Running !top !Yukawa ! ! for !the !naturalness GGI !2018 ! - - PowerPoint PPT Presentation
Running !top !Yukawa ! ! for !the !naturalness GGI !2018 ! Florence, !Italy ! Aug !23, !2018 Hyung !Do !Kim ! (Seoul !National !University) ! with !Raffaele !Dagnolo Higgs as pNGB works in Nnaturalness works in running Yukawa couplings 2
Hyung !Do !Kim ! (Seoul !National !University) ! with !Raffaele !D’agnolo GGI !2018 ! Florence, !Italy ! Aug !23, !2018
2
works in Nnaturalness works in running Yukawa couplings
MULTIVERSE
NATURALNESS
?
by S Dimopoulos
3
It is important to fill up the loophole in all possible explanation
4
Arkani-Hamed !Cohen !D’agnolo ! ! Hook !HDK !Pinner, !PRL !(2016)
1m 1m Higgs mass : random dart to 1m*1m in the disk of the solar system
6
by N Arkani-Hamed
7
if reheaton is a pNGB
Arkani-Hamed !Cohen !D’agnolo ! ! Hook !HDK !Pinner, !PRL !(2016) Dvali !Redi !PRD(2009)
N = 1032 N = 1016 N = 104 Λ∗ = ΛH = 1010 GeV Λ∗ = 100 GeV Λ∗ = 1016 GeV ΛH = 10 TeV scenario I scenario II
enormous reduction of dof
⇣
2 H
⌘
us−4
3 × ( Q , U
c
, D
c
, L , E
c
)
SU(2) (1) SU(3)
⇣ m
2 H
⌘
u s − 3
3 × ( Q , U
c
, D
c
, L , E
c
)
SU(2) U(1) SU(3) ⇣ m2
H
⌘
us−2
3 × ( Q , U
c
, D
c
, L , E
c
)
SU(2) U(1) SU(3)
⇣ m2
H
⌘
us−1
3 × ( Q , U
c
, D
c
, L , E
c
)
SU(2) U(1) SU(3)
3 × ( Q , U
c
, D
c
, L , E
c
)
SU(2) U(1) SU(3)
⇣ m
2 H
⌘
u s
3 × ( Q , U
c
, D
c
, L , E
c
)
SU(2) U(1) SU(3)
⇣ m2
H
⌘
u s + 1
3 × ( Q , U
c
, D
c
, L , E
c
)
SU(2) U(1) SU(3)
⇣ m2
H
⌘
u s + 2
3 × ( Q , U
c
, D
c
, L , E
c
)
SU(2) U(1) SU(3)
⇣ m2
H
⌘
u s + 3
3 × ( Q , U
c
, D
c
, L , E
c
)
SU(2) U(1) SU(3) ⇣ m2
H
⌘
u s + 4
3
SU U(1) SU ⇣ m
2 H
⌘
m2
H
v = 0
vus = 246 GeV
Λ2
H
−Λ2
H
H
H
N
N 2 i N 2 ,
seen as dark sector seen as dark sector dominantly reheated
H H
H H T Ton φHH
H+ H-
γγ γγ
H,W,Z H,W,Z
W,Z W,Z
H
H B B
m2
H > 0
m2
H < 0
LhHi6=0
φ
Cφ
1 a yq v m2
h q qc ;
LhHi=0
φ
Cφ
3 a g2 16 π2 1 m2
H WµνW µν ,
9
AφH†H λSLH
scalar reheat fermion reheat
population of the sectors
Arkani-Hamed !Cohen !D’agnolo ! ! Hook !HDK !Pinner, !PRL !(2016)
different phase of deconstruction
phase A : extra dimension phase B : Nnaturalness
∆Neff ∼ O(1) 4.4 + 3 = 7.4
photon neutrino Br(i=2)~ 0.1 VEV no VEV dark radiation generic prediction
11
Cosmological solution to the naturalness Nnaturalness It might explain no new physics at the LHC Cosmological observables might be interesting
12
Why is it working? Reheaton is pNGB (not Higgs itself) The presence of light scalar can be explained by pNGB idea and extra assumption of decay via Higgs can explain why it decays predominantly to the lightest Higgs sector
13
Higgs as pNGB For the relevant operators, it is more important (relevant) at IR yt ∼ O(1) does not work well since geff(µ) = cΛ µ c = ✏ ⌧ 1
14
15
† ‡One possible way out is to make the SM Yukawa and gauge couplings to be relevant.
