameters attributable to an additional neutrino, the model can be in part constrained by low-energy experiments such as sterile neutrino searches and neutrinoless double-beta decays, as well as the observed baryon asymmetry in the universe.Comment: 23 pages, 7 figure

The small mixing angle θ13\theta_{13} and the lepton asymmetry

We present the correlation of low energy CP phases, both Dirac and Majorana, and the lepton asymmetry for the baryon asymmetry in the universe, with a certain class of Yukawa matrices that consist of two right-handed neutrinos and include one texture zero in themselves. For cases in which the amount of the lepton asymmetry $Y_L$ turns out to be proportional to $\theta_{13}^2$, we consider the relation between two types of CP phases and the relation of $Y_L$ versus the Jarlskog invariant or the amplitude of neutrinoless double beta decay as $\theta_{13}$ varies.Comment: 17 pages, 14 figures, information for figures added, version published in PR

Conflict between the identification of cosmic neutrino source and the sensitivity to mixing angles in neutrino telescope

Neutrino fluxes at telescopes depend on both initial fluxes out of astronomical bursts and flavor mixing during their travel to the earth. However, since the information on the initial composition requires better precision in mixing angles and vice versa, the neutrino detection at telescopes for itself cannot provide solutions to the both problems. Thus, a probability to be measured at long baseline oscillation is considered as a complement to the telescope, and problems like source identification and parameter degeneracy are examined under a few assumptions.Comment: 17 pages with 7 figures, published versio

ON DEVELOPMENT OF STATISTICAL LEARNING METHODS IN PRECISION MEDICINE

Precision medicine is an area that seeks to maximize clinical effectiveness by assigning treatment regimes tailored to individuals. In this dissertation, we present three topics that advance the methods and applications in the field of precision medicine.The first topic introduces a novel methodology termed random forest informed tree-based learning to discover underlying patient characteristics associated with differential improvement in knee osteoarthritis (OA) symptoms and to identify the individualized treatment regime (ITR) among three available treatments. The proposed algorithm suggests decision rules that divide participants into subgroups based on their characteristics. In our analysis, the estimated treatment rule yielded greater improvements in OA symptoms that could ultimately guide patients toward suitable treatment strategies.In the second topic, we propose a doubly robust estimator for patient-specific utilities and ITRs based on the inverse reinforcement framework from Luckett et al. (2021). This framework optimizes patient-utility for two outcomes by leveraging experts’ decisions on observational data. The suggested doubly robust estimator guarantees consistency even whenincorrect outcome models or incorrect propensity score models are applied, alleviating the need for exact formulation of the outcome model and improving the previous estimator. We also present asymptotic distributions for the estimators of boundary and utility functions using the newly developed indexed argmax theorem, which can be used for deriving weak convergence ofM-estimators with multiple layers.Lastly, we suggest an estimator for utilities when there are more than two treatments. Specifically, we utilize stabilized direct learning to estimate ITRs. Subsequently, we apply the inverse reinforcement framework once again to obtain an estimator for a composite outcome and the balance of the two outcomes. Also, the proposed estimator for utilities considers theheterogeneity in the variance of patients, leveraging the benefits of stabilized direct learning.Doctor of Philosoph

A complex-angle rotation and geometric complementarity in fermion mixing

The mixing among flavors in quarks or leptons in terms of a single rotation angle is defined such that three flavor eigenvectors are transformed into three mass eigenvectors by a single rotation about a common axis. We propose that a geometric complementarity condition exists between the complex angle of quarks and that of leptons in $\mathbb{C}^2$ space. The complementarity constraint has its rise in quark-lepton unification and is reduced to the correlation among $\theta_{12}, \theta_{23}, \theta_{13}$ and the CP phase $\delta$. The CP phase turns out to have a non-trivial dependence on all the other angles. We will show that further precise measurements in real angles can narrow down the allowed region of $\delta$. In comparison with other complementarity schemes, this geometric one can avoid the problem of the $\theta_{13}$ exception and can naturally keep the lepton basis being independent of quark basis.Comment: 9 pages, 4 figures, APPC 10 Pohan