a viable rs model for quarks and leptons with t´ flavor symmetry felix yu university of california,...
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![Page 1: A viable RS Model for Quarks and Leptons with T´ Flavor Symmetry Felix Yu University of California, Irvine Pheno 2010 M-C. Chen, K. T. Mahanthappa, FY](https://reader035.vdocument.in/reader035/viewer/2022062322/5697bff71a28abf838cbec7d/html5/thumbnails/1.jpg)
A viable RS Model for Quarks and Leptons with
T´ Flavor SymmetryFelix Yu
University of California, IrvinePheno 2010
M-C. Chen, K. T. Mahanthappa, FY – Phys. Rev. D 81, 036004 (2010)[arXiv: 0907.3963 [hep-ph]]
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Motivation• Fermion mass hierarchy unexplained• Gauge hierarchy problem motivates new
physics at about TeV• Randall-Sundrum (RS1) model with bulk
fermions provides a good framework– Can get fermion mass hierarchy with O(1)
coefficients– Need to suppress FCNCs
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Randall-Sundrum• RS1 Model – warped geometry
– 5th dimension compactified via S1/2
– Higgs field confined to TeV brane (y = R), other fields propagate in bulk
– From compactification and boundary conditions, can find Fourier modes for bulk fields
– SM masses and mixings arise from zero modes• Integrate out y to find overlap between SM fields and
Higgs
Gherghetta, Pomarol (2000), Huber, Shafi (2000), Grossman, Neubert (1999)
222 dydxdxeds )y(
yk)y(
Randall, Sundrum (1999)
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Flavor Changing Neutral Currents in RS• Change from gauge interaction basis to mass basis
• Generically get FCNCs if bulk masses are not equal• Solutions: (1) alignment, (2) degeneracy
233
222
211
4
00
00
00
)c,c(f
)c,c(f
)c,c(f
GgDiedy MM|y|k
mm V
)c,c(f
)c,c(f
)c,c(f
VGg
233
222
211
00
00
00†
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The Finite Group T´• Double covering of A4
– A4 is the discrete invariant rotations of a tetrahedron
• Has two generators: S=(1234) (4321), T=(1234) (2314)– S2=R, T3=1, (ST)3=1, R2=1
• R=1: 1, 1´, 1´´, 3 (vector) [use for leptons]• R=-1: 2, 2´, 2´´ (spinorial) [use for quarks]
Frampton, Kephart (1995)
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Assignment of T´ Representations• Motivated by neutrino mixing data: assign L ~ 3 (LH
lepton doublets), N ~ 3 (RH neutrinos) under T to obtain the tri-bimaximal mixing pattern– Introduce e ~ 1, ~ 1, ~ 1 for charged lepton masses– Tree-level lepton FCNCs are eliminated via degeneracy
(left-handed lepton doublets share a common bulk mass term) and alignment (right-handed lepton singlets can freely rotate)
• Motivated by quark masses, use 2 1 assignment– Tree-level quark FCNCs involving first and second
generations are eliminated via degeneracy (up- and down-type first two generations share a common bulk mass term)
• Require additional flavon fields to break T symmetry on the IR brane
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.c.h
NLyHk
Ry
yyNNk
yL
Dc,SS,
SSD
b,Dc,SSD
a,SS,T
lepSS,,Yuk
5
55
1
1
Leptons in T´
.c.hLyLyeLyHk
)Ry(L DDDe
lepl,Yuk
5551)NcNcceceLcL(kL
LLLLL
NeLlepBulk
,Yukawal,YukawaBulkKineticleptonic
.c.hyyNLHk
)Ry(L DcDb,Dc,
DcDa,Dc,
lepDc,,Yuk
551
Purely Dirac neutrino masses
Seesaw type 1 neutrino masses
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Quarks in T´: 2 1 Framework
.c.h)]TQyTQy
UQy)(UQy(H)[Ry(L
TUT
UUUUYukawa
331212
331212
)BcBDcD
TcTUcUQcQQcQ(kL
BD
TUQQBulk
331212 312
Down-type Yukawa Lagrangian is exactly analogous
YukawaBulkKineticquark LLLL
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Parameter Counting• Input parameters (Naïve counting)
– Charged lepton: 8 (= 4 bulk + 3 Yukawa + 1 flavon)– Neutrino: [seesaw] 6 [7] (= 2 bulk + 2 [3] Yukawa + 2
flavon) – Quark: 24 = (6 bulk + 8 Yukawa + 10 flavon)
• Actual number of independent input combinations– 16 = Lepton matrix (3) + Neutrino matrix (2) + Quark
matrices (6 + 5)
• Contrast with anarchic case– 36 [30] for leptons, 36 for quarks
• Fit parameters– Lepton and quark masses (3 + 6 = 9)– CKM matrix (+ CP violating phase) (3 + 1 = 4)– Neutrino mixing angles (3)
16 Inputs, 16 Outputs
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Results –Leptons
571260664960829250400000 .c,.c,.c,.c eL
Set all leptonic Yukawas to 1. Renormalization effects negligible.
