bootstrap bootstrap dsb-4 george w.s. hou (ntu) th seminar @ taida, 12/5/2012 1 dynamical...

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


Dynamical Electroweak Symmetry Breaking

by Heavy 4th Generation Bootstrap

December 5, 2012, TH Seminar @ Taida

12

6 G

eV

12

6 G

eV


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


–I. Why go on with 4G ?

“Physics Highlights” Talk by Riccardo Barbieri @ ICHEP 2012

explained later ...


12/17 Outreach Talk in R204

Physics Colloquiumon 12/18 Tue


PostMortem ... Alex Pomarol @ ICHEP

Riccardo Barbieri


PostMortem ...; or (future) Resurrection

Alex Pomarol @ ICHEP


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


• mode > SM• no convincing evidence for VBF (Vector Boson Fusion)

or VH (Higgsstrahlung off V), e.g. fermionic modes

Dilaton Not Ruled Out !


Coupling weaker by v/f, except to & gg


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


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


4G Is Still 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.


4G Is Still SM



● 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.


My own busy slide from ICHEP2010 (and ICHEP2008).

Point is, great gain in CPV from

3G means

CPV-4-BAU

4G Is Still SM



● But concentrate first on Flavor/CPVCPV, as SM Higgs is flavor-blind

WSH, CJP 47 (2009) 134 [arXiv:0803.1234]


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


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.


I. Unitarity Bound, QQ Scattering

_

from Self-Energy to Gap Equation


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]



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


Gap Equation?

WSH, ICHEP2010;& arXiv:1201.6029

(Chin. J. Phys., 6/2012)Q


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


II. Dynamical Symmetry Breaking: Two Examples

NJL Strong Scale-inv. QED ― Setting up


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


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



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


noting

plus B.C.:

Miransky scaling ... ?



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


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]


GGQ

(gauge symm.)



““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



““MassMass” = ” = BB//AADrop Higgs for now;return later.




GGQ

(gauge symm.)


So,

We find, numerically, ~ 1.4~ 1.4

➜ ➜ ➜ ➜

Gap Equation: Yukawa “Bootstrap”Higgs or not, absorbed in


● 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


● Gap Eq.: Integrate over q22, so < 2mQ for GG to remain Goldstone


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 !!




This raises to ,

OR

q22


● Can this be made Lower?

Pion-Nucleon very analogous !


Pion-Nucleon very analogous !



This raises to ,

OR

q22


● Can this be made Lower?

Perhaps:Perhaps:

Yes, other tight Bound States ➜

~ NJL (but much q-dep.)


IV. Discussion and Conclusion


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” ...


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



““MassMass” = ” = BB//AADropped “Higgs”; if dilaton, if dilaton, vv22/F/F22 suppressedsuppressed.

➜ self-consistentself-consistent




GGQ

(gauge symm.)


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.


Possible Phenomenology: QQ → nVL

An Intriguing Analogy

➨

Example

WSH, PRD’2012 [arXiv:1206.1453]

data

bootstrap bootstrap dsb-4 george w.s. hou (ntu) th seminar @ taida, 12/5/2012 1 dynamical...

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