cosmological phase transitions in the early universecosmological phase transitions in the early...
TRANSCRIPT
IIT_Guwahati_joint_workshop_uploadKohei Fujikura (TiTech)
Sin Kyu Kang (SeoulTech) Arnab Dasgupta (SeoulTech)
Devabrat Mahanta (IIT Guwahati)
Content Introduction
Scotogenic Model
3
SM cannot explain tiny neutrino masses.
Problems in the SM The SM cannot explain following phenomena:
We need a beyond standard model physics! 4
Scotogenic Model
Dark matter
Neutrino masses
SM + additional SU(2)w doublet + 3 right-handed neutrinos can explain following phenomena:
5
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Dark Matter (DM) Candidates Masses for Z2 odd particles
m±
Scotogenic Model
Dark matter
SM + additional SU(2)w doublet + 3 right-handed neutrinos can explain following phenomena:
8
9
Three sources of the Gravitational Wave:
Bubble collisions
Turbulence of the plasma
http://gwplotter.com 11
Electroweak Phase Transition (EWPT) : EWPT is not of first order. (La6ce simula;on)mh 125GeV
[ A. I. Bochkarev and M.E. Shaposhnikov (1987)]
[ K. Kajan;e, M. Laine, K. Rummukainen and M.E. Shaposhikov(1996)]
EWPT in the scotogenic model can be of first order.
S particle, which couples to the SM- like Higgs boson, generates the
potential barrier!
(Thermal fluctuation)
Solve bounce eq.
Fix a model
etc.. Duration of phase transition:
Energy difference:
13
T > 1
p 4
S > 0, 1 + 2 p SMS > 0, 1 + 2
|3| 2
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10-6
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EWPT is of (strong) first order is almost ruled out by a direct detection constraint!
Gravitational Wave Signals (Fermion DM)
17
10-19
10-14
10-9
10-4
10
e x p ( - > e )
LFV constraint can be evaded with small Yukawa couplings!
In the SM, LFV is generated at one-loop which is suppressed by tiny neutrino masses.
5
III. ANALYTICAL RESULTS
In this section we present our analytical results for the LFV processes #! ! #"$, #! ! 3 #" and
µ" e conversion in nuclei. Before we proceed to the analytical discussion a comment is in order. It
is well-known that the rates for LFV processes get greatly enhanced in models with right-handed
neutrinos at the electroweak scale [34–42]. This is due to the fact that the GIM suppression at
work in the SM contribution is spoiled by the mixing between left- and right-handed neutrinos.
One could naively think that this is also the case in the scotogenic model. However, the unbroken
Z2 symmetry forbids this mixing, (see footnote 2), and thus the enhancement in the W " % loops
is not present. We will show that the enhancement is still possible, but with &±"N loops instead.
A. #! ! #"$
The most popular searches for LFV have focused on the radiative process #! ! #"$. This is
described by the e!ective Lagrangian
Le! = !µ"!
#"' µ##!Fµ# , (12)
where µ"! is a transition magnetic moment. It proves convenient to define it in terms of the
dipole form factor AD as µ"! = em!AD/2, where terms proportional to m" have been neglected
and e is the electromagnetic coupling, related to the electromagnetic fine structure constant as
!em = e2/(4(). In the model under consideration, AD gets contributions at the 1-loop level from
the Feynman diagrams in Fig. 1. They lead to the following expression
AD = 3 #
i=1
Summary •The inert scalar and RH neutrinos are introduced in
scotogenic model.
•GW signals within reach of U-DECIGO-corr with 100% DM are almost ruled out by the DM direct detection experiment in the scalar DM scenario.
•First-order (electroweak) phase transitions realized in beyond the standard model produce GW signals.
19
•GW signals within reach of U-DECIGO-corr with 100% DM are not ruled out in the fermion DM scenario.
Back up
+ m 2 1|S|2 + 1|H|2|S|2
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How is the strength of the phase transition changed?
SM
Standard Model: SU(2)W U(1)Y
loop order
22
Important parameters for GW GW amplitude is related to two important parameters.
Vacuum energy difference:
Tunneling occurs at
Bubble volume
Large vacuum energy and long- duration enhance the GW amplitude.GW
H
+ m 2 1|S|2 + 1|H|2|S|2
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m1 ! 1
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S is heavy so that it does not contribute to the thermal effective potential. 25
H(A) 1 + 2 ± 23
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Standard Model (small E) SM + one scalar doublet (large E)
SM
27
SM
Standard Model (small E) SM + one scalar doublet (large E)
SM
SM
Standard Model (small E) SM + one scalar doublet (large E)
SM
One-loop suppression!
