susy meets its twin · sus-16-014, 0-lep (h t), 12.9 fb-1 sus-16-015, 0-lep (m t2), 12.9 fb-1...
TRANSCRIPT
SUSY MEETS ITS TWIN Andrey Katz
based on work w/ A. Mariotti, S. Pokorski, D. Redigolo and R. Ziegler
This is an output file created in Illustrator CS3
Colour reproductionThe badge version must only be reproduced on a plain white background using the correct blue: Pantone: 286 CMYK: 100 75 0 0 RGB: 56 97 170 Web: #3861AA
If these colours can not be faithfully reproduced, use the outline version of the logo.
Clear spaceA clear space must be respected around the logo: other graphical or text elements must be no closer than 25% of the logo’s width.
Placement on a documentUse of the logo at top-left or top-centre of a document is reserved for official use.
Minimum sizePrint: 10mmWeb: 60px
CERN Graphic Charter: use of the black & white version of the CERN logo
“Is SUSY Alive and Doing Well”, IFT Workshop September, 30, Madrid, Spain
Little About the Main Question.
Is SUSY alive and doing well??
Why Supersymmetry? Hierarchy problem
Gauge coupling unification
WIMP dark matter
For 30 years, experiments testing these suggestive reasons were “right around
the corner”, and SUSY became the dominant BSM paradigm.
The experiments are now here.
HP: Theory
GUT: data DM: D
ATA
3
What kind of SUSY are we talking about?
Original idea of 80’s and 90’s?
The LHC is finally here. What do we know about the FT in garden-variety SUSY
UDD
⇤
2ùñ
UDDU :D:D:
m
⇤
4(64)
G´1F
9 pmh
q
20 `
3y2t
4⇡2⇤
2` . . . “ 174 GeV (65)
L “ |H|
2O (66)
�pt¯tq “ 0.82 nb at
?
s “ 13 TeV (67)
�pt¯tq “ 0.97 nb at
?
s “ 14 TeV (68)
�pt¯tq « 32 nb at
?
s “ 100 TeV (69)
BRpt Ñ e b {ET
q “ 13.3% ˘ 0.4% ˘ 0.4% (70)
BRpt Ñ µ b {ET
q “ 13.4% ˘ 0.3% ˘ 0.5% (71)
BRpt Ñ ⌧h
b {ET
q “ 7.0% ˘ 0.3% ˘ 0.5% (72)
⌦h29
1
x�vy
(73)
T⌫
“
ˆ10.75
75
˙1{3T⌫
(74)
�Neff
« 0.075 (75)
�phidden Ñ SMq9
´mhidden
TeV
¯n
(76)
⌦
DM
« 5 ⌦
Baryon
(77)
⌦
DM
„
mDM
mp
⌦
B
(78)
m „ �T with � " 1 . (79)
↵ ° ↵8 (80)
↵ ”
�V
⇢rad
(81)
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
5
Bounds and Fine Tunings
[GeV]t~m200 400 600 800 1000 1200
[GeV
]10 χ∼
m
0
100
200
300
400
500
600
700
800
900
CMS Preliminary
10χ∼ t→ t~, t~t~ →pp ICHEP 2016
13 TeVExpectedObserved
-1), 12.9 fbmissTSUS-16-014, 0-lep (H
-1), 12.9 fbT2SUS-16-015, 0-lep (M-1), 12.9 fbTαSUS-16-016, 0-lep (-1SUS-16-029, 0-lep stop, 12.9 fb
-1SUS-16-030, 0-lep (top tag), 12.9 fb-1SUS-16-028, 1-lep stop, 12.9 fb
-1Combination 0-lep and 1-lep stop, 12.9 fb
01χ∼
+ m
t
= m
t~m
[GeV]g~m800 1000 1200 1400 1600 1800 2000
[GeV
]10 χ∼
m
0
200
400
600
800
1000
1200
1400
1600
1800
2000 CMS Preliminary
10χ∼t t→ g~, g~g~ →pp ICHEP 2016
(13 TeV)-112.9 fbExpectedObserved
)missTSUS-16-014, 0-lep (H
)T2SUS-16-015, 0-lep (M)TαSUS-16-016, 0-lep ()φ∆SUS-16-019, 1-lep (
2-lep (SS)≥SUS-16-020, 3-lep≥SUS-16-022,
SUS-16-030, 0-lep (top tag)
Generic bound on stops ~900 GeV
UDD
⇤
2ùñ
UDDU :D:D:
m
⇤
4(64)
G´1F
9 pmh
q
20 `
3y2t
4⇡2⇤
2` . . . “ 174 GeV (65)
L “ |H|
2O (66)
�pt¯tq “ 0.82 nb at
?
