4th Generation: Dead or Alive?
Dynamical Electroweak Symmetry Breaking
by Heavy 4th Generation Bootstrap
December 21, 2012, BSM/RdV @ Quy Nhon
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 1
!?
DEWSB w/ 4G Quark Bootstrap
0. Why go on? What SM, w/ 4G, could still do for you ...
flavor/CPV in SM4
* 4G Is Still SM
* SM4 seemingly has sufficient CPV-4-BAU
Two Biggest Problems
* Bootstrap DSB from large lQ (this talk)
_
I. Unitarity Bound, QQ Scattering
self-energy
Gap Equation
II. Dynamical Symmetry Breaking: Two Examples
* NJL
* Strong Scale-inv. QED ― Set up shop
III. Yukawa “Bootstrap” Gap Eq.: Dynamical EWSB
cf. PQ’s talk
formulate & solve
IV. Discussion and Conclusion
Bootstrap DSB-4
George W.S. Hou (NTU)
WSH, Chin. J. Phys. ’12 [arXiv:1201.6029]
Mimura, WSH, Kohyama, arXiv:1206.6063
BSM/RdV @ Quy Nhon, 12/21/12 2
–I. Why go on with 4G ?explained later ...
“Physics Highlights” Talk by Riccardo Barbieri @ ICHEP 2012
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 3
PostMortem ...
Alex Pomarol @ ICHEP
Riccardo Barbieri
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 4
PostMortem ...; or (future) Resurrection
Alex Pomarol @ ICHEP
TC Yuan
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 5
But it’s hard to believe we are seeing
a Dilaton “just now” ...
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 6
Summary by Michelangelo Mangano
@ HCP 2012, Kyoto, 11/2012
Bhimji
MASS !?
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 7
Summary by Michelangelo Mangano
@ HCP 2012, Kyoto, 11/2012
Bhimji
MASS !?
• gg mode > SM
• no convincing evidence
for VBF (Vector Boson Fusion)
or VH (Higgsstrahlung off V),
e.g. fermion/gg modes
Dilaton Not Ruled Out
!
Coupling weaker by v/f,
except to gg & gg
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 8
0. What SM, w/ 4G, could still be doing for you
flavor/CPV in SM4
* 4G Is Still SM
* SM4 seemingly has sufficient CPV-4-BAU
* Bootstrap DSB from large lQ
(main part of this talk)
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 9
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.
R.I.P.
And, the 126 GeV
could be “dilaton”
still ...
Keep on Searching
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 10
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]
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 11
SM4 seemingly has Sufficient CPV-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.
Perhaps
more natural
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 12
_
_
I. Unitarity Bound, QQ Scattering
from Self-Energy
to Gap Equation
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 13
_
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
(influenced, e.g. Francois)
↷ LHC), re-learned Yukawa-induced condensate
Holdom ’06
Nambu’s prize in 10/2008 made me think QQ condensation is NJL-like
Intuitively saw
4q operator
Puzzled:
Scattering
As mQ rose, mQ/mW increased;
the scattering that sets
lQ
the Unitarity Bound
Associated with left-handed gauge
coupling:
is a “long
distance” effect
(ca. 2009)
(UBV)
Not quite NJL-like.
~ “long-distance”
Yukawa Coupling
of Goldstone Mode Established,
(vs 1/mQ)
Of course, leading UBV occurs
Independent
of Higgs’ Existence
for G in s-channel (but this is repulsive).
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 14
_
I. Unitarity Bound, QQ Scattering
self-energy
Scattering
(UBV)
Gap Equation
lQ
Self
Energy
~ “long-distance”
(vs 1/mQ)
lQ
1-2-3 TeV
summer 2010,
while discussing w/
Felipe Llanes-Estrada
summer 2011: No New Physics
Gap Equation?
Summing over large range
of exchange momentum q
q2
WSH, ICHEP2010;
& arXiv:1201.6029
(Chin. J. Phys., 6/2012)
Bootstrap DSB-4
George W.S. Hou (NTU)
lQ
BSM/RdV @ Quy Nhon, 12/21/12 15
II. Dynamical Symmetry Breaking: Two Examples
* NJL
Bootstrap DSB-4
* Strong Scale-inv. QED ― Set up shop
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 16
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
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 17
Gap Equation: Strong Scale-invariant QED
Gap equation for QED in the ladder approx.
w/ m0 = 0
Self-energy
momentum-dep.
w.fn. renorm
“Mass” = B/A
follow Fukuda−Kugo, NPB’76
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 18
Gap Equation: Strong Scale-invariant QED
noting
plus B.C.:
Miransky scaling ... ?
