Supersymmetryafter
Higgs discovery
Koichi Hamaguchi (University of Tokyo)
@ ECFA LC 2013, DESY, May 29
a Higgs boson was discovered !
-1.0 -0.5 0.5 1.0
-0.2
-0.1
0.1
0.2
0.3
126 GeV Higgs
-1.0 -0.5 0.5 1.0
-0.2
-0.1
0.1
0.2
0.3
126 GeV Higgs
-1.0 -0.5 0.5 1.0
-0.2
-0.1
0.1
0.2
0.3
=1
2p2GF
' (174 GeV)2We knew...
126 GeV Higgs
-1.0 -0.5 0.5 1.0
-0.2
-0.1
0.1
0.2
0.3
=1
2p2GF
' (174 GeV)2We knew...
126 GeV Higgs
Now we also know' (126 GeV)2
-1.0 -0.5 0.5 1.0
-0.2
-0.1
0.1
0.2
0.3
=1
2p2GF
' (174 GeV)2We knew...
126 GeV Higgs
Now we also know' (126 GeV)2
-1.0 -0.5 0.5 1.0
-0.2
-0.1
0.1
0.2
0.3
completely determined !
126 GeV Higgs
It seems...Higgs sector is also described byweakly coupled, perturbative QFT. (at least no sign of strong interaction, so far...)
Higgs
126 GeV Higgs
By the way... perturbative, weakly coupled Higgs sectoris consistent with the existence of heavy right-handed neutrinos which are (weakly) coupled to Higgs.
Higgs
R.H.neutrino
L = LSM +1
2NR(i/@ +MR)NR + y⌫NR`LH + h.c.
(3) Leptogenesis
(1) small neutrino masses
(2) matter unification in 16 of SO(10)
126 GeV Higgs
... implying weakly coupled, perturbative QFTup to right-handed neutrino scale. (say, > 1010 GeV.)
fine-tuning problem
(fine tuning like 1.0000000000000001 - 1)
no fine-tuning
(“little” fine tuning 1.01-1 or 1.001-1 or...)
“little”
�1
2m2
Higgs ' |µ|2 +m2 (tree)Hu
+m2 (loop)Hu
126 GeV HiggsPerturbative Higgs sector up to intermediate scale?
... then, Supersymmetry is the most attractive candidate for BSM physics.
naturalness
gauge coupling unification DM muon g-2
Supersymmetryafter
Higgs discovery
Let’s recall the motivations of TeV scale SUSY.....
naturalness
muon g-2
Dark Matter
Coupling Unification
.....
126 GeV Higgs and SUSY
Let’s recall the motivations of TeV scale SUSY.....
naturalness
muon g-2
Dark Matter
Coupling Unification
.....
126 GeV Higgs and SUSY
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
Let’s recall the motivations of TeV scale SUSY.....
naturalness
muon g-2
Dark Matter
Coupling Unification
.....
126 GeV Higgs and SUSY
Today
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
Let’s recall the motivations of TeV scale SUSY.....
naturalness
muon g-2
Dark Matter
Coupling Unification
.....
126 GeV Higgs and SUSY
Today
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
Let’s recall the motivations of TeV scale SUSY.....
naturalness
muon g-2
Dark Matter
Coupling Unification
.....
126 GeV Higgs and SUSY
Today
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
See also the next H.Baer’s talk
126 GeV Higgs and naturalness
in SUSY...
126 GeV Higgs and naturalness
in SUSY...
too small...
g2 cos2 2�
8 cos
2 ✓W' 0.069 cos
22�
126 GeV Higgs and naturalness
...requires heavy stop and/or large A-term
for large tan�. (↵ ' At/mstop
)
g2 cos2 2�
8 cos
2 ✓W' 0.069 cos
22�
in SUSY...
126 GeV Higgs and naturalness
P.Draper, P.Meade, M.Reece, S.Shih ’11
forsmall A-term
...requires heavy stop and/or large A-term
for large tan�. (↵ ' At/mstop
)
g2 cos2 2�
8 cos
2 ✓W' 0.069 cos
22�
in SUSY...
126 GeV Higgs and naturalness
P.Draper, P.Meade, M.Reece, S.Shih ’11
forsmall A-term
...requires heavy stop and/or large A-term
for large tan�. (↵ ' At/mstop
)
~ 10 TeV
g2 cos2 2�
8 cos
2 ✓W' 0.069 cos
22�
in SUSY...