s “ 13 TeV (67)
�pt¯tq “ 0.97 nb at
?
s “ 14 TeV (68)
�pt¯tq « 32 nb at
?
s “ 100 TeV (69)
BRpt Ñ e b {ET
q “ 13.3% ˘ 0.4% ˘ 0.4% (70)
BRpt Ñ µ b {ET
q “ 13.4% ˘ 0.3% ˘ 0.5% (71)
BRpt Ñ ⌧h
b {ET
q “ 7.0% ˘ 0.3% ˘ 0.5% (72)
⌦h29
1
x�vy
(73)
T⌫
“
ˆ10.75
75
˙1{3T⌫
(74)
�Neff
« 0.075 (75)
�phidden Ñ SMq9
´mhidden
TeV
¯n
(76)
⌦
DM
« 5 ⌦
Baryon
(77)
⌦
DM
„
mDM
mp
⌦
B
(78)
m „ �T with � " 1 . (79)
↵ ° ↵8 (80)
↵ ”
�V
⇢rad
(81)
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
5
Comparable result from gluino bounds
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
6
FT ~ 2%
Ways Out?
Pick the two:
Keep naturalness and Unification — RPV (also cornered , but in better shape). Give up on the DM. Choose a mechanism to bridge over the little hierarchy (NN ?). Usually screws unification. Mini-split — perfectly addresses unification + DM. OK w. 125 GeV higgs. Just give up on the little (?) hierarchy
Or one can keep believing in miracles
Outline
• Twin Higgs: Basic Idea and Fine Tuning
• Why marrying the Twin Higgs with SUSY?
• SUSY Twin Higgs: Natural, Non-Minimal
• Comments on Phenomenology — there is still a (weak) hope for the LHC
• Conclusions and Outlook
Logic: we can neither confirm nor rule out perturbative unification at the LHC. DM is also a long shot.
Let us see if we can bridge over the little hierarchy problem.
Twin Higgs (Still Alive and Well!!)
The idea fits into the paradigm of neutral naturalness (NN) solutions to the little hierarchy problem.
Why neutral?
Expect to get a natural model without light
colored particles — mild
constraints from the LHC
The Twin Higgs
In the Twin Higgs the lightness of the EW scale is explained by the fact, that the SM like higgs is a pGB of an approximate SU(4)
[enhanced to SO(8)] symmetry of the Lagrangian. This symmetry is not exact, but holds up to good approximation due to
a mirror symmetry of the Lagrangian
Chacko, Goh, Harnik; 2005
Z2 yt yt
−ytf
ytf
h h h h
t
t
Cancellation of the leading divergencies:
At the leading order only Z2 is needed
The Twin Higgs Potential
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
V “ m2p|A|
2` |B|
2q ` �p|A|
2` |B|
2q
2(86)
6
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
V “ m2p|A|
2` |B|
2q ` �p|A|
2` |B|
2q
2(86)
`p|A|
4` |B|
4q (87)
`�f 2|A|
2` ⇢|A|
4(88)
6
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
V “ m2p|A|
2` |B|
2q ` �p|A|
2` |B|
2q
2(86)
`p|A|
4` |B|
4q (87)
`�f 2|A|
2` ⇢|A|
4(88)
6
Standard SU(4) conserving and mirror symmetric term — massless higgs
Mirror symmetric, but breaks SU(4). We expect the SM higgs mass to come from
this term
Need to break the mirror symmetry, otherwise the SM higgs would be an equal mixture of our higgs and the twin higgs. The correct
alignment can be achieved via σ or ρ
Break SU(4) at a scale f ≫ v
Mirror Symmetry Breaking by the Higgs Potential
Most of the works until now considered soft mirror symmetry breaking — relative radiative safety.
