electroweak baryogenesis in the next-to-mssm · 2007. 3. 6. · features of the nmssm • 5 neutral...
TRANSCRIPT
Electroweak Baryogenesis in theNext-to-MSSM
SHUICHIRO TAO (KYUSHU UNIV.)
WITH KOICHI FUNAKUBO (SAGA UNIV.)
YITP - June 30, 2004 – p.1
Summary
• One-loop formulation with all CP phases
• Parameter search→ mass bounds for the charged Higgs boson
• EWPT in CP conserving case
• Higgs spectrum in CP violating case
Todo
• EWPT in CP violated case
YITP - June 30, 2004 – p.2
Features of the NMSSM
• 5 neutral and 1 charged scalars(3 scalar and 2 pseudoscalar when CP cons.)The lightest Higgs scalar H1 can escape from the bound
mHSM > 114GeV
because of small gH1ZZ , ⇒ HSM = H2 [Miller, et. al. NPB681]
M2N =
0@ M2
S M2SP
(M2SP )T M2
P
1A , M2
SP =
0BB@
0 32
sin β
0 32
cos β
− 12
− sin 2β
1CCA Ivnv
YITP - June 30, 2004 – p.3
Features of the NMSSM
• 5 neutral and 1 charged scalars
• CP violation at the tree level: I
I = Im(λκ∗ei(θ−2φ))
from the vacuum condition, I related to the other combinations
I ∼ Im(λAλei(θ+φ)) ∼ Im(κAκe3iφ)
• Only one combination of the phases is physical
• Our formalism is independent of prametrisation for the phases
• One can escape from the EDM constraint
YITP - June 30, 2004 – p.3
Features of the NMSSM
• 5 neutral and 1 charged scalars
• CP violation at the tree level: I• Pure NMSSM regime
vn → ∞ with λvn and κvn fixed ⇒ MSSM [Ellis, et. al. PRD39]
→ new features expected for vn = O(100)GeV
we focus on this regime
YITP - June 30, 2004 – p.3
NMSSM
Superpotential:
W = ydHdQDc − yuHuQU c − λNHdHu − κ
3N 3
λ〈N〉 ∼ µ in the MSSM
• Z3 symmetry← We assume it’s already broken by higher dimensional operatorIf one include tadpole term → nMSSM [Menon, et. al. hep-ph/0404184]
• All couplings are dimensionless
YITP - June 30, 2004 – p.4
NMSSM
Superpotential:
W = ydHdQDc − yuHuQU c − λNHdHu − κ
3N 3
λ〈N〉 ∼ µ in the MSSM
SUSY X soft terms:
Lsoft � −m2Nn∗n +
[λAλnΦdΦu +
κ
3Aκn
3 + h.c.]
λAλ〈n〉 ∼ µB in the MSSM
YITP - June 30, 2004 – p.4
NMSSM - Higgs sector
The tree-level Higgs potential:
V =m21Φ
†dΦd + m2
2Φ†uΦu + m2
Nn∗n − (λAλnΦdΦu +κ
3Aκn
3 + h.c.)
+g22 + g2
1
8(Φ†
dΦd − Φ†uΦu)
2 +g22
2(Φ†
dΦu)(Φ†uΦd)
+ |λ|2n∗n(Φ†dΦd + Φ†
uΦu) + |λΦdΦu + κn2|2
Order parameters:
〈Φd〉 =1√2
( vd
0
), 〈Φu〉 =
eiθ
√2
( 0
vu
), 〈n〉 =
eiφ
√2vn
YITP - June 30, 2004 – p.5
Tadpole conditions
m21 = Rλvn tan β − 1
2m2
Z cos(2β) − 12|λ|2(v2
u + v2n) − 1
2Rv2
n tanβ
m22 = Rλvn cot β +
12m2
Z cos(2β) − 12|λ|2(v2
d + v2n) − 1
2Rv2
n cotβ
m2N = Rλ
vdvu
vn+ Rκvn − 1
2|λ|2(v2
d + v2u) − |κ|2v2
n −Rvdvu
Iλ =12Ivn, Iκ = −3
2I vdvu
vn.
R = Re[λκ∗ei(θ−2ϕ)], I = Im[λκ∗ei(θ−2ϕ)],
Rλ =1√2Re[λAλei(θ+ϕ)], Iλ =
1√2Im[λAλei(θ+ϕ)],
Rκ =1√2Re[κAκei3ϕ], Iκ =
1√2Im[κAκei3ϕ].
