SO(10) inspired GMSB
MEK, W. Porod, F. Staub, Phys.Rev. D88 (2013) 015014
– SUSY, Trieste 2013 –
Manuel E. Krauss
in collaboration with W. Porod and F. Staub
Würzburg University
Department of Theoretical Physics II
August 27th, 2013
Introduction
How does SUSY breaking work?
1
introduce terms in the Lagrangian which explicitly break SUSY
often considered scenario: CMSSM-like boundaries at MGUT
easy to handle, based on strong assumptions
appealing alternative:
Gauge Mediated Supersymmetry Breaking:
SUSY masses dynamically generated by gauge interactions
Manuel E. Krauss
SUSY, Trieste 2013
Introduction
How does SUSY breaking work?
introduce terms in the Lagrangian which explicitly break SUSY
often considered scenario: CMSSM-like boundaries at MGUT
easy to handle, based on strong assumptions
appealing alternative:
Gauge Mediated Supersymmetry Breaking:
SUSY masses dynamically generated by gauge interactions
secluded sector
X̂; hXi = M + θ2F
ˆ
W = λi X̂ Φ̂i Φ̄
i
messenger sector
Φ̂
fermion masses: λi M
p
boson masses: |λi M |2 ± |λi F |
⇒ SUSY breaking!
[see, e.g., Giudice, Rattazzi, ’99; Martin, ’97]
visible world
1
Manuel E. Krauss
SUSY, Trieste 2013
Introduction
Problem:
Higgs mass in the MSSM:
m m
3m 2 Y 2 + ...
mh20 = MZ2 cos2 2β + t 2 t ln( t̃1 2 t̃2 ) + δt
| {z }
4π
mt
|{z}
tree-level mass
2
Manuel E. Krauss
⊃Au
SUSY, Trieste 2013
Introduction
Problem:
Higgs mass in the MSSM:
m m
3m 2 Y 2 mh20 = MZ2 cos2 2β + t 2 t ln( t̃1 2 t̃2 ) + δt
+ ...
| {z }
4π
mt
|{z}
tree-level mass
⇒ either: large stop masses
⊃Au
or: large trilinear couplings
but: minimal GMSB predicts very small trilinear terms
⇒ Stop mass has to be very large, mt̃1 & 5 TeV
[Ajaib, Gogoladze, Nasir, Shafi, ’12 ]
2
Manuel E. Krauss
SUSY, Trieste 2013
Introduction
Problem:
Higgs mass in the MSSM:
m m
3m 2 Y 2 mh20 = MZ2 cos2 2β + t 2 t ln( t̃1 2 t̃2 ) + δt
+ ...
| {z }
4π
mt
|{z}
tree-level mass
⇒ either: large stop masses
⊃Au
or: large trilinear couplings
but: minimal GMSB predicts very small trilinear terms
⇒ Stop mass has to be very large, mt̃1 & 5 TeV
[Ajaib, Gogoladze, Nasir, Shafi, ’12 ]
ideas:
enlarge trilinear terms by introducing direct messenger-matter
interactions
[several studies in the literature/see previous plenary and parallel talks]
2
enlarge tree-level mass by considering a larger gauge group
Manuel E. Krauss
SUSY, Trieste 2013
The Model
GMSB version of [Hirsch, Porod, Reichert, Staub, ’12]
consider a gauge group inspired by a SO(10) GUT group:
M
GUT
SO(10) −−−
−→ SU (3)c × SU (2)L × SU (2)R × U (1)B−L