Why bothering with the hard mirror symmetry?
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
V “ m2p|A|
2` |B|
2q ` �p|A|
2` |B|
2q
2(86)
`p|A|
4` |B|
4q (87)
`�f 2|A|
2` ⇢|A|
4(88)
v2
f 2«
1
2
2 ´ �
2(89)
m2h
« 8v2 (90)
6
The experimental bound is ~0.4, we have to fine tune σ against to make it small
In fact, in the soft-broken mirror symmetry scenario is not a free parameter:
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
V “ m2p|A|
2` |B|
2q ` �p|A|
2` |B|
2q
2(86)
`p|A|
4` |B|
4q (87)
`�f 2|A|
2` ⇢|A|
4(88)
v2
f 2«
1
2
2 ´ �
2(89)
m2h
« 8v2 (90)
6
It is simply a SM quartic!
leads to inevitable FT ≈ v2/f2
On the FT, More Carefully
What is our real gain in the FT due to the little Higgs?
multiple talks by Riccardo Rattazzi; 2015-2016
Sources: 1. IR effective theory — v/f FT 2. Is the scale f is stable??
Let us now be very naive, assume that these two sources perfectly factorize and neglect other caveats:
2 3 4 5 6
1
2
3
4
5
fêv
Lt@TeV
Dfêv>2.3
Lt < lf
mhsoft êmh
mhhard êmh
Lt < lf
0.75
0.7
0.65
0.6
0.5
1
1.5
2
Figure 2. The blue contours indicates the irreducible contributions to the Higgs mass coming fromtop loops normalized to mh = 125 GeV, while the red dashed contours indicate the irreduciblecontributions to the Higgs mass in the pure hard breaking case (�
0
= 0) where we fix ⇤⇢ = 250 GeVand ✏ = +1 to minimize the soft Z
2
-breaking generated by radiative corrections (2.7). The greyshaded region at f < 2.3 v is excluded by Higgs coupling measurements and the grey region at thebottom of the plot is inconsistent due to ⇤ < �f .
2.3 Fine-Tuning in the Low Energy E↵ective Theory and Beyond
We are now ready to discuss the fine-tuning in the general Twin Higgs model quantitatively
and show that if hard Z2
-breaking is involved, one in fact expects to improve on the fine-
tuning compared to the soft breaking case. For illustration purposes let us start from the
pure soft case, where the IR fine-tuning is well-known to scale as ⇠ f2/v2. More precisely,
quantifying the fine tuning a la Barbieri-Giudice [31], one gets for the logarithmic derivative
of v2 with respect to �: �soft
v/f = f2�2v2
2v2. Of course, this is just a part of the total fine-tuning
that one estimates in the IR e↵ective theory. On top of that one should also consider a
fine-tuning of the scale f with respect to the top cuto↵ scale ⇤t. Strictly speaking this
fine-tuning should be computed in the full UV theory, but it turns out that one can get a
reasonable estimate by analyzing the threshold corrections to the scale f in the e↵ective
theory and further varying it with respect to the top Yukawa. These radiative corrections
are
�f2 =1
32⇡2
✓3y2t�
⇤2
t � 5⇤2
�
◆. (2.8)
We will see in the next section how they reproduce the dominant RGE e↵ects of the UVI see that there is
an overall factor of
2 mismatch with my
notes. Did you
check it and we dis-
agree? I think it is
just the normaliza-
tion of the CW po-
tential.
