A crisis in physics? LHC results so far do not confirm the
dominant theoretical paradigm about the origin of the weak scale
Is Nature Natural?
— A modified naturalness principle and its experimental tests —
1) What was found
2) What was not found
3) What does it mean?
Alessandro Strumia, Pisa University, INFN and NICPB
Talk at Madrid, September 26, 2013
1) What was found
But should not have been found
3
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CDF-D0
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4
ZZ
ZZ
WW
WW
WW
ΓΓ
ΓΓ-0
ΓΓ-0
ΓΓ-1
ΓΓ-1
ΓΓ-1{
ΓΓ-2
ΓΓ-2
ΓΓ-2j
ΓΓ-3
ΓΓ-3
ΓΓ-cch
ΓΓ-cch
ΓΓ-ccl
ΓΓ-ccl
ΓΓ-crh
ΓΓ-crh
ΓΓ-crl
ΓΓ-crl
ΓΓ-ct
ΓΓ-ct
ΓΓ-e
ΓΓ-jj
ΓΓjj-l
ΓΓjj-t
ΓΓ-lhm2j
ΓΓ-lm2j
ΓΓ-ET
ΓΓ-ET
ΓΓ-thm2j
ΓΓ-uch
ΓΓ-uch
ΓΓ-ucl
ΓΓ-ucl
ΓΓ-urh
ΓΓ-urh
ΓΓ-url
ΓΓ-url
ΓΓ-Μ
ZΓ
ZΓ
h®ΤΤ
ΤΤ jj
ΤΤV
ΤΤ
ΤΤ
bbV
bbV
bbV
ΜΜ
Zhinv
RateSM rate
Only the Higgs
mh = 125.6 GeV
2
1
The SM Higgs
New physics only in loops
t
2.0
pr
ed
ic
tio
n
BRHh®ΓΓLSM
0.3
0.1
SM
Higgs coupling
1
partner
Τ
b
W
Z
Composite Higgs
1.5
Higgs coupling to fermions c
2.5
Τ partner
Fit to Higgs couplings
1.5
SM
1.0
b partner
t
0.03
0.5
90,99% CL
0.01
3
10
30
100
300
0.0
SM
0.5
0.0
FP
-0.5
90,99% CL
-1.0
0.0
1
1.0
1.0
0.5
Mass of SM particles in GeV
0.6
2.0
1.5
1.2
1.4
20
Higgs or dilaton?
4
400
SM + BRinv
Pure
dilaton
4Σ
15
350
300
DΧ2
3
QED anomaly bΓ
Pseudo-scalar Higgs mass mA in GeV
1.0
Higgs coupling to vectors a
BRHh®ggLSM
MSSM fit HtanΒ >> 1L
0.8
2
10
3Σ
SM+BRinv +
+BRgg +BRΓΓ
1
5
250
0
90,99% CL
SM
1Σ
90,99% CL
0
200
0.6
0.8
1.0
1.2
1.4
Stop correction to the htt coupling
1.6
2Σ
-8
-6
-4
-2
QCD anomaly b3
0
2
4
0.0
0.2
0.4
0.6
Invisible Higgs BR
0.8
1.0
And nothing else
Maybe up to the Planck scale
For the measured Mh, Mt the SM can go up to MPl and is close to meta-stability
1.0
200
0.4
0.0 yb
m in TeV
12
ty
bili 910
a
t
s
8
ta7
Me
6
5
LI =104 GeV
150
100
14
16
Stability
50
1010
19
Top pole mass Mt in GeV
Top pole mass Mt in GeV
g1
0.2
109
178
g2
0.6
108
Instability
g3
yt
107
Instability
Non-perturbativity
SM couplings
0.8
180
6 8 10
1011
1012
1013
176
1016
174
1019
172
Λ
170
102 104 106 108 1010 1012 1014 1016 1018 1020
RGE scale Μ in GeV
1,2,3 Σ
Meta-stability
1018
1014
0
0
50
100
150
Higgs pole mass Mh in GeV
200
168
120
10
17
Stability
122
124
126
128
Higgs pole mass Mh in GeV
Mt
− 173.35) +
GeV
α (MZ ) − 0.1184
M
+0.0018 3
+ 0.0029( h − 125.66)
0.0007
GeV
λ(µ̄ = MPl) = −0.0128 − 0.0065(
130
132
Fixing the SM parameters
Threshold corrections at the weak scale
for
1 loop
2 loop
3 loop
g3
full
full?
