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Three Family SU(5) GUT · Three Family SU(5) GUT Zurab Tavartkiladze Low Dimensional Physics &...
Transcript of Three Family SU(5) GUT · Three Family SU(5) GUT Zurab Tavartkiladze Low Dimensional Physics &...
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Three Family SU(5) GUT
Zurab Tavartkiladze
Low Dimensional Physics & Gauge Principles (Tbilisi Sep. 28 – 29, 2011)
[Anomaly-free U(1)Flavor x SU(5) Models]
(Ilia State Univ, Georgia)
hep-ph/1109.2642
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Aim of the work:
● Within SUSY GUT, find anomaly free U(1)F flavor Symmetries (with simplest content possible)
● Classify U(1)F charge assignments & Yukawa textures YU,D,E leading to natural explanation of hierarchies in fermion sector.
Some related works:
-- Within MSSM, anom. free U(1)F ‘s with successful YU,D,E
Dudas, Pokorski, Savoy, hp/9504292;
-- Within MSSM & SU(5) GUT, some examples/models of anom. free U(1)F ‘s : Mu-Chun Chen, et al, ph/0612017, 0801.0248;
-- Within SM, non-Abelian anom. free fl. symmetries have been listed:Babu, Frank, Rai, 1104.4782
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● Intro: Shortcomings, Problems & Puzzles of SM / MSSM New Physics
● Motivations for GUT
● Some shortcomings & problems
● New SUSY SU(5)xU(1)Flavor models are built:
- Non-anomalous flavor sym. with economical setup ;
- several successful charged fermion mass patterns
emerged
● Summary
Outline
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c c=
c=l
uq u d
d
νe
e
( (1) 12)SM Interactions : 3( ) ( EW B(3) 8 gluo oso )ns nsL YC USUSU
-( , 2 ,3 1/3) ( , ,13 4/3) -( ,1,3 2/3)
(1, 2 ,1) (1,1, -2)
Fractional charges-Charge quantizat( ) n1 io ?YU
C L Y C emBreaking: SU(3) ×SU(2) ×U(1) SU(3) ×U(1)H
Higgs H(1,2, 1) is required (undiscovered yet)Why/how it is light? –Gauge Hierarchy Problem
---- ---- ----
---- ----
Shortcomings of SM:
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Interactions : (2 (1)(
(1
)
))
)3
(3
YC
C
L
em
S UUU
SU U
S
SM model of EW interactions ~ Matter: 3 gen. quarks & leptons
That's all the matter we have? (additions, extensions?)
Dark Matter:
Dominant part (~85% ) of total matter is unknown – Dark Matter
Dark matter is EM neutral, interacting gravitationally.
Strong evidence of physics beyond the SM. The SM fails to explain DM.
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The ‘Whirlpool galaxy’ - "M51"
Rotational velocity remains constant,
or "flat", with increasing distance
away from the galactic center.
Distance to M51 is 9 Mpc (30 million light yrs)moving away from us at 500 km/s.
Based on Newton's law, the velocity would steadily decrease for stars further away from the galactic center,
since the rotation speed satisfies v^2=GM/r
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Atmospheric & Solar Neutrino Data
● Origin of these scales and mixings?
Unexplained in SM/MSSM
Third mixing angle: 13 0.2
Unknown phase: lept
are of great importance for leptonic CP viol.
Evidences for New Physics:
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1) Cosm. Observation -- Dark Matter (DM):
Dominant part (~85% ) of total matter is unknown – DM
DM is EM neutral, interacting gravitationally.
Evidences for New Physics:
Additional strong evidences of physics beyond SM
2) Baryon Asymmetry 1010B
How this asymmetry is generated?
Big puzzles of particle physics models.
No explanation within SM/MSSM.
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● Charged fermion masses & mixings
With λ=0.2
Observed Noticeable Hierarchies:
What is origin of these hierarchies?Is there any relation or sum rule?
Why three families?
Within SM no answer to these questions…
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Each SM State SUSY Partner
, ,
, , ,
e u d
W Z G
H
SUSY: Symmetry between Bosons & Fermions
, , (sfermions)
, , , (gauginos)
, (Higgsinos)
e u d
W Z G
H Hu d
SM Scale ~ 100 GeV SUSY Scale: Not far above
few TeV
SUSY Breaking scale & br.patternare very important…
SUSY solves some problems/puzzles
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● Solution of Hierarchy problem
● SUSY “Zoo” near TeV…
● Automatic coupling unification
GUT is revamped!