−−−−→ SU (3)c × SU (2)L × U (1)R × U (1)B−L
M ∼TeV
R
−−−
−−−→ SU (3)c × SU (2)L × U (1)Y
U (1)R × U (1)B−L can be rotated into another basis:
U (1)Y × U (1)χ
additional fields:
ˆR to break
two additional Higgs fields χ̂R , χ̄
U (1)Y × U (1)χ → U (1)Y
singlet fields Ŝ generate neutrino masses via inverse Seesaw
ˆR χ̂R
Wh,add = −µR χ̄
Wν = Yν ν̂ c L̂Ĥu + YS ν̂ c Ŝ χ̂R + µS Ŝ Ŝ
3
Manuel E. Krauss
SUSY, Trieste 2013
The Model
Messenger fields
introduce n copies of messenger 10-plets
Φ̂1
ˆ
Φ̄
1
Φ̂2
ˆ
Φ̄
2
(1, 2)
(1, 2)
(3, 1)
(3, 1)
U (1)R × U (1)B−L
( 12 , 0)
(− 12 , 0)
(0, − 13 )
(0, 13 )
U (1)Y × U (1)χ
( 21 , − 12 )
(− 21 , 12 )
(− 13 , − 12 )
( 13 , 12 )
soft masses calculated at M including gauge kinetic mixing
numerical implementation in SARAH, SPheno
require gauge coupling unification
free model parameters: n, F , M , tan β(R) , vR , sign µ(R) , YS , Yi , µS
4
SU (3)c × SU (2)L
Manuel E. Krauss
(code publicly available)
SUSY, Trieste 2013
Higgs Physics
recall: tree level mass in the MSSM:
1
2
≤ MZ2 = (g 2 + g 02 )v 2
mh,tree
4
MSSM
now, with additional U (1)χ sector:
1
2
mh,tree
≤ MZ2 + gχ2 v 2
4
but: dependent on ratio of the two new vevs, tan βR = vχR /vχ̄R
1.0
h1
h2
R2Li ,tree
mhi ,tree [GeV]
h2
0.8
150
0.6
100
MZ
0.4
h1
50
0.2
0.0
0
1.00
1.01
1.02
1.03
tan βR
5
Manuel E. Krauss
1.04
1.05
1.00
1.01
1.02
1.03
tan βR
SUSY, Trieste 2013
1.04
1.05
Higgs Physics
130
128
⇒ Stop masses of
2–3 TeV are able to
generate large enough
Higgs masses
(MSSM: mt̃1 & 5 TeV)
mh [GeV]
126
124
122
120
118
116
1000
2000
3000
4000
mt̃1 [GeV]
5000
135.
mhi [GeV]
130.
dependent on messenger
scale M
(with constant F /M ):
125.
120.
115.
1 ´10 10
5 ´10 10
M [GeV]
6
Manuel E. Krauss
SUSY, Trieste 2013
1 ´10 11
Higgs Physics
h → γγ
∃ hints to enhanced BR(h → γγ) at the LHC
[ATLAS, ’12; CMS, ’12]
What does this model predict?
1.0
Rh→γγ
0.8
Rh→γγ
0.6
=
0.4
σ(pp → h) × BR(h → γγ)
σ(pp → h) × BR(h → γγ)|SM
0.2
0.0
600
800
1000
1200
1400
mτ̃1 [GeV]
⇒ Rh→γγ ≤ 1
complies with recent data from CMS
7
Manuel E. Krauss
[CMS, ’13]
SUSY, Trieste 2013
Phenomenology of the NLSP and the Z 0
LSP and NLSP
Gravitino G̃ is the LSP:
m3/2 = √
F
∼ O(MeV)
3mPl
∃ three possibilities for NLSP:
lightest neutralino χ̃01 (B̃ or χ̃R ):
(n ≤ 2 and YS nonhierarchical, or small µR )
lightest slepton τ̃ :
(n > 2, YS nonhierarchical and large tan β)
lightest sneutrino ν̃ (S̃ ):
(YS hierarchical)
⇒ new with respect to usual GMSB considerations:
S̃ - and χ̃R -like NLSP
8
Manuel E. Krauss
SUSY, Trieste 2013
χ̃01
NLSP:
µR > M1 :
