Towards a scale free electroweak baryogenesis Teppei Kitahara U.of - - PowerPoint PPT Presentation
Towards a scale free electroweak baryogenesis Teppei Kitahara U.of Tokyo KEK Karlsruhe Collaborators K. Ishikawa, M. Takimoto Based on PRD . 91(2015) 055004, PRL .113(2014) 131801 U.of Toyama theory seminar May 22, 2015,
Teppei Kitahara （U.of Tokyo → KEK→ Karlsruhe） Collaborators：K. Ishikawa, M. Takimoto Based on PRD. 91(2015) 055004, PRL.113(2014) 131801 U.of Toyama theory seminar May 22, 2015, University of Toyama
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Standard Model (SM)
July 2012, Observation of a Higgs boson particle
indiatimes.com
Nobel prize, 2013 2
[ATLAS-CONF-2015-007] [CMS-HIG-14-009]
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
[レオ・レオニ フェイスタオル スイミー]
3
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
[レオ・レオニ フェイスタオル スイミー]
MATTER Anti-MATTER current the Universe
3
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
[レオ・レオニ フェイスタオル スイミー]
MATTER Anti-MATTER
[Planck ’14]
current the Universe
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
[レオ・レオニ フェイスタオル スイミー]
MATTER Anti-MATTER
[Planck ’14]
nB − n ¯
B
s ∼ 10−10
current the Universe
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Baryon Asymmetry of the Universe (BAU)
YB is constant during the expansion of the Universe
A suitable Big Bang Nucleosynthesis (BBN) requires Observed value by Planck/WMAP is consistent with BBN
Planck ’14]
s = π2 45g∗T 3
g∗
YB ≡ nB − n ¯
B
s = (0.86 ± 0.01) × 10−10
[WMAP ’12,
: entropy density : massless degrees of freedom ~ O(10 -100)
nB ∝ a(t)−3 ∝ T 3
[Copi, et.al. ’95]
0.4 × 10−10 . YB . 0.9 × 10−10
nB ∼ n ¯
B + s × 10−10
where
4
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Baryon Asymmetry of the Universe (BAU)
YB is constant during the expansion of the Universe
A suitable Big Bang Nucleosynthesis (BBN) requires Observed value by Planck/WMAP is consistent with with BBN
Planck ’14]
s = π2 45g∗T 3
g∗
YB ≡ nB − n ¯
B
s = (0.86 ± 0.01) × 10−10
[WMAP ’12,
: entropy density : massless degrees of freedom ~ O(10 -100)
nB ∝ a(t)−3 ∝ T 3
[Copi, et.al. ’95]
0.4 × 10−10 . YB . 0.9 × 10−10
nB ∼ n ¯
B + s × 10−10
where
4
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
The following 3 necessary conditions are required for the Baryogenesis
i) Baryon number violating process ii) Violation of C and CP symmetries iii) Out of thermal equilibrium
[Sakharov, ’67]
5
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
The following 3 necessary conditions are required for the Baryogenesis
i) Baryon number violating process ii) Violation of C and CP symmetries iii) Out of thermal equilibrium SM is satisfied the conditions (i) and (ii)
(i) Anomalous process (sphaleron), Next Slide (ii) SM dose not have C symmetry, SM has CKM matrix
[Sakharov, ’67]
5
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Anomaly calculations of Baryon number and Lepton number axial current
✓ uL dL ◆ ✓ ν eL ◆ ¯ uR ¯ dR ¯ eR a b c d e B + L B − L 1/3 1/3 −1/3 −1/3 −1/3 −1/3 −1 −1 1 1
B+L/B-L axial current Gauge Gauge
SU(3)c SU(2)L U(1)Y
∝ 2a + b + c = ⇢ 0 (B + L) 0 (B − L) / 3a + d = ⇢ 2 6= 0 (B + L) 0 (B L)
/6 ✓1 6 ◆2 a + 3 ✓ 2 3 ◆2 3 ✓1 3 ◆ + 2 ✓ 1 2 ◆ d + (1)2e = ⇢ 1 6= 0 (B + L) 0 (B L)
6
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Anomaly calculations of Baryon number and Lepton number axial current
✓ uL dL ◆ ✓ ν eL ◆ ¯ uR ¯ dR ¯ eR a b c d e B + L B − L 1/3 1/3 −1/3 −1/3 −1/3 −1/3 −1 −1 1 1
B+L/B-L axial current Gauge Gauge
SU(3)c SU(2)L U(1)Y
∝ 2a + b + c = ⇢ 0 (B + L) 0 (B − L) / 3a + d = ⇢ 2 6= 0 (B + L) 0 (B L)
/6 ✓1 6 ◆2 a + 3 ✓ 2 3 ◆2 3 ✓1 3 ◆ + 2 ✓ 1 2 ◆ d + (1)2e = ⇢ 1 6= 0 (B + L) 0 (B L)
B-L axial current is anomaly free in the SM, but B+L axial current is anomalous 6
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 B+L chiral anomaly SU(2) gauge field has a topologically non-trivial field configuration in 3(4) dimensional Euclidean space
∂µjµ,5
B+L =
3 16π2 ⇣ g2Tr(Fµν ˜ F µν) − g02Bµν ˜ Bµν ⌘ F µν ≡ 1 2✏µνρσFρσ
where
sphaleron (instanton) solution
V Winding #
1
2 ∝ B+L #
vacuum tunneling (instanton) thermal tunneling (sphaleron)
[’t Hooft ’76 ]
7
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Sphaleron process is a non-perturbative 9 left handed quarks and 3 left handed lepton vertex
[Illustrated by Morrissey, Ramsey-Musolf]
∆B = 3 ∆L = 3
condition (i)! T > TC TC : Electroweak phase transition temperature (Symmetric vacuum, massless weak bosons)
Γsph ∼ α4
W T
At high temperature, the sphaleron process is always active 8
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Decoupling condition
[Funakubo, Senaha ’09]
Once electroweak symmetry is broken, the sphaleron process becomes decouple T < TC Γsph ∼ T Exp " −24 √ 2π g v T # ⌧ H(T) Decouple!