—
yt
full
full
O(α3
3)
g1,2
full
in progress
—
λ
full
full
—
m
full
full
—
Renormalization Group Equations
for
1 loop
2 loop
3 loop
g1,2,3
full
full
full
yt
full
full
full
λ
full
full
full
m
full
full
full
Mt
Mh
− 125.66 −0.00004
− 173.35 ±0.0003th .
λ(µ̄ = Mt) = 0.1271+0.0021
GeV
GeV
Mt
α (M ) − 0.1184
yt(µ̄ = Mt) = 0.9370+0.0055
− 173.35 −0.0004 3 Z
±0.0005th
GeV
0.0007
The SM close to criticality?
Mh = (129.6 ± 1.5) GeV comes from V ≈ 0h2 + 0h4 at MPl
Mt = 171.4 GeV
0.00
Αs HMZ L = 0.1205
Αs HMZ L = 0.1163
-0.02
Mt = 175.3 GeV
-0.04
102
104
106
108 1010 1012 1014 1016 1018 1020
16
14
12
10
8
0.4 6
104
10
64
12
8
14
10
18
Stability
Metastability
4
14
18
14 16
104
14
12
10
68 10
0.2 16
18
14
16
6
4
12
10
84 14
16
10
10
6
12
68 10
816
16
4
14
12
10
6 18
16 10
18
8
No EW vacuum
0.0
-0.06 -0.04 -0.02
RGE scale Μ in GeV
0.00
4
1010
684
10
68
10
0.02
Higgs coupling ΛHMPl L
0.04
0.06
1010
Xh\ » MPl
105
0
10
105
1010
1015
-0.10
Xh\ » m
stable
Xh\ » m
meta
stable
Xh\ » m
unstable
Anthropic band
Xh\ = 0
meta-stable
0.02
1015
Higgs mass term mHMPl L in GeV
Hpositive quadraticL
Hnegative quadraticL
0.04
0.6
Instability
Higgs quartic coupling Λ
0.06
Top Yukawa coupling yt HMPl L
3Σ bands in
Mt = 173.4 ± 0.7 GeV HgrayL
Α3 HMZ L = 0.1184 ± 0.0007HredL
Mh = 125.7 ± 0.3 GeV HblueL
0.08
Phase diagram of the SM potential
Planck-scale
dominated
Xh\ = 0
unstable
0.8 18
0.10
-0.05
Xh\ = 0
stable
0.00
0.05
0.10
Higgs coupling ΛHMPl L
For the measured masses even the β-function of λ ∼vanishes around MPl
An accident or a big message?
• Easy to explain λ ≈ 0. Pseudo-Goldstone? SUSY with tan β = 1?
• Difficult to explain β(λ) ≈ g 4 − yt4 ≈ 0. Criticality? RGE above MPl?
2) What was not found
But it should have been found
A solution to the hierarchy problem
In quantum “Everything not forbidden is mandatory” (Hassan i Sabbah).
−32 M 2 .
∼
10
No symmetry forbids a large quantum correction to m2
Higgs
Pl
New physics must cut-off the loop integral before it gets unnaturally big.
Divergent correction
Z Λ 4
d k
2
δmHiggs ∼
=
k2
Naive cut-off
Physical cut-off?
LUV
Energy
The naturalness principle: light scalars do not exist unless they come together
with new physics that protects their lightness, such as SUSY, technicolor ...
