Quark mixing from softly broken symmetries

Quark flavor mixing may originate in the soft breaking of horizontal symmetries. Those symmetries, which in the simplest case are three family U(1) groups, are obeyed only by the dimension-4 Yukawa couplings and lead, when unbroken, to the absence of mixing. Their breaking may arise from the dimension-3 mass terms of SU(2)-singlet vector-like quarks. Those gauge-singlet mass terms break the horizontal symmetries at a scale much higher than the Fermi scale, yet softly, leading to quark mixing while the quark masses remain unsuppressed.Comment: 9 pages, plain Latex, no figure

慈円『仙洞句題五十首』『最勝四天王院障子和歌』校注

In 1201，the year of Ken-nin 1st，Ex-Emperor Gotoba ordered Six Poets at that time to compose the 50 Poems consisting of Four Chinese Characters . And Gotoba constructed the Saisho Shitenno-in Temple for the honor of himself. That Temple was drawed 46 pictures on Shoji Screen，famous place in Japan. Then Gotoba ordered Ten Poets to compose 46 poems concerning that pictures . This Annotation is dealing with Jien's Waka Poems on both contents

Professional Culture: Let’s Talk Tackling of Inequity, Injustice, and Absent Talent

Progressive reforms and community kindness are encouraged; terminology common among DEI discussions is explored here

Interface Hamiltonians and bulk critical behavior

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