Flavor-Symmetry based Flavor Violation in Supersymmetry Jisuke Kubo (kanazawa Univ.) at NCTS LHC Topical Program 1 based on: Babu and JK, PRD71, 056006 (2005); Itou, Kajiyama and JK, NPB743, 74 (2006); Kifune, JK and Lenz, PRD77, 076010 (2008); Araki and JK, IJMod.A24, 5831 (2009); Kawashima, JK and Lenz, PLB681,60 (2009); JK and Lenz, PRD82,075001 (2010) Text
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Flavor-Symmetry based Flavor Violation in Supersymmetry Jisuke Kubo (kanazawa Univ.) at NCTS LHC Topical Program 1 based on: Babu and JK, PRD71, 056006.
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Flavor-Symmetry basedFlavor Violation
in Supersymmetry
Jisuke Kubo (kanazawa Univ.)
at NCTS LHC Topical Program
1
based on: Babu and JK, PRD71, 056006 (2005); Itou, Kajiyama and JK, NPB743, 74 (2006);Kifune, JK and Lenz, PRD77, 076010 (2008); Araki and JK, IJMod.A24, 5831 (2009); Kawashima, JK and Lenz, PLB681,60 (2009);JK and Lenz, PRD82,075001 (2010)
II Where do non-abelian discrete family symmetries come from?
IV Conclusion
PLAN
6
The classification of the finite groups has been completed; 1981 Gorenstein, 1995 Aschbacher+Smith more than 100 years later than the case of the continues group.
g= order of a finite group = # of the group elements
7
I Non-abelian finite group
1. No non-abelian finite group exists for prime g.2. For smaller g (<31) there exist only three types:
3. The smallest non-abelian finite group is S3=D3.
a) Permutation groups
b) Dihedral groups and Binary dihedral (Dicyclic) groups
c) Twisted products like
Non-abelian Finite groups of lower ordersfrom Frampton and Kephart
8
Frampton and Kephart, `o1,Frampton,Kephart+Rohm, `09
direct products
twisted products
32+13=45 groups
II Where do discrete family symmetries come from?
*It is simply there!
*It comes from the geometry of extra dimensions.
*It comes from SSB of a non-abelian continuous G.
10
Discrete translational inv.+parity
From the geometry of a discrete dimension (dim. deconstruction)(Kubo, `05)
DN
Flavor group11
A4 From orbifolding extra dimensions
(Altarelli,Feruglio+Lin, `06)
with 120 degrees=> root vectors of SU(3)
Z2
In field theory:
12
Abe, K-S Choi, Kobayashi, Ohki, Sakai,`10Extended by