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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Dynamical Electroweak Symmetry Breaking by Heavy 4th Generation Bootstrap December 5, 2012, TH Taida

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Dynamical Electroweak Symmetry Breaking by Heavy 4th Generation Bootstrap December 5, 2012, TH Taida 126 GeV 126 GeV

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ I. Unitarity Bound, QQ Scattering self-energy II. Dynamical Symmetry Breaking : Two Examples NJL Strong Scale-inv. QED ― Set up shop III. Yukawa “ Bootstrap ” Gap Eq.: Dynamical EWSB IV. Discussion and Conclusion DEWSB w/ 4G Quark Bootstrap WSH, Chin. J. Phys. ’12 [arXiv: ] Mimura, WSH, Kohyama, arXiv: !? 0. Why go on? What SM, w/ 4G, could still do for you Gap Equation solve formulate & solve _ 4G Is Still SM SM4 seemingly has sufficient CPV-4-BAU Bootstrap DSB from large Q (this talk) Two Biggest Problems flavor/CPV in SM4

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ – I. Why go on with 4G ? “Physics Highlights” Talk by Riccardo ICHEP 2012 explained later...

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ /17 Outreach Talk in R204 Physics Colloquium on 12/18 Tue

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ PostMortem... Alex ICHEP Riccardo Barbieri

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ PostMortem...; or (future) Resurrection Alex ICHEP

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Summary by Michelangelo HCP 2012, Kyoto, 11/2012

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Summary by Michelangelo HCP 2012, Kyoto, 11/2012

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ mode > SM no convincing evidence for VBF ( Vector Boson Fusion ) or VH (Higgsstrahlung off V ), e.g. fermionic modes Dilaton Not Ruled Out ! Summary by Michelangelo HCP 2012, Kyoto, 11/2012 Coupling weaker by v/f, except to & gg

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ What SM, w/ 4G, could still be doing for you 4G Is Still SM SM4 seemingly has sufficient CPV-4-BAU Bootstrap DSB from large Q (main part of this talk) flavor/CPV in SM4

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ G Is Still SM ● 4G does not take anything that did not exist in SM Even Scaling or Dilatation Invariance is built into SM ( turn off all couplings ) ● But concentrate first on Flavor/CPV, as SM Higgs is flavor-blind

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ G Is Still SM ● 4G does not take anything that did not exist in SM Even Scaling or dilatation invariance is built into SM ( turn off all couplings ) ● But concentrate first on Flavor/CPV, as SM Higgs is flavor-blind Sheldon Stone R.I.P.

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ G Is Still SM ● 4G does not take anything that did not exist in SM Even Scaling or dilatation invariance is built into SM ( turn off all couplings ) ● But concentrate first on Flavor/CPV, as SM Higgs is flavor-blind Sheldon Stone However, Flavor people should keep the CKM-extension in mind. Higgs does not enter these loops. And, the 126 GeV dilaton could be “dilaton” still... Keep on Searching R.I.P.

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ My own busy slide from ICHEP2010 (and ICHEP2008). Point is, great gain in CPV from 3G means CPV-4-BAU 4G Is Still SM ● 4G does not take anything that did not exist in SM Even Scaling or dilatation invariance is built into SM ( turn off all couplings ) CPV ● But concentrate first on Flavor/CPV, as SM Higgs is flavor-blind WSH, CJP 47 (2009) 134 [arXiv: ]

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Not much affected by absence of hint for New Physics in sin s ; B s → ; A FB ( B → K* ) SM4 seemingly has Sufficient CPV-4-BAU Sheldon ICHEP CJP 47 (2009) 134

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Not much affected by absence of hint for New Physics in sin s ; B s → ; A FB ( B → K* ) SM4 seemingly has Sufficient CPV-4-BAU Sheldon ICHEP CJP 47 (2009) 134 Consistent w/ small |V t’s V t’b |, which consists with observed CKM pattern.