The top loop gives a quadratically divergent correction to Mh, cut-offing at M :
2 (top) =
δm2
≈
δm
h
h
≈
12λ2
top
2×
M
(4π)2
(
1
2 /M 2
ln MPl
< m2 × ∆ up to a fine-tuning ∆,
Imposing naturalness δm2
h∼ h
(
√
400 GeV
<
M∼ ∆×
Not many TeV!
50 GeV
Past performance
√
√
√
√
Those Higgs-like scalars present in field theories of condensed matter are
not unnaturally lighter than their ultimate cut-off: the atomic lattice.
The electron mass receives divergent electromagnetic corrections
Naturalness holds thanks to new physics: chiral symmetry of e± fermions.
2 receives power divergent electromagnetic corrections.
m2
−
m
±
π
π0
Naturalness holds thanks to new physics: π are QCD composite of fermions.
K mixing receives power divergent corrections.
Naturalness holds thanks to new physics: the charm.
? The Higgs mass receives power divergent corrections.
Naturalness wants new physics to again appear at the right energy.
The solution to the hierarchy problem
SUSY is an entirely theoretical idea – there is no experimental evidence for it … yet → talk by Mihoko Nojiri
The
scalar
precipice
Mrs. SUSY
EW scale—1
?If weak-scale
SUSY stabilizes
Higgs:
the weak
scale
SUSY existed,
it could
…
is the scale of SUSY breaking.
•  Moderate
the hierarchy
problem
? SUSY
extends
Lorentz.
by cancelling quadratic
? SUSY
unifiesoffermions
divergence
SM scalar with bosons.
? SUSY unifies gauge couplings.
•  Equalise the number of
fermionic and bosonic degrees
of freedom, render existence
of scalar particles natural
Mr. Higgs
•  Realise grand unification of the
gauge couplings
•  Provide a suitable dark matter
candidate
GUT scale—1
Fundamental scalar
length scale
Lepton-Photon, 24–29 June, 2013
? SUSY gives DM aka ‘neutralino’.
? SUSY is predicted by super-strings.
? Worry: too many sparticles at LHC?
Andreas Hoecker — Searches for Supersymmetry at Colliders
2
After LHC run I the missing super-partner problem can no longer be ignored
The CMSSM
The SUSY scale should have been the scale of EWSB breaking
M3
)2 + · · ·
110 GeV
Use adimensional ratios as parameters and fix the SUSY scale from MZ : LEP
and later LHC excluded all the parameter space away from the critical line v = 0
2
2
2
MZ2 ≈ 0.2m2
0 + 0.7M3 − 2µ = (91 GeV) × (
CMSSM parameter space with tanΒ = 3, A0 = 0
2.5
experimentally
excluded
ed
ow
all
2.0
excluded
vev = 0
m0 Μ
1.5
excluded
by LHC
1.0
0.5
excluded
vev = ¥
0.0
0.0
0.2
0.4
0.6
0.8
M12 Μ
1.0
1.2
1.4
Beyond the CMSSM
Many models, even at the level of one-letter extensions of the MSSM
AMSSM, BMSSM, CMSSM, DMSSM, EMSSM, FMSSM, GMSSM, HMSSM,
IMSSM,
KMSSM,
MMSSM, NMSSM, OMSSM, PMSSM, QMSSM,
RMSSM, SMSSM, TMSSM, UMSSM, VMSSM, XMSSM, YMSSM, ZMSSM
All of them have similar problems: the unit of measure is the kilo-fine-tuning.
A possibility often considered after LHC is ‘natural SUSY’: abandon models and
maximise naturalness keeping only the sparticles more relevant for it: t̃, b̃L, g̃:
δMZ2 ∝ yt2m2
t̃
2M 2
δm2
∝
g
3
3
t̃
So searches for gluinos and stops are particularly important.
Stop bounds
Gren band: correct DM abundance thanks to neutralino/stop coannihilations.