∼ 0.9
vC TC >
Γins ∼ 1 R Exp ✓ −8π2 g2 ◆ cf.
∆B = 3 ∆L = 3
9
vC TC & 0.9 : Condition of a “strongly” 1st order phase transition
(Breaking vacuum, massive weak bosons)
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Electroweak Baryogenesis (EWBG) is one of the baryogenesis scenarios A first order phase transition involved with electroweak symmetry breaking gives the out of thermal equilibrium Experimentally testable scenario thermal tunneling
[Morrissey, Ramsey-Musolf ’12] [Kuzmin, Rubakov, Shaposhnikov ’85, Shaposhnikov ’86, ’87 ] [’t Hooft ’76 ]
10 V thermal tunneling
vEW
[Illustrated by Morrissey, Ramsey-Musolf]
Bubble expansion
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
[Kuzmin, Rubakov, Shaposhnikov ’85, Shaposhnikov ’86, ’87 ] [Morrissey, Ramsey-Musolf ’12] [’t Hooft ’76 ]
Baryon number violation
hφi = 0
Symmetric vacuum Breaking vacuum Bubble W all Bubble W all ① Interaction between matter and bubble generate spacial CP (Baryon) asymmetric distribution
hφi 6= 0
② Baryon # is fixed because sphaleron process is decoupled when 11 vC TC & 0.9
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Within the standard model, EWBG mechanism can not be realized Within the MSSM, EWBG mechanism is still alive, but severe Higgs (scalar) sector extended models can achieve the electroweak phase transition easily MSSM+singlet, 2HDM, SM + complex singlet, etc... , CKM phase is insufficient
mh . 70 GeV
[Bochkarev, Shaposhnikov ’87, Kajantie, Laine, Rummukainen, Shaposhnikov ’96 ]
m˜
tL 50 TeV, m˜ tR . 110 GeV
σ(gg→h)が2.5倍以上。和らげるにはBr(h→inv.) > 30 - 60 % →excluded by global fit... [Carena, Nardini, Quiros, W agner ’13 ]
Constraints: EDM, direct search for additional scalar, Higgs coupling, Bphys. etc... These scenario are alive and testable by the future experiments! 12
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Within the standard model, EWBG mechanism can not be realized Within the MSSM, EWBG mechanism is still alive, but severe Higgs (scalar) sector extended models can achieve the electroweak phase transition easily MSSM+singlet, 2HDM, SM + complex singlet, etc... , CKM phase is insufficient
mh . 70 GeV
[Bochkarev, Shaposhnikov ’87, Kajantie, Laine, Rummukainen, Shaposhnikov ’96 ]
m˜
tL 50 TeV, m˜ tR . 110 GeV
σ(gg→h)が2.5倍以上。和らげるにはBr(h→inv.) > 30 - 60 % →excluded by global fit... [Carena, Nardini, Quiros, W agner ’13 ]
Constraints: EDM, direct search for additional scalar, Higgs coupling, Bphys. etc... These scenario are alive and testable by the future experiments! 12
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Within the standard model, EWBG mechanism can not be realized Within the MSSM, EWBG mechanism is still alive, but severe Higgs (scalar) sector extended models can achieve the electroweak phase transition easily MSSM+singlet, 2HDM, SM + complex singlet, etc... , CKM phase is insufficient
mh . 70 GeV
[Bochkarev, Shaposhnikov ’87, Kajantie, Laine, Rummukainen, Shaposhnikov ’96 ]
m˜
tL 50 TeV, m˜ tR . 110 GeV
σ(gg→h)が2.5倍以上。和らげるにはBr(h→inv.) > 30 - 60 % →excluded by global fit... [Carena, Nardini, Quiros, W agner ’13 ]
Constraints: EDM, direct search for additional scalar, Higgs coupling, Bphys. etc... These scenario are alive and testable by the future experiments! 12
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Since electroweak phase transition occurs at T ～100 GeV (electroweak scale), the relevant dimensional parameters must be set at ～100 GeV so that the experimental constraints are severe How about if phase transition occurs much higher the electroweak scale? But when a Lagrangian has L violating interactions that are relevant only the broken phase, the B-L number is generated from B+L which is generated by phase transition, and baryon asymmetry can survive Scale free electroweak baryogenesis Baryon asymmetry is washed out by the sphaleron process