Low scale SUSY insures all order quantum stability of the construction.
Due to Bose Fermi symmetry all unwantedQuantum corrections cancel out.
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SUSY Unification vs. non-SUSY
MSSMSM
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● Neutral Higgs
is accompanied by neutral SUSY partners
0H
0 0 0, , ,H W Z
Lightest (LSP) Neutralino is stabile ~ 100 GeV
● Good Dark Matter candidate!
(mass ~ 100 GeV)
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● Matter Unification
SUSY Grand Unification
offers more solutions to some problems/puzzles
And interesting asymptotic relations [in SO(10)]:
, ...Dt b tm m
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SO(10) νR
Neutrino masses via see-saw
Oscillations
Leptogenesis
m
M
(1, 1,0)c N
l N H M N N
SM singlet
Δ L=2 Lepton number viol.
0 H
H M
2
Hm
M
NM M
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SUSY GUT
● Charge Quantization,Unification of multiplets
● Neutrino Masses (via νR of SO(10)); L-violation
● Successful Coupling Unification
● Stab. Hierarchy (Light Higgs) low SUSY scale
● Dark Matter Candidate (LSP)
● Baryogenesis via Leptogenesis
● Prediction: B-violation proton decay
16 (10)of SO
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SUSY GUT puzzles:
● GUT Symmetry Breaking? (flat directions/goldstones)
● Doublet-Triplet Splitting
● How/why mu-Term ~ 100 GeV ? (harder in GUT)
● Proton Stability (especially d=5 decay)
● Fermion Masses & Mixings (flavor problem)(Discussed Below)
● SUSY FCNC (sflavor problem)
● Minimal & Economical System- Calculability of GUT Threshold Corrections
- Perturbativity all the way up to MPlanck
Unless Unified solution is found, none of the predictions can be trusted..
All these issues are closely related and
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Within SUSY & GUT, the problem of flavor remains unsolved.
Flavor symmetry GF acting between families can help to explain hierarchies
Simplest possibility: GF=U(1)F (Froggatt, Nielsen’79)
Models with gauged U(1)F are highly constrained(anomaly cancellation conds.)
-- Anomalous U(1)F (of string origin); GS mechanism for anomaly cancellation.
-- Alternatively: Anomaly free U(1)F
Within GUTs become more non-trivial [multiplet charges related]
Challenge to find simple anom. free U(1)F x GGUT
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New SUSY SU(5) x U(1)Flavor
Models
U(1)Flavor : Non-Anomalous Flavor Symmetry
SU(5) Matter: 10i , 5i*
U(1)Flavor Charge: Q[10i] , Q[5i*]
SU(5) Scalars: H(5) , H*(5*) , Σ(24)
Charge: Q[H] , Q[H*] , 0
Extra matter : Only SU(5) Singlets (# = or < 3)For anomaly cancellation & RH Neutrinos
Flavons: X[q] , X*[-q] For U(1)Flavor Breaking
Search for Economical Setup..
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Anomaly Cancellation
Singlets
Vanishes with:
Minimal Setup: No states beyond min. SUSY SU(5)
i.e. Three 10’s + four 5* ’s + one H(5) + one
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Search for Anomaly Free Economical Setup
Finding I. Try to find embedding of SU(5)xU(1)F (matter) inAnomaly free non-Abelian G
Example:
[Vertical embedding]
Finding II. Embed U(1)F in anomaly free non-Abelian GF (Babu’2011)
Example:[Horizontal embedding]
*With and ‘minimal flavon’ setup, no realistic model emerges
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We follow Finding I. However, if other possibilities [without G, GF
embeddings of U(1)F] exist, worthwhile of searching & makingclassification of realistic models.
Finding I: Embeddings
I.a.
I.b.
SO(10)SU(5)xU(1)’: 16= 10[1] + 5*[-3]+1[5]
(Flipped SU(5) type) 10=5[2q]+ 5*[-2q] (q=-1)
U(1)’ charges in brackets
E6->SO(10)xU(1)’’SU(5)xU(1)’’:
(Flipped SO(10) type)
27= 16[1] + 10[-2]+1’[4]=
(10+ 5*+1)[1]+(5+5’*)[-2]+1’[4]
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I.c.
