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Dynamical Electroweak Symmetry Breaking by Heavy 4th Generation Bootstrap

Dynamical Electroweak Symmetry Breaking by Heavy 4th Generation Bootstrap. December 5, 2012, TH Seminar @ Taida. Dynamical Electroweak Symmetry Breaking by Heavy 4th Generation Bootstrap. December 5, 2012, TH Seminar @ Taida. 126 GeV. !?. DEWSB w/ 4G Quark Bootstrap.

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Dynamical Electroweak Symmetry Breaking by Heavy 4th Generation Bootstrap

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  1. Dynamical Electroweak Symmetry Breaking by Heavy 4th Generation Bootstrap December 5, 2012, TH Seminar @Taida

  2. Dynamical Electroweak Symmetry Breaking by Heavy 4th GenerationBootstrap December 5, 2012, TH Seminar @Taida 126 GeV

  3. !? DEWSBw/4G Quark Bootstrap 0.Why go on? What SM, w/ 4G, could still do for you... *4G Is Still SM * SM4 seemingly has sufficientCPV-4-BAU *Bootstrap DSB from large lQ(this talk) flavor/CPV in SM4 Two Biggest Problems _ I. Unitarity Bound, QQ Scattering Gap Equation self-energy II. Dynamical Symmetry Breaking:Two Examples * NJL * Strong Scale-inv. QED ― Set up shop III. Yukawa “Bootstrap” Gap Eq.: Dynamical EWSB formulate & solve IV. Discussion and Conclusion WSH, Chin. J. Phys. ’12 [arXiv:1201.6029] Mimura,WSH,Kohyama,arXiv:1206.6063

  4. –I. Why go on with 4G? explained later ... “Physics Highlights” Talk by Riccardo Barbieri @ ICHEP 2012

  5. 12/17 Outreach Talk in R204 Physics Colloquium on 12/18 Tue

  6. PostMortem ... Alex Pomarol @ ICHEP Riccardo Barbieri

  7. PostMortem ...;or (future) Resurrection Alex Pomarol @ ICHEP

  8. Summary by Michelangelo Mangano @ HCP 2012, Kyoto, 11/2012

  9. Summary by Michelangelo Mangano @ HCP 2012, Kyoto, 11/2012

  10. Summary by Michelangelo Mangano @ HCP 2012, Kyoto, 11/2012 • ggmode > SM • no convincing evidence • for VBF (Vector Boson Fusion) • or VH (Higgsstrahlung off V), • e.g. fermionic modes DilatonNot Ruled Out ! Coupling weaker by v/f, except to gg & gg

  11. 0.What SM, w/ 4G, could still be doing for you *4G Is Still SM * SM4 seemingly has sufficientCPV-4-BAU *Bootstrap DSB from large lQ(main part of this talk) flavor/CPV in SM4

  12. 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) ● But concentrate first on Flavor/CPV, as SM Higgs is flavor-blind

  13. 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) ● But concentrate first on Flavor/CPV, as SM Higgs is flavor-blind Sheldon Stone R.I.P.

  14. 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) ● 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 could be “dilaton” still ... R.I.P. Keep on Searching

  15. 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) ● But concentrate first on Flavor/CPV, as SM Higgs is flavor-blind My own busy slide from ICHEP2010 (and ICHEP2008). Point is, great gain in CPV from 3G means CPV-4-BAU WSH, CJP 47 (2009) 134 [arXiv:0803.1234]

  16. SM4 seemingly has SufficientCPV-4-BAU CJP 47 (2009) 134 Not much affected by absence of hint for New Physics in sinfs;Bs→ m+m-;AFB(B → K*0m+m-) Sheldon Stone @ ICHEP

  17. SM4 seemingly has SufficientCPV-4-BAU CJP 47 (2009) 134 Not much affected by absence of hint for New Physics in sinfs;Bs→ m+m-;AFB(B → K*0m+m-) Sheldon Stone @ ICHEP Consistent w/ small |Vt’sVt’b|, which consists with observed CKM pattern.

  18. _ I. Unitarity Bound, QQ Scattering from Self-Energy to Gap Equation

  19. _ I. Unitarity Bound, QQ Scattering I re-entered 4G study, since 2004, due to flavor/CPV [CPV-4-BAU] Since 2006-7, 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

  20. _ I. Unitarity Bound, QQ Scattering I re-entered 4G study, since 2004, due to flavor/CPV [CPV-4-BAU] Since 2006-7, 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 Holdom ’06 _ Nambu’s prize in 10/2008 made me think QQ condensation is NJL-like Puzzled: (ca. 2009) 4q operator Scattering (UBV) As mQ rose, mQ/mW increased; the scattering that sets the Unitarity Bound is a “long distance” effect Not quite NJL-like. lQ ~ “long-distance” (vs 1/mQ) Of course, leading UBV occurs for G in s-channel (but this is repulsive).