bino NLSP
µR < M1 :
new higgsino NLSP
mχ̃0i [GeV]
Phenomenology of the NLSP and the Z 0
χ̃03...7
1000
χ̃02
500
χ̃01
100
50
0
200
400
600
800
1000
1200
1400
1200
1400
µR [GeV]
possibly interesting:
new Higgs hχR in
SUSY cascade decays
BR(χ̃01 → X)
1
hχR G̃
γ G̃
Z G̃
0.1
0.01
0.001
hG̃
10 - 4
0
200
400
600
800
µR [GeV]
9
Manuel E. Krauss
SUSY, Trieste 2013
1000
Phenomenology of the NLSP and the Z 0
ν̃ (S̃ ) NLSP
fermionic (bosonic) singlet fields S (S̃ ) mix with (s)neutrinos
m2
≈ vR2 sin2 βR YS† YS /2
S̃ S̃
hierarchical diagonal YS entries can give a light S̃ -like NLSP:
ν̃2
1500
mi [GeV]
χ̃02
1000
τ̃1
χ̃01
500
ν̃1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
YS33
possibly interesting:
heavy neutrino νh in SUSY cascade decays: χ̃01 → ν̃1 νh → ν G̃W (∗) l
10
Manuel E. Krauss
SUSY, Trieste 2013
Phenomenology of the NLSP and the Z 0
bounds on Z 0 mass
using ATLAS ’13 data:
σ(Z ′ ) × BR(Z ′ → l+ l− ) [pb]
Z 0 Phenomenology
0.010
0.005
0.002
0.001
5 ´ 10 - 4
MZ 0 & 2.4 TeV
vR & 6.6 TeV
2 ´ 10 - 4
1 ´ 10 - 4
1600 1800 2000 2200 2400 2600 2800 3000
MZ ′ [GeV]
possibly interesting Z 0 decays: Z 0 → νh νh , Z 0 → ν̃ ν̃
11
Manuel E. Krauss
SUSY, Trieste 2013
Conclusions
12
Higgs mass is a major problem for minimal GMSB models
extended gauge structure allows for enhanced tree-level Higgs
mass
in a SO(10)-inspired model: minimal GMSB is not dead yet!
Manuel E. Krauss
SUSY, Trieste 2013
Conclusions
Higgs mass is a major problem for minimal GMSB models
extended gauge structure allows for enhanced tree-level Higgs
mass
in a SO(10)-inspired model: minimal GMSB is not dead yet!
Thank you for your attention!
interested?
MEK, Porod, Staub, Phys.Rev. D88, 015014, arXiv:1304.0769
12
Manuel E. Krauss
SUSY, Trieste 2013
BACKUP
13
Manuel E. Krauss
SUSY, Trieste 2013
λ, mλ ∼
f˜, m2f˜ ∼
14
Manuel E. Krauss
SUSY, Trieste 2013
F2
M2
F
M
The superpotential reads
W =Yuij ûic Q̂j Ĥu − Ydij d̂ic Q̂j Ĥd − Yeij êic L̂j Ĥd + µ Ĥu Ĥd
ˆR χ̂R + µijS Ŝi Ŝj
+ Yνij ν̂ic L̂j Ĥu + YSij ν̂ic Ŝj χ̂R − µR χ̄
The soft SUSY breaking terms are
1
Vsoft = mij2 φ∗i φj +
Mab λa λb + Bµ Hu Hd + BµR χ̄R χR
2
+ BµS S̃ S̃ + Tdij Hd d̃ic Q̃j + Tuij Hu ũic Q̃j
+
15
Teij Hd ẽic L̃j
Manuel E. Krauss
+
Tνij Hu ν̃ic L̃j
+
TSij χR ν̃ic S̃j
+ h.c.
SUSY, Trieste 2013
Rotations
The gauge couplings and charges of U (1)R × U (1)B−L and
U (1)Y × U (1)χ are (without GUT normalization) related via
µ
AY
qB−L + qR
µ
0µ
0
,
A →A =
, Q →Q = 3
Aµχ
2 qB−L − qR
g
gY χ
G → G0 = Y
,
0
gχ
with
gBL gR − gBLR gRBL
gY = p
,
(gBLR − gR )2 + (gBL − gRBL )2