NOTE: phase transitionをトリガーにしてバリオン数を生成しているので、Leptogenesisとは 異なる
制限さえなければ、Baryon数は稼げる
13
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Since electroweak phase transition occurs at T ～100 GeV (electroweak scale), the relevant dimensional parameters must be set at ～100 GeV so that the experimental constraints are severe How about if phase transition occurs much higher the electroweak scale? But when a Lagrangian has L violating interactions that are relevant only the broken phase, the B-L number is generated from B+L which is generated by phase transition, and baryon asymmetry can survive Scale free electroweak baryogenesis Baryon asymmetry is washed out by the sphaleron process
NOTE: phase transitionをトリガーにしてバリオン数を生成しているので、Leptogenesisとは 異なる
制限さえなければ、Baryon数は稼げる
13
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Since electroweak phase transition occurs at T ～100 GeV (electroweak scale), the relevant dimensional parameters must be set at ～100 GeV so that the experimental constraints are severe How about if phase transition occurs much higher the electroweak scale? But when a Lagrangian has L violating interactions that are relevant only the broken phase, the B-L number is generated from B+L which is generated by phase transition, and baryon asymmetry can survive Scale free electroweak baryogenesis Baryon asymmetry is washed out by the sphaleron process
NOTE: phase transitionをトリガーにしてバリオン数を生成しているので、 Leptogenesisとは異なる 制限さえなければ、Baryon数は稼げる
13
/45
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
① Introduction to the electroweak baryogenesis ② Towards scale free electroweak baryogenesis
Resonant singlino dark matter via SM Higgs boson Radiative Singlino mass Experimental constraints
③ Singlino dark matter
Towards scale free electroweak baryogenesis
④ Result and summary Next 14
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 15
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
vEW vEW
～100 GeV sphaleron ON sphaleron ON sphaleron ON sphaleron ON sphaleron OFF sphaleron OFF sphaleron OFF sphaleron OFF
Lepton number violation process is decouple by the Boltzmann suppression
Γ6L < H
B − L > 0
B-L number is generated via the Lepton number violation process
Usual Our proposal
Sphaleron rate (chiral anomaly)
∼ MSUSY
Γsph ∼ α4
W T @T > TC
∆B = 3 ∆L = 3
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
vEW vEW
～100 GeV sphaleron ON sphaleron ON sphaleron ON sphaleron ON sphaleron OFF sphaleron OFF sphaleron OFF sphaleron OFF
Lepton number violation process is decouple by the Boltzmann suppression
Γ6L < H
B − L > 0
B-L number is generated via the Lepton number violation process
Usual Our proposal
Sphaleron rate (chiral anomaly)
∼ MSUSY
Γsph ∼ α4
W T @T > TC
∆B = 3 ∆L = 3
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Main motivation : the hierarchy problem cancelation of the quadratic divergence due to the SUSY particle loop SUSY models have a candidate of the dark matter as a lightest supersymmetric particle (LSP) But, EWMG in the MSSM is difficult
[Illustration: CERN & IES de SAR]
Minimal Supersymmetric Standard Model (MSSM)
×2 ×2
17
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Superpotential of the Minimal Supersymmetric Standard Model (MSSM) Some mass parameters are related to the electroweak scale (Z boson mass) via a spontaneous symmetry breaking μ : Higgsino mass parameter μ parameter must know the SUSY breaking scale...