3 Talk at LHCP2017 , May 15-20 1709.00766
∆[Qtc] = 2 ∆[yt] = 1 yt(Λ) = ( µ Λ)yt(µ) ⌧ yt(µ)
16
δm2
H ∝ −y2 t m2 soft
:SUSY as an example −m2
h
2 = µ2 + m2
H + δm2 H
µ > 100 GeV (bound from Higgsino mass)
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h h
<latexit sha1_base64="DhAlNTFpFxaeBG+LzwHvu3p9BwQ=">ACJXicbVDLSgMxFM34rPU16tJNsAiCtcyIoMuCG6ECvYBnaFk0kwbmRCkhG0q/wI/wGt7p2J4Ir8U9M21nY1gP3cjnXm5yIsmoNp735Swtr6yurRc2iptb2zu7t5+QyepwqSOE5aoVoQ0YVSQuqGkZUBPGIkWY0uB7zUeiNE3Eg8kCTnqCRpTjIyVOu5ZBoNyIPs0KEMYREjBQGo6bafwbk7quCWv4k0AF4mfkxLIUeu4P0E3wSknwmCGtG7njThEClDMSOjYpBqIhEeoB5pWyoQJzocTr41gsdW6cI4UbaEgRP178YQca0zHtlJjkxfz3tj8T+vnZr4KhxSIVNDBJ4eilMGTQLHGcEuVQblmCsKL2rRD3kULY2CRnrkR8ZDPx5xNYJI3ziu9V/PuLUvUmT6cADsEROAE+uARVcAtqoA4weAIv4BW8Oc/Ou/PhfE5Hl5x85wDMwPn+Be7uo6Y=</latexit><latexit sha1_base64="DhAlNTFpFxaeBG+LzwHvu3p9BwQ=">ACJXicbVDLSgMxFM34rPU16tJNsAiCtcyIoMuCG6ECvYBnaFk0kwbmRCkhG0q/wI/wGt7p2J4Ir8U9M21nY1gP3cjnXm5yIsmoNp735Swtr6yurRc2iptb2zu7t5+QyepwqSOE5aoVoQ0YVSQuqGkZUBPGIkWY0uB7zUeiNE3Eg8kCTnqCRpTjIyVOu5ZBoNyIPs0KEMYREjBQGo6bafwbk7quCWv4k0AF4mfkxLIUeu4P0E3wSknwmCGtG7njThEClDMSOjYpBqIhEeoB5pWyoQJzocTr41gsdW6cI4UbaEgRP178YQca0zHtlJjkxfz3tj8T+vnZr4KhxSIVNDBJ4eilMGTQLHGcEuVQblmCsKL2rRD3kULY2CRnrkR8ZDPx5xNYJI3ziu9V/PuLUvUmT6cADsEROAE+uARVcAtqoA4weAIv4BW8Oc/Ou/PhfE5Hl5x85wDMwPn+Be7uo6Y=</latexit><latexit sha1_base64="DhAlNTFpFxaeBG+LzwHvu3p9BwQ=">ACJXicbVDLSgMxFM34rPU16tJNsAiCtcyIoMuCG6ECvYBnaFk0kwbmRCkhG0q/wI/wGt7p2J4Ir8U9M21nY1gP3cjnXm5yIsmoNp735Swtr6yurRc2iptb2zu7t5+QyepwqSOE5aoVoQ0YVSQuqGkZUBPGIkWY0uB7zUeiNE3Eg8kCTnqCRpTjIyVOu5ZBoNyIPs0KEMYREjBQGo6bafwbk7quCWv4k0AF4mfkxLIUeu4P0E3wSknwmCGtG7njThEClDMSOjYpBqIhEeoB5pWyoQJzocTr41gsdW6cI4UbaEgRP178YQca0zHtlJjkxfz3tj8T+vnZr4KhxSIVNDBJ4eilMGTQLHGcEuVQblmCsKL2rRD3kULY2CRnrkR8ZDPx5xNYJI3ziu9V/PuLUvUmT6cADsEROAE+uARVcAtqoA4weAIv4BW8Oc/Ou/PhfE5Hl5x85wDMwPn+Be7uo6Y=</latexit><latexit