2p
gχ =
(gBLR − gR )2 + (gBL − gRBL )2 ,
5
2 + g2
2
2(gBL
) + gBLR gR + gBL gRBL − 3(gR2 + gRBL
)
BLR
p
gY χ =
5 (gBLR − gR )2 + (gBL − gRBL )2
16
Manuel E. Krauss
SUSY, Trieste 2013
boundary conditions from GMSB
masses of SUSY particles [e.g. Giudice, Rattazzi, ’99; Martin, ’97]:
Ma =
X
ga2
Λ
na (i )g(xi )
2
16π
i
mk2 =2Λ2
X
Ca (k )
a
ga4 X
na (i )f (xi )
(16π 2 )2 i
including gauge kinetic mixing effects
using [Fonseca, Malinskyi, Porod, Staub, ’11]
2
X
gA
Λ
nA (i )g(xi )
2
16π
i
X
1
T
T
Mkl=Abelian =
Λ
g(x
)G
NQ
Q
NG
i
i
i
16π 2
kl
i
X
X
2
4
mk2 =
Λ2
CA (k )gA
f (xi )nA (i )
(16π 2 )2
i
A6=Abelian
X
+
f (xi )(QkT NGG T NQi )2
MA6=Abelian =
i
17
Manuel E. Krauss
SUSY, Trieste 2013
Particle Content
Q̂
d̂ c
û c
L̂
ê c
ν̂ c
Ŝ
Ĥd
Ĥu
χ̂R
ˆR
χ̄
18
s=0
s= 12
Gen.
Q̃
d̃ c
ũ c
L̃
ẽ c
ν̃ c
S̃
Hd
Hu
χR
χ̄R
Q
dc
uc
L
ec
νc
S
H̃d
H̃u
χ̃R
˜R
χ̄
3
3
3
3
3
3
3
1
1
1
1
Manuel E. Krauss
SU (3)c × SU (2)L
(3, 2)
(3, 1)
(3, 1)
(1, 2)
(1, 1)
(1, 1)
(1, 1)
(1, 2)
(1, 2)
(1, 1)
(1, 1)
U (1)R × U (1)B−L
(0, 61 )
( 21 , − 61 )
(− 12 , − 61 )
(0, − 21 )
( 12 , 21 )
(− 21 , 21 )
(0, 0)
(− 12 , 0)
( 21 , 0)
( 21 , − 21 )
(− 21 , 21 )
SUSY, Trieste 2013
U (1)Y × U (1)χ
( 16 , 41 )
( 13 , − 34 )
(− 23 , 14 )
(− 12 , − 43 )
(1, 14 )
(0, 54 )
(0, 0)
(− 12 , 12 )
( 12 , − 12 )
(0, − 54 )
(0, 54 )
Tadpole equations
5v 2
tβ 2
v2
2
2
mHd − mH
c2β gL2 + gY
+ (gχ − gY χ )2 + R c2βR gχ (gχ − gY χ ) ,
+
u
tβ2 − 1
4
8
2
tβ
25vR
5v 2
BµR = 2 R
mχ̄2 R − mχ2 R −
c2β gχ (gχ − gY χ ) +
c2βR gχ2 ,
tβ − 1
8
16
R
2
1
v
2
2
2
|µ|2 = 2
g 2 + gY
+ (gχ − gY χ )2 (tβ2 − 1)
mH
− mH
t2 −
u β
d
tβ − 1
8 L
5v 2
+ R c2βR (1 + tβ2 )gχ (gχ − gY χ ) ,
16
2
25vR
1
5v 2
2
mχ̄2 R − mχ2 R tβ2R +
|µR | = 2
c2β (tβ2R + 1)gχ (gχ − gY χ ) −
(tβ2R − 1)gχ2
tβ − 1
16
32
Bµ =
R
19
Manuel E. Krauss
SUSY, Trieste 2013
1.06
2000
1.05
tan βR
1500
1.04
1000
1.03
500
1.02
1.01
5000
0
6000
7000
8000
9000 10000 11000 12000
vR [GeV]
20
Manuel E. Krauss
SUSY, Trieste 2013
Messenger Fields
Φ̂1
ˆ
Φ̄
1
Φ̂2
ˆ
Φ̄
2
SU (3)c × SU (2)L
U (1)R × U (1)B−L
( 12 , 0)
(− 12 , 0)
(0, − 13 )
(0, 13 )
(1, 2)
(1, 2)
(3, 1)
(3, 1)
U (1)Y × U (1)χ
( 21 , − 12 )
(− 21 , 12 )
(− 13 , − 12 )
( 13 , 12 )
X
gA2
Λ
nA (i )g(xi ) ,
16π 2
i
X
1
T
T
Λ
g(x
)G
NQ
Q
NG
Mkl=Abelian =
,
i
i
i
16π 2
kl
i
X
X
2
2
4
mk2 =
Λ
C
(k
)g
f (xi )nA (i )
A
A
(16π 2 )2
i
A6=Abelian
X
+
f (xi )(QkT NGG T NQi )2
MA6=Abelian =
i
21
Manuel E. Krauss
SUSY, Trieste 2013
inverse Seesaw mechanism
singlet fields Ŝ generate neutrino masses via inverse Seesaw
Wν = Yν ν̂ c L̂Ĥu + YS ν̂ c Ŝ χ̂R + µS Ŝ Ŝ