μ problem
[Kim, Nilles, ’84]
µ2 = −1 2M 2
Z + m2 2 tan2 β − m2 1
1 − tan2 β ∼ MSUSY
18
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
[Nilles, Srednicki, Wyler ’83]
Singlet extension of the MSSM can solve the μ problem through the vev of the singlet scalar
W = λ ˆ S ˆ H2 ˆ H1 + f[ ˆ S] + WYukawa
µeff = λhSi ⇠ MSUSY
W e should control the singlet superfield potential f[S] properly in order to avoid other μ- like problem and an undesirable NG boson
ˆ
One of the models: Next-to Minimal Supersymmetric standard model (NMSSM)
Discrete Z3 symmetry Main motivation
W = λ ˆ S ˆ H2 ˆ H1+κ 3 ˆ S3 + WYukawa
However NMSSM suffers from a dangerous domain wall problem! MSSM + gauge singlet superfield ˆ
S = (S, ˜ S)
19
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
[Nilles, Srednicki, Wyler ’83]
Singlet extension of the MSSM can solve the μ problem through the vev of the singlet scalar
W = λ ˆ S ˆ H2 ˆ H1 + f[ ˆ S] + WYukawa
µeff = λhSi ⇠ MSUSY
W e should control the singlet superfield potential f[S] properly in order to avoid other μ- like problem and an undesirable NG boson
ˆ
One of the models: Next-to Minimal Supersymmetric standard model (NMSSM)
Discrete Z3 symmetry Main motivation
W = λ ˆ S ˆ H2 ˆ H1+κ 3 ˆ S3 + WYukawa
However NMSSM suffers from a dangerous domain wall problem! MSSM + gauge singlet superfield ˆ
S = (S, ˜ S)
19
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
W e discuss the phenomenology of the following Lagrangian In such a case, the effective μ term is If one assumes the following model as a UV theory, the above Lagrangian is generated as a low energy effective theory
with [Panagiotakopoulos, Pilaftsis ’01]
m2
12 ∼ O(M 2 SUSY),
tS ∼ O(M 3
SUSY)
W e used this Lagrangian
µeff ∼ −λ tS m2
S
∼ O(MSUSY)
e.g.
Fat Higgs Model
[Jeong, Shoji, Y amaguchi ’12]
Peccei-Quinn invariant NMSSM
[Harnik, Kribs, Larson, Murayama ’04]
WnMSSM = λ ˆ S ˆ H2 ˆ H1+m2
12
λ ˆ S + WYukawa
Vsoft = m2
S|S|2 + (λAλH2H1S+tSS + h.c.) + V MSSM soft
Nearly Minimal Supersymmetric Standard Model (nMSSM)
[Panagiotakopoulos, Tamvakis ’99]
20
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
The nearly Minimal Supersymmetric standard model (nMSSM) Discrete Z5 R-symmetry
[Panagiotakopoulos, Tamvakis ’99]
W = λ ˆ S ˆ H2 ˆ H1 + WYukawa+ Planck suppress terms
Discrete R-symmetry breaking [Panagiotakopoulos, Pilaftsis ’01]
Wtad ' M 2
SUSY ˆ
S, Vtad ' M 3
SUSYS
Linear conbi. of the R and PQ symmetry
WnMSSM = λ ˆ S ˆ H2 ˆ H1+m2
12
λ ˆ S + WYukawa
,
Domain wall is not a problem because it can be diluted by inflation
21
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
W e have considered about the MSSM+Singlet with Lepton violation sector The nearly MSSM with vector-like multiplets
WnMSSM = λ ˆ S ˆ H2 ˆ H1+m2
12
λ ˆ S + WYukawa
Z5
R
Z3
Z2
Solution of the μ problem Forbid a rapid decay of a dark matter The vector-like multiplet parity
To obtain a sizable thermal corrections to Higgs potential
22
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 W e have considered about the MSSM+Singlet with Lepton violation sector The nearly MSSM with vector-like multiplets
WnMSSM = λ ˆ S ˆ H2 ˆ H1+m2
12
λ ˆ S + WYukawa
Z5
R
Z3
Z2
Solution of the μ problem Forbid a rapid decay of a dark matter The vector-like multiplet parity
+W6Z2
slightly broken
・small mixing ε ・small Lepton number violation ε
W6Z2 / ✏ ⌧ 1
To obtain a sizable thermal corrections to Higgs potential
22
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
W6Z2 ✏N
✏
✏S
(✏, ✏S, ✏N ⌧ 1)
a small Lepton number violation term
23
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
W6Z2 ✏N
✏
✏S
(✏, ✏S, ✏N ⌧ 1)
a small Lepton number violation term W e have considered a thermal potential as follows zero temperature Coleman-W einberg potential T ree level potential improved one-loop thermal potential
x = m(φ) T
V (φi, T)
Full potential
vEW
sphaleron ON sphaleron ON sphaleron OFF sphaleron OFF sphaleron OFF εN process is decouple by the
Boltzmann suppression of
Γ6L < H
B − L > 0
Generated Lepton # decreases by εN process
∼ MSUSY
¯ N 0 23
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
