Partial Compositeness - Lattice at LLNL · 2015-04-24 · Partial Compositeness Luca Vecchi...
Transcript of Partial Compositeness - Lattice at LLNL · 2015-04-24 · Partial Compositeness Luca Vecchi...
Partial CompositenessLuca Vecchi
(University of Maryland)
LLNL Lattice BSM Workshop (4/2015)
Friday, April 24, 15
Main hurdles:
1) Electro-weak data + LHC (Higgs)2) Flavor
Strong Dynamics for the TeV scale
MPl
~CFT
⇤ ⇠ 4⇡f
-- higher-dimensional operators? -- top quark mass?!
Friday, April 24, 15
if SM fermions (q) are weakly-coupled to the strong dynamics, ONLY TWO OPTIONS:
Top quark?
Extended Technicolor Partial Compositeness
�qqO �qOreview by Contino (2010)
and no elementary scalars...
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1
Id[O]
not allowed irrelevant
Extended Technicolor Partial Compositeness
�qqO �qO
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MPl
⇤
⇤Fwhat is the flavor dynamics?what is its impact on low energy?
LEFT � �qqO
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3/2
Id[O]
not allowed irrelevant
5/2
I
Extended Technicolor Partial Compositeness
�qqO �qO
d[qO]<4
1
Id[O]
not allowed irrelevant {Friday, April 24, 15
MPl
⇤
⇤F
Partial Compositenessfor d<5/2 no flavor issues to be addressed!
~CFT
5D Randall-Sundrum scenarios are an effective realization
LEFT � �qO
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qL qR
y ⇠ 1
4⇡�L(⇤)�R(⇤)
�L
4⇡�R
4⇡4⇡
SM Yukawas
xv
SM fermions are “partially composite”...
need RG evolution of�qOFriday, April 24, 15
d[O]<5/2 d�
d lnµ=
✓dO � 5
2
◆�+
C
16⇡2�3
� ! 4⇡pC
s✓5
2� dO
◆
l
mdl
dmo positive by
unitarity
Top quarkthe coupling reaches the IR fixed point
Lighter fermionsdo not reach the IR fixed point
(perturbative enough)
�(⇤) ⇠ �(µ0)
✓⇤
µ0
◆d�5/2
mass hierarchy?in 5D: Gherghetta-Pomarol (2000), ...
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What is ? �qO
...
�q 1 2 3
�q��µ⌫
aGaµ⌫
��q�
...
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no asymptotic freedom
best option on the lattice?
-- unitarity: >-3-- SU(3) SQCD gives -1.2-- NJL model: -2 seems possible-- ...
What is ? �qO
...
�q 1 2 3
�q��µ⌫
aGaµ⌫
��q�
...
� ' �2
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Here is one example where the lattice is KEY
What can the lattice do for BSM physics?
✓⇤
⇤cuto↵
◆�⇤
O(1) NDA estimates are totally useless when it comes to anomalous dimensions!!!
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G/H ⊃ Higgs doublet: robust way to get a parametrically light Higgs
H ⊃ custodial SU(2)
Realistic phenomenology (ex: v<f and Higgs mass)
Partners O for the top quark
Partners O for all SM quarks (to decouple the flavor scale!)
Proton is stable
Anomalies cancel
No Landau poles at low energy
A strong IR fixed point (conformal window)
d[O]<5/2 within the CFT?
Model-building Wish-list
Georgi-Kaplan (‘80s)
Sikivie et al. (1980)
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G/H ⊃ Higgs doublet
H ⊃ custodial SU(2)
Realistic phenomenology
Partners O for the top quark
Partners O for all SM quarks
Proton is stable
Anomalies cancel
No Landau poles at low energy
A strong IR fixed point (conformal window)
d[O]<5/2 within the CFT?
Ferretti-Karateev (2013): SU(N)/SO(N), SU(N)/Sp(N) with ≧2 irrepsWish-list
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G/H ⊃ Higgs doublet
H ⊃ custodial SU(2)
Realistic phenomenology
Partners O for the top quark
Partners O for all SM quarks
Proton is stable
Anomalies cancel
No Landau poles at low energy
A strong IR fixed point (conformal window)
d[O]<5/2 within the CFT?
for SU(3) and N_f Dirac flavors...Wish-list
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plus the right handed components
An QCD-like SU(3) candidate model with N_f ≥ 9 Dirac flavors
PC
ETC
exit CFT
SU(3) SU(3)c SU(2)w U(1)YT 3 3 1 aD 3 1 2 1
3 � 12a
S 3 1 1 � 16 � 1
2aS0 3 1 1 5
6 � 12a
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MPl
CW with
⇤CW ⇠ MPle� 2⇡
↵b
d[ ] . 5
2
SU(N)xSU(N)/SU(N)
the key assumption}SU(3), N≥9
⇤ ⇠ m
✓m
⇤CW
◆� 3�d[ ]4�d[ ]
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Conclusion 2 options: ETC or PC
Partial Compositeness is very attractive -- simple* UV-complete models without fundamental scalars -- bonus: may account for fermion mass hierarchy
Test the d=5/2 hypothesis on the lattice!
Ex: QCD-like models -- SU(3) gauge with ≥9 Dirac flavors: use existing data? -- satisfy all basic requirements that are theoretically under control -- have realistic vacuum alignment (v<f) and (PNGB) Higgs mass -- very rich collider phenomenology (colored scalars, TC-hadrons)
* ONLY 1 TUNING as in the SM, but numerically MUCH MUCH LESS
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Back-up slides
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Id[O]
not allowed irrelevant
d[OO]>4+O(1/N)...
I
Extended Technicolor Partial Compositeness
�qqO �qO
2
I
d[qO]<4{
1
Id[O]
not allowed irrelevant
d[OO]=2+O(1/N)...
3/2 5/2
best case scenario: Luty-Okui (2004)
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Main hurdles:
1) Electro-weak data + LHC (Higgs)2) Flavor
Strong Dynamics for the TeV scale
MPl
~CFT
⇤ ⇠ 4⇡f
-- higher-dimensional operators? -- top quark mass?!
Friday, April 24, 15
TC or CH? v<f is generic
v=0
v=f
v<fCH
a
b
Vacuum alignment ⟺ NGB potential. Example:
v ⌘ f sinhhif
V = ↵ sin2h
f+ � sin4
h
f
v<f generic ONLY when ≥2 G-breaking parameters of comparable size PC typically has 2 comparable contributions from top L and R
CH
“TC”
SM-like Higgs up to v/f<1:parametric
SM-like Higgs up to v/f=1!!!accidental
Giudice et al. (2007)
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NGB Higgs is pseudo-scalar?! When writing the Standard Model Lagrangian we do not demand anything but gauge invariance...
hZZ( proportional to the CP-odd spurion v)CP spontaneously broken by v
� 6= 0
CP explicitly broken by yqqh
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NGB = (2, 2) + (2, 2) + (3, 1) + (1, 3) + (1, 1)
SU(2)w ⇥ SU(2)cust ⇢ SU(4)Vunder
Phenomenology of SU(4)xSU(4)/SU(4) models
() IR is effectively SU(4)/Sp(4) -- realistic vacuum alignment -- the Higgs mass is light (OK for b=4)
() 3 accidental symmetries -- Baryon & Lepton numbers !!!! -- techni-fermion number (TC-hadrons!)
m2h =
Nc
2⇡2y4t (⇤)v
2
✓⇤
4⇡f
◆2
b
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