Anomaly free:
With ‘flips’:
Three family of (anomaly free):
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All other G findings, such as E7, E8, SU(N>7) give extra SU(5) states and are rejected
-- Possible to build superpositios of U(1)s:
With , is anomaly free
is automatically anomaly free
(I)
(II)
Other superpositions are also possible..
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ABB BBB DABC BBC
Four classes of U(1)F assignment emerge:
Many combinations.. , but restrictions – no extra `exotics’
Give 6 combined options:
Or with
Three family SU(5) GUT!
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For example, ABB: 100+5*0
10α +5*-3 α+15 α
10α' +5*-3 α’+15 α’
Hq+H*-q
Some selection rules (‘guide’):
AAB: rejected because of two 10’s same 0-chage (no hierarchical up-Yukawas)
ACC: rejected for extra 5-plets
In case of ABB, α and α’ should be relatedα/α’=m/n, to avoid two U(1)s
Classify acceptable up type quark mass matrices...
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ABB: 100+5*0
10α +5*-3 α+15 α
10α' +5*-3 α’+15 α’
ABB Scenario includes GF case of O(3) isotriplet:
For a’=-a=1 we obtain horizontal embedding:
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Up Quark Mass Matrices
U(1)Flavor breaking:
Higher operators are suppressed by powers of and
3 Sub-Cases (giving different down sector):n=0 U1; n=3 U5; n=1 U7
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3 Sub-Cases (giving different down sector):n=0 U3; n=1 U4; n=1 U9
3 Sub-Cases (giving different down sector):n=0 U2; n=-1 U6; n=-3 U8
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Content:
Make selection & identification(s):
Three Family SU(5)xU(1)F -
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Mass matrices
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Is a Good choice
For charged fermion mass hierarchies & CKM
Naturally large mixing:
Neutrino sector needs more detailed study..
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● Discussed problem of hierarchies between fermionmasses and mixings within SUSY SU(5) GUT
● New SUSY SU(5)xU(1)Flavor models are built:Non-anomalous flavor sym. with economical setup
● Successful charged fermion mass patterns emerged within three family SU(5)xU(1)Flavor model
(more cases/details in: )
● Neutrino sector may discriminate some scenarios(?)
Thank You
Summary
hep-ph/1109.2642
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Backup Slides:
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U(1)F Breaking
Flavon(s) needed for U(1)F Breaking & for generating Yukawacouplings
Tempting to use singlet(s) (1 or/and 1’) responsible for anomaly cancellation.-However, no realistic model has been found.
-- Introduce flavons – Minimal flavon setup
In SU(5)x U(1)F , the FI-term is allowed
D-term:
& superpotential:
*Without S, higher order superpotential/Kahler terms may do the job
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U(1)F Breaking (contd.)
All F’s & D =0 unique solution (no degeneracy) fixed VEVs:
a)
b)
c)
ExpansionParameters:
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Two Favorite models
Content:
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With selection
and identification =
We get down quark/ch. Lepton mass matrices:
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Is a Good choice
Charged fermionmass hierarchies:
CKM mixings:
Large neutrino mixing:
Neutrino sector needs more detailed study..
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Content and charge assignment:
Make selection:
With identification:
![Page 41: Three Family SU(5) GUT · Three Family SU(5) GUT Zurab Tavartkiladze Low Dimensional Physics & Gauge Principles (Tbilisi Sep. 28 –29, 2011) [Anomaly-free U(1)Flavor x SU(5) Models]](https://reader034.fdocuments.us/reader034/viewer/2022042323/5f0e30127e708231d43e07bc/html5/thumbnails/41.jpg)
Mass matrices
For n=-2/5:
![Page 42: Three Family SU(5) GUT · Three Family SU(5) GUT Zurab Tavartkiladze Low Dimensional Physics & Gauge Principles (Tbilisi Sep. 28 –29, 2011) [Anomaly-free U(1)Flavor x SU(5) Models]](https://reader034.fdocuments.us/reader034/viewer/2022042323/5f0e30127e708231d43e07bc/html5/thumbnails/42.jpg)
Is a Good choice
For obtaining Charged fermionmass hierarchies and CKM mixings
Naturally large mixing:
Neutrino sector needs more detailed study..