YITP - June 30, 2004 – p.6
Constraints for the parameters
The parameters are restricted
The vacuum that break electroweak symmetryis the absolute minimum of the potential
• V (vac.) = min{V }• Positive mass2 of the all scalars
YITP - June 30, 2004 – p.7
Constrained parameter - example
Charged Higgs mass bound
• Positive mass2 of pseudo-scalar
detM2P > 0 =⇒ lower bound of mH±
mH± >3R2v2v2
n
4Rκ − 3Rv2 sin 2β+ m2
W − 12|λ|2v2
where
R = Re[λκ∗ei(θ−2ϕ)], Rκ =1√2Re[κAκei3ϕ]
� In the MSSM : m2H± = m2
W + m2A =⇒ m2
H± > m2W
YITP - June 30, 2004 – p.8
Constrained parameter - example
Charged Higgs mass bound
• Positive mass2 of pseudo-scalar
• Higgs potential at the vac. is lower than that at origin
V (vac.) < V (0) =⇒ upper bound of mH±
m2H± < 2|λ|2v2
n
1sin2 2β
+ 2|κ|2 v4n
v2
1sin2 2β
+ m2Z cot2 2β + m2
W
+ Rv2n
v2
1sin 2β
− 43Rκ
v3n
v2
1sin2 2β
.
� In the MSSM limit : this bound → ∞
YITP - June 30, 2004 – p.8
Constrained parameter - example
Charged Higgs mass bound
• Positive mass2 of pseudo-scalar
• Higgs potential at the vac. is lower than that at origin
CP cons.
Pure NMSSM regime
YITP - June 30, 2004 – p.8
Constrained parameter - example
Charged Higgs mass bound
• Positive mass2 of pseudo-scalar
• Higgs potential at the vac. is lower than that at originGeVGeV
GeV
κ = −0.3 κ = 0.3
Aκ GeVAκ
tan β = 5, vn = 300GeV, ⇒ κAκ > 0 is favored
YITP - June 30, 2004 – p.8
Constrained parameter - example
Charged Higgs mass bound
• Positive mass2 of pseudo-scalar
• Higgs potential at the vac. is lower than that at origin
In fact, we search the allowed parameternumerically and systematically at one-loop level
YITP - June 30, 2004 – p.8
Allowed parameters
1. The masses of the Higgs bosons are heavier than114GeV, or their coupling to Z boson is less than 0.1
2. The electroweak vacuum is the global minimum of theeffective potential
3. The mass-squared of the squarks are positive
tanβ = 2, 3, 5, 10, 20 and vn = 100, 150, 200, , , 1000 GeV
• heavy-squark scenario (mq̃, mt̃R) = (1000, 800)GeV
• light-squark scenario-1 (mq̃, mt̃R) = (1000, 10)GeV
• light-squark scenario-2 (mq̃, mt̃R) = (500, 10)GeV
YITP - June 30, 2004 – p.9
Allowed parametersA
κ(G
eV)
vn = 100GeV
mH±(GeV)
vn = 200GeV vn = 300GeV
vn = 400GeV vn = 500GeV vn = 600GeV
-1000
-900
-800
-700
-600
-500
-400
-300
-200
-100
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-1000
-900
-800
-700
-600
-500
-400
-300
-200
-100
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-1000
-900
-800
-700
-600
-500
-400
-300
-200
-100
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-1000
-900
-800
-700
-600
-500
-400
-300
-200
-100
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-1000
-900
-800
-700
-600
-500
-400
-300
-200
-100
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-1000
-900
-800
-700
-600
-500
-400
-300
-200
-100
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
x
YITP - June 30, 2004 – p.9
Allowed parameters
crit
κ
λ
light Higgs
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
YITP - June 30, 2004 – p.9
Electroweak phase transition
• The effective potential at finite temperature
V (T ) = Vtree + ∆qV + ∆q̃V + ∆gV + ∆T V
• For the Baryogenesis
• Strong 1st order PT : vC > TC
• CPV (but now we investigate the PT in CP cons. case)
YITP - June 30, 2004 – p.10
Electroweak phase transition
tan β mH± Aκ vn λ κ mq̃ mt̃R
3 400GeV −200GeV 200GeV 0.9 −0.1 1000GeV 800GeV
H1 H2 H3 H4 H5
mass(GeV) 64.1156 145.332 187.338 436.500 5964.78
g2HiZZ 2.69889 × 10−3 0.996300 0 1.00092 × 10−3 0
T=0
v
vn
0
50
100
150
200
250
300
0 50 100 150 200 250 300
T=100GeV
0
50
100
150
200
250
300
0 50 100 150 200 250 300
T=155GeV TC=155.4GeV
0
50
100
150
200
250
300
0 50 100 150 200 250 3000
50
100
150
200
250
300
0 50 100 150 200 250 300
vC = 163.2GeV
TC = 155.4GeV
vC
example of strong 1st order in light-mass and small-coupling case
YITP - June 30, 2004 – p.10
CP violation
We used light-mass and small-coupling
• 3 scalar mixing in NMSSM [Miller, et. al. NPB681]
light Higgs mass ⇒ strong 1st order PTAnd more, CPV is nessesary for BaryogenesisBut now we weren’t include CP phase
Is there other mixing that related to CPV?