sha1_base64="DhAlNTFpFxaeBG+LzwHvu3p9BwQ=">ACJXicbVDLSgMxFM34rPU16tJNsAiCtcyIoMuCG6ECvYBnaFk0kwbmRCkhG0q/wI/wGt7p2J4Ir8U9M21nY1gP3cjnXm5yIsmoNp735Swtr6yurRc2iptb2zu7t5+QyepwqSOE5aoVoQ0YVSQuqGkZUBPGIkWY0uB7zUeiNE3Eg8kCTnqCRpTjIyVOu5ZBoNyIPs0KEMYREjBQGo6bafwbk7quCWv4k0AF4mfkxLIUeu4P0E3wSknwmCGtG7njThEClDMSOjYpBqIhEeoB5pWyoQJzocTr41gsdW6cI4UbaEgRP178YQca0zHtlJjkxfz3tj8T+vnZr4KhxSIVNDBJ4eilMGTQLHGcEuVQblmCsKL2rRD3kULY2CRnrkR8ZDPx5xNYJI3ziu9V/PuLUvUmT6cADsEROAE+uARVcAtqoA4weAIv4BW8Oc/Ou/PhfE5Hl5x85wDMwPn+Be7uo6Y=</latexit><latexit sha1_base64="DhAlNTFpFxaeBG+LzwHvu3p9BwQ=">ACJXicbVDLSgMxFM34rPU16tJNsAiCtcyIoMuCG6ECvYBnaFk0kwbmRCkhG0q/wI/wGt7p2J4Ir8U9M21nY1gP3cjnXm5yIsmoNp735Swtr6yurRc2iptb2zu7t5+QyepwqSOE5aoVoQ0YVSQuqGkZUBPGIkWY0uB7zUeiNE3Eg8kCTnqCRpTjIyVOu5ZBoNyIPs0KEMYREjBQGo6bafwbk7quCWv4k0AF4mfkxLIUeu4P0E3wSknwmCGtG7njThEClDMSOjYpBqIhEeoB5pWyoQJzocTr41gsdW6cI4UbaEgRP178YQca0zHtlJjkxfz3tj8T+vnZr4KhxSIVNDBJ4eilMGTQLHGcEuVQblmCsKL2rRD3kULY2CRnrkR8ZDPx5xNYJI3ziu9V/PuLUvUmT6cADsEROAE+uARVcAtqoA4weAIv4BW8Oc/Ou/PhfE5Hl5x85wDMwPn+Be7uo6Y=</latexit>Let’s accept and focus on the remaining parts
µ
17
∆ = δm2
H
( m2
H
2 )
∼ δm2
H
(100 GeV)2 δm2
H ∼ (200 GeV)2
δm2
H ∼ (300 GeV)2
∆ ∼ 5 ∆ ∼ 10 20% 10%
10% to 20% fine tuning would be acceptable
18
δm2
H ∝ − 3y2 t
16π2 ⇣ m2
˜ t1 + m2 ˜ t2 + |At|2⌘
log ✓ Λ m˜
t
◆ ∼ 10−2 3 ∼ 30 −(m˜
t
3 )2 −m2
˜ t
−(200 GeV)2 m˜
t ∼ 600 GeV : 20% to 2%
(M3, M2 ∼ 900 GeV)
19
βm2
h =
dm2
h
d log ¯ µ = 3m2
h
8π2 ⇣ 2λ + y2
t 3g2
4 g02 4 ⌘
<latexit sha1_base64="mHVczkRVY87Xy8BK7q2k6nsUNpQ=">ACEnicbVDLSsNAFJ3UV62vqDvdDBahipSkCLosiOCygn1Ak4bJdNIOnUnCzEQoeBH+A1ude1O3PoDLv0Tp2kWtvXA5R7OuZc7c/yYUaks69sorKyurW8UN0tb2zu7e+b+QUtGicCkiSMWiY6PJGE0JE1FSOdWBDEfUba/uhm6rcfiZA0Ch/UOCYuR4OQBhQjpSXPOK9mjesODw5g84FhE48pL3zrHlm2apaGeAysXNSBjkanvnj9COcBIqzJCUXduKlZsioShmZFJyEklihEdoQLqahogT6abZHybwVCt9GERCV6hgpv7dSBGXcsx9PcmRGspFbyr+53UTFVy7KQ3jRJEQzw4FCYMqgtNAYJ8KghUba4KwoPqtEA+RQFjp2Oau+HyiM7EXE1gmrVrVtqr2/W5fpunUwTH4ARUgA2uQB3cgQZoAgyewAt4BW/Gs/FufBifs9GCke8cgjkYX78TAZxl</latexit><latexit