W e have considered a full thermal potential as follows Zero temperature Coleman-W einberg potential T ree level potential Improved one-loop thermal potential
V (φi, T)
Full potential
24
VCW(φi) =
with
m(φ) → m(φ, T), Thermal potential → Improved one-loop thermal potential
x = m(φ, T) T
for scalers and longitudinal gauge bosons
→ Vthermal mass = m(φ, T)2T 2
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Scalar potential (T ree + thermal mass) Minimization condition φs = −
tS m2
s,0 + λ2φ2 + y2 ST 2 ∼ O(MSUSY)
∼ −M 2 + y2
φT 2 +
λ2t2
S
(m2
s,0 + y2 ST 2)2
! φ2 + ¯ λ2 − λ4t2
S
(m2
s,0 + y2 ST 2)3
! φ4 + O(φ6)
This potential can have negative effective quartic coupling 25
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 Analyses on benchmark point ① ② ③ ④ ⑤ ⑥ ⑦ 3 scalar fields potential Minimal direction 26
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 Analyses on benchmark point ① ② ③ ④ ⑤ ⑥ ⑦ 3 scalar fields potential Minimal direction Phase transition
26
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
wall
Analyses on the benchmark point Action
Γ V ∼ T 4e−S(T ), S(T) ≡ S3 T
S(T) . 130:Tunneling
∆φ T & 0.9
(∆φ T & 1.3 @ v = 246 GeV nortation)
:Sphaleron decoupling Bounce profile Behavior of tanβ Analyses on the benchmark point
LwT ∼ 30, ∆β ∼ 0.1
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Lepton number violation rate The strongly 1st order phase transition occurs (T = T1st) At the broken vacuum ( Troll < T < T1st )
with
✏N
λ1
S
N 0
¯ N 0 ¯ N 0 ¯ N 0
with
B-L number is generated from B+L number via Lepton number decreasing Assumption in our study 28
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
At the symmetric vacuum (after turn back, T < Troll) Final Baryon asymmetry
with
✏N
λ1
S
N 0
¯ N 0 ¯ N 0 ¯ N 0
When are satisfied, the baryon asymmetry generated by the phase transition can exist until today Boltzmann suppressed (T << MV
ector)
6= 0 6= 0
Ndec 1, Nw ⌧ 1
Ndec ∼ 8, Nw ∼ 0.2 @Benchmarck + ✏N = 10−5 YB(Tf) ∼ 0.3 × YB(T1st)
, 29
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 30
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
In the nMSSM, Singlino belongs to the neutralinos, and its tree-level mass is obtained by the Higgsino-Singlino mixing Typically Singlino mass is 1-10 GeV due to the SUSY breaking suppression If one imposes a matter parity originated from U(1)B-L symmetry, the LSP (Singlino- like) becomes stable and a candidate of the dark matter
Basis
m˜
s ∼ λ2
v2 MSUSY sin 2β
∼ O(1 − 10)GeV
SUSY breaking suppression
No mass term
a ad u
31
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
In the nMSSM, Singlino belongs to the neutralinos, and its tree-level mass is obtained by the Higgsino-Singlino mixing Typically Singlino mass is 1-10 GeV due to the SUSY breaking suppression If one imposes a matter parity originated from U(1)B-L symmetry, the LSP (Singlino- like) becomes stable and a candidate of the dark matter
Basis
m˜
s ∼ λ2
v2 MSUSY sin 2β
∼ O(1 − 10)GeV
SUSY breaking suppression
No mass term
a ad u
31
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 Singlino mass receive a significant one-loop radiative correction This contribution was not treated / noticed in literature Charged Higgs (NG) boson and charged Higgsino loop is dominant contribution tree mass radiative mass
m˜
s ∼ λ2
v2 MSUSY sin 2β
m1-loop
˜ s
∼ λ2 (4π)2 MSUSY sin 2β
[Ishikawa, TK, Takimoto ’14]
Novelty 32
a ad u
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
1 2 5 10 20 50 1 5 10 50 100 0.5
m [GeV]
s
~
M [ T e V ]
S
tree
tanβ = 2 tanβ = 5 tanβ = 10
λ = 0.75
All dimensionful parameters = MS
Plot of the radiative singlino mass: including full one-loop radiative corrections to the neutralino 5×5 matrix
m˜
s ∼ λ2
v2 MSUSY sin 2β
m1-loop
˜ s
∼ λ2 (4π)2 MSUSY sin 2β
[Ishikawa, TK, Takimoto ’14]
33
/45
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
Typically, Singlino dark matter becomes overabundance of the Universe due to the small couplings to the SM particle When the radiative Singlino mass is about 60GeV , the annihilation cross section is enhanced thanks to the s-channel SM Higgs boson exchange In order to understand this “resonant Singlino scenario”, at first we consider the following low energy effective theory : Free parameters are Singlino mass and Singlino-Higgs coupling