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ I. Unitarity Bound, QQ Scattering _ from Self-Energy to Gap Equation

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ I. Unitarity Bound, QQ Scattering _ I re-entered 4G study, since 2004, due to flavor/CPV Since , start to think about Physics at CMS/LHC ➜ Set-up 4G quark search as program for NTU CMS group. Since 2008, as bounds rose (Tev ↷ LHC), re-learned Yukawa-induced condensate Intuitively saw Holdom ’ 06 Associated with left-handed gauge coupling: Yukawa Coupling of Goldstone Mode Established, Independent of Higgs ’ Existence [CPV-4-BAU]

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ I. Unitarity Bound, QQ Scattering _ Since , start to think about Physics at CMS/LHC ➜ Set-up 4G quark search as program for NTU CMS group. Since 2008, as bounds rose (Tev ↷ LHC), re-learned Yukawa-induced condensate Nambu’s prize in 10/2008 made me think QQ condensation is NJL-like Puzzled: ( ca ) _ Scattering UBV (UBV) ~ “long-distance” ( vs 1/m Q ) ( vs 1/m Q ) Q As m Q rose, m Q /m W increased; the scattering that sets the Unitarity Bound is a “long distance” effect Not quite NJL-like. Of course, leading UBV occurs for G in s-channel (but this is repulsive). I re-entered 4G study, since 2004, due to flavor/CPV [CPV-4-BAU] 4q operator Holdom ’ 06

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Gap Equation? WSH, ICHEP2010; & arXiv: (Chin. J. Phys., 6/2012) Q I. Unitarity Bound, QQ Scattering _ Scattering UBV (UBV) ~ “long-distance” ( vs 1/m Q ) ( vs 1/m Q ) Q Self Energy Q summer 2010, while discussing w/ Felipe Llanes-Estrada self-energy Gap Equation 2q 22q 2 summer 2011: No New Physics TeV Summing over large range of exchange momentum q

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ II. Dynamical Symmetry Breaking : Two Examples NJL Strong Scale-inv. QED ― Setting up

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Gap Equation : Nambu − Jona-Lasinio Model Self-energy Does Not depend on momentum ➜ infinite number of diagrams... factor out m N Eventually trade G and for f and m N

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Gap Equation : Strong Scale-invariant QED Gap equation for QED in the ladder approx. m 0 = 0 w/ m 0 = 0 Self-energy momentum-dep. w.fn. renorm

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Gap Equation : Strong Scale-invariant QED Gap equation for QED in the ladder approx. m 0 = 0 w/ m 0 = 0 angular integration Wick rotation Self-energy momentum-dep. Simplification w.fn. renorm “Mass” = B/A Set up Notation follow Fukuda − Kugo

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ noting plus B.C.: Miransky scaling... ? Gap Equation : Strong Scale-invariant QED

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ III. Yukawa “ Bootstrap ” Gap Eq.: Dynamical EWSB Q 2q22q2 2q22q2 Summing over large range of exchange momentum q Large Q through massless G generates m Q, but in turns assures G as Goldstone

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Gap Equation : Yukawa “ Bootstrap ” Gap equation for large Yukawa in the ladder approx. m 0 = 0 w/ m 0 = 0 (and neglect gauge couplings) “Mass” = B/A incorporate Higgs in calc. [Hung-Xiong ’11] Self-energy momentum-dep. G Q (gauge symm.)

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Gap Equation : Yukawa “ Bootstrap ” “Mass” = B/A If follow HX ’11 sign and ignore A ( p 2 ) equation, then ~ Scale-inv. QED, w/ critical Q = , or, and If we use correct sign, but continue to use A ( p 2 ) = 1 in B ( p 2 ) equation, then, i.e. higher But one should not ignore A ( p 2 ) equation ! vs. Hung-Xiong ’11 massless doublet

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Gap Equation : Yukawa “ Bootstrap ” “Mass” = B/A Drop Higgs for now; return later. Gap equation for large Yukawa in the ladder approx. m 0 = 0 w/ m 0 = 0 (and neglect gauge couplings) Self-energy momentum-dep. G Q (gauge symm.)