D
M
lin
e
500
t1 Ž t Ž
® 1®
Nb N
{Ν c
Ž
t 1 LSP
200
CMS razor
hadronic only
our analysis
4.7 fb-1
100
0
0
100
200
Nt
t1 Ž
®
Nb
W
300
t1 Ž
®
Neutralino mass in GeV
400
ATLAS 2013
21 fb-1
300
400
500
600
700
Lightest stop mass in GeV
Small stop/neutralino mass difference: 30 GeV. Stop decays are ≈ invisible.
Bound from theorist re-analyses of 7 TeV data relying on jet initial state
radiation. Big and fully model independent QCD cross section pp → t̃ t̃∗ + jets.
Natural SUSY: “not very satisfactory”
Fine tuning for low L » 10 TeV
1800
24yt2 2
Xt2
Λ
2
δMZ ≈
(1
+
)
ln
m
(4π)2 t̃
3
mt̃
for tan β 1, and
32g32
2
2 ln Λ ,
δmt̃ ≈
M
3(4π)2 3 M3
the fine-tuning now is ∆ ∼ 10 − 20.
1600
Gluino mass M3 in GeV
Even including quantum corrections
only below a relatively low cut-off Λ,
30
30
1400
1200
20
1000
800 10
600
200
400
600
800
1000
Stop mass mŽt in GeV
Reducing tan β does not help, worse FT to get a heavy enough Higgs:



2
mt̃
3yt2m2
2
2
2
t


 + X2
Mh = MZ cos 2β +
ln
t
4π 2
m2
t
!
Xt2 
1−
12
At + µ cot β
Xt =
mt̃
Jumping the shark
> 1.1 TeV:
Break R-parity to try to weaken the experimental bound M3 ∼
• Leptonic RPV give leptonic gluino decays making bounds on M3 stronger.
• Hadronic RPV is crazy and does not allow to go at M3 < 700 GeV.
Dirac gauginos reduce ln Λ/M3 → O(1) but increase the exp bound on M3.
Compressed sparticle spectra to reduce signals, but µ should naturally be
light because of MZ2 = −2µ2 + · · ·. And having all sparticles light is bad.
“We must be careful to rashly reject a new idea. Yet I dare say that this
assumption ... is not very satisfactory” (Lorentz about the Stokes-Planck
proposal that the aether can be compressed by gravity in the vicinity of earth).
Fine-tuning started and we do not know where it will stop: TeV? PeV? EeV?
Getting the SUSY scale from Mh
SUSY might exist above the weak scale for reasons
unrelated to naturalness.
√
The MSSM predicts 0 < λ < (g22 + gY2 )/8, so Mh ∼ λv offers a new handle to
guess where SUSY could be. 125 GeV means λ just below 0 at high scale.
Predicted range for the Higgs mass
160
tanΒ = 50
tanΒ = 4
tanΒ = 2
tanΒ = 1
Higgs mass mh in GeV
150
Split SUSY
140
High-Scale SUSY
130
Experimentally favored
120
110
104
106
108
1010
1012
1014
1016
1018
Supersymmetry breaking scale in GeV
Like ambiguos oracles: Ibis redibis non morieris in bello
3) What does it mean?
The Great Leap Backward
Theorists proposed a beautiful plausible detailed scenario beyond the SM
...
Warped extra dimensions
.?.
?
Weak scale
Anthropic
?
Technicolor
...
?
Extra Singlet
...
?
Gauge-mediated
...
?
GUT masses
Natural
SUSY
MSSM
SUGRA
CMSSM
Finite Naturalness
Little Higgs
Extra gauge
Anomaly-mediated
NUH-MSSM
.?.
Large Extra Dimensions
...
...
...
...
LHC brings us to reconsider the most interesting and basic question
Is Nature Natural?
Data do not support the naturalness principle. Waiting for the 14 TeV run,
the present situation is often presented as a dichotomy, even as a monochtomy
From talks of Arvinataki, Dimopoulos, and Villadoro with the wall
There is at least one more possibility...