Gives me=511 keV, m=105.7 MeV, m=1.777 GeV10
For normal hierarchy
For inverted hierarchy
Normal, Dc: msol2 = 7.6370 10-5 eV2, matm
2 = 2.4031 10-3 eV2
Inverted, SS: msol2 = 7.6560 10-5 eV2, matm
2 = –2.4009 10-3 eV2
Experimental: msol2 = 7.65 10-5 eV2, matm
2 = 2.40 10-3 eV2
Fusaoka, Koide (1998), Schwetz, Tortola, Valle (2008)
0944.0,1768.0,27000.1,40000.0 ,0,0 DcDcNL cc
Normal, SS: msol2 = 7.6520 10-5 eV2, matm
2 = 2.4001 10-3 eV2
06191.0,07427.0,40000.0,40000.0 ,0,0 SSSSNL cc
115241.0,02321.0,40000.0,40000.0 ,0,0 SSSSNL cc
For normal hierarchy
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Results – Quarks
508.0350.0150.0
503.0512.0503.0
3
12
BTQ
DUQ
ccc
ccc
Bulk mass parameters
Flavons and Yukawas
060.0
00.1
540.0540.0
1135.0
00230.0
181.0
448.0
00200.0
00104.000143.0
3
3
0
0
00
0
0
B
T
D
D
D
U
UU
y
y
i
i
Prediction (3 TeV) Fit bounds
mu 1.49 MeV 0.75-1.5 MeV
md 2.92 MeV 2-4 MeV
mc 0.541 GeV 0.56 ± 0.04 GeV
ms 36.6 MeV 47 ± 12 MeV
mt 134.8 GeV 136.2 ± 3.1 GeV
mb 2.41 GeV 2.4 ± 0.04 GeV
Csaki, Falkowski, Weiler (2008)Other Yukawas set to 1
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Results – CKM and Jarlskog
Fusaoka, Koide (1998), Charles, et al. (CKMfitter Group) (2009)
000078.0000047.0
0011.00020.0
00057.000064.0
0011.00019.0
00053.000052.0
0022.00022.0
00044.000032.0
0022.00022.0
00052.000052.0
999146.00404.000859.0
0412.097349.02250.0
00351.02251.097433.0
|| ExpCKMV
999176.00395649.000910164.0
040450.0973485.0225147.0
003464.0225305.0974282.0
|| TheoryCKMV Corrections to quark mixings from running are small.
Perform fit at mZ
510023 .Jth5450
250 10932 .