theory once the cut-o↵ scales are identified with physical mass thresholds. A-priori both
the sensitivity to the thresholds ⇤t and ⇤� are equally dangerous and, unlike in the SM,
it is not clear that the dominant sensitivity comes from the tops rather than the higgses
– 9 –
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
V “ m2p|A|
2` |B|
2q ` �p|A|
2` |B|
2q
2(86)
`p|A|
4` |B|
4q (87)
`�f 2|A|
2` ⇢|A|
4(88)
v2
f 2«
1
2
2 ´ �
2(89)
m2h
« 8v2 (90)
FT
twin`SUSY
FT
SUSY
„
�SM
�(91)
6
This coupling is measured to be ~0.06, the effect cannot be
moderate at best
Up to the denominator it is the
SUSY FT
Can be cancelled by
higgsinos, mild LHC bounds
What is the Full Parameter Space?
-0.10-0.05 0.00 0.05 0.10 0.15 0.20-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
mé2ê f 2
r
0.25
0.2
0.15
0.1
0.05
0
fêv > 2.3mh=130 GeVmh=125 GeVmh=120 GeV
k<0
soft Z2-breaking
k
pure hard breaking
pure soft breaking
With the given measurement of the higgs mass we are always constrained to a narrow strip
Always need small κ. Radiative corrections?
On the FT, Hard Breaking
Can we do a better job if we allow the hard symmetry breaking?
Simple answer: YES
vacuum, and only one of the Higgses, either HA or HB, gets a VEV. This possibility
usually does not lead to a viable phenomenology and we will not further consider it
here (see however [? ]). On the other hand, if is bigger than zero, the Z2
symmetry
is preserved by the vacuum, and HA and HB get equal VEVs vA = vB = f/p2.
In the following we will always consider 0 < ⌧ � such that the SU(4) breaking
term gives a sub-leading contribution to the mass of the radial mode. but generates
a small SM-like higgs massp2f . The hierarchy between the two quartics in the
potential is technically natural and so is the hierarchy between the radial mode (the
“Twin Higgs”) and the SM Higgs. The latter is a pseudo-Goldstone-boson (PGB) in
the limit ⌧ �. The main problem with the model at the present stage is that the
unbroken Z2
implies that the SM-like Higgs mass eigenstate is an equal superposition
of the visible and the mirror Higgs. This would mean that SM Higgs couplings to
(visible) gauge bosons and fermions would be reduced by a factor 1/p2, a possibility
which is excluded both by LEP EWPM and the LHC Higgs coupling measurements.
Therefore we must include also explicit Z2
-breaking terms.
3. Z2
-breaking terms. In general one can break the mirror symmetry at the renormal-
izable level in two ways: with a relevant operator proportional to µ and/or with a
marginal operator proportional to ⇢. We will conveniently define µ2 ⌘ �f2 and work
with the dimensionless parameters � and ⇢, which are responsible for the Higgs VEV
misalignment v ⌘ vA 6= vB and a mixing between the SM and the twin Higgs. As
we have made clear before, maximal mixing and misalignment are already excluded
and the largest possible misalignment allowed by data translates into the bound
f/v & 2.3.
2.2 Electroweak Symmetry Breaking and Radiative Corrections
In order to analyze EWSB and the Higgs mass in the Twin Higgs it is instructive to
integrate out the heavy radial mode and switch to an e↵ective Higgs theory, where we can
write the Higgs fields in a non-linear realization as
HA = f sin�p2f
, HB = f cos�p2f
. (2.2)
Hereafter we identify � with the SM-like Higgs. It is straightforward to plug these expres-
sions into Eq. (??) and obtain the e↵ective SM Higgs potential in the low energy e↵ective
theory. Minimization of this potential with respect to � yields the following expressions
for the VEV and the mass of the SM-like Higgs:6
2v2
f2
=
✓2� �
2+ ⇢
◆, (2.3)
m2
h = 4v2 (2+ ⇢)
✓1� v2
f2
◆= 2f2 (2� �)
✓1� v2
f2
◆. (2.4)
6The same expressions can alternatively be obtained at the level of the linear sigma model (??) by
solving the EWSB conditions and expanding them at leading order in ,� ⌧ �. We refer to appendix ??
for a discussion of the subleading corrections in this expansion.