126 GeV Higgs and naturalness
on the other hand
for large tan�. (↵ ' At/mstop
)
...requires heavy stop and/or large A-term
g2 cos2 2�
8 cos
2 ✓W' 0.069 cos
22�
126 GeV Higgs and naturalness
on the other hand
for large tan�. (↵ ' At/mstop
)
...requires heavy stop and/or large A-term
g2 cos2 2�
8 cos
2 ✓W' 0.069 cos
22�
126 GeV Higgs and naturalness
up to O✓
1
tan
2 �
◆' |µ|2 +m2 (tree)
Hu+ �m2 (loop)
Hu�m2
for large tan�. (↵ ' At/mstop
)
up to O✓
1
tan
2 �
◆
large µ -----> fine-tuning.e.g.,
' |µ|2 +m2 (tree)
Hu+ �m2 (loop)
Hu
requires Light Higgsinoto avoid a fine-tuning.
...requires heavy stop and/or large A-term
g2 cos2 2�
8 cos
2 ✓W' 0.069 cos
22�
126 GeV Higgs and naturalness
on the other hand
�m2
for large tan�. (↵ ' At/mstop
)
Moreover,
�m2 (loop)
Hu⇠ �3y2t
8⇡2
⇣m2
ftL+m2
ftR+ |At|2
⌘log
✓M
mess
met
◆+ · · ·
requires Light stop and small A-term to avoid a fine-tuning.
' |µ|2 +m2 (tree)
Hu+ �m2 (loop)
Hu
...requires heavy stop and/or large A-term
g2 cos2 2�
8 cos
2 ✓W' 0.069 cos
22�
on the other hand
126 GeV Higgs and naturalness
�m2
for large tan�. (↵ ' At/mstop
)
Moreover,
�m2 (loop)
Hu⇠ �3y2t
8⇡2
⇣m2
ftL+m2
ftR+ |At|2
⌘log
✓M
mess
met
◆+ · · ·
requires Light stop and small A-term to avoid a fine-tuning.
' |µ|2 +m2 (tree)
Hu+ �m2 (loop)
Hu
...requires heavy stop and/or large A-term
inconsistent !!
g2 cos2 2�
8 cos
2 ✓W' 0.069 cos
22�
on the other hand
126 GeV Higgs and naturalness
�m2
Fine-tuning worse than 1% seems unavoidable in MSSM.
126 GeV Higgs and naturalness
difficult to reconcile within MSSM
Fine-tuning worse than 1% seems unavoidable in MSSM.
L.J.Hall, D.Pinner, J.T.Ruderman, 1112.2703 (Λmess = 10 TeV is assumed.)
mh = 124-126 GeV
fine tuning 1%fine tuning 0.5 %
126 GeV Higgs and naturalness
difficult to reconcile within MSSM
Fine-tuning worse than 1% seems unavoidable in MSSM.
L.J.Hall, D.Pinner, J.T.Ruderman, 1112.2703 (Λmess = 10 TeV is assumed.)
mh = 124-126 GeV
fine tuning 1%fine tuning 0.5 %
126 GeV Higgs and naturalness
difficult to reconcile within MSSM
But see also the next H.Baer’s talk. (cf. “Radiatively-driven natural SUSY”, Baer, Barger, Huang, Mickelson, Mustafayev,Tata, [1212.2655].)
implies Beyond MSSM models.
126 GeV Higgs and naturalness
difficult to reconcile within MSSMFine-tuning worse than 1% seems unavoidable in MSSM.
But see also the next H.Baer’s talk. (cf. “Radiatively-driven natural SUSY”, Baer, Barger, Huang, Mickelson, Mustafayev,Tata, [1212.2655].)
implies Beyond MSSM models.
126 GeV Higgs and naturalness
�m2Higgs / �H (' 0.13)
= �(tree)H + ��(loop)
H
�treeH ' 0.069 cos
22� +
�2NMSSM
4
sin
22�
can be large if
(�2NMSSM > O(0.1)
and tan� ⇠ O(1)
example: NMSSM WNMSSM = �NMSSMSHuHd
Model buildings and collider studies of NMSSM with less fine-tuningare interesting and important... See, e.g.,L.J.Hall, D.Pinner, J.T.Ruderman, [1112.2703], G.G.Ross, K.Schmidt-Hoberg, F.Staub [1205.1509], and many related works...
difficult to reconcile within MSSMFine-tuning worse than 1% seems unavoidable in MSSM.
But see also the next H.Baer’s talk. (cf. “Radiatively-driven natural SUSY”, Baer, Barger, Huang, Mickelson, Mustafayev,Tata, [1212.2655].)