.ex .J
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Leading FCNC Estimate• Leading contribution is from dim-6
operators arising from fermion zero-modes mixing with KK modes
• Scaled to Z-coupling, leading contribution is
• Using MKK ~ 3 TeV, kR ~ 11, v = 246 GeV:– coefficient is 2.96510-6 for u-c transition– coefficient is 4.15610-6 for d-s transition
2
42
222
)0()0(2)1(2
00 4 KK
kRkji
M
ve
Rk
fff
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Conclusions• RS1 + T´ provides a framework for
realistic fermion masses and mixings– Motivated by neutrino mixings and quark
masses, we choose T´ representations• This choice eliminates tree-level lepton FCNCs
and first-second generation quark FCNCs
– Can fit for all SM fermion masses, CKM matrix, and Jarlskog invariant with 16 input parameter combinations
– Allows a low first KK mass scale, testable at colliders
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Group Algebra of T´
ie
eiA
/i
/i
12
12
12
2
3
1
2 S=A1, T=A2,
2´ S=A1, T=2A2,
2´´ S=A1, T=A2
1 S=1, T=1,1´ S=1, T=,1´´ S=1, T=2
10
02A
122
212
221
3
1
2
2
2
S
200
00
001
T
Feruglio, Hagedorn, Lin, Merlo (2007)
3
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Neutrino Constraints• Neutrino measurements (at 2)
• (at 1)• Well-fit by Tri-Bimaximal Mixing
(TBM) Harrison, Perkins, Scott (1999)
14012023
2 50 ...sin
0440032012
2 3040 ...sin
0160011013
2 010 ...sin
213161
213161
03132
///
///
//
UTBM
TBM can be easily obtained from A4 or T´ group symmetries
Schwetz, Tortola, Valle (2008)
Ma, Rajasekeran (2001)
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Leptons in T´ 3
3
2
1
~
L
L
L
L
1
1
1
~
~
~e3
0
0
1
0 ~
1113333 AS
)c,c(fy
)c,c(fy
)c,c(fy
hM
LD
LD
eLD
e
e
5
5
5
0
00
00
00
2332111 1221331 1331221
T´ contraction:
Diagonal charged lepton mass matrixbecause of T´ assignments and flavon VEVs
.c.hLyLyeLyHk
)Ry(L DDDe
lepl,Yuk
5551
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Quarks in T´: The 2 1 Framework
)c,c(fy)c,c(f
)c,c(fcos)c,c(f)c,c(fi
)c,c(fsin)c,c(fi
)c,c(fi
hM
TQT
TQU
UQUU
UQUQ
UQUU
UQUQ
U
312
31212
31212
30
0000
0000
02
12
1
2 1
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Quarks in T´: The 2 1 Framework
)c,c(fy)c,c(f
)c,c(fcos)c,c(f)c,c(fi
)c,c(fsin)c,c(fi
)c,c(fi
hM
BQB
BQD
DQDD
DQDQ
DQDD
DQDQ
D
312
31212
31212
30
0000
0000
02
12
1
2 1
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ph]CKMfitter Group (J. Charles et al.), Eur. Phys. J. C41, 1-131 (2005). arXiv:hep-ph/0406184M.C. Chen and S.F. King, arXiv:0903.0125 [hep-ph]M.C. Chen and K.T. Mahanthappa, arXiv:0904.1721 [hep-ph]V. Cirigliano, B. Grinstein, G. Isidori and M. B. Wise, Nucl. Phys. B 728, 121 (2005).
arXiv:hep-ph/0507001G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Nucl. Phys. B 645, 155 (2002).
arXiv:hep-ph/0207036G. Engelhard, J.L. Feng, I. Galon, D. Sanford and FY, arXiv:0904.1415 [hep-ph]J.L. Feng, C.G. Lester, Y. Nir and Y. Shadmi, Phys. Rev. D 77, 076002 (2008) arXiv:0712.0674 [hep-ph].F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo, Nucl. Phys. B 775, 120 (2007) arXiv:hep-ph/0702194P.H. Frampton and T.W. Kephart, Int. J. Mod. Phys. A 10, 4689 (1995). arXiv:hep-ph/9409330T. Gherghetta and A. Pomarol, Nucl. Phys. B 586, 141 (2000). arXiv:hep-ph/0003129Y. Grossman and M. Neubert, Phys. Lett. B 474, 361 (2000). arXiv:hep-ph/9912408 P.F. Harrison, D.H. Perkins and W.G. Scott, Phys. Lett. B 458, 79 (1999). arXiv:hep-ph/9904297S.J. Huber and Q. Shafi, Phys. Lett. B 544, 295 (2002). arXiv:hep-ph/0205327C.I. Low and R.R. Volkas, Phys. Rev. D 68, 033007 (2003). arXiv:hep-ph/0305243E. Ma and G. Rajarasekaran, Phys. Rev. D 64, 113012 (2001). arXiv:hep-ph/0106291L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999). arXiv:hep-th/9906064L. Randall and R. Sundrum, Phys. Rev. Lett 83, 3370 (1999). arXiv:hep-ph/9905221L. Randall and R. Sundrum, Nucl. Phys. B 557, 79 (1999). arXiv:hep-th/9810155T. Schwetz, M. Tortola and J.W.F. Valle, New J. Phys. 10, 113011 (2008). arXiv:0808.2016 [hep-ph]