sha1_base64="mHVczkRVY87Xy8BK7q2k6nsUNpQ=">ACEnicbVDLSsNAFJ3UV62vqDvdDBahipSkCLosiOCygn1Ak4bJdNIOnUnCzEQoeBH+A1ude1O3PoDLv0Tp2kWtvXA5R7OuZc7c/yYUaks69sorKyurW8UN0tb2zu7e+b+QUtGicCkiSMWiY6PJGE0JE1FSOdWBDEfUba/uhm6rcfiZA0Ch/UOCYuR4OQBhQjpSXPOK9mjesODw5g84FhE48pL3zrHlm2apaGeAysXNSBjkanvnj9COcBIqzJCUXduKlZsioShmZFJyEklihEdoQLqahogT6abZHybwVCt9GERCV6hgpv7dSBGXcsx9PcmRGspFbyr+53UTFVy7KQ3jRJEQzw4FCYMqgtNAYJ8KghUba4KwoPqtEA+RQFjp2Oau+HyiM7EXE1gmrVrVtqr2/W5fpunUwTH4ARUgA2uQB3cgQZoAgyewAt4BW/Gs/FufBifs9GCke8cgjkYX78TAZxl</latexit><latexit sha1_base64="mHVczkRVY87Xy8BK7q2k6nsUNpQ=">ACEnicbVDLSsNAFJ3UV62vqDvdDBahipSkCLosiOCygn1Ak4bJdNIOnUnCzEQoeBH+A1ude1O3PoDLv0Tp2kWtvXA5R7OuZc7c/yYUaks69sorKyurW8UN0tb2zu7e+b+QUtGicCkiSMWiY6PJGE0JE1FSOdWBDEfUba/uhm6rcfiZA0Ch/UOCYuR4OQBhQjpSXPOK9mjesODw5g84FhE48pL3zrHlm2apaGeAysXNSBjkanvnj9COcBIqzJCUXduKlZsioShmZFJyEklihEdoQLqahogT6abZHybwVCt9GERCV6hgpv7dSBGXcsx9PcmRGspFbyr+53UTFVy7KQ3jRJEQzw4FCYMqgtNAYJ8KghUba4KwoPqtEA+RQFjp2Oau+HyiM7EXE1gmrVrVtqr2/W5fpunUwTH4ARUgA2uQB3cgQZoAgyewAt4BW/Gs/FufBifs9GCke8cgjkYX78TAZxl</latexit><latexit sha1_base64="mHVczkRVY87Xy8BK7q2k6nsUNpQ=">ACEnicbVDLSsNAFJ3UV62vqDvdDBahipSkCLosiOCygn1Ak4bJdNIOnUnCzEQoeBH+A1ude1O3PoDLv0Tp2kWtvXA5R7OuZc7c/yYUaks69sorKyurW8UN0tb2zu7e+b+QUtGicCkiSMWiY6PJGE0JE1FSOdWBDEfUba/uhm6rcfiZA0Ch/UOCYuR4OQBhQjpSXPOK9mjesODw5g84FhE48pL3zrHlm2apaGeAysXNSBjkanvnj9COcBIqzJCUXduKlZsioShmZFJyEklihEdoQLqahogT6abZHybwVCt9GERCV6hgpv7dSBGXcsx9PcmRGspFbyr+53UTFVy7KQ3jRJEQzw4FCYMqgtNAYJ8KghUba4KwoPqtEA+RQFjp2Oau+HyiM7EXE1gmrVrVtqr2/W5fpunUwTH4ARUgA2uQB3cgQZoAgyewAt4BW/Gs/FufBifs9GCke8cgjkYX78TAZxl</latexit><latexit sha1_base64="mHVczkRVY87Xy8BK7q2k6nsUNpQ=">ACEnicbVDLSsNAFJ3UV62vqDvdDBahipSkCLosiOCygn1Ak4bJdNIOnUnCzEQoeBH+A1ude1O3PoDLv0Tp2kWtvXA5R7OuZc7c/yYUaks69sorKyurW8UN0tb2zu7e+b+QUtGicCkiSMWiY6PJGE0JE1FSOdWBDEfUba/uhm6rcfiZA0Ch/UOCYuR4OQBhQjpSXPOK9mjesODw5g84FhE48pL3zrHlm2apaGeAysXNSBjkanvnj9COcBIqzJCUXduKlZsioShmZFJyEklihEdoQLqahogT6abZHybwVCt9GERCV6hgpv7dSBGXcsx9PcmRGspFbyr+53UTFVy7KQ3jRJEQzw4FCYMqgtNAYJ8KghUba4KwoPqtEA+RQFjp2Oau+HyiM7EXE1gmrVrVtqr2/W5fpunUwTH4ARUgA2uQB3cgQZoAgyewAt4BW/Gs/FufBifs9GCke8cgjkYX78TAZxl</latexit>Below the sparticle mass scales, the correction is negligible m2