[GeV]1t
~m100 200 300 400 500 600 700
10
r¾
+mt <
m1t~
m
10
r¾
+ m
W
+ m
b
< m
1t~m
200 300 400 500 600
)1
0r¾ m×
= 2 1
±r¾ ( m
1±r¾+m
b < m1t~m
< 106 GeV 1±r¾ m
+5 G
eV)
10
r¾
= m
1±
r¾
( m1±
r¾
+mb
< m
1t~m
< 103.5 GeV1±r¾m
[GeV
]10 r¾
m0
100
200
300
400
500
600
Observed limits)theomObserved limits (-1
Expected limits
10
r¾ m× = 2 ±
1rm
-1 = 20-21 fbintL
- 10 GeV1t
~ = m±1
rm-1 = 20.3 fbintL
= 150 GeV±1
rm-1 = 20.7 fbintL = 106 GeV±
1rm
-1 = 4.7 fbintL
+ 5 GeV10
r¾ = m±
1rm
-1 = 20.1 fbintL
-1 = 4.7 fbintL -1 21 fb5 intL10
r¾W b -1 = 20 fbintL
ATLAS Preliminary
production1t~1t
~ Status: LHCP 2013
=8 TeVs -1 = 20 - 21 fbintL =7 TeVs -1 = 4.7 fbintL0L ATLAS-CONF-2013-024
1L ATLAS-CONF-2013-037
-
2L ATLAS-CONF-2013-048
0L ATLAS-CONF-2013-053
-
1L ATLAS-CONF-2013-037
2L ATLAS-CONF-2013-048
1L CONF-2013-037, 2L CONF-2013-048
0L [1208.1447]
1L [1208.2590]
2L [1209.4186]
-
-
2L [1208.4305], 1-2L [1209.2102]
-
-
1-2L [1209.2102]
10
r¾ (*) WA1±r¾,
1±r¾ b A 1t
~10
r¾ W b A1t~ /
10
r¾ t A1t~
10
r¾ t A1t~0L,
10
r¾ t A1t~1L,
10
r¾ t A1t~2L,
10
r¾ W b A1t~2L,
+ 5 GeV10
r¾ = m±
1r
0L, m = 106 GeV±
1r
, m1±r¾ b A 1t
~1-2L, = 150 GeV±
1r
, m1±r¾ b A 1t
~1L, - 10 GeV
1t~ = m±
1r
, m1±r¾ b A 1t
~2L,
10
r¾ m× = 2 ±
1r
, m1±r¾ b A 1t
~1-2L,
�m2 (loop)
Hu⇠ �3y2t
8⇡2
⇣m2
ftL+m2
ftR+ |At|2
⌘log
✓M
mess
met
◆+ · · ·
Naturalness requires light Higgsino and light stop,which are searched for at the LHC.If discovered, Higgsino can be further studied at LC.
' |µ|2 +m2 (tree)
Hu+ �m2 (loop)
Hu
In any case,...
e.g., by NMSSM
126 GeV Higgs and naturalness
�m2
Motivations of TeV scale SUSY.....
naturalness
muon g-2
Dark Matter
Coupling Unification
.....
126 GeV Higgs and SUSY
Today
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs +
126 GeV Higgs and SUSY
Today
126 GeV Higgs +
126 GeV Higgs +based on recent works
M.Endo, KH, S.Iwamoto, N.Yokozaki, arXiv:1108.3071, 1112.5653, 1202.2751 M.Endo, KH, S.Iwamoto, K.Nakayama, N.Yokozaki, arXiv:1112.6412 M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935 M.Endo, KH, S.Iwamoto, T.Yoshinaga, arXiv:1303.4256M.Endo, KH, T.Kitahara, T.Yoshinaga, arXiv:1306.xxxx (to appear soon)
Motivations of TeV scale SUSY.....
naturalness
muon g-2
126 GeV Higgs + muon g-2
126 GeV Higgs + muon g-2
[Hagiwara, Liao, Martin, Nomura, Teubner, arXiv: 1105.3149. See also references therein!]
> 3σ deviation !
muon g-2
> 3σ deviation !
...can be explained by SUSY.
... if smuon andchargino/neutralinoare O(100 GeV).
126 GeV Higgs + muon g-2
muon g-2
difficult to reconcile in typical models(mSUGRA/GMSB/AMSB/NMSSM (small tanβ) ...)
heavy stop light smuon/ inos
126 GeV Higgs + muon g-2
difficult to reconcile in typical models(mSUGRA/GMSB/AMSB/NMSSM (small tanβ) ...)
heavy stop light smuon/ inos
126 GeV Higgs + muon g-2
Example in mSUGRA:Higgs mass is maximized by A-term, while b -> sγ constraint is satisfied.
(Figure thanks to Motoi Endo.)[ See M.Endo, KH, S.Iwamoto, K.Nakayama, N.Yokozaki ’11 ]
difficult to reconcile in typical models(mSUGRA/GMSB/AMSB/NMSSM (small tanβ) ...)
heavy stop light smuon/ inos
126 GeV Higgs + muon g-2
(1) general MSSM(2) model building
2 approaches
difficult to reconcile in typical models(mSUGRA/GMSB/AMSB/NMSSM (small tanβ) ...)
heavy stop light smuon/ inos
126 GeV Higgs + muon g-2
(1) general MSSM(2) model building
2 approaches
“g-2 motivated” MSSM
>> 1 TeVto explain Higgs mass
= O(100 GeV)to explain muon g-2
Can we test it ??
