BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 1
Dynamical Electroweak Symmetry Breaking
by Heavy 4th Generation Bootstrap
December 5, 2012, TH Seminar @ Taida
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 2
Dynamical Electroweak Symmetry Breaking
by Heavy 4th Generation Bootstrap
December 5, 2012, TH Seminar @ Taida
12
6 G
eV
12
6 G
eV
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 3
I. Unitarity Bound, QQ Scatteringself-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:1201.6029]Mimura, WSH, Kohyama, arXiv:1206.6063
!?
0. Why go on? What SM, w/ 4G, could still do for you
Gap Equation
formulate & solvesolve
_
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
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 4
–I. Why go on with 4G ?
“Physics Highlights” Talk by Riccardo Barbieri @ ICHEP 2012
explained later ...
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 5
12/17 Outreach Talk in R204
Physics Colloquiumon 12/18 Tue
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 6
PostMortem ... Alex Pomarol @ ICHEP
Riccardo Barbieri
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 7
PostMortem ...; or (future) Resurrection
Alex Pomarol @ ICHEP
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 8
Summary by Michelangelo Mangano @ HCP 2012, Kyoto, 11/2012
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 9
Summary by Michelangelo Mangano @ HCP 2012, Kyoto, 11/2012
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 10
• 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 Mangano @ HCP 2012, Kyoto, 11/2012
Coupling weaker by v/f, except to & gg
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 11
0. 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
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 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
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 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.R.I.P.
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 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-extensionin mind.
Higgs does not enterthese loops.
And, the 126 GeV could be “dilatondilaton” still ...
Keep on Searching
R.I.P.R.I.P.
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 15
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)
● But concentrate first on Flavor/CPVCPV, as SM Higgs is flavor-blind
WSH, CJP 47 (2009) 134 [arXiv:0803.1234]
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 16
Not much affected by absence of hint for New Physics in
sins; Bs → ; AFB(B → K* )
SM4 seemingly has Sufficient CPV-4-BAU
Sheldon Stone @ ICHEP
CJP 47 (2009) 134
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 17
Not much affected by absence of hint for New Physics in
sins; Bs → ; AFB(B → K* )
SM4 seemingly has Sufficient CPV-4-BAU
Sheldon Stone @ ICHEP
CJP 47 (2009) 134
Consistent w/
small |Vt’sVt’b|,
which consists
with observed
CKM pattern.
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 18
I. Unitarity Bound, QQ Scattering
_
from Self-Energy to Gap Equation
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 19
I. Unitarity Bound, QQ Scattering _
I re-entered 4G study, since 2004, due to flavor/CPV
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
[CPV-4-BAU]
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 20
I. Unitarity Bound, QQ Scattering _
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
Nambu’s prize in 10/2008 made me think QQ condensation is NJL-like
Puzzled: (ca. 2009)
_
Scattering(UBVUBV)
~ “long-distance”~ “long-distance” ((vs vs 1/m1/mQQ))
Q
As mQ rose, mQ/mW increased;the scattering that sets the Unitarity Boundis 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
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 21
Gap Equation?
WSH, ICHEP2010;& arXiv:1201.6029
(Chin. J. Phys., 6/2012)Q
I. Unitarity Bound, QQ Scattering _
Scattering(UBVUBV)
~ “long-distance”~ “long-distance” ((vs vs 1/m1/mQQ))
Q
SelfEnergy
Q
summer 2010,while discussing w/
Felipe Llanes-Estrada
self-energy
Gap Equation
q 22
summer 2011: No New Physics1-2-3 TeV
Summing over large range of exchange momentum q
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 22
II. Dynamical Symmetry Breaking: Two Examples
NJL Strong Scale-inv. QED ― Setting up
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 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 for f and
mN
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 24
Gap Equation: Strong Scale-invariant QED
Gap equation for QED in the ladder approx. w/ mm00 = 0 = 0 Self-energy
momentum-dep.
w.fn. renorm
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 25
Gap Equation: Strong Scale-invariant QED
Gap equation for QED in the ladder approx. w/ mm00 = 0 = 0
angular integration
Wick ro
tation
Self-energy momentum-dep.
Simplification
w.fn. renorm
““MassMass” = ” = BB//AA
Set up Notation
follow Fukuda−Kugo
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 26
noting
plus B.C.:
Miransky scaling ... ?
Gap Equation: Strong Scale-invariant QED
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 27
III. Yukawa “Bootstrap” Gap Eq.: Dynamical EWSB
Q
q22
q22
Summing over large range of exchange momentum q
Large Q through massless G generates mQ,
but in turns assures G as Goldstone
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 28
Gap Equation: Yukawa “Bootstrap”
Gap equation for large Yukawa in the ladder approx. w/ mm00 = 0 = 0
(and neglect gauge couplings)
““MassMass” = ” = BB//AAincorporate
Higgs in calc.[Hung-Xiong ’11]
Self-energy momentum-dep.