MSUSY MEW
SM particles + singlino Other SUSY particles
Singlino mass Singlino-Higgs coupling
−Leff ⊃ +m˜
s
2 ˜ s˜ s+λeff 2 h˜ s˜ s
SM particles
h S
～
S
～
λeff
Singlino resonant pair-annihilation process
mh ' m˜
s
2
34
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Typically, Singlino dark matter becomes overabundance of the Universe due to the small couplings to the SM particle When the radiative Singlino mass is about 60GeV , the annihilation cross section is enhanced thanks to the s-channel SM Higgs boson exchange In order to understand this “resonant Singlino scenario”, at first we consider the following low energy effective theory : Free parameters are Singlino mass and Singlino-Higgs coupling
MSUSY MEW
SM particles + singlino Other SUSY particles
Singlino mass Singlino-Higgs coupling
−Leff ⊃ +m˜
s
2 ˜ s˜ s+λeff 2 h˜ s˜ s
SM particles
h S
～
S
～
λeff
Singlino resonant pair-annihilation process
mh ' m˜
s
2
34
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Typically, Singlino dark matter becomes overabundance of the Universe due to the small couplings to the SM particle When the radiative Singlino mass is about 60GeV , the annihilation cross section is enhanced thanks to the s-channel SM Higgs boson exchange In order to understand this “Resonant Singlino Scenario”, at first we consider the following low energy effective theory : Free parameters are Singlino mass and Singlino-Higgs coupling
MSUSY MEW
SM particles + singlino Other SUSY particles
Singlino mass Singlino-Higgs coupling
−Leff ⊃ +m˜
s
2 ˜ s˜ s+λeff 2 h˜ s˜ s
SM particles
h S
～
S
～
λeff
Singlino resonant pair-annihilation process
mh ' m˜
s
2
34
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 40 45 50 55 60 65 0.002 0.005 0.01 0.02 0.05 0.1
m [GeV]
s
~
λ eff
Ω /Ω = 1 0.1 0.5
c s ~
[Ishikawa, TK, Takimoto ’14]
W e estimated a thermal relic abundance of the Singlino dark matter by calculating Boltzmann eqs.
Singlino mass Singlino-Higgs coupling
−Leff ⊃ +m˜
s
2 ˜ s˜ s+λeff 2 h˜ s˜ s
SM particles
h S
～
S
～
λeff
ΩCDMh2 = 0.1199
[Planck ’14]
35
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
singlino mass singlino-Higgs coupling
m1-loop
˜ s
∼ λ2 (4π)2 MSUSY sin 2β
λ1-loop
eff
∼ λ4 (4π)2 v MSUSY sin 2β
−Leff ⊃ +m˜
s
2 ˜ s˜ s+λeff 2 h˜ s˜ s
λtree
eff
∼ √ 2λ v MSUSY sin 2β
36
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
singlino mass singlino-Higgs coupling
m1-loop
˜ s
∼ λ2 (4π)2 MSUSY sin 2β
λ1-loop
eff
∼ λ4 (4π)2 v MSUSY sin 2β
negligible
∼ 60 GeV ∼ O(0.01)
−Leff ⊃ +m˜
s
2 ˜ s˜ s+λeff 2 h˜ s˜ s
λtree
eff
∼ √ 2λ v MSUSY sin 2β
MSUSY ∼ O(10) TeV, tan β ∼ O(1), λ ∼ O(1)
21
40 45 50 55 60 65 0.002 0.005 0.01 0.02 0.05 0.1
m [GeV]
s
~λ eff
Ω / Ω = 1 0.1 0.5 c s ~[Ishikawa, TK, Takimoto ’14]
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
This resonant Singlino scenario can be probed by the following two type experiments
① Precision measurement of Higgs invisible decay ② Direct dark matter detection
37
[http://graphics.latimes.com/]
Search for the dark matter-nucleon scattering Search for the Higgs invisible decay to the dark matter
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
a Direct DM detection constrains the spin-independent scattering cross section between the dark matter and the nucleons When the SM Higgs boson is integrated out, the following Singlino-fermions (gluons) 4- point effective vertex are obtained
② Direct dark matter detection
Leff = λeff 2 √ 2m2
h
¯ ˜ s˜ s X
i
(yi ¯ fifi) − αs 4πvEW GµνGµν ! fN is Higgs - nucleons coupling fN strongly depends on a hadronic matrix elements, which are evaluated by a lattice simulation
σ(˜ sN → ˜ sN) = λ2
eff
2πv2
EW
f 2
N
m4
Nm2 ˜ s
m4
h(m˜ s + mN)2
fNmN ⌘ hN| X
q
mq¯ qq αs 4π GµνGµν|Ni
fN ' 0.33
[Y
σSI ' 10−46 ✓ λeff 0.01 ◆2 [cm2]
[Andreas, Hambye, Tytgat ’08]
様々なestimateがある dominant uncertaintyを生む
38
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Current experimental bounds and Future prospects
detection exp.