Chargino contribution Neutralino contribution
. .
˜W−˜H−
µL µRν̃µ
(a)
˜B
µL µ̃L
m2LR
µ̃R µR
(b)
˜B˜H0
µL µRµ̃L
(c)
˜W 0 ˜H0
µL µRµ̃L
(d)
˜H0 ˜B
µL µRµ̃R
(e)
Figure 1: The SUSY contributions to the muon g − 2 which give the leading terms of theexpansion in mZ/mSUSY. The photon (wavy line) is attached to all the charged particles.
where
G1(x) =1
12(x− 1)4[(x− 1)(x2 − 5x− 2) + 6x ln x
], (5a)
G2(x) =1
12(x− 1)4[(x− 1)(2x2 + 5x− 1)− 6x2 ln x
], (5b)
G3(x) =1
2(x− 1)3[(x− 1)(x− 3) + 2 lnx] , (5c)
G4(x) =1
2(x− 1)3[(x− 1)(x+ 1)− 2x ln x] . (5d)
Even though these expressions are useful for numerical calculations, they are not particularlyilluminating for the purpose of understanding their dependences on the SUSY parameters.The main disadvantage of the above expressions is that they are written in terms of themass eigenstates, in terms of which the dependences on the SUSY breaking parameters arehidden by the electroweak symmetry breaking that causes complex mixings.
In the weak eigenstates, the structure of the one-loop contributions becomes much moretransparent. This simplification occurs since the expressions in the weak eigenstates areequivalent to the mZ/mSUSY expansion, where mSUSY is the typical SUSY breaking massscale. The price we have to pay is that the leading terms in the expansion are not usefulwhen mSUSY ∼ mZ . However, we will find below that this expansion is very useful whenanalyzing the SUSY parameter dependence.
The leading terms in the mZ/mSUSY expansion are given by the five diagrams (a) to (e)
4
. .
˜W−˜H−
µL µRν̃µ
(a)
˜B
µL µ̃L
m2LR
µ̃R µR
(b)
˜B˜H0
µL µRµ̃L
(c)
˜W 0 ˜H0
µL µRµ̃L
(d)
˜H0 ˜B
µL µRµ̃R
(e)
Figure 1: The SUSY contributions to the muon g − 2 which give the leading terms of theexpansion in mZ/mSUSY. The photon (wavy line) is attached to all the charged particles.
where
G1(x) =1
12(x− 1)4[(x− 1)(x2 − 5x− 2) + 6x ln x
], (5a)
G2(x) =1
12(x− 1)4[(x− 1)(2x2 + 5x− 1)− 6x2 ln x
], (5b)
G3(x) =1
2(x− 1)3[(x− 1)(x− 3) + 2 lnx] , (5c)
G4(x) =1
2(x− 1)3[(x− 1)(x+ 1)− 2x ln x] . (5d)
Even though these expressions are useful for numerical calculations, they are not particularlyilluminating for the purpose of understanding their dependences on the SUSY parameters.The main disadvantage of the above expressions is that they are written in terms of themass eigenstates, in terms of which the dependences on the SUSY breaking parameters arehidden by the electroweak symmetry breaking that causes complex mixings.
In the weak eigenstates, the structure of the one-loop contributions becomes much moretransparent. This simplification occurs since the expressions in the weak eigenstates areequivalent to the mZ/mSUSY expansion, where mSUSY is the typical SUSY breaking massscale. The price we have to pay is that the leading terms in the expansion are not usefulwhen mSUSY ∼ mZ . However, we will find below that this expansion is very useful whenanalyzing the SUSY parameter dependence.
The leading terms in the mZ/mSUSY expansion are given by the five diagrams (a) to (e)
4
Case1 Case2
(usually dominant) (subdominant)
two representative parameter regions
enhanced whenHiggsino, Wino, smuon(L)
are light.
enhanced whenBino, smuon(L+R)
are light (and µ is large).
“g-2 motivated” MSSM
Results
slep
ton_
L m
ass
wino mass
M.Endo, KH, S.Iwamoto, T.Yoshinaga [1303.4256]
“g-2 motivated” MSSM
Results
slep
ton_
L m
ass
wino mass
light Wino, Higgsino, smuon(L).
M.Endo, KH, S.Iwamoto, T.Yoshinaga [1303.4256]
“g-2 motivated” MSSM
Results
slep
ton_
L m
ass
wino mass
light Wino, Higgsino, smuon(L).
light Bino, smuon(L+R),
+ large µ.