– 5 –
There is a-priori no need to fine-tune σ against κ. But…
ρ is a hard breaking term, we expect σ to be quadratically sensitive to it
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
V “ m2p|A|
2` |B|
2q ` �p|A|
2` |B|
2q
2(86)
`p|A|
4` |B|
4q (87)
`�f 2|A|
2` ⇢|A|
4(88)
6
And w/o UV completion we even do not know the sign of this term
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
�� „
3⇢
16⇡2
⇤
2⇢
f 2(86)
6
FT, Hard Breaking
Let us assume for simplicity that we have only hard mirror symmetry breaking at the “cutoff ” scale. Of course in the real
theory we will have soft + hard.
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0-2-1012345
fêveLr@TeV
D
0.1
0.2
0.3
0.40.5
0.60.7
0.8
FHLr , fLe=+1 e=-1
Figure 3. Contours of F (v, f ;⇤⇢). The two di↵erent colors correspond to to the two di↵erent signsof ✏. maybe we can shaded in gray the region where ⇤⇢ < �f? - DR
IR e↵ective theory is given by the logarithmic variation of v2 with respect to the parameter
⇢ and reads
�hard
v/f =f2 � 2v2
2v2⇥ F (v, f ;⇤⇢) , (2.11)
where we traded ⇢ for the EW scale using the EWSB condition (2.3) and we have dropped
the log⇤⇢ contributions to � because they are largely subdominant to the quadratic con-
tributions in most portions of the parameter space (but not all!). Here we have introduced
for further convenience
F (v, f ;⇤⇢) ⌘3✏⇤2
⇢ + 32⇡2v2
3✏⇤2
⇢ + 16⇡2f2
. (2.12)
Interestingly the first piece in (2.11) is precisely the fine-tuning in the pure soft breaking
scenario, but in the hard breaking case it is multiplied by a function F (v, f ;⇤⇢). We
illustrate the behavior of this function on Fig. 3. This function is always smaller than 1
and in the limit 3⇤2
⇢ ⌧ 32⇡2v2 reduces to 2v2/f2, while in the limit 3⇤2
⇢ � 16⇡2f2 this
function simply becomes 1. If we assume that the fine-tuning of the scale f2 with respect to
the top cuto↵ scale is not di↵erent from the soft case and the factorization works, this tells
us, at least naively that the reduction of the fine-tuning with respect to common SUSY
scenarios should now be �SM/� ⇥ F (v, f ;⇤⇢), which can be a significant improvement
compared to the Twin Higgs with softly broken Z2
.