0
 √1 v Y
mν =  2 u ν
0
mνIS ' −
√1 vu Y T
ν
2
0
0
√1 vχ Y T
2 R S

√1 vχ YS 

2 R
µS
vu2 T −1
Y Y µS (YST )−1 Yν
vχ2R ν S
i.e.
22
vu
vχR
smallness of ν masses: µS small and/or
ν mixing: structure of µS and/or Yν and/or YS
Manuel E. Krauss
small
SUSY, Trieste 2013
Higgs mass matrix
On tree level, the scalar Higgs mass matrix in the basis (σd , σu , σ̄R , σR )
is given by
2
mh 0 =
 1 2 2 2
2 2
sβ
g̃Σ v cβ + mA
 4s
2 2
2
− 2β (g̃Σ
)
v + 4mA
8


5 g̃ 2 vv c c

8 χ R β βR

5 g̃ 2 vv c s
−8
χ R β β
R
s
2 2
2
− 2β
)
(g̃Σ
v + 4mA
8
1 g̃ 2 v 2 s 2 + m 2 c 2
A β
β
4 Σ
g̃ 2 vv s c
−5
8 χ R β βR
5 g̃ 2 vv s s
8 χ R β βR
5 g̃ 2 vv c c
8 χ R β βR
−5
g̃ 2 vv s c
8 χ R β βR
25 g 2 v 2 c 2 + m 2 s 2
AR βR
16 χ R βR
s2β
2 2
2
)
− 32R (25gχ
vR + 16mA
R
5 g̃ 2 vv c s
−8
χ R β β
2
where g̃Σ2 = gL2 + gY
+ (gχ − gY χ )2 , g̃χ2 = gχ (gχ − gY χ ), and
sx , cx = sin x , cos x .
The parameters mA and mAR are the tree-level masses of the
pseudoscalar Higgs bosons, which are given by
2
2
mA
= Bµ /(sβ cβ ) and mA
= BµR /(sβR cβR ).
R
23
Manuel E. Krauss

R

5 g̃ 2 vv s s

8 χ R β βR

s2β

2 2
2
)
− 32R (25gχ
vR + 16mA
R 
25 g 2 v 2 s 2 + m 2 c 2
AR βR
16 χ R βR
SUSY, Trieste 2013
Neutralino mass matrix

M1

0


 gY vd
− 2

 g v
Mχ̃0 =  Y2 u
 M

Yχ

2


0

0
24
0
M2
gL vd
2
g v
− L2 u
g v
− Y2 d
gY vu
g2 v
− L2 u
gL vd
2
0
−µ
−µ
0
0
(gχ −gY χ )vd
2
0
0
0
0
0
0
Manuel E. Krauss
−
(gχ −gY χ )vu
2
MY χ
2
0
(gχ −gY χ )vd
2
(gχ −gY χ )vu
−
2
Mχ
5gχ vχ̄
R
4
5gχ vχ
R
−
4
SUSY, Trieste 2013
0
0
0
0
5gχ vχ̄
R
4
0
−µR
0
0





0



 .
0

5gχ vχ 
R 
−
4


−µR 
0
Sneutrino mass matrix
2
Mν̃ =

2
v 2 sβ
†
0
2
mL + 2 Yν Yν + DL 1


 √v
Tν sβ − µ∗ Yν cβ

2


1 vv Y † Y s s
R S ν β β
2
2
mν
c
R
+
v
√
Tν† sβ
2
2 s2
vR
βR
†
YS YS
2
v
√R
2
†
TS sβ
R
− µYν† cβ
+
2
v 2 sβ
2
1 vv Y † Y s s
R ν S β βR
2
Yν Yν†
†
− µR YS cβ
R
+
0
1
DR
v
√R
2
TS sβ
mS2 +
−
R
2 s2
vR
βR
2
†
YS YS
1 2
2
2
2
2
2
,
2 − 3gχ + gχ gY χ + 2(gL + gY + gY χ ) v c2β − 5gχ (3gχ + 2gY χ )vR c2β
R
32
5g
χ
0
2
2
DR =
2(gχ − gY χ )v c2β + 5gχ vR c2β
.
R
32
0
25
Manuel E. Krauss
SUSY, Trieste 2013




µ∗
R YS cβR 

with
DL =


,