h(mSUSY) = m2 h(Λ) + δm2 h(Λ → mSUSY)
− 6y2
t
8π2 m2
SUSY log(
Λ mSUSY ) O(m2
SUSY)
= Fine tuning is determined at the sparticle mass scales, Focus on the couplings bounds from direct search < 10% correction
Top Yukawa : constrained at the weak scale
20
m2
H(m˜ t) = cy2 t (m˜ t)
16π2 m2
˜ t
µ = m˜
t
µ = M exit from conformal window µ = MZ, Mh electroweak symmetry breaking
computed at high scale All the fine tuning issues are at this scale
21
δm2
h(mSUSY) = cy2 t∗m2 SUSY
yt∗ = yt(µ = mSUSY) If is drastically different at , EWSB can be natural with heavy stops. yt mSUSY, mt mSUSY yt mt
22
δm2
h(mSUSY) = cy2 t∗m2 SUSY
yt∗ = yt(µ = mSUSY) If is drastically different at , EWSB can be natural with heavy stops. yt mSUSY, mt mSUSY yt mt M marginal relevant
23
mSUSY yt mt M marginal relevant γ = 1
: optimum of the slop
γ < 1
: UV dominates
γ > 1
: IR dominates
γ ≥ 1
The idea works for
yt(mSUSY) = ( M mSUSY )γyt(mt)
∆[Qtc] = 3 − γ
24
X X t t H H
strongly interacting
yt ⇠ ✏ ⌧ 1
weakly interacting
yt ∼ O(1) mSUSY M
25
26
Conformal window of QCD
s + (34 − 13x)a3 s + · · ·
xc = 3.25 > 0 < 0 5.5 > x > 2.6
:fixed point for x close to 11/2
as∗ ∼ 11 − 2x 13x − 34 ∼ 0.5 x = Nf Nc
27
a>a* a=a* a<a*
g- g* g+ g bHg, aL g* tIR tUV gUV t g
UV fixed point IR fixed point Walking for α < α∗
β(g; α) = ∂g ∂t = (α − α∗) − (g − g∗)2
external parameter
t = log µ
coupling (IR attractive) (IR repulsive)
g± = g∗ ± √α − α∗ Conformal window
28
Conformal window of QCD Banks-Zaks fixed point
from Peskin
8 < Nf∗ < 12 7.8 < Nf < 16.5
(Nc=3 from large Nc)
Nf∗ = 3xc = 9.75 Nf∗ = 11
no chiral symmetry breaking above 12
γ = 33 − 2Nf Nf = 1
anomalous dimension conjecture from SUSY
γ = 2 → Nf∗ = 8.25
29
✏ = 11 2 − Nf Nc xc = Nf Nc = 3.25
Gardi Grunberg 1998
as∗ = 0.2
30
Gardi Grunberg 1998
31
=11/2
+
from D Kaplan et al : conformality lost
x = Nf Nc xc = 3.25 5.5
32
Conformal window of QCD at the critical point ⇥ ¯ ψψ ⇤ = 2 Nf∗ ' 10 g2
s∗ ' 10
αs∗ ' 0.8 as∗ = Ncαs∗ 4π ' 0.2
33
Conformal window of SQCD SU(Nc) Nf Q, ˜ Q 3Nc 2 < Nf < 2NC 2Nc < Nf < 3NC