Alternatively one can understand the parametric of the fine tuning measure in the
hard-breaking scenario fixing the cut-o↵ scale ⇤⇢ using the EWSB condition (2.3) so that
the fine tuning in (2.11) can be rewritten as
�hard
v/f =f2 � 2v2
2v2⇥ 2
2+ ⇢=
f2 � 2v2
2v2⇥ 8v2
m2
h
✓1� v2
f2
◆. (2.13)
– 11 –
Limits:
Λ goes to infinity ☛ the function F reduces to 1, no gain
Λ ≪ 4πf ☛ the function F ~ v2/f2
In the IR:
There is a true gain if the “cutoff ” is low enough 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0-2
-1
0
1
2
3
4
5
fêv
eLr@TeV
D
FHv, f ; LrL
Lr<l f
0.80.7
0.60.5
0.40.3
0.2
0.1
Caveats
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
1
2
3
4
5
fêv
Lt@TeV
D
0.001
0
-0.02
-0.01
0.1
0.2
0.3
0.4 e=+1, Lr=1 TeV______________________
k 0DhardêDsoft
k0<0 k0>0
Gains in the FT
Desired values of quartic at the “cutoff ” scale
The desired values of the quartic are of order 10-2, but…dimensionless parameters then read
� =3y4t16⇡2
log⇤2
t
m2
tB
+3�⇢
32⇡2
log
⇤2
⇢
m2
rad
+ log⇤2
⇢
m2
h
!, (2.5)
�⇢ =3y4t16⇡2
logf2
v2, (2.6)
�� =3⇢
16⇡2
✏⇤2
⇢
f2
+ 2� log⇤2
⇢
m2
h
!. (2.7)
Several clarifications are needed at this point. First, we have introduced in these expressions
two di↵erent mass thresholds: ⇤t and ⇤⇢. Usually one assumes that there is a single scale,
often loosely dubbed “the cut-o↵ of the IR e↵ective theory”. Here we will be slightly more
precise. Strictly speaking ⇤t and ⇤⇢ are the mass scales at which one finds the new states
of the UV complete, natural theory that cut the corresponding quantum contributions of
the low-energy theory. In strongly coupled UV completions of the Twin Higgs it is hard to
imagine the situation in which these scales are qualitatively separated. However in weakly
coupled UV completions, e.g. SUSY, one might expect appreciable di↵erences between
these mass scales, because of naturally small couplings that control these expressions.
Therefore we will keep track of these scales separately and we will later see that in the
concrete models that we analyze in the next section these scales are indeed di↵erent. Of
course, due to higher orders corrections these scales cannot be arbitrarily di↵erent from
one another.
Second, in the above expressions we have kept the Higgs dependence in the logarithms
frozen. Moreover we have expanded these expressions to the first order in and v/f .
Third, in Eq. (2.7) we have introduced a new parameter ✏. This parameter stand for
the sign of the UV mass threshold corrections and a-priori ✏ = ±1. Since one cannot
calculate the sign of these radiative corrections within the IR e↵ective theory, we will be
agnostic about the sign of ✏ and consider both positive and negative threshold corrections.
As will see in the next section, within a full UV complete theory this sign is determined
unambiguously.
Having at hand all the radiative contributions to ⇢, and �, we can estimate how
big are the contributions of the radiative corrections to the Higgs mass. Because it would
be di�cult to illustrate this point for generic Z2
-breaking, we concentrate on two extreme
cases: pure soft breaking, defined as ⇢0
= 0, and pure hard breaking, defined as �0
= 0.
From Eq. (2.4) we can infer that the radiative contributions to the Higgs mass squared,
up to O(v2/f2) corrections, are given by �m2
h = 4v2(2�+�⇢). We show the results in
Fig. 2. The first important conclusion that we draw from this figure is that while in the soft-
breaking radiative corrections contribute at least ⇠ 60% of the Higgs mass, the radiative
corrections of the hard Z2
-breaking typically overshoot for the Higgs mass, though not by
orders of magnitude. In the soft breaking case the contributions grow with ⇤t, showing
only mild dependence on the value of f . On the other hand, in the hard breaking case this
contributions grow significantly with the value of f . This fact will be very important for
the next subsection, where we will see that in the hard breaking case the fine tuning �v/f
can be ameliorated compared to the soft case at the price of adjusting the Higgs mass.
– 8 –
Should we FT the higgs mass?yes, but the extra FT is of order 1
Typically full models with hard breaking will slightly overshoot for the Higgs mass, and will lack perfect factorization, but these caveats
turn to be minor.
UV Completion. Why Do We Prefer SUSY?
• The scale f is unstable by itself and requires a natural UV completion. Known options: strong coupling, SUSY or “turtles all the way down”.
• Examples of the latest version are not know in the Twin Higgs context.
• Strongly coupled Twin Higgs has its own problems, e.g. precisions EW. In the strongly coupled models all the mass scales should come out similar.