M.Endo, KH, S.Iwamoto, T.Yoshinaga [1303.4256]
“g-2 motivated” MSSM
slep
ton_
L m
ass
wino mass
muon g-2: 2σ1σ
“g-2 motivated” MSSMResults
M.Endo, KH, S.Iwamoto, T.Yoshinaga [1303.4256]
slep
ton_
L m
ass
wino mass
when GUT relationM1:M2:M3 = 1:2:6 holds,
this region is excluded byjets + missing pT search[ATLAS 5.8fb-1@8TeV].
even if gluino is heavythis region is excluded by 3-lepton search[ATLAS 13fb-1@8TeV].
“g-2 motivated” MSSMResults
M.Endo, KH, S.Iwamoto, T.Yoshinaga [1303.4256]
slep
ton_
L m
ass
wino mass
m˜̀>m�2
>m�1
m�2>m ˜̀
>m�1
m�2> m�1
> m˜̀
“g-2 motivated” MSSMResults
M.Endo, KH, S.Iwamoto, T.Yoshinaga [1303.4256]
even if gluino is heavythis region is excluded by 3-lepton search[ATLAS 13fb-1@8TeV].
slep
ton_
L m
ass
wino mass
“g-2 motivated” MSSMResults
M.Endo, KH, S.Iwamoto, T.Yoshinaga [1303.4256]
LHC started exclude
g-2 motivated regions !
(1) If discovered at LHC,
--> further test at LC
whether they are really
responsible for the g-2.
(2) Some regions are
difficult to cover at LHC.
--> LC may cover them.
. .
˜W−˜H−
µL µRν̃µ
(a)
˜B
µL µ̃L
m2LR
µ̃R µR
(b)
˜B˜H0
µL µRµ̃L
(c)
˜W 0 ˜H0
µL µRµ̃L
(d)
˜H0 ˜B
µL µRµ̃R
(e)
Figure 1: The SUSY contributions to the muon g − 2 which give the leading terms of theexpansion in mZ/mSUSY. The photon (wavy line) is attached to all the charged particles.
where
G1(x) =1
12(x− 1)4[(x− 1)(x2 − 5x− 2) + 6x ln x
], (5a)
G2(x) =1
12(x− 1)4[(x− 1)(2x2 + 5x− 1)− 6x2 ln x
], (5b)
G3(x) =1
2(x− 1)3[(x− 1)(x− 3) + 2 lnx] , (5c)
G4(x) =1
2(x− 1)3[(x− 1)(x+ 1)− 2x ln x] . (5d)
Even though these expressions are useful for numerical calculations, they are not particularlyilluminating for the purpose of understanding their dependences on the SUSY parameters.The main disadvantage of the above expressions is that they are written in terms of themass eigenstates, in terms of which the dependences on the SUSY breaking parameters arehidden by the electroweak symmetry breaking that causes complex mixings.
In the weak eigenstates, the structure of the one-loop contributions becomes much moretransparent. This simplification occurs since the expressions in the weak eigenstates areequivalent to the mZ/mSUSY expansion, where mSUSY is the typical SUSY breaking massscale. The price we have to pay is that the leading terms in the expansion are not usefulwhen mSUSY ∼ mZ . However, we will find below that this expansion is very useful whenanalyzing the SUSY parameter dependence.
The leading terms in the mZ/mSUSY expansion are given by the five diagrams (a) to (e)
4
(What is the minimal set of particles that can explain muon g-2 ?)
M.Endo, KH, T.Kitahara, T.Yoshinaga [1306.xxxx]
minimal “g-2 motivated” MSSMonly smuon(L), smuon(R), andBino are light.(and µ is large)
. .
˜W−˜H−
µL µRν̃µ
(a)
˜B
µL µ̃L
m2LR
µ̃R µR
(b)
˜B˜H0
µL µRµ̃L
(c)
˜W 0 ˜H0
µL µRµ̃L
(d)
˜H0 ˜B
µL µRµ̃R
(e)
Figure 1: The SUSY contributions to the muon g − 2 which give the leading terms of theexpansion in mZ/mSUSY. The photon (wavy line) is attached to all the charged particles.
where
G1(x) =1
12(x− 1)4[(x− 1)(x2 − 5x− 2) + 6x ln x
], (5a)
G2(x) =1
12(x− 1)4[(x− 1)(2x2 + 5x− 1)− 6x2 ln x
], (5b)
G3(x) =1
2(x− 1)3[(x− 1)(x− 3) + 2 lnx] , (5c)
G4(x) =1
2(x− 1)3[(x− 1)(x+ 1)− 2x ln x] . (5d)
Even though these expressions are useful for numerical calculations, they are not particularlyilluminating for the purpose of understanding their dependences on the SUSY parameters.The main disadvantage of the above expressions is that they are written in terms of themass eigenstates, in terms of which the dependences on the SUSY breaking parameters arehidden by the electroweak symmetry breaking that causes complex mixings.