  21. _ I. Unitarity Bound, QQ Scattering self-energy Scattering (UBV) Gap Equation lQ Self Energy ~ “long-distance” (vs 1/mQ) 1-2-3 TeV lQ summer 2011:No New Physics summer 2010, while discussing w/ Felipe Llanes-Estrada Gap Equation? Summing over large range of exchange momentumq q2 WSH, ICHEP2010; & arXiv:1201.6029 (Chin. J. Phys., 6/2012) lQ

  22. II. Dynamical Symmetry Breaking:Two Examples * NJL * Strong Scale-inv. QED ― Setting up

  23. Gap Equation: Nambu−Jona-Lasinio Model Self-energy Does Not depend on momentum ➜ infinite number of diagrams ... factor out mN Eventually trade G and L for fp and mN

  24. Gap Equation: Strong Scale-invariant QED Gap equation for QED in the ladder approx. w/ m0 = 0 Self-energy momentum-dep. w.fn. renorm

  25. Gap Equation: Strong Scale-invariant QED Set up Notation Gap equation for QED in the ladder approx. w/ m0 = 0 Self-energy momentum-dep. w.fn. renorm “Mass” = B/A angular integration Wick rotation Simplification follow Fukuda−Kugo

  26. Gap Equation: Strong Scale-invariant QED noting plus B.C.: Miransky scaling ... ?

  27. Large lQ through massless G generates mQ, but in turns assures G as Goldstone III.Yukawa“Bootstrap” Gap Eq.: Dynamical EWSB lQ q2 q2 Summing over large range of exchange momentumq

  28. Gap Equation: Yukawa “Bootstrap” Gap equation for large Yukawa in the ladder approx. w/ m0 = 0 (and neglect gauge couplings) Self-energy momentum-dep. (gauge symm.) G lQ “Mass” = B/A incorporate Higgs in calc. [Hung-Xiong ’11]

  29. Gap Equation: Yukawa “Bootstrap” vs. Hung-Xiong ’11 masslessf doublet + “Mass” = B/A • If follow HX ’11 sign and ignore A(p2) equation, then ~ Scale-inv.QED, • w/ critical aQ = p/2, or , and • If we use correct sign, but continue to use A(p2) = 1 in B(p2) equation, • then , i.e. higher • But one should not ignore A(p2)equation!

  30. Gap Equation: Yukawa “Bootstrap” Gap equation for large Yukawa in the ladder approx. w/ m0 = 0 (and neglect gauge couplings) Self-energy momentum-dep. (gauge symm.) G lQ “Mass” = B/A Drop Higgs for now; return later.

  31. Gap Equation: Yukawa “Bootstrap” So, Higgs or not, absorbed in We find, numerically, ~ 1.4 ➜ ➜

  32. q2 ● Gap Eq.: Integrate over q2, but need L< 2mQfor G to remain Goldstone ➜ Lcannot be taken arbitrarily large This raises to , OR depressingly large !

  33. q2 ● Gap Eq.: Integrate over q2, so L< 2mQfor G to remain Goldstone ➜ Lcannot be taken arbitrarily large This raises to , OR depressingly large ! ● Put back the light Higgs (126 GeV close to 80 GeV)? ~ 1.4 ➜ ➜ ~ 13.7 ! ➜ ➜ No Good!

  34. q2 ● Gap Eq.: Integrate over q2, so L< 2mQfor G to remain Goldstone ➜ Lcannot be taken arbitrarily large This raises to , OR Pion-Nucleon very analogous! depressingly large ! ● Can this be made Lower?

  35. q2 ● Gap Eq.: Integrate over q2, so L< 2mQfor G to remain Goldstone ➜ Lcannot be taken arbitrarily large This raises to , OR Pion-Nucleon very analogous! depressingly large ! ● Can this be made Lower? Perhaps: ~ NJL (but much q-dep.) Yes, other tight Bound States ➜

  36. IV. Discussion and Conclusion

  37. 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) My first reaction: Hard to believe we are seeing a Dilaton “just now” ...

  38. 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) My first reaction: Hard to believe we are seeing a Dilaton “just now” ... But the Bootstrap Gap Eq. is nominally Scale-Inv. (no scale) ! Used in aid of numerical solution. What is the true source of Scale Breaking? 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, Yamawaki, ’12; 7/12; 9/12etc. Elander, Piai, 8/12 Chacko, Franceschini, Mishra, 9/12 “holographic techni-dilaton gives as good a fit as SM Higgs” Not Yet Ruled Out Treat 3 parameters a = v/F, cg, cg N.B. We did not touch UV ... N.B. 4G + 2HDM? Perhaps, but 1) Why h0 light; 2) Gap Eq. not applicable

  39. Gap Equation: Yukawa “Bootstrap” Gap equation for large Yukawa in the ladder approx. w/ m0 = 0 (and neglect gauge couplings) Self-energy momentum-dep. (gauge symm.) G lQ “Mass” = B/A Dropped “Higgs”; if dilaton, v2/F2 suppressed. ➜ self-consistent

  40. Conculsion ● A Dynamical Gap Eq., by Goldstone, or VL 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-p] This implies 4G masses in 2-3 TeV Range. Boundstate Resonance Production with Decay into Multi-VL (backup slide) should be considered. lQ≳ 4p ● The new 126 GeV Boson poses difficulties for 4G. It would have to be a Dilaton ... Our Gap Eq. is nominally Scale-invariant! Let’s wait what Nature reveals to us, thru LHC.

  41. Possible Phenomenology: QQ → nVL ➨ An Intriguing Analogy Example data WSH, PRD’2012 [arXiv:1206.1453]

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