Electroweak Baryogenesis inNon-Standard Cosmology
Germano Nardini
Universitat Bielefeld
.............................KOSMOLOGIETAG ’12
.............................
Related to works in colloboration withM. Carena, A. Delgado, A. De Simone, M. Quiros,
A. Riotto, N. Sahu, C. Wagner
Germano Nardini EWBG in non-standard cosmology
Outline
Outline
1 EWBG Mechanism Review
2 Effective Theory of the LSS (MSSM)
3 EWBG in the MSSM (Standard Cosmology)
4 EWBG in the MSSM (Non-Standard Cosmology)
Germano Nardini EWBG in non-standard cosmology
EWBG Mechanism Review
The Question: Why this asymmetry?
The Universe is populated by matter. BBN and CMB furnishindependently:
η ≡ nB − nB
nγ= (6.11± 0.19)× 10−10
Mechanisms attempting to produce η must contain theingredients [Sakharov,1967] (if CPT symmetry)
1 B violation
2 C and CP violation
3 Departure from thermal equilibrium
How did the Universe arrive to this asymmetry?
One possible mechanism: EWBG (alternatives: Drewes,Domcke,Wu,Herranen’s talks)
Germano Nardini EWBG in non-standard cosmology
EWBG Mechanism Review
EWBG in the SM and MSSM
Kuzmin, Rubakov and Shapshnikov, Phys.Lett.B155:36,1985;.........
Some EWBG reviews:M. Quiros, hep-ph/9901312A. Riotto, hep-ph/9807454J. Cline, hep-ph/0609145
SM(even with mν = 0) and MSSM contain the Sakh. condts:1 B number is non-perturbative violated
at T 6= 0 (sphalerons) [’t Hooft,76]�������������������������������������������������������������������������������������������
�������������������������������������������������������������������������������������������
L
L
L
Q
Q
Qτ
e
µ
1
2
32 CKM matrix (SM) or Soft Breaking terms (MSSM)contain CP violating phases
3 EWPT (when of 1st order) proceeds by bubble nucleation.Expanding bubbles break the thermal equilibrium.
Germano Nardini EWBG in non-standard cosmology
EWBG Mechanism Review
EWBG in the SM and MSSM
V (φ, T ) ≃ m(T )φ2 + F (T )φ3 + λ(T )φ4
φ
SM(even with mν = 0) and MSSM contain the Sakh. condts:1 B number is non-perturbative violated
at T 6= 0 (sphalerons) [’t Hooft,76]�������������������������������������������������������������������������������������������
�������������������������������������������������������������������������������������������
L
L
L
Q
Q
Qτ
e
µ
1
2
32 CKM matrix (SM) or Soft Breaking terms (MSSM)contain CP violating phases
3 EWPT (when of 1st order) proceeds by bubble nucleation.Expanding bubbles break the thermal equilibrium.
Germano Nardini EWBG in non-standard cosmology
EWBG Mechanism Review
EWBG in the SM and MSSM
V (φ, T ) ≃ m(T )φ2 + F (T )φ3 + λ(T )φ4
φ
φ =0φ >0
φ >0
φ >0
φ >0
φ >0
φ >0
⇒ .
SM(even with mν = 0) and MSSM contain the Sakh. condts:1 B number is non-perturbative violated
at T 6= 0 (sphalerons) [’t Hooft,76]�������������������������������������������������������������������������������������������
�������������������������������������������������������������������������������������������
L
L
L
Q
Q
Qτ
e
µ
1
2
32 CKM matrix (SM) or Soft Breaking terms (MSSM)contain CP violating phases
3 EWPT (when of 1st order) proceeds by bubble nucleation.Expanding bubbles break the thermal equilibrium.
Germano Nardini EWBG in non-standard cosmology
EWBG Mechanism Review
EWBG in the SM and MSSM
V (φ, T ) ≃ m(T )φ2 + F (T )φ3 + λ(T )φ4
φ
CP asymmetry
z
wall
φ 6= 0
φ = 0
qL>qL⇒ .
In (front of) the wall CP asymm. generates temporally qL > qL⇒ There are more sphalerons B↑ than those B↓⇒ Temporally B asymm. is present beyond the wall ⇒ The wallexpansion introduces B > 0 inside the bubble, where
it remains there forever IF sphalerons do not wash out it!!!
Germano Nardini EWBG in non-standard cosmology
EWBG Mechanism Review
EWBG in the SM and MSSM
Sphalerons do not wash out η if ...
Dilution: “Bf ∼ Bi exp[−Γsp(Tn)/H]”
Γsp(Tn) = KTn e−
Esp(Tn)
Tn
⇓ (taking H in rad. era).