• We would like to have some moderate separation between the top partners mass scale and the higgs partners mass scale — hard in a strongly coupled theory
• SUSY can naturally explain why various mass scales that we have introduced are slightly different from one another — technically natural, moderately small couplings.
SUSY Meets Its TwinFalkowski, Pokorski, Schmaltz; 2006;; Chang, Hall, Weiner; 2006
Z2
How do we get the necessary
couplings?
Getting SU(4) conserving quartic: NMSSM (well, almost)
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
�� „
3⇢
16⇡2
⇤
2⇢
f 2(86)
� “ 0.9 � “ 1.4 (87)
tan � “ 1.2 tan � “ 2.0 (88)
W “ �SHu
Hd
(89)
6
full multiplets of the approximate SU(4)
assume to be order-1 The singlet should be integrated out non-
supersymmetrically (soft mass ≫ SUSY mass)
The Soft SUSY Model
Straightforward, but do not expect big gains in the FT!
κ — comes out from the D-terms. Given that the SM higgs mass ~ κ, it very similar to the MSSM (but factor of 2 helps!) Mirror symmetry breaking terms — simply assume asymmetric soft masses (definitely soft).
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
1
2
3
4
5
fêv
Ms
lS=1
2.7
33.3 3.6
Dsoft
100
200
300
400
500
600
-6-4-20246
Rattazzi’s logic clearly works — no FT better than 1% (in agreement with Craig
& Howe)
Higgs mass condition cannot be satisfied for any tan β.
The Hard SUSY Model — Wrong Way
Very naive way to break the mirror symmetry:
Just introduce a mirror symmetry breaking W:
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
�� „
3⇢
16⇡2
⇤
2⇢
f 2(86)
� “ 0.9 � “ 1.4 (87)
tan � “ 1.2 tan � “ 2.0 (88)
W “ �SHu
Hd
(89)
W “ �1HA
u
HA
d
(90)
6
Perfectly maps on a ρ-term. Small problem:
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
�� „
3⇢
16⇡2
⇤
2⇢
f 2(86)
6
Now we can really calculate the sign, and it turns out to be negative
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
�� „
3⇢
16⇡2
⇤
2⇢
f 2(86)
� “ 0.9 � “ 1.4 (87)
tan � “ 1.2 tan � “ 2.0 (88)
W “ �SHu
Hd
(89)
W “ �1HA
u
HA
d
(90)
⇤
⇢
„ mSA (91)
6
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
1
2
3
4
5
fêvLt@TeV
D0
2
4
6
0.5
0.3
0.1
k0=0__________________
e Lr @TeVDFHv, f; LrLe=+1 e=-1
This negative threshold drags the soft mass negative, allows only low values of the stop masses.
Way out — negative κ.
The Bi-Doublets
Desiderata: negative mirror symmetry preserving quartic, hard mirror symmetry breaking terms. Any way to get this?
Trick: introduce vectorlike bidoublets:
The simplest setup to get a negative contribution to is to integrate out a bi-doublet
transforming both under SU(2)A and SU(2)B. Consider for example a vectorlike bidoublet
B +B with hypercharge ±1, with the superpotential and soft mass term
�W = �BBhAu hBu +MBDBB , V
soft
= m2
BD
�|B|2 + |B|2
�. (3.18)
Integrating out the bidoublet in the limit of mBD � MBD and matching gives
�V = s2As2
B|�B|2|HA|2|HB|2 , (3.19)
which in our general parametrization gives a negative contribution to (and positive to
�):
� = ��� = �1
2s2As
2
B|�B|2 . (3.20)
However, the presence of a state charged under both A and B gauge group would generically
generate a large mixing between the photon and the dark photon and makes it non-trivial
to achieve gauge coupling unification.
