supersymmetry after higgs discovery...supersymmetry after higgs discovery koichi hamaguchi...

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

126 GeV Higgs

-1.0 -0.5 0.5 1.0

126 GeV Higgs

-1.0 -0.5 0.5 1.0

' (174 GeV)2We knew...

126 GeV Higgs

-1.0 -0.5 0.5 1.0

126 GeV Higgs

Now we also know' (126 GeV)2

-1.0 -0.5 0.5 1.0

126 GeV Higgs

Now we also know' (126 GeV)2

-1.0 -0.5 0.5 1.0

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...)

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.

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”

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

naturalness

muon g-2

Dark Matter

126 GeV Higgs +

naturalness

muon g-2

Dark Matter

126 GeV Higgs +

naturalness

muon g-2

Dark Matter

126 GeV Higgs +

naturalness

muon g-2

Dark Matter

126 GeV Higgs +

See also the next H.Baer’s talk

126 GeV Higgs and naturalness

in SUSY...

too small...

g2 cos2 2�

2 ✓W' 0.069 cos

...requires heavy stop and/or large A-term

for large tan�. (↵ ' At/mstop

g2 cos2 2�

2 ✓W' 0.069 cos

in SUSY...

P.Draper, P.Meade, M.Reece, S.Shih ’11

forsmall A-term

g2 cos2 2�

2 ✓W' 0.069 cos

in SUSY...

P.Draper, P.Meade, M.Reece, S.Shih ’11

forsmall A-term

~ 10 TeV

g2 cos2 2�

2 ✓W' 0.069 cos

in SUSY...

on the other hand

g2 cos2 2�

2 ✓W' 0.069 cos

on the other hand

g2 cos2 2�

2 ✓W' 0.069 cos

up to O✓

◆' |µ|2 +m2 (tree)

Hu+ �m2 (loop)

Hu�m2

up to O✓

large µ -----> fine-tuning.e.g.,

' |µ|2 +m2 (tree)

Hu+ �m2 (loop)

requires Light Higgsinoto avoid a fine-tuning.

g2 cos2 2�

2 ✓W' 0.069 cos

on the other hand

Moreover,

�m2 (loop)

Hu⇠ �3y2t

ftL+m2

ftR+ |At|2

⌘log

◆+ · · ·

requires Light stop and small A-term to avoid a fine-tuning.

' |µ|2 +m2 (tree)

Hu+ �m2 (loop)

g2 cos2 2�

2 ✓W' 0.069 cos

on the other hand

Moreover,

�m2 (loop)

Hu⇠ �3y2t

ftL+m2

ftR+ |At|2

⌘log

◆+ · · ·

requires Light stop and small A-term to avoid a fine-tuning.

' |µ|2 +m2 (tree)

Hu+ �m2 (loop)

inconsistent !!

g2 cos2 2�

2 ✓W' 0.069 cos

on the other hand

Fine-tuning worse than 1% seems unavoidable in MSSM.

difficult to reconcile within 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 %

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 %

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.

difficult to reconcile within MSSMFine-tuning worse than 1% seems unavoidable in MSSM.

implies Beyond MSSM models.

�m2Higgs / �H (' 0.13)

= �(tree)H + ��(loop)

�treeH ' 0.069 cos

22� +

�2NMSSM

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.

[GeV]1t

~m100 200 300 400 500 600 700

200 300 400 500 600

0r¾ m×

±r¾ ( m

1±r¾+m

b < m1t~m

< 106 GeV 1±r¾ m

( m1±

< 103.5 GeV1±r¾m

]10 r¾

Observed limits)theomObserved limits (-1

Expected limits

r¾ m× = 2 ±

-1 = 20-21 fbintL

- 10 GeV1t

~ = m±1

rm-1 = 20.3 fbintL

= 150 GeV±1

rm-1 = 20.7 fbintL = 106 GeV±

-1 = 4.7 fbintL

+ 5 GeV10

r¾ = m±

-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

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]

r¾ (*) WA1±r¾,

1±r¾ b A 1t

r¾ W b A1t~ /

r¾ t A1t~

r¾ t A1t~0L,

r¾ t A1t~1L,

r¾ t A1t~2L,

r¾ W b A1t~2L,

+ 5 GeV10

r¾ = m±

0L, m = 106 GeV±

, m1±r¾ b A 1t

~1-2L, = 150 GeV±

, m1±r¾ b A 1t

~1L, - 10 GeV

1t~ = m±

, m1±r¾ b A 1t

r¾ m× = 2 ±

, m1±r¾ b A 1t

~1-2L,

�m2 (loop)