Esp(Tn) & 35 Tn
⇓〈φ(Tn)〉 & Tn
... the 1st order phase transition is STRONG
Germano Nardini EWBG in non-standard cosmology
EWBG Mechanism Review
EWBG in the SM and MSSM
EWBG in the SM is ruled out:
The EWPT turns out not to be strong for mh > 75GeV[Kajantie et al.,97]
Small CP asymmetry
And in the MSSM ?New physics at the EW scale may modify the EWPT
New couplings violating CP
Germano Nardini EWBG in non-standard cosmology
Effective Theory
LSS Framework [Carena et al.,96;Delepine et al.,96;Cline et al.,98]
The main features of the LSS spectrum are:
Fermions are at the EW scale (gluino may be a bit heavy)
The tR is lighter than the top quark
The other scalars MQ ≃ mA ≃ ... ≡ m ≫ few TeV
At ≪ m (enhancing the strength of the EWPT)
(A sort of light-stop scenario in SS)
⇓LOW ENERGY EFFECTIVE THEORY
(to avoid large logs)
[Carena,GN,Quiros,Wagner 08,09]
Germano Nardini EWBG in non-standard cosmology
Effective Theory
LE Lagrangian [Carena,GN,Quiros,Wagner 08,09]
The effective Lagrangian is
Leff = m2H†H − λ
2
(H†H
)2 − ht [qLǫH∗tR] + Yt
[HuǫqLt
∗R
]
−√2G Θg tRg
aTatR +
√2J t∗RBtR − 1
6K|tR|2 |tR|2 −Q
∣∣tR∣∣2 |H|2
+H†√2
(guσ
aW a + g′uB)Hu +
HT ǫ√2
(−gdσ
aW a + g′dB)Hd + h.c.
−M3
2Θg g
aga − M2
2WAWA − M1
2BB − µHT
u ǫHd −M2U t∗RtR
EEW (M3) m
tL, bL, Hh, . . .SUSYEFF.
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Standard Cosmology)
Higgs-Stop window 〈φ(Tn)〉/Tn > 1 (µ = 100,M3 = 500)
Condt. 1: tanβ . 15 by EDM and BAUCondt. 2: stab. or metastab. (Tn
SP→CB < T fSP→EWB)
Based on effect. parameters. g3, ht 2-loops T 6= 0 at g3, ht approx
For EDM: Chang et al.,99For BAU: Carena et al.,03; Konstandin et al.,06; D. J. H. Chung et.al.,09
m = 500 TeV m = 8000 TeV
1 1
2 2
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Standard Cosmology)
Higgs-Stop window 〈φ(Tn)〉/Tn > 1 (µ = 100,M3 = 500)
Condt. 1: tanβ . 15 by EDM and BAUCondt. 2: stab. or metastab. (Tn
SP→CB < T fSP→EWB)
EWBG bounds (LEP bound):
mh . 127 GeV mtR. 120 GeV
m & 7 TeV
m = 500 TeV m = 8000 TeV
1 1
2 2
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Standard Cosmology)
Produced B-asymmetry
Different approaches: Carena et al.,03; Konstandin et al.,06;D. J. H. Chung et.al.,09. We apply the intermediate one
2 4 6 8 10 12 14 16 18 20 22 24 26 28 300
2
4
6
8
10
µ = 100 GeV sin φ = 1µ = 250 GeV sin φ = 1µ = 100 GeV sin φ = 0.6µ = 250 GeV sin φ = 0.6
η/ηBBN
tanβ
Calculation strongly depends on details (M1,M2, µ):
⇓Good choice: tanβ ≤ 15 Very conservative: tanβ ≤ 5
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Relaxing Assumption (NON-SC)
-14 -12 -10 -8 -6 -4 -2 0-14 -12 -10 -8 -6 0
replacements
〈φ(Tn)〉Tn
>1
〈φ(Tn)〉Tn
<1
log10 Γ
log10GeVT
T = O(100 GeV) radiation domination
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Relaxing Assumption [Joyce et al.’98]
-14 -12 -10 -8 -6 -4 -2 0-14 -12 -10 -8 -6 0
replacements
〈φ(Tn)〉Tn
>1
〈φ(Tn)〉Tn
<1
log10 Γ
log10GeVT
.
No entropy injection(gain strength,loose η)
[GN, Sahu 11]
Fig. from ’Particle Dark Matter: Observations, Models and Searches’, edited by G. Bertone
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Relaxing Assumption [Joyce et al.’98]
-14 -12 -10 -8 -6 -4 -2 0-14 -12 -10 -8 -6 0
〈φ(Tn)〉Tn
>1
〈φ(Tn)〉Tn
<1
log10 Γ
log10GeVT
Sphal. in equil. in unbroken phase
Hew/Hsc < 1011
Sphal. out-of-equil. in broken phase
〈φ(T )〉T
∣∣∣T=Tn
> D + 135 log
HscHew
, D = 1
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Relaxed window [Carena,GN,Quiros,Wagner in progress]
Hew/Hsc = 1, 103, 106
112 114 116 118 120 122
95
100
105
110
115
120
125
m = 8TeV
mh [GeV]
mt
[GeV
]
112 114 116 118 120 122 124 126 128 130 132
95
100
105
110
115
120
125
m = 106 TeV
mh [GeV]
mt
[GeV
]New upper bounds: mh . 135GeV and mt . 125GeV
New parameter region of the effective couplings: different fingerprintof LSS at LHC for SC/NSC?