GGQ
(gauge symm.)
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 29
Gap Equation: Yukawa “Bootstrap”
““MassMass” = ” = BB//AA
• If follow HX ’11 sign and ignore A(p2) equation, then ~ Scale-inv. QED,
w/ critical Q = , 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 !
vs. Hung-Xiong ’11
masslessmassless doublet doublet
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 30
Gap Equation: Yukawa “Bootstrap”
““MassMass” = ” = BB//AADrop Higgs for now;return later.
Gap equation for large Yukawa in the ladder approx. w/ mm00 = 0 = 0
(and neglect gauge couplings)
Self-energy momentum-dep.
GGQ
(gauge symm.)
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 31
So,
We find, numerically, ~ 1.4~ 1.4
➜ ➜ ➜ ➜
Gap Equation: Yukawa “Bootstrap”Higgs or not, absorbed in
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 32
● Gap Eq.: Integrate over q22, but need < 2mQ for GG to remain Goldstone
➜ cannot be taken arbitrarily large
This raises to ,
OR depressingly large !depressingly large !
q22
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 33
● Gap Eq.: Integrate over q22, so < 2mQ for GG to remain Goldstone
➜ cannot be taken arbitrarily large
This raises to ,
OR
q22
depressingly large !depressingly large !
● Put back the light Higgs (126 GeV close to 80 GeV) ? ~ 1.4~ 1.4
➜ ➜ ➜ ➜
~ 13.7 !~ 13.7 !
➜ ➜ ➜ ➜No GoodNo Good !!
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 34
● Gap Eq.: Integrate over q22, so < 2mQ for GG to remain Goldstone
➜ cannot be taken arbitrarily large
This raises to ,
OR
q22
depressingly large !depressingly large !
● Can this be made Lower?
Pion-Nucleon very analogous !
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 35
Pion-Nucleon very analogous !
● Gap Eq.: Integrate over q22, so < 2mQ for GG to remain Goldstone
➜ cannot be taken arbitrarily large
This raises to ,
OR
q22
depressingly large !depressingly large !
● Can this be made Lower?
Perhaps:Perhaps:
Yes, other tight Bound States ➜
~ NJL (but much q-dep.)
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 36
IV. Discussion and Conclusion
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 37
So, what about 126 GeV boson ? Has to be DilatonDilaton.
4G (chiral Q) seemingly bites the dust, again ... (not that it did not happen before)
My first reaction: Hard to believebelieve we are seeing a DilatonDilaton “just now” ...
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 38
Dynamical Mass Generation also means Breaking of Scale Invariance.
Could there be a Dilaton ? (Radion via AdS/CFT or warped)Goldberger, Grinstein, Skiba, ’08Barger, Ishida, Keung, ’12 Cheung, Yuan, ’12Campbell, Ellis, Olive, ’12 Grzadkowski, Gunion, Toharia, ’12Coleppa, Gregroire, Logan, ’12Matsuzaki, YamawakiMatsuzaki, Yamawaki, ’12; 7/127/12; 9/129/12 etc.Elander, Piai, 8/12Elander, 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, cg, 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 h0 light; 2) Gap Eq. not applicable
My first reaction: Hard to believebelieve we are seeing a DilatonDilaton “just now” ...
Cha
cko,
Fra
nces
chin
i, M
ishr
a, 9
/12
Cha
cko,
Fra
nces
chin
i, M
ishr
a, 9
/12
What is the true source
of Scale Breaking ?
So, what about 126 GeV boson ? Has to be DilatonDilaton.
Not YetRuled Out
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 39
Gap Equation: Yukawa “Bootstrap”
““MassMass” = ” = BB//AADropped “Higgs”; if dilaton, if dilaton, vv22/F/F22 suppressedsuppressed.
➜ self-consistentself-consistent
Gap equation for large Yukawa in the ladder approx. w/ mm00 = 0 = 0
(and neglect gauge couplings)
Self-energy momentum-dep.
GGQ
(gauge symm.)
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 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] This implies 4G masses in 2-3 TeV Range.
Boundstate Resonance Production with Decay into Multi-VL (backup slide) should be considered.
● The new 126 GeV Boson poses difficulties for 4G.
It would have to be a DilatonDilaton ... Our Gap Eq. is nominally Scale-invariant !
Q≳
Let’s wait what Nature reveals to us, thru LHC.
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 41
BootstrapBootstrap DSB-4 George W.S. Hou (NTU) TH Seminar @ Taida, 12/5/2012 42
Possible Phenomenology: QQ → nVL
An Intriguing Analogy
➨
Example
WSH, PRD’2012 [arXiv:1206.1453]
data
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