In the weak eigenstates, the structure of the one-loop contributions becomes much moretransparent. This simplification occurs since the expressions in the weak eigenstates areequivalent to the mZ/mSUSY expansion, where mSUSY is the typical SUSY breaking massscale. The price we have to pay is that the leading terms in the expansion are not usefulwhen mSUSY ∼ mZ . However, we will find below that this expansion is very useful whenanalyzing the SUSY parameter dependence.
The leading terms in the mZ/mSUSY expansion are given by the five diagrams (a) to (e)
4
Priliminary
200 250 300 350 400 450 500
500
1000
1500
2000
mµ̃1=
400GeV
300GeV
500GeV
(What is the minimal set of particles that can explain muon g-2 ?)
M.Endo, KH, T.Kitahara, T.Yoshinaga [1306.xxxx]
minimal “g-2 motivated” MSSMonly smuon(L), smuon(R), andBino are light.(and µ is large)
200 250 300 350 400 450 500
500
1000
1500
2000
mµ̃1=
400GeV
300GeV
500GeV
(What is the minimal set of particles that can explain muon g-2 ?)
M.Endo, KH, T.Kitahara, T.Yoshinaga [1306.xxxx]
minimal “g-2 motivated” MSSMonly smuon(L), smuon(R), andBino are light.(and µ is large) Prilim
inary
. .
˜W−˜H−
µL µRν̃µ
(a)
˜B
µL µ̃L
m2LR
µ̃R µR
(b)
˜B˜H0
µL µRµ̃L
(c)
˜W 0 ˜H0
µL µRµ̃L
(d)
˜H0 ˜B
µL µRµ̃R
(e)
Figure 1: The SUSY contributions to the muon g − 2 which give the leading terms of theexpansion in mZ/mSUSY. The photon (wavy line) is attached to all the charged particles.
where
G1(x) =1
12(x− 1)4[(x− 1)(x2 − 5x− 2) + 6x ln x
], (5a)
G2(x) =1
12(x− 1)4[(x− 1)(2x2 + 5x− 1)− 6x2 ln x
], (5b)
G3(x) =1
2(x− 1)3[(x− 1)(x− 3) + 2 lnx] , (5c)
G4(x) =1
2(x− 1)3[(x− 1)(x+ 1)− 2x ln x] . (5d)
Even though these expressions are useful for numerical calculations, they are not particularlyilluminating for the purpose of understanding their dependences on the SUSY parameters.The main disadvantage of the above expressions is that they are written in terms of themass eigenstates, in terms of which the dependences on the SUSY breaking parameters arehidden by the electroweak symmetry breaking that causes complex mixings.
In the weak eigenstates, the structure of the one-loop contributions becomes much moretransparent. This simplification occurs since the expressions in the weak eigenstates areequivalent to the mZ/mSUSY expansion, where mSUSY is the typical SUSY breaking massscale. The price we have to pay is that the leading terms in the expansion are not usefulwhen mSUSY ∼ mZ . However, we will find below that this expansion is very useful whenanalyzing the SUSY parameter dependence.
The leading terms in the mZ/mSUSY expansion are given by the five diagrams (a) to (e)
4
Vacuum stability bound:(too large µ --> slepton-Higgs potential unstable --> Lifetime < Age of Universe
O(100 GeV) slepton and bino ... can be tested at LC !!
(for m
stau =
msmuon
)
(1) general MSSM(2) model building
2 approaches
difficult to reconcile in typical models(mSUGRA/GMSB/AMSB/NMSSM (small tanβ) ...)
heavy stop light smuon/ inos
126 GeV Higgs + muon g-2
(1) general MSSM(2) model building
2 approaches
difficult to reconcile in typical models(mSUGRA/GMSB/AMSB/NMSSM (small tanβ) ...)
heavy stop light smuon/ inos
126 GeV Higgs + muon g-2
MSSM + vector-like matter Endo,KH,Iwamoto,Yokozaki,+ Ishikawa’11-12, Moroi,Sato,Yanagida,’11, Sato,Tobioka,Yokozaki,’12, Nakayama,Yokozaki,’12,...MSSM + U(1) Endo,KH,Iwamoto,Nakayama,Yokozaki’11,...split family Ibe Yanagida Yokozaki,’13,...modified GMSB Evans,Ibe,Shirai,Yanagida,’12, Ibe,Matsumoto,Yanagida,Yokozaki’12,...non-universal gaugino Mohanty,Rao,Roy,’13,...other models.....
(2) model building
difficult to reconcile in typical models(mSUGRA/GMSB/AMSB/NMSSM (small tanβ) ...)
heavy stop light smuon/ inos
126 GeV Higgs + muon g-2
MSSM + vector-like matter Endo,KH,Iwamoto,Yokozaki,+ Ishikawa’11-12, Moroi,Sato,Yanagida,’11, Sato,Tobioka,Yokozaki,’12, Nakayama,Yokozaki,’12,...MSSM + U(1) Endo,KH,Iwamoto,Nakayama,Yokozaki’11,...split family Ibe Yanagida Yokozaki,’13,...modified GMSB Evans,Ibe,Shirai,Yanagida,’12, Ibe,Matsumoto,Yanagida,Yokozaki’12,...non-universal gaugino Mohanty,Rao,Roy,’13,...other models.....