The good, the bad, the ugly
The good possibility of naturalness is in trouble.
The bad possibility is that the Higgs is light because of ant**pic selection.
(A bigger vev makes atoms impossible; a bigger Λ makes galaxies impossible).
Then, one expects that H is the only light scalar. So DM — if at the weakscale (but why?) — would be a fermion: Split SUSY, Minimal Dark Matter.
Axions/Higgs unification, special fermionic models can fit the g − 2 anomaly...
The ugly possibility is that a modified Finite Naturalness applies, where
quadratic divergences are ignored. They are unphysical, so nobody knows
if they vanish or not. Scale invariance does not help, because the answer is
chosen by the unknown physical cut-off. Surely it is not a Lorentz-breaking
lattice. Maybe it behaves like dimensional regularization.
I don’t want to advocate, but to explore its consequences and tests.
Finite naturalness is here considered only as a pure
mathematical hypothesis without any pretence of truth
The SM satisfies Finite Naturalness
Quantum corrections to the dimensionful parameter m2 ' Mh2 in the SM La1 m2 |H|2 − λ|H|4 are small for the measured values of the parameters
grangian 2
Finite natualness in the SM
10
200
3
0.3
D=1
Top mass Mt in GeV
150
0
100
Fine tuning D < 1
50
-1-0.3
-0.1
From arXiv:1303.7244
0.1
Fine tuning
D>1
-3
0
0
20
40
60
80
100
120
140
Higgs mass Mh in GeV
Mh = 125.6 GeV ⇒ m(µ̄ = Mt) = 132.7 GeV ⇒ m(µ̄ = MPl) = 140.9 GeV
Finite Naturalness and new physics
FN would be ruined by new heavy particles coupled to the SM (such as GUT).
FN holds if the top really is the top — if the weak scale is the highest scale.
New physics is demanded by data: DM, neutrino masses, maybe axions...
FN still holds if such new physics lies not much above the weak scale.
Is this possible? If yes what are the signals?
Finite Naturalness and new physics
Neutrino mass models add extra particles with mass M
√

3
7

∆ type I see-saw model,
×
 0.7 10 GeV
√
< 200 GeV × ∆
M∼
type II see-saw model,
√


940 GeV × ∆
type III see-saw model.
Leptogenesis is compatible with FN only in type I.
> 109 GeV. Axion
Axion and LHC usually are like fish and bicycle because fa ∼
models can satisfy FN, e.g. KSVZ models employ heavy quarks with mass M
√
< ∆×
M∼


 0.74 TeV if Ψ = Q ⊕ Q̄
4.5 TeV

 9.1 TeV
if Ψ = U ⊕ Ū
if Ψ = D ⊕ D̄
Inflation does not need big scales and anyhow flatness implies small couplings.
Absolute gravitational limit on HI and on any mass [Arvinataki, Dimopoulos..]
δm2 ∼
yt2M 6
4 (4π)6
MPl
so
< ∆1/6 × 1014 GeV
M∼
Dark Matter: extra scalars/fermions with/without weak gauge interactions.
DM with EW gauge interactions
Consider a Minimal Dark Matter n-plet. 2-loop quantum corrections to Mh2:

2

M
2
2

for a fermion
6 ln Λ2 − 1
cnM n − 1 4
2
4
2
g2 + Y gY ) × 3 2 M 2
δm =
(
2
M
7 for a scalar

(4π)4
4
 2 ln
+
2
ln
+
2
2
2
Λµ
Λ
Quantum numbers
SU(2)L U(1)Y Spin
2
2
3
3
3
3
4
4
4
4
5
5
7
1/2
1/2
0
0
1
1
1/2
1/2
3/2
3/2
0
0
0
0
1/2
0
1/2
0
1/2
0
1/2
0
1/2
0
1/2
0
mDM± − mDM Finite naturalness
σSI in
in MeV bound in TeV, Λ ∼ MPl 10−46 cm2
√
EL
0.54
350
0.4 × √∆
(2.3 ± 0.3) 10−2
EH
1.1
341
1.9 × √∆
(2.5 ± 0.8) 10−2
HH ∗
2.0 → 2.5
166
0.22 ×√ ∆
0.60 ± 0.04
LH
2.4 → 2.7
166
1.0 × √∆
0.60 ± 0.04
HH, LL
1.6 → ?