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ So, ~ 1.4 We find, numerically, ~ 1.4 ➜ ➜ ➜ ➜ Gap Equation : Yukawa “ Bootstrap ” Higgs or not, absorbed in

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ G ● Gap Eq.: Integrate over q 2, but need < 2m Q for G to remain Goldstone ➜ cannot be taken arbitrarily large This raises to, OR depressingly large ! 2q22q2

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ G ● Gap Eq.: Integrate over q 2, so < 2m Q for G to remain Goldstone ➜ cannot be taken arbitrarily large This raises to, OR 2q22q2 depressingly large ! ● Put back the light Higgs (126 GeV close to 80 GeV) ? ~ 1.4 ~ 1.4 ➜ ➜ ➜ ➜ ~ 13.7 ! ~ 13.7 ! ➜ ➜ ➜ ➜ No Good !

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ G ● Gap Eq.: Integrate over q 2, so < 2m Q for G to remain Goldstone ➜ cannot be taken arbitrarily large This raises to, OR 2q22q2 depressingly large ! ● Can this be made Lower? Pion-Nucleon very analogous !

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Pion-Nucleon very analogous ! 2 G ● Gap Eq.: Integrate over q 2, so < 2m Q for G to remain Goldstone ➜ cannot be taken arbitrarily large This raises to, OR 2q22q2 depressingly large ! ● Can this be made Lower? Perhaps: Yes, other tight Bound States ➜ ~ NJL (but much q-dep.)

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ IV. Discussion and Conclusion

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Dilaton So, what about 126 GeV boson ? Has to be Dilaton. 4G (chiral Q) seemingly bites the dust, again... (not that it did not happen before) believeDilaton My first reaction: Hard to believe we are seeing a Dilaton “just now”...

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Dynamical Mass Generation also means Breaking of Scale Invariance. Could there be a Dilaton ? (Radion via AdS/CFT or warped) Goldberger, Grinstein, Skiba, ’08 Barger, Ishida, Keung, ’12 Cheung, Yuan, ’12 Campbell, Ellis, Olive, ’12 Grzadkowski, Gunion, Toharia, ’12 Coleppa, Gregroire, Logan, ’12 Matsuzaki, Yamawaki7/129/12 Matsuzaki, Yamawaki, ’12; 7/12; 9/12 etc. Elander, Piai, 8/12 4G (chiral Q) seemingly bites the dust, again... (not that it did not happen before) But the Bootstrap Gap Eq. is nominally Scale-Inv. (no scale) ! Used in aid of numerical solution. Treat 3 parameters a = v/F, c g, c “holographic techni-dilaton gives as good a fit as SM Higgs” N.B. We did not touch UV... N.B. 4G + 2HDM? Perhaps, but 1) Why h 0 light; 2) Gap Eq. not applicable believeDilaton My first reaction: Hard to believe we are seeing a Dilaton “just now”... Chacko, Franceschini, Mishra, 9/12 What is the true source of Scale Breaking ? Dilaton So, what about 126 GeV boson ? Has to be Dilaton. Not Yet Ruled Out

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Gap Equation : Yukawa “ Bootstrap ” “Mass” = B/A Dropped “Higgs”; if dilaton, v 2 /F 2 suppressed suppressed. self-consistent ➜ self-consistent Gap equation for large Yukawa in the ladder approx. m 0 = 0 w/ m 0 = 0 (and neglect gauge couplings) Self-energy momentum-dep. G Q (gauge symm.)

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Conculsion ● A Dynamical Gap Eq., by Goldstone, or V L exch. with Strong Yukawa Coupling is constructed, and solved. This can, in principle, replace usual Higgs Condensation ● The Needed Yukawa Coupling is above 10 !! [~ -p] This implies 4G masses in 2-3 TeV Range. Boundstate Resonance Production with Decay into Multi-V L (backup slide) should be considered. ● The new 126 GeV Boson poses difficulties for 4G. Dilaton It would have to be a Dilaton... Our Gap Eq. is nominally Scale-invariant ! Q ≳ Let’s wait what Nature reveals to us, thru LHC.

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/

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Bootstrap Bootstrap DSB-4 George W.S. Hou (NTU) TH Taida, 12/5/ Possible Phenomenology : QQ → nV L An Intriguing Analogy ➨ Example WSH, PRD’2012 [arXiv: ] data

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