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 19
Large lQ through massless G generates mQ,
but in turns assures G as Goldstone
III. Yukawa “Bootstrap” Gap Eq.: Dynamical EWSB
q2
lQ
Summing over large range
of exchange momentum q
Bootstrap DSB-4
George W.S. Hou (NTU)
q2
BSM/RdV @ Quy Nhon, 12/21/12 20
Gap Equation: Yukawa “Bootstrap”
Gap equation for large Yukawa in the ladder approx.
w/ m0 = 0
(and neglect gauge couplings)
(gauge symm.)
lQ
G
Self-energy
momentum-dep.
“Mass” = B/A
incorporate
Higgs in calc.
[Hung-Xiong ’11]
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 21
Gap Equation: Yukawa “Bootstrap”
• 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 !
vs. Hung-Xiong ’11
massless f doublet
+
“Mass” = B/A
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 22
Gap Equation: Yukawa “Bootstrap”
Gap equation for large Yukawa in the ladder approx.
w/ m0 = 0
(and neglect gauge couplings)
(gauge symm.)
lQ
G
Self-energy
momentum-dep.
“Mass” = B/A
Drop Higgs
for now;
return later.
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 23
Gap Equation: Yukawa “Bootstrap”
Higgs or not, absorbed in
So,
We find, numerically,
➜
Bootstrap DSB-4
~ 1.4
➜
George W.S. Hou (NTU)
!!
BSM/RdV @ Quy Nhon, 12/21/12 24
Gap Equation: Yukawa “Bootstrap”
q2
● Gap Eq.: Integrate over q2, but need L < 2mQ for G to remain Goldstone
➜ L cannot be taken arbitrarily large
This raises
to
,
OR
● Put back the light Higgs (126 GeV close to 80 GeV) ?
~ 1.4
➜
➜
~ 13.7 !
➜
Bootstrap DSB-4
➜
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 25
Gap Equation: Yukawa “Bootstrap”
q2
● Gap Eq.: Integrate over q2, but need L < 2mQ for G to remain Goldstone
➜ L cannot be taken arbitrarily large
This raises
to
,
Pion-Nucleon very analogous !
OR
● Can this be made Lower?
Perhaps:
~ NJL (but much q-dep.)
Yes, other tight Bound States ➜
Enkhbat
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 26
IV. Discussion and Conclusion
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 27
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, m0 = 0) !
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
Campbell, Ellis, Olive, ’12
Coleppa, Gregroire, Logan, ’12
Matsuzaki, Yamawaki, ’12; 7/12; 9/12
Elander, Piai, 8/12
Treat 3 parameters
a = v/F, cg, cg
Bootstrap DSB-4
Cheung, Yuan, ’12
Grzadkowski, Gunion, Toharia, ’12
etc.
“holographic techni-dilaton gives
as good a fit as SM Higgs”
Even after HCP
Not Yet
Ruled Out
N.B. We did not touch UV ... (our whole development is empirical)
N.B. 4G ➙ 2HDM? Perhaps, but 1) Why h0 light; 2) Gap Eq. not applicable
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 28
Gap Equation: Yukawa “Bootstrap”
Gap equation for large Yukawa in the ladder approx.
w/ m0 = 0
(and neglect gauge couplings)
(gauge symm.)
lQ
G
Self-energy
momentum-dep.
“Mass” = B/A
Dropped “Higgs”;
if dilaton, v2/F2
suppressed.
➜ self-consistent
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 29
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 !!
This implies 4G masses in 2-3 TeV Range.
[~ p-p]
lQ ≳ 4p
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 Dilaton ...
Our Gap Eq. is nominally Scale-invariant !
Let’s wait what Nature reveals to us, thru the LHC.
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 30
Bootstrap DSB-4
George W.S. Hou (NTU)
BSM/RdV @ Quy Nhon, 12/21/12 31
Possible Phenomenology: QQ → nVL
➨
An Intriguing Analogy
data
Example
WSH, PRD’2012 [arXiv:1206.1453]
Bootstrap DSB-4
George W.S. Hou (NTU)
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