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
[Ishikawa, TK, Takimoto ’14]
Blue/Green Line Direct DM detection
Current bound (solid lines), and future prospects (dashed lines)
40
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 41
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
,
Blue, Green Green ¯ B → Xsγ Constraint by
This scenario works in Green region
(T = 0)
Benchmark point 42 Singlino dark matter
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
eL eL eR eR ˜ eR ˜ eL ˜ νe
where therefore
43
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
W e have proposed a new type of the electroweak baryogenesis scenario with the nMSSM including vector-like multiples that have the Lepton number violation process The thermal mass term for the singlet scalar field generates the global minimum of the potential for the Higgs field far from the origin at T ～ MSUSY The Lepton number violating process converts the B + L number to the B - L number, and the Lepton number violating process is decoupled at the low energy scale In this baryogenesis process, MSUSY can be an arbitrary value and it is almost a free parameter If MSUSY ～ O(10) TeV , this scenario is compatible with the proper Higgs boson mass and the right amount of the singlino dark matter without SUSY flavor/CP problem (Resonant Singlino DM scenario) This scenario is testable in the future direct dark matter search and the EDM experiments
44 Strongly 1st-order phase transition at T ～ MSUSY ! Baryogenesis! Scale free!
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Including the CP-violation sources explicitly, the concrete estimation of the B+L number which is generated by the first-order phase transition The full analysis of the stability against the charged Higgs field direction More simplified toy model
45 Kadanoff-Baym equation, diffusion equation, Resonant flavor oscillation effect
nMSSM模型は荷電Higgsの方向にポテンシャルが不安定になりやすい。もし荷電Higgs方向 に真空期待値を持つと、U(1)EMが破れてしまう。これを理論的な制限ととらえて解析を行う
M 2
charged = m2 1 + m2 2 + 2λ2s2 + g2
2 (v2
1 + v2 2)
Teppei KITAHARA, Phys.Rev. D91 (2015) 5, 055004, [arXiv:1410.5432]
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 40 45 50 55 60 65 0.002 0.005 0.01 0.02 0.05 0.1
m [GeV]
s
~
λ eff
I L C 2 5 G e V HL - LHC Ω /Ω = 1 0.1 0.5
c s ~
global ft CMS
[Ishikawa, TK, Takimoto ’14]
Pink Line Higgs invisible decay
① recision measurement of Higgs invisible decay
Current bound (solid lines) and future prospects (dashed line)
SM particles
h S
～
S
～
λeff
Γ(h → ¯ ˜ s˜ s) = λ2
eff
16π mh ✓ 1 − 4m2
˜ s
m2
h
◆ 3
2
HL-LHC ILC
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
VB = − 8 π2 T 4 1 Γ(5) Z ∞ y4dy p x2 + y2 1 e √
x2+y2 − 1
VF = − 8 π2 T 4 1 Γ(5) Z ∞ y4dy p x2 + y2 1 e √
x2+y2 + 1
x = m(φ) T
with [Joseph I. Kapusta ’89]
m(φ) → m(φ, T), Thermal potential → Improved one-loop thermal potential Note:
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Thermal tunneling rate per unit volume Thermal tunneling condition Euclidean action in three dimensions: Bounce solutions:
S3 = SE3[¯ φ] − SE3[φf]
¯ φ
Γtrans. V ∼ T 4e−S(T ), S(T) ≡ S3 T
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
10 50 20 30 15 1 10 5 2 8
M [ T e V ]
S
tanβ
λ(mh= 125.5 GeV)
λ=λ max λ=0 mh < 125.5 GeV mh > 125.5 GeV
0 ≤ λ ≤ λmax
Resonant Singlino DMシナリオをnMSSMのパラメータ上で見る 最初にHiggsの質量を125.5 GeVに固定する
[Ishikawa, TK, Takimoto ’14]