(2) model building
difficult to reconcile in typical models(mSUGRA/GMSB/AMSB/NMSSM (small tanβ) ...)
heavy stop light smuon/ inos
126 GeV Higgs + muon g-2
MSSM + vector-like matter
Idea:In MSSM, Ytop (and Atop) raises the Higgs mass.--> Add new vector-like matters with a Yukawa coupling to Higgs. W = Ytop Q3U3Hu + Y’Q’U’Hu
�m2Higgs / �H (' 0.13)
= �(tree)H + ��(loop)
H
��(loop)H / Y 4
top · (top, stop-loop)
126 GeV Higgs + muon g-2
Idea:In MSSM, Ytop (and Atop) raises the Higgs mass.--> Add new vector-like matters (10+10bar) with a Yukawa coupling to Higgs. W = Ytop Q3U3Hu + Y’Q’U’Hu
[Okada,Moroi,’92;.....Babu,Gogoladze,Rehman,Shafi,’08; Martin,’09]
�m2Higgs / �H (' 0.13)
= �(tree)H + ��(loop)
H
��(loop)H / Y 4
top · (top, stop-loop)
+Y04 · (new vector-loop)
126 GeV Higgs + muon g-2
MSSM + vector-like matter
Resultsfor “V-GMSB”
= gauge mediation (GMSB) + vector-like matter
126 GeV Higgs + muon g-2M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935
muon g-2 explained (1σ)(2σ)
126 GeV Higgs + muon g-2
for “V-GMSB”Results M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935
muon g-2 explained (1σ)(2σ)Higgs mass 125-126 GeV
126 GeV Higgs + muon g-2
for “V-GMSB”Results M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935
muon g-2 explained (1σ)(2σ)Higgs mass 125-126 GeV
g-2 and
Higgs mass
are
explaine
d simulta
neously!
126 GeV Higgs + muon g-2
for “V-GMSB”Results M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935
muon g-2 explained (1σ)(2σ)Higgs mass 125-126 GeV
LHC constraints ?
126 GeV Higgs + muon g-2
for “V-GMSB”Results M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935
NLSP = stauLHC signal= long-lived charged particle
NLSP = neutralinoLHC signal= jets + missing energy
126 GeV Higgs + muon g-2
for “V-GMSB”Results M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935
already excluded
126 GeV Higgs + muon g-2
for “V-GMSB”Results M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935
[* using ATLAS result (5.8fb-1@8TeV) for jets + missing and CMS result (5.0fb-1@7TeV) for long-lived charged particle.]
already excluded
126 GeV Higgs + muon g-2
for “V-GMSB”Results
New LHC resultswere reported
after our analysis.
M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935
[* using ATLAS result (5.8fb-1@8TeV) for jets + missing and CMS result (5.0fb-1@7TeV) for long-lived charged particle.]
stau NLSP region is completely excluded.
(CMS: m(stau) > 339 GeVwith Drell-Yang direct)
neutralino NLSP regionis still allowed.
8TeV 20fb^-1[ATLAS-CONF-2013-047]
for “V-GMSB”
New analysis: thanks to Kazuya Ishikawa.
Results
126 GeV Higgs + muon g-2
Now...
stau NLSP region is completely excluded.
(CMS: m(stau) > 339 GeVwith Drell-Yang direct)
neutralino NLSP regionis still allowed.
8TeV 20fb^-1[ATLAS-CONF-2013-047]
allowedregion
for “V-GMSB”
New analysis: thanks to Kazuya Ishikawa.
Results
126 GeV Higgs + muon g-2
Now...
motivations model LHC/LC signal
126 GeV Higgs+ naturalness
impliesbeyond MSSM (e.g. NMSSM)
light stop and light Higgsino.
126 GeV Higgs+ muon g-2 (>3σ !!)
difficult in simple models
(1) general MSSM(2) model building
(1) “g-2 motivated MSSM”--> can be tested by non-colored particle search at LHC/LC.(2) example: “V-GMSB”--> barely alive. tested soon.
126 GeV Higgs+ Dark Matter
* No problem in simple models (e.g., mSUGRA). * O(TeV) gauginos/Higgsinos are sufficient (split/spread SUSY). AMS-02 result on anti-proton will be important.
* No problem in simple models (e.g., mSUGRA). * O(TeV) gauginos/Higgsinos are sufficient (split/spread SUSY). AMS-02 result on anti-proton will be important.