YITP - June 30, 2004 – p.11
CP violation
We used light-mass and small-coupling
• 3 scalar mixing in NMSSM [Miller, et. al. NPB681]
• The squark phase, also in MSSM [Carena, et. al. NPB586]
Scalar-pseudoscalar mixing at one-loop levelWe investigated the effect of this phase in MSSM
Im(µAt)
on the PT in previous paper [Funakubo, et. al. PTP109]
We gain light Higgs, but 1st order PT is weakened by this phaseIs there other phase?
YITP - June 30, 2004 – p.11
CP violation
We used light-mass and small-coupling
• 3 scalar mixing in NMSSM [Miller, et. al. NPB681]
• The squark phase, also in MSSM [Carena, et. al. NPB586]
• The tree level CP phase in NMSSMScalar-pseudoscalar mixing at tree levelOne can escape EDM constraint
We expect good result
YITP - June 30, 2004 – p.11
CP violation
We used light-mass and small-coupling
• 3 scalar mixing in NMSSM [Miller, et. al. NPB681]
• The squark phase, also in MSSM [Carena, et. al. NPB586]
• The tree level CP phase in NMSSM
-15000
-10000
-5000
0
5000
10000
15000
20000
0 0.2 0.4 0.6 0.8 1
m_H1^2
m_H2^2
m_H3^2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
g_H1ZZ
g_H2ZZ
g_H3ZZ
g_H4ZZ
g_H5ZZ
del_kappa/pi
YITP - June 30, 2004 – p.11
Summary
• One-loop formulation with all CP phases
• Parameter search→ mass bounds for the charged Higgs boson
• EWPT in CP conserving case
• Higgs spectrum in CP violating case
Todo
• EWPT in CP violated case
YITP - June 30, 2004 – p.12
EWPT in the NMSSM
order parameters :
vd = v cos β = y cosα cosβ
vu = v sinβ = y cos α sinβ
vn = y sinα
−→ y3-term, even at the tree level [Pietroni, NPB402]
0
50
100
150
200
250
0
50
100
150
200
-5·107
0
5·107
1·108
50
100
150
200
250
0
50
100
150
200 vn
v
V
VEV
0 50 100 150 200 250 3000
50
100
150
200
250
v
vn
YITP - June 30, 2004 – p.13
CP phase and the EDM
The phases apear in following 3 combinations
I = Im[λκ∗ei(θ−2ϕ)], Iλ =1√2Im[λAλei(θ+ϕ)], Iκ =
1√2Im[κAκei3ϕ]
from vacuum condition, these are related
Iλ =1
2Ivn, Iκ = −3
2I vdvu
vn.
EDM related phases that appear in Higgs sector are
δEDM ⊃ δλ + ϕ + θ
YITP - June 30, 2004 – p.14
CP phase and the EDM
define
δ′λ ≡ δλ + θ + ϕ, δ′κ ≡ δκ + 3ϕ
so, describe the phases explicitly
Arg(λκ∗ei(θ−2ϕ)) = δλ − δκ + θ − 2ϕ = δ′λ − δ′κ,
Arg(λAλei(θ+ϕ)) = δλ + δAλ+ θ + ϕ = δ′λ + δAλ
,
Arg(κAκei3ϕ) = δκ + δAκ + 3ϕ = δ′κ + δAκ
and
δEDM ⊃ δλ + ϕ + θ = δ′λ
Although one choose the phase δ′λ = 0, the vacuum condition can be satisfied.
YITP - June 30, 2004 – p.14
Maximal effect of the CP phase
now we have
R = Re[λκ∗], I = Im[λκ∗],
Rλ =1√2Re[λAλ], Iλ =
1√2Im[λAλ],
Rκ =1√2Re[κAκ], Iκ =
1√2Im[κAκ].
from the vacuum condition, Iλ and Iκ are described by the function of I. The inputparameters are λ, κ, δκ, mH± , δAκ = 0, π. The input mH± gives Rλ, and the inputδAκ = 0, π gives following simple relation,
Aκ = ±3λvdvu√2vn
,
so the parameter Aκ becomes dependent one. Then Rκ determined.
Note : in this situation, we can see the effect of the CP phase δκ maximally.YITP - June 30, 2004 – p.15