∆[Q ˜ Q] = 3 2R[Q ˜ Q] = 3(Nf − Nc) Nf
γ = 1 2 γ = 1 M = Q ˜ Q γ = 1 2 SU(Nf − Nc) Nf q, ˜ q electric description magnetic description g− → 0 g− → ∞ g−(magnetic) → 0
Seiberg gauge group gauge group
34
Conformal window of SQCD Nf
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weakly coupled weakly coupled free magnetic free electric
35
One concrete realization : how to make ? ∆[Qtc] = 2 γ = 1
36
The setup SU(3)1 × SU(3)2 → SU(3)C
All the SM quarks are charged under
g2
1 ' 10
g2
2 ' 1
1 g2
s
= 1 g2
1
+ 1 g2
2
hΣi = diag(f, f, f) (3, ¯ 3)
conformal window
SU(3)1
37
mSUSY yt mt M marginal relevant SU(3)1 × SU(3)2 SU(3)C gs hΣi = f ⇠ M
38
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R.S. Chivukula et al. /Physics Letters B 353 (1995) 289-294
vacuum polarizations, with top and bottom quarks in the loop.
6497~~~ f4
This effect is suppressed by f:/M* and is not included in the leading order (in l/M*) analysis of the gap equation.
A& = _A
µ
g1 g1
as∗ = Ncαs∗ 4π ' 0.2 Two loop corrections : Higgs, top, hidden color M can be 1 TeV or higher Higgs modified by hidden sector
39
Flavor Universal Coloron MG0 = g1f ∼ 3f g1¯ qγµT aG0a
µ q
f ∼ 1 − 2 TeV 3 − 6 TeV
:
18 = 1 + 1 + 8 + 8 Σ = φR + φI + Θ + Goldstone
(massive color octet vector boson)
Σ = (3, ¯ 3) SU(3)1 × SU(3)2
under
40
p p Θ φI
j
j j
j
j
j
G
J
p p Θ φI
j
j
G
2.5 3.0 3.5 4.0 4.5 5.0 5.5 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
MG' (TeV) tan θ
MΘ=MG'/2, MϕI=MG'/10 dijet 36 fb-
1
100 fb-
1
BP 2 6j, 95% 5σ fat jet strategy 95%
Bai Lu Xiang (2018)
Coloron physics
41
Excluded by S - T at 95% C.L.
0.0 0.2 0.4 0.6 0.8 1.0 500 1000 1500 2000 2500 3000 sin Χ ms HGeVL
Electroweak precision
Chivukula et al (2013)
h φS t t t G0
µ
G0
µ
sin χ ∝ 3yt 16π2 as∗ v f ∼ 10−2 − 10−3
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h h
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R.S. Chivukula et al. /Physics Letters B 353 (1995) 289-294
vacuum polarizations, with top and bottom quarks in the loop.