126 GeV Higgs+ coupling unification
* No problem in simple models (e.g., mSUGRA). * O(TeV) gauginos/Higgsinos are sufficient (split/spread SUSY). AMS-02 result on anti-proton will be important.
* No problem in simple models (e.g., mSUGRA). * O(TeV) gauginos/Higgsinos are sufficient (split/spread SUSY). AMS-02 result on anti-proton will be important.
SUMMARY SUSY < O(TeV) after Higgs discovery
•backup
simplest possibility: heavy SUSY
Fig. from P.Draper, P.Meade, M.Reece, S.Shih ’11 Fig. from L.Hall, Y.Nomura, S.Shirai ’12
no stop mixinglarge tanβ
heavy scalar scenario
+ many related works
A-term small
(not so large)
126 GeV Higgs and SUSY
Fig. fromN.Arkani-Hamed, A.Gupta, D.E.Kaplan, N.Weiner, T.Zorawski’12
[ L.J.Hall, D.Pinner, J.T.Ruderman, 1112.2703 ]
Example: in mSUGRA, Higgs mass is maximized by A-term,while b -> sγ constraint is satisfied. (Thanks to Motoi Endo)
[ See M.Endo, KH, S.Iwamoto, K.Nakayama, N.Yokozaki ’11 ]
example: mSUGRA126 GeV Higgs can be consistentwith light stop,if maximally enhanced by A-term.
�m2Higgs / �H
/
difficult to reconcile within MSSM
126 GeV Higgs and naturalness
Example: in mSUGRA, Higgs mass is maximized by A-term,while b -> sγ constraint is satisfied. (Thanks to Motoi Endo)
[ See M.Endo, KH, S.Iwamoto, K.Nakayama, N.Yokozaki ’11 ]
example: mSUGRA126 GeV Higgs can be consistentwith light stop,if maximally enhanced by A-term. but fine-tuned.
difficult to reconcile within MSSM
126 GeV Higgs and naturalness
126 GeV Higgs and naturalness
requires beyond MSSM.difficult to reconcile within MSSM
example: NMSSM
can realize 126 GeV + O(a few) % tuning.[e.g., L.J.Hall, D.Pinner, J.T.Ruderman,1112.2703 + many related works]
Any concrete model, perturbativeup to GUT ??
generalizedNMSSM
G.G.Ross, K.Schmidt-Hoberg, F.Staub [1205.1509]
Higgsmass
a few % fine-tuning
M.Endo, KH, K.Ishikawa, S.Iwamoto, N.Yokozaki, arXiv:1212.3935
200 400 600 800 1000 1200 14000
20000
40000
60000
80000
100000
. .
˜W−˜H−
µL µRν̃µ
(a)
˜B
µL µ̃L
m2LR
µ̃R µR
(b)
˜B˜H0
µL µRµ̃L
(c)
˜W 0 ˜H0
µL µRµ̃L
(d)
˜H0 ˜B
µL µRµ̃R
(e)
Figure 1: The SUSY contributions to the muon g − 2 which give the leading terms of theexpansion in mZ/mSUSY. The photon (wavy line) is attached to all the charged particles.
where
G1(x) =1
12(x− 1)4[(x− 1)(x2 − 5x− 2) + 6x ln x
], (5a)
G2(x) =1
12(x− 1)4[(x− 1)(2x2 + 5x− 1)− 6x2 ln x
], (5b)
G3(x) =1
2(x− 1)3[(x− 1)(x− 3) + 2 lnx] , (5c)
G4(x) =1
2(x− 1)3[(x− 1)(x+ 1)− 2x ln x] . (5d)
Even though these expressions are useful for numerical calculations, they are not particularlyilluminating for the purpose of understanding their dependences on the SUSY parameters.The main disadvantage of the above expressions is that they are written in terms of themass eigenstates, in terms of which the dependences on the SUSY breaking parameters arehidden by the electroweak symmetry breaking that causes complex mixings.
In the weak eigenstates, the structure of the one-loop contributions becomes much moretransparent. This simplification occurs since the expressions in the weak eigenstates areequivalent to the mZ/mSUSY expansion, where mSUSY is the typical SUSY breaking massscale. The price we have to pay is that the leading terms in the expansion are not usefulwhen mSUSY ∼ mZ . However, we will find below that this expansion is very useful whenanalyzing the SUSY parameter dependence.
The leading terms in the mZ/mSUSY expansion are given by the five diagrams (a) to (e)
4
Priliminary
vacuum bound (smuon)
vacuum
bound (m
stau = 10 msm
uon)
(mstau = 5 ms
muon)
(mstau = 2 msmuon)
(mstau = msmuon)
(What is the minimal set of particles that can explain muon g-2 ?)
M.Endo, KH, T.Kitahara, T.Yoshinaga [1306.xxxx]
minimal “g-2 motivated” MSSMonly smuon(L), smuon(R),Bino are light.(and µ is large)