Thanks to the one-loop suppression, tiny neutrino masses are generated with TeV scale Majorana masses!
e.g.) 3 = 0.01
Sin Kyu Kang (SeoulTech) Arnab Dasgupta (SeoulTech)
Devabrat Mahanta (IIT Guwahati)
Content Introduction
Scotogenic Model
3
SM cannot explain tiny neutrino masses.
Problems in the SM The SM cannot explain following phenomena:
We need a beyond standard model physics! 4
Scotogenic Model
Dark matter
Neutrino masses
SM + additional SU(2)w doublet + 3 right-handed neutrinos can explain following phenomena:
5
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Dark Matter (DM) Candidates Masses for Z2 odd particles
m±
Scotogenic Model
Dark matter
SM + additional SU(2)w doublet + 3 right-handed neutrinos can explain following phenomena:
8
9
Three sources of the Gravitational Wave:
Bubble collisions
Turbulence of the plasma
http://gwplotter.com 11
Electroweak Phase Transition (EWPT) : EWPT is not of first order. (La6ce simula;on)mh 125GeV
[ A. I. Bochkarev and M.E. Shaposhnikov (1987)]
[ K. Kajan;e, M. Laine, K. Rummukainen and M.E. Shaposhikov(1996)]
EWPT in the scotogenic model can be of first order.
S particle, which couples to the SM- like Higgs boson, generates the
potential barrier!
(Thermal fluctuation)
Solve bounce eq.
Fix a model
etc.. Duration of phase transition:
Energy difference:
13
T > 1
p 4
S > 0, 1 + 2 p SMS > 0, 1 + 2
|3| 2
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15
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10-9
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<latexit sha1_base64="Dfq9fBulaWNW937JJClOdvb6E0g=">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</latexit>
EWPT is of (strong) first order is almost ruled out by a direct detection constraint!
Gravitational Wave Signals (Fermion DM)
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e x p ( - > e )
LFV constraint can be evaded with small Yukawa couplings!
In the SM, LFV is generated at one-loop which is suppressed by tiny neutrino masses.
5
III. ANALYTICAL RESULTS
In this section we present our analytical results for the LFV processes #! ! #"$, #! ! 3 #" and
µ" e conversion in nuclei. Before we proceed to the analytical discussion a comment is in order. It
is well-known that the rates for LFV processes get greatly enhanced in models with right-handed
neutrinos at the electroweak scale [34–42]. This is due to the fact that the GIM suppression at
work in the SM contribution is spoiled by the mixing between left- and right-handed neutrinos.
One could naively think that this is also the case in the scotogenic model. However, the unbroken
Z2 symmetry forbids this mixing, (see footnote 2), and thus the enhancement in the W " % loops
is not present. We will show that the enhancement is still possible, but with &±"N loops instead.
A. #! ! #"$
The most popular searches for LFV have focused on the radiative process #! ! #"$. This is
described by the e!ective Lagrangian
Le! = !µ"!
#"' µ##!Fµ# , (12)
where µ"! is a transition magnetic moment. It proves convenient to define it in terms of the
dipole form factor AD as µ"! = em!AD/2, where terms proportional to m" have been neglected
and e is the electromagnetic coupling, related to the electromagnetic fine structure constant as
!em = e2/(4(). In the model under consideration, AD gets contributions at the 1-loop level from
the Feynman diagrams in Fig. 1. They lead to the following expression
AD = 3 #
i=1
Summary •The inert scalar and RH neutrinos are introduced in
scotogenic model.
•GW signals within reach of U-DECIGO-corr with 100% DM are almost ruled out by the DM direct detection experiment in the scalar DM scenario.
•First-order (electroweak) phase transitions realized in beyond the standard model produce GW signals.
19
•GW signals within reach of U-DECIGO-corr with 100% DM are not ruled out in the fermion DM scenario.
Back up
+ m 2 1|S|2 + 1|H|2|S|2
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How is the strength of the phase transition changed?
SM
Standard Model: SU(2)W U(1)Y
loop order
22
Important parameters for GW GW amplitude is related to two important parameters.
Vacuum energy difference:
Tunneling occurs at
Bubble volume
Large vacuum energy and long- duration enhance the GW amplitude.GW
H
+ m 2 1|S|2 + 1|H|2|S|2
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m1 ! 1
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S is heavy so that it does not contribute to the thermal effective potential. 25
H(A) 1 + 2 ± 23
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Standard Model (small E) SM + one scalar doublet (large E)
SM
27
SM
Standard Model (small E) SM + one scalar doublet (large E)
SM
SM
Standard Model (small E) SM + one scalar doublet (large E)
SM
One-loop suppression!
Thanks to the one-loop suppression, tiny neutrino masses are generated with TeV scale Majorana masses!
e.g.) 3 = 0.01