540
0.22 ×√ ∆
0.06 ± 0.02
LH
1.9 → ?
526
1.0 × √∆
0.06 ± 0.02
HHH ∗
2.4 → ?
353
0.14 ×√ ∆
1.7 ± 0.1
(LHH ∗ )
2.4 → ?
347
0.6 × √∆
1.7 ± 0.1
HHH
2.9 → ?
729
0.14 ×√ ∆
0.08 ± 0.04
(LHH)
2.6 → ?
712
0.6 × √∆
0.08 ± 0.04
(HHH ∗ H ∗ ) 5.0 → 9.4
166
0.10 ×√ ∆
5.4 ± 0.4
stable
4.4 → 10
166
0.4 × √∆
5.4 ± 0.4
stable
8 → 25
166
0.06 × ∆
22 ± 2
DM could DM mass
decay into
in TeV
DM without EW gauge interactions
DM coupling to the Higgs determines ΩDM, σSI and Finite Naturalness δm2
Fermion DM singlet HmS =300 GeVL
scalar DM singlet
10-42
Finite Naturalness
Λ=
10-43
1
D=
0
1
db
ude
Excl
ΣSI in cm2
ΣSI in cm2
10-45
00
E
by
Xen
D=1
ded
u
l
c
x
10-43
012
2
n
o
D»1
10-44
D=
10
non
y Xe
2012
10-44
10-45
DM thermal abundance
10-46
DM thermal
abundance
Finite naturalness
10-46
10-47
102
103
DM mass in GeV
102
103
DM Mass in GeV
Observable DM satisfies Finite Naturalness if lighter than ≈ 1 TeV
What is the weak scale?
In the context of FN
1. Could be the only scale of particle physics. Just so.
2. Could be the shadow of a new particle with mass M ∼ 1014 GeV coupled
only gravitationally to the SM. At 3 loops it gives ± the Higgs mass.
t
g
H
H
M
M
g
t
Other scalars (DM?) would similarly be at the weak scale.
3. Could be generated dynamically from nothing, like the QCD scale...
Dynamical generation of the weak scale
Goals:
1) Dynamically generate the weak scale and weak scale DM
2) Preserve the successful automatic features of the SM: B, L...
3) Get DM stability as one extra automatic feature.
Model: GSM ⊗ SU(2)X with one extra scalar S, doublet under SU(2)X and
V = λH |H|4 − λHS |HS|2 + λS |S|4.
Dynamical generation of the weak scale
1) λS runs negative at low energy:
1
S(x) = √
2
1
√
H(x) =
2
4
9gX
βλS '
8(4π)2
with
0
w + s(x)
!
w ' s∗e−1/4
Couplings
s
λS ' βλS ln
s∗
1 gX
10-1
g3
g2
g1
yt
ΛH
ΛS
10-2
0
v + h(x)
!
s
λHS
v'w
2λH
S acts as the Higgs boson of the Higgs boson.
ΛHS
10-3
102 104 106 108 1010 1012 1014 1016 1018 1020
RGE scale Μ in GeV
2) No new Yukawas.
1 g w and are automatically stable [Hambye].
3) SU(2)X vectors get mass MX = 2
X
4) Bonus: threshold effect stabilises λH = λ + λ2
HS /βλS .
Experimental implications
1) New scalar s: like another h with suppressed couplings; s → hh if Ms > 2Mh.