λを変化させる stopの寄与 extra F term の寄与 白い領域はmh = 125.5
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
10 50 20 30 15 1 10 5 2 8
M [ T e V ]
S
tanβ
λ(mh= 125.5 GeV)
λ=λ max λ=0 mh < 125.5 GeV mh > 125.5 GeV
0 ≤ λ ≤ λmax
Resonant Singlino DMシナリオをnMSSMのパラメータ上で見る 最初にHiggsの質量を125.5 GeVに固定する
[Ishikawa, TK, Takimoto ’14]
λを変化させる stopの寄与 extra F term の寄与 白い領域はmh = 125.5
λ . 0.75 - 0.85
Landau pole constraint:
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
10 50 20 30 15 1 10 5 2 8
M [ T e V ]
S
tanβ
0.005
λ(mh= 125.5 GeV)
λ=λ max λ=0 mh < 125.5 GeV mh > 125.5 GeV
ms = 60 GeV
～100 200 20 λef = 0.01 0.001
40 45 50 55 60 65 0.002 0.005 0.01 0.02 0.05 0.1
m [GeV]
s
~λeff
XENON1T XENON100 (2012) LUX - 300 live days LUX (2013) - 85 live days I L C 2 5 G e V HL - LHC Ω /Ω = 1 0.1 0.5 c s ˜ g lFull One-loop radiative correctionsを含んだ Singlino 質量 (赤線) Singlino-Higgs coupling (青線)
[Ishikawa, TK, Takimoto ’14]
λtree
eff
= √ 2λ
11N ⇤ 14N ⇤ 15 + ZH 12N ⇤ 13N ⇤ 15 + ZH 13N ⇤ 13N ⇤ 14
ZH
11N ⇤ 11N ⇤ 13 − ZH 12N ⇤ 11N ⇤ 14
11N ⇤ 12N ⇤ 13 + ZH 12N ⇤ 12N ⇤ 14
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
10 50 20 30 15 1 10 5 2 8
M [ T e V ]
S
tanβ
0.005
λ(m
h
= 125.5 GeV)
λ = λmax λ = mh < 125.5 GeV mh > 125.5 GeV
ILC 250 GeV
ms = 60 GeV
～100 200 20 λeff = 0.01 0.001
XENON1T
L U X
Singlino 暗黒物質の残存量 (紫線) 観測からの制限 (① Higgs invisible decay, ② Direct DM detections )
Ω˜
s/Ωc = 1
Ω˜
s/Ωc < 1
40 45 50 55 60 65 0.002 0.005 0.01 0.02 0.05 0.1
m [GeV]
s
~λeff
XENON1T XENON100 (2012) LUX - 300 live days LUX (2013) - 85 live days I L C 2 5 G e V HL - LHC Ω /Ω = 1 0.1 0.5 c s ˜ g l[Ishikawa, TK, Takimoto ’14]
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
Fat Higgs模型
[Harnik, Kribs, Larson, Murayama ’04]
Weff = λ ˆ N( ˆ H2 ˆ H1 − v2
0)
Strong dynamicsの模型。Higgs場は 他の場がcompositeしたmesonと考える
[Jeong, Shoji, Y amaguchi ’12]
Peccei-Quinn invariant NMSSM
κm3/2 f 2
a
MPl ∼ O(M 2
SUSY)
U(1)PQ
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45
GUT scale ( ) 以下は摂動論で扱えると仮定 (no Landau pole)
λは基本的には繰り込みスケールに対して単調増加
λ(Q = MGUT) = √ 4π (Q = MSUSY) top Y ukawaが Landau poleを持つ bottom/tau Y ukawaが Landau poleを持つ
λ . 0.75 - 0.85
Landau pole constraint:
但し、additional gauge symmetryや extra particleの導入で、制限は和らぐ [Kyae, Shin ’13]
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
/45 In the nMSSM, there is a sizable tree-level contribution to the Higgs boson mass. When integrating out heavy SUSY particles and matching with the SM, the SM Higgs quartic coupling is Large λ and small tanβ can give a sizable contribution to the Higgs boson mass In this paper, we calculate the Higgs boson mass using the two- loop renormalization group equation including the above matching condition
λSM = g2 + g02 4 cos2 2β+λ2 2 m2
S − A2 λ
m2
S
sin2 2β
[Giudice, Strumia ’12]
/45
May 22, 2015, Theory Seminar, University of Toyama, Teppei KITAHARA - KEK
However these interactions cause a quadratic divergence of tadpole term “Minimal” NMSSM
. L. White ’95]
W = λ ˆ S ˆ H2 ˆ H1 + κ 3 ˆ S3 + WYukawa+ λ0 MPl ⇣ ˆ S4 + ˆ S2 ˆ H1 ˆ H2 + ( ˆ H1 ˆ H2)2⌘
Wtad ' 1 (16π2)2 λ0 MPl MSUSYΛ2 ˆ S µeff ∼ 1 (16π2)2 λ0 MPl Λ2
λ0 ⌧ 1
with
λ0 < 1011
µeff ∼ MSUSY
The minimal NMSSM cannot solve the μ problem and the domain wall problem simultaneously. Condition that the domain wall collapse before the BBN: λ0 > 107
To solve the μ problem,
explicit Z3 breaking term
Typical effective μ term