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Minimal m for (mh,mtR) = (114.7, 95)GeV
100
101
102
103
104
105
106
107
108
109
4000
5000
6000
7000
Hew/Hsc
m[G
eV]
larger Hew/Hsc, less hierarchy problem !
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Conclusions
Hew = Hsc ⇒ mh . 127 ,GeV, mt . 120GeV
Hew 6= Hsc ⇒ mh . 135 GeV, mt . 125 GeV
GW [D.Chung et al.’10]
Growth of DM (if freeze-out) → no neutralino DM[M.Kamionkowski et al.’90]
Magnetic field evolution ? [T.Stevens et al.’11]
At LHC signatures different from SC? [Menon et al.’09, Cohen etal.’12, Curtin et al.’12, Carena,GN,Quiros,Wagner ’12*]
Applied on MSSM, but general!
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Why EWBG interesting? Pheno connections with
In cosmology (at the electroweak epoch):
Primordial magnetic field
Gravitational waves
Pre-BBN cosmology
...
In particle physics (new physics at the EW scale):
Signatures at colliders
Precision physics (EDMs, ...)
...
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
bkp
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Stop-neutralino
]2 Stop Mass [GeV/c
60 80 100 120 140 160 180
]2
Neu
tral
ino
Mas
s [G
eV/c
40
60
80
100
120
]2 Stop Mass [GeV/c
60 80 100 120 140 160 180
]2
Neu
tral
ino
Mas
s [G
eV/c
40
60
80
100
120
Observed Limit (95% CL)
)σ1±Expected Limit (
]2 Stop Mass [GeV/c
60 80 100 120 140 160 180
]2
Neu
tral
ino
Mas
s [G
eV/c
40
60
80
100
120
c
+ m
1o
χ∼
= m
t~m
1o
χ∼
+ m
b
+ m
W
= m
t~
m
o = 56θLEP o = 0θLEP
-1CDF 295 pb
-1DØ 995 pb
CDF Run II Preliminary -1
L dt=2.6 fb∫
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Matter-Decay Domination
te τ
ΡX
ΡR
S
ΡX
ΡR
19 20 21 22 23-2
0
2
4
6
Log10@t/GeV−1
D
Log 1
0@Ρ
�ΡX
HΤL
D
3 �
4S�
S i
Hew
Hsc
.Hew
Hsc
∣∣∣∣t≡
√teτ
.
√ρXρR
∣∣∣∣t
≃ ρ+Rρ−R
∣∣∣∣1/4
t=τ
= ∆1/6 =
(ηmax
ηexp
)1/6
NO ENHANCEMENT!
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
bkp
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Gauge Coupling Unification
EWBG suggests m ≫TeV. Large modif. from the usualparameter region of the MSSM, which unifies.
EWBG compatible with unification?
(4π)2 ddtgi = g3i bi+
+g3i
(4π)2
[∑3j=1Bijg
2j − dui h
2t − dGi G
2 − dJi J2 − · · ·
]g21 = (5/3)g′2
bLSS =(143
30,− 7
6,− 41
6+ 2Θg
)
bSUSY =(33
5,−2,−3
)
mZ
m
MGUT
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Gauge Coupling Unification
EWBG suggests m ≫TeV. Large modif. from the usualparameter region of the MSSM, which unifies.
EWBG compatible with unification? YES
103
104
105
106
107
1080.11
0.112
0.114
0.116
0.118
0.12
0.122
0.124
0.126
0.128
0.13
α3(M
Z)
m [GeV]
1-σ prediction:
M3 = 500GeV:m = 103.3±0.6 TeV
M3 = 150GeV:m = 101.6±0.6 TeV
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Metastability
Is the transition EWB→CB possible ? NO
150 100 50 0 50 100 150 200
-2e+06 -2e+06
0 0
2e+06 2e+06
4e+06 4e+06
V[G
eV4]
←t | h→300 200 100 0 100 200 300
-2e+08
-1.5e+08
-1e+08
-5e+07
0
V[G
eV4]
←t | h→
SEWB→CB ≫ 135
IT DOESN’T DECAY !60 70 80 90 100 110 120
T0
1000
2000
3000
4000
5000
6000
S 3 / T
Tnh
Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
Carena, Quiros, Riotto, Vilja, Wagner Nucl.PhysB 503Germano Nardini EWBG in non-standard cosmology
EWBG in the MSSM (Non-Standard Cosmology)
mA = 2000GeV
mA = 300GeV
D. Curtin, P. Jaiswal, P. Meade, arXiv:1203.2932Germano Nardini EWBG in non-standard cosmology