2) Dark Matter coupled to s, h. Assuming that DM is a thermal relict
2
2
11gX
gX
cm3
1
26
+
≈ 2.3 × 10
σvann + σvsemi−ann =
2
2
2
1728πw
64πw
s
fixes gX = w/1.9 TeV, so all is predicted in terms of one parameter λHS :
10-43
0.008
Bound
from LEP
ATLAS, CMS
0.007
Bound from
Xenon 2012
10-44
0.006
ΛHS
0.005
ΣSI in cm2
10-1
SM Higgs
Cross section in SM Higgs units
100
10-45
-2
10
0.004
10-3
50
100
150
200
250
Mass in GeV of the extra Higgs
0.003
10-46
10-47
30
100
300
DM mass in GeV
(Insignificant hint in ZZ and γγ data around 143 GeV)
1000
3000
Dark/EW phase transition
<v
In the SM h smoothly goes from 0 to v at T ∼
The model predicts a first order phase transition for s
The universe remains trapped at s = 0 until the potential energy ∆V is violently
4.
released via thermal tunnelling: Γ ∼ T 4e−S/T with S ∝ gX
Model HgX = 1L
1 ´ 108
VHh,TL - VH0,TL in GeV4
VHh,TL - VH0,TL in GeV4
Standard Model
5 ´ 107
0
-5 ´ 107
-1 ´ 108
0
50
100
150
200
250
300
1 ´ 108
0
-1 ´ 108
-2 ´ 108
-3 ´ 108
-4 ´ 108
0
h in GeV
200
400
600
800
1000
1200
s in GeV
• For the critical value gX ≈ 1.2 one has ∆V ≈ ρ such that
fpeak ≈ 0.3 mHz
Ωpeakh2 ≈ 2 10−11
detectable at LISA
• For gX > 1.2 gravitational waves become weaker.
• For gX < 1.2 the universe gets trapped in a (too long?) inflationary phase.
Finite naturalness and gravity
2 !?
But non-perturbative quantum gravity gives δMh2 ∼ MPl
Nobody knows: maybe 1/MPl is just a small coupling and there are either no
new particles around MPl (as in a 2-dim model by Dubovsky et al.) or weakly
coupled particles. Then, the SM RGE would hold above MPl and Landau
poles for gY and λ become a problem.
To modify the SM into a theory that holds up to infinity energy one needs:
SM-UH1LY for Mt = 194.0 GeV
1. A special value for yt, predicted in terms
of gauge couplings:
1
for gY ∼ 0
λ must become negative at large energy.
2. Hypercharge made non-abelian.
All
models (Pati-Salam, trinification) include
SU(2)R and so two Higgs coupled to u and
d: K0/K̄0 mixing and K → µe demand that
this can only happen at unnaturally large E.
g2
ÈSM couplingsÈ
Mt ≈ 194 GeV
g3
yt
0.3
Λ
0.1
0.03
0.01
101
1010
10100
101000
1010000
RGE scale Μ in GeV
FN needs that quantum gravity cures itself and the SM UV problems.
Conclusions
Naturalness?
1) Stick to it like mussels. Naturalness should be fresh, spontaneous. Present
bounds are so strong that it can only be imposed with kicks in ...
2) Abandon it. Go ant**pic. Multiverse is the only ‘rationale’ we have for Λ.
3) Modify it. Naturalness is satisfied by the SM if quadratic divergences vanish.
Mh at the meta/stability border: a deep meaning in λ(MPl) ∼ β(λ(MPl)) ∼ 0?
Higgs mass
Cosmological constant
Naturalness
Wrong?
Wrong
Finite naturalness
Viable
Wrong
Ant**pic multiverse Not even wrong
Not even wrong
Exploring higher energies is the only way to clarify.
Unnaturalness would have bigger significance than the discovery of SUSY.
From Feynman:
‘There was a Princess
Somebody of Denmark
sitting at a table ...
She turned to me and
said, ‘In what field did
you do your work?’
‘In physics,’ I said.
‘Oh.
Nobody knows
anything about that, so
we can’t talk about it.’
Naturalness is a great topic for a Dialogo sopra i Massimi Sistemi