Hu⇠ �3y2t

ftL+m2

ftR+ |At|2

⌘log

◆+ · · ·

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)

In any case,...

e.g., by NMSSM

Motivations of TeV scale SUSY.....

naturalness

muon g-2

Dark Matter

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

[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).

muon g-2

difficult to reconcile in typical models(mSUGRA/GMSB/AMSB/NMSSM (small tanβ) ...)

heavy stop light smuon/ inos

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 ]

(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

µL µ̃L

µ̃R µR

˜B˜H0

µL µRµ̃L

˜W 0 ˜H0

µL µRµ̃L

˜H0 ˜B

µL µRµ̃R

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.

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)

˜W−˜H−

µL µRν̃µ

µL µ̃L

µ̃R µR

˜B˜H0

µL µRµ̃L

˜W 0 ˜H0

µL µRµ̃L

˜H0 ˜B

µL µRµ̃R

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)

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).

Results

wino mass

M.Endo, KH, S.Iwamoto, T.Yoshinaga [1303.4256]

Results

wino mass

light Wino, Higgsino, smuon(L).

Results

wino mass

light Wino, Higgsino, smuon(L).

light Bino, smuon(L+R),

+ large µ.

wino mass

muon g-2: 2σ1σ

“g-2 motivated” MSSMResults

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].

wino mass

m˜̀>m�2

>m�1

m�2>m ˜̀

>m�1

m�2> m�1

> m˜̀

even if gluino is heavythis region is excluded by 3-lepton search[ATLAS 13fb-1@8TeV].

wino mass

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

µL µ̃L

µ̃R µR

˜B˜H0

µL µRµ̃L

˜W 0 ˜H0

µL µRµ̃L

˜H0 ˜B

µL µRµ̃R

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)

(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

µL µ̃L

µ̃R µR

˜B˜H0

µL µRµ̃L

˜W 0 ˜H0

µL µRµ̃L

˜H0 ˜B

µL µRµ̃R

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)

Priliminary

200 250 300 350 400 450 500

mµ̃1=

400GeV

300GeV

500GeV

minimal “g-2 motivated” MSSMonly smuon(L), smuon(R), andBino are light.(and µ is large)

200 250 300 350 400 450 500

mµ̃1=

400GeV

300GeV

500GeV

minimal “g-2 motivated” MSSMonly smuon(L), smuon(R), andBino are light.(and µ is large) Prilim

˜W−˜H−

µL µRν̃µ

µL µ̃L

µ̃R µR

˜B˜H0

µL µRµ̃L

˜W 0 ˜H0

µL µRµ̃L

˜H0 ˜B

µL µRµ̃R

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)

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

2 approaches

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

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

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)

��(loop)H / Y 4

top · (top, stop-loop)

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)

��(loop)H / Y 4

top · (top, stop-loop)

+Y04 · (new vector-loop)

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)

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

explaine

d simulta

neously!

LHC constraints ?

NLSP = stauLHC signal= long-lived charged particle

NLSP = neutralinoLHC signal= jets + missing energy

already excluded

[* using ATLAS result (5.8fb-1@8TeV) for jets + missing and CMS result (5.0fb-1@7TeV) for long-lived charged particle.]

already excluded

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

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

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) “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.

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.

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)

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

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.

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

100000

˜W−˜H−

µL µRν̃µ

µL µ̃L

µ̃R µR

˜B˜H0

µL µRµ̃L

˜W 0 ˜H0

µL µRµ̃L

˜H0 ˜B

µL µRµ̃R

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)

Priliminary

vacuum bound (smuon)

vacuum

bound (m

stau = 10 msm

(mstau = 5 ms

(mstau = 2 msmuon)

(mstau = msmuon)

minimal “g-2 motivated” MSSMonly smuon(L), smuon(R),Bino are light.(and µ is large)

supersymmetry after higgs discovery...supersymmetry after higgs discovery koichi hamaguchi...

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