CP violation of quarks in A4A_4 modular invariance

We discuss the quark mass matrices in the $A_4$ modular symmetry, where the $A_4$ triplet of Higgs is introduced for each up-quark and down-quark sectors, respectively. The model has six real parameters and two complex parameters in addition to the modulus $\tau$. By inputting six quark masses and three CKM mixing angles, we can predict the CP violation phase $\delta$ and the Jarlskog invariant $J_{CP}$. The predicted ranges of $\delta$ and $J_{CP}$ are consistent with the observed values. The absolute value of $V_{ub}$ is smaller than $0.0043$, while $V_{cb}$ is lager than $0.0436$. In conclusion, our quark mass matrices with the $A_4$ modular symmetry can reproduce the CKM mixing matrix completely with observed quark masses.Comment: 15 pages, 1 table, 3 figures, accepted version for publication in Physics Letters

Non-Abelian Discrete Symmetries in Particle Physics

We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive, conjugacy classes, characters, representations, and tensor products for these groups (with a finite number). We discussed them explicitly for $S_N$, $A_N$, $T'$, $D_N$, $Q_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$, $T_7$, $\Sigma(3N^3)$ and $\Delta(6N^2)$, which have been applied for model building in the particle physics. We also present typical flavor models by using $A_4$, $S_4$, and $\Delta (54)$ groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetry. We discuss these breaking patterns of the non-Abelian discrete group, which are a powerful tool for model buildings. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach.Comment: 179 pages, 8 figures, section 15 is changed, some references are adde

Long wavelength characteristics of Earth structure

Considerable efforts have been paid to analyse digital seismic network data and ISC (International Seismological Center) data during the last decade. Although there are still uncertainties in seismic maps, some consistent results for long wavelength characteristics of Earth's heterogeneity have emerged. We briefly summarize those features in this paper

A case of esophageal atresia with the bronchial-like lower esophagus which originates from the left lower lobe bronchus

Background Esophageal atresia with or without a trachea-esophageal fistula occurs due to the failure of separation or incomplete development of the foregut. Therefore, esophageal atresia is often associated with various forms of tracheobronchial anomalies. We report an extremely rare case of esophageal atresia. Case presentation A female infant was born at 37 weeks of gestation and weighed 2596 g. A diagnosis of esophageal atresia and total anomalous pulmonary vein return type III were confirmed. The infant had respiratory distress that required tracheal intubation and ventilatory support soon after birth. Temporary banding of the gastroesophageal junction and gastrostomy were performed on the second day of life. However, her respiratory condition deteriorated due to atelectasis of the left lung and compensatory hyperinflation of the right lung. Preoperative examinations showed the unilobe and atelectatic left lung. The trachea was trifurcated in three directions, and the branch that was expected to be the left main bronchus was blind-ended. The dorsal branch was cartilaginous and bifurcated into the left lower lobe bronchus and lower esophagus approximately 1 cm distal from the tracheal trifurcation. The cartilaginous tissue continued to the lower esophagus. The diagnosis of esophageal atresia with the lower esophagus which originated from the left lower lobe bronchus was made. Esophageal atresia repair was performed when the patient was 4 months of age. The esophagus was dissected distally to the bifurcation of the left lower lobe bronchus via right thoracotomy. The lower esophagus was bronchial-like in appearance, transitioning to the normal esophageal wall approximately 7 mm distal to the transected edge. The cartilage tissue was completely resected during surgery, and a primary end-to-end anastomosis of the esophagus was successfully performed. Histopathological findings revealed that the extracted specimen was surrounded by tracheal cartilage and that the inner surface was covered by stratified squamous epithelium that originated from the esophagus. Conclusions In cases of esophageal atresia with an atypical clinical presentation, there may be unique structural abnormalities of the foregut. We emphasize the importance of a preoperative surgical planning since an inadequate operation can lead to fatal complications

A case of esophageal atresia complicated by a right-sided aortic arch with right ductus arteriosus and inferior vena cava interruption with hemiazygos continuation

During the repair of esophageal atresia with tracheoesophageal fistula (EA/TEF), cardiovascular malformations occasionally create a technical challenge. We report a novel case of a 4-day-old girl with EA/TEF and multiple cardiovascular malformations, including right-sided aortic arch (RAA), right ductus arteriosus (RDA), single ventricle with single atrium, common atrioventricular valve, pulmonary atresia, bilateral superior vena cava, and interruption of the inferior vena cava (IVC) with hemiazygos continuation. In this case, a right-sided approach would require the mobilization of the RAA and RDA, which were supplying the pulmonary blood flow due to pulmonary atresia. Alternatively, the left-sided approach would require the mobilization of the hemiazygos vein, which was essential for venous return from the lower body due to IVC interruption. We performed the less intrusive left-sided approach, and the postoperative course was uneventful. Right-sided EA/TEF repair should be avoided because RDA spasm or injury caused by RAA mobilization would be fatal. In cases of interrupted IVC with azygos or hemiazygos vein continuation, care must be taken not to ligate these vessels or block the venous return. Preoperative evaluation is important to prevent complications in such complicated cases. If sufficient information is not available, the left-sided approach may be preferred

Quark mixing from Delta(6N^2) family symmetry

We consider a direct approach to quark mixing based on the discrete family symmetry Delta (6N^2) in which the Cabibbo angle is determined by a residual Z_2 times Z_2 subgroup to be $|V_{us}|=0.222521$, for $N$ being a multiple of 7. We propose a particular model in which unequal smaller quark mixing angles and CP phases may occur without breaking the residual Z_2 times Z_2 symmetry. We perform a numerical analysis of the model for $N=14$, where small Z_2 times Z_2 breaking effects of order 3% are allowed by model, allowing perfect agreement within the uncertainties of the experimentally determined best fit quark mixing values.Comment: 14 pages, 6 figures. arXiv admin note: text overlap with arXiv:1403.439