⇡ ��t��2
S
4s4�c
2
� , (3.21)
µ2 ⇡ �t�c2
�
⇥�m2
u �m2
d
�s2� � 2b c
2�
⇤(3.22)
⇢ ⇡ �t�2
s4�c
2
�
�2
S � g2ew
2
�. (3.23)
4 Higgs sector phenomenology
In the previous sections we have studied the (SUSY) Twin Higgs model in full generality
and identified the regions in the parameter space which exhibit the lowest amount of fine
tuning, allowing for generic soft as well as hard breaking Z2
terms. In this section we
discuss possible phenomenological signatures of the (SUSY) Twin Higgs. We focus on the
Higgs sector of the (SUSY) Twin Higgs, which features the most distinctive signatures of
the model that we expect to be accessible at the LHC. We have seen that, for interesting
viable scenarios, also the SUSY (visible) spectrum can be quite light, at the edge of LHC
reach. For such states the expected signals are the canonical ones of SUSY, possibly
augmented with extra missing energy when mixing with the dark sector is relevant (i.e. for
very small f/v).
The Higgs sector of the SUSY Twin Higgs presents new properties with respect to
the standard SUSY case, being e↵ectively a double copy of the MSSM. This includes new
scalar states that can be possibly probed directly at the LHC. In Table 1 we summarize
the complete scalar spectrum of the Higgs sector of the Twin SUSY model at leading order
in the expansion �2 � g2eff , f2 � v2, m2
A � �2f2.
The CP-even states exhibit a rich structure with possible sizeable mixing. The CP-odd
Higgs mixing is exact and depends only on vf , and we have indicated with AT the CP-odd
– 19 –
Automatically get negative quartic which can outweigh the D-terms 20
10
6
5
252.5 3.0 3.5 4.0 4.5 5.01.0
1.5
2.0
2.5
3.0
fêvMsusyHTeV
L
Min D
Contours of the FT (scan!!) We can improve the situation
qualitatively
Hopes for the LHC Pheno?
We have plenty of the Higgses in the story? Who is the next to the lightest higgs
Red — more radial mode-like
Blue — more MSSM heavy-
higgs—like
Green, black — contours of the other CP-even higgs masses.
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
�� „
3⇢
16⇡2
⇤
2⇢
f 2(86)
� “ 0.9 � “ 1.4 (87)
6
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
�� „
3⇢
16⇡2
⇤
2⇢
f 2(86)
� “ 0.9 � “ 1.4 (87)
6
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
�� „
3⇢
16⇡2
⇤
2⇢
f 2(86)
� “ 0.9 � “ 1.4 (87)
tan � “ 1.2 tan � “ 2.0 (88)
6
↵8 “
30
24⇡2
ca
�m2a
p'q
g˚T 2˚(82)
m2h
9
3y2t
4⇡2M2
stops
log
ˆ⇤
2
M2stops
˙(83)
�
´1«
ˇˇ m2
h
2�m2h
ˇˇ
« 1.4% (84)
�m2h
«
y2t
↵s
⇡3M
g
log
2
ˆ⇤
2
Mg
˙(85)
�� „
3⇢
16⇡2
⇤
2⇢
f 2(86)
� “ 0.9 � “ 1.4 (87)
tan � “ 1.2 tan � “ 2.0 (88)
6
Searches for the New Higgses
What can we search for? Decays into di-Z and di-h — very promising, BRs are not independent
due to the Higgs equivalence theorem. Decays into tops — very challenging due to the interference with the
SM background.
Promising
coverage for the
HL LHC and
future b ⇾ sɣ
Conclusions
• Twin Higgs is still an alive mechanism to bridge over the looming little hierarchy problem
• Hard mirror symmetry breaking can reduce the FT, with certain caveats
• Twin SUSY is a natural candidate to UV complete the Twin Higgs + hard mirror symmetry breaking
• A model with bidoublets and generic terms in the superpotential can do the job
• LHC signals are possible, both in the searches for the extra higgses and in the precsion measurements of the higgs couplings
• Where are the stops??