Introducing new interactions for the top and bottom quarks will also generate additional contributions to Ap*. In this section, we will focus on the contributions to Ap, coming from loops of top and bottom quarks. The contribution to Ap* from one top-color gauge boson exchange (expressed in terms of vacuum polar- izations for left-handed currents) is: (3.1) where we have made explicit the dependence
fermions (i.e. top and bottom) propagating in the two- loop graph7 (see Fig. 2). We are neglecting terms suppressed by (mb/mr) 2. In the Nambu-Jona-Lasinio approximation we are considering, the two-loop vac- uum polarization calculation reduces to the product
vacuum polarizations. Keeping only (universal) logarithmically divergent terms in each of these one-loop pieces we find:
6497~~~ f4
rI&j2 =
O,m,,m,) = --f 9
M2' 8nKtc f" H&/2 =O.WZ,,mb) =--L
9
M2'
where
NC f,"s
8rr2 (3.2) (3.3) (3.4) Note that, with this definition, in the TC2 model the
piece of the Z self-energy contributes e2
4s2c2 t
(3.5) to M;.
7
This effect is suppressed by f:/M* and is not included in the leading order (in l/M*) analysis of the gap equation.
Putting everything together we find the top-color exchange contribution to be: 41Te2Kt, f"
A& = _A
3s2c2 M2,M2 (3.6) Since KI must be small, Eq. (1.2) implies that ~~~ must be close to 3rr/8. Taking K,~ M 3~/8, m, = 175 GeV and M = 1 TeV, we have: A& = 0.53%) (3.7) which is about one half of the one-loop top quark con- tribution to Ap in the standard model. Note that this contribution is nonzero, even though the top-color in- teractions themselves are isospin-symmetric - isospin violation is present in the form of the t-b mass split-
data constrain Ap* to be less than this value. There is also a contribution to Ap* from the cI( 1) interaction with one top quark loop and one tech- nifermion
(again) that the techni- quarks are degenerate, this contribution is:
(3.8)
Thus for m t = 175 GeV and M =
1
TeV: APT.’ = 10.2% KI . (3.9) The contribution from one (/( 1) gauge boson ex- change with two quark loops is even smaller.
with data In order to extract the S and T parameters, we have performed (using the procedure described in
electroweak data. We have used the most precise measurement [IO] of
a,(M'$) =
0.115 & 0.002. In Fig. 3 we show the el- lipse in the S-T plane which projects onto the 95% confidence interval on the T
< T
< 0.52 (-0.19%
< Ape < 0.40%) as the 95% confidence
LY, results in an even tighter bound on T. For exam- ple, using a,( M:) =
0.124
(which is obtained from a global fit to precision electroweak data [ I I] > we find
< T
<
0.30 (-0.36% < Ap, < 0.23%).
G0
µ
W, Z W, Z
42
conformal technicolor relevant SM relevant to marginal marginal to relevant ∆[H2] = 2 → 4 ∆[Qtc] = 3 → 2
43
One concrete realization : how to make ? γ = 1 It was only half-way successful Task : keep the anomalous dimension to be 1 while avoid large couplings : SU(2) and U(1) extension?
44
2
10
3
10
4
10
5
10
6
10
7
10
Top-quark pairs
(13 TeV)
35.9 fb
CMS Preliminary
Dilepton
Data signal t t
t t Single t W+jets Z+jets +Z/W t t Diboson Uncertainty
400 600 800 1000 1200 1400 1600 1800 2000
GeV
t t
m
0.5 1 1.5
Pred. Data
45
Summary Light Higgs might be due to smaller couplings at high energy (off-shell) It is consistent with Higgs being a pseudo- Nambu-Goldstone boson at high energy To realize the idea in the SM, we can take several possibilities (strongly interacting QFT above M) Measuring off-shell top Yukawa coupling would be important to check this idea