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Baryogenesis in non-minimal split Sup ersymmetry mo del
Kirpichnikov D.V.

Institute for Nuclear Research RAS
kirp@ms2.inr.ac.ru

June 26 2015


Setup of non-minimal split SUSY model (split NMSSM)
CMB (PDG 2013): 6.1 в 10-
10

<

nB < 6.9 в 10-10 . n

(1)

Higgs discovery (ATLAS, CMS 2012): D. Gorbunov and S. Demidov 2006:

mH = 125.6 ± 0.3 GeV.

Additional sinlet field N non-minimal coupled to Higgs ^^ ^ ^ ^^ ^ W = N Hu Hd + 1 k N 3 + µHu Hd + r N . 3 Spectrum of the particles is splitted: (1) ~, q , A and H ± decouple from the spectrum at Q < MS . l~ ~ ~ ~~ (2) SM + ( Hu,d , W , B , g , N , n) have masses near O(MEW ) ~ Soft trilinear couplings H 2 N and N 3 provide the mechanism of strengthen the first order EWPT. N -H mass squared mixing is absent at electroweak scale, Q < MS .
Kirpichnikov D.V. (INR RAS) Split NMSSM 2 / 15


Scaninng over dimensionless couplings at MS scale
10 Ms Ms Ms Ms = = = = 4 5 6 7 TeV TeV TeV TeV

8

6 tan 4 2 0 0 0.1 0.2 0.3 0.4 0.5 0.6

Allowed regions of tan and at MS scale. (g , g , gs , yt ), (gu,d , gu,d , u,d , , ~ ~
2 2 1,2

~ k , N , , , ).

g Ї ~ cos2 2 + sin2 2 . (MS ) = 4 2 mH = ~ (MEW )v : 125.3 GeV < mH < 125.9 GeV,
Split NMSSM

v = 246 GeV
3 / 15

Kirpichnikov D.V. (INR RAS)


Dimensionful parameters:
~ ~ -Ltrilinear = +i A1 H H (N - N ) + A2 H H (N + N ) + 1~ + Ak N 3 + N 3
3

~ + Ar (N + N ) +

1~ 2 A3 N N + h.c . , 2 - P ) squared mass the appropriate and A2 . P = vP ,

Higgs-scalar (H - S ) and Higgs-pseudoscalar (H mixings are absent at EW energies. This implies electroweak fine-tuning for trilinear couplings A1 N = (S + iP )/ 2, S = vS ,

There are only seven independent dimensionful parameters of the model at EW scale ~ ~ ~ (vS , vP , M1 , M2 , Ak , A3 , Ar ). (2) ~ ~ A3 = Ar = 0,
Kirpichnikov D.V. (INR RAS)

~ Ak = -1.1 GeV.

(3)
4 / 15

Split NMSSM


Strong first order EWPT
Three necessary conditions (Sakharov conditions) must be fulfilled in the early Universe to produce the baryon asymmetry: Departure from thermal equilibrium. Baryon number violation, C- and CP-violation Departure from thermodynamic equilibrium is induced by the rapidly-expanding bubble walls through the cosmological plasma. Violation of baryon number comes from the rapid sphaleron transitions in the symmetric phase. C- and CP-violating scattering processes are needed at the phase boundaries to create the particle number asymmetries that bias the sphalerons to create more baryons than antibaryons.
Kirpichnikov D.V. (INR RAS) Split NMSSM 5 / 15


Strong first order EWPT
We define Tc as a temperature at which one bubble of the broken phase begin to nucleate within a casual space-time volume of the Universe. The last one is defined by the Hubble parameters H(T ) as H
-4 (T ) = (MPL /T 2 )4 .

(4)

The bubble nucleates with the rate (T ) (prefactor) в T 4 exp(-S3 /T ). (5)

where S3 is a free energy of the critical bubble


S3 (T ) = 4
0

dr r

2

1 2

dh dr

2

+

1 2

dS dr

2

+

1 2

dP dr

2

eff + VT (h, S , P ) .

Here h(r ), S (r ) and P (r ) are the radial configurations of the scalar field, which minimize S3 .
Kirpichnikov D.V. (INR RAS) Split NMSSM 6 / 15


Strong first order EWPT
The probability of bubble nucleation inside a casual volume is given by
4 MPL exp(-S3 /T ). T4

P

(6)

The first bubble nucleates when P 1, so that, one can obtain a rough nucleation criteria S3 (T )/T 4 ln
MPL T

150,

where T is a typical temperature of order the electroweak energy scale, T = 100 GeV. More stringent result gives (Anderson et al. 1991) S3 (Tc )/Tc
Kirpichnikov D.V. (INR RAS) Split NMSSM

140.

(7)
7 / 15


Strong first order EWPT
By using the iterative procedure for anzats configurations, we find the absolute minimum of the functional


F (h, S , P ) = 4
0

dr r

2

2 2 2 Eh (r ) + ES (r ) + EP (r ) ,

(8)

where Eh (r ), ES (r ) and EP (r ) are the equations of motion for bubble wall profiles Eh (r ) =
eff d 2 h 2 dh VT + - = 0, dr 2 r dr h

E S (r ) =

eff d 2 S 2 dS VT + - = 0, dr 2 r dr S

eff VT d 2P 2 dP - = 0. + dr 2 r dr P Note that the critical bubble obey the following boundary conditions

EP (r ) =

(h(r ), S (r ), P (r ))
Kirpichnikov D.V. (INR RAS)

r =

= (0, Ss , Ps ),
Split NMSSM

dh dS dP , , dr dr dr

r =0

= (0, 0, 0).
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Strong first order EWPT
350 300 250 GeV GeV 200 150 100 50 0 0 0.05 0.1 r, GeV 0.15
-1

h(r) S(r) P(r)

300 250 200 150 100 50 0

h(r) S(r) P(r)

0.2

0.25

0

0.05

0.1

0.15

0.2

0.25

r, GeV-1

The critical bubbles. Left panel: Tc = 73 GeV. Right panel Tc = 81 GeV.

(1) (2)

vS 53 72

vP 242 263

Tc 81.0 73.0

vc 218.8 229.5

Sc 53.7 72.4
Split NMSSM

Pc 252.2 261.9

Ss 240.4 277.5

Ps 33.8 30.1

S3 /Tc 139.6 141.2
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All dimensionful parameters are in GeV.
Kirpichnikov D.V. (INR RAS)


Baryogenesis
2 1.5 1 0.5 0 -0.5 -1000 0 = 8.7 10-11 Tc=81 GeV Tc=73 GeV

B/0

-500

0

500

1000

M2, GeV

Baryon asymmetry ratio B /0 versus gaugino mass parameter M2 . M
Kirpichnikov D.V. (INR RAS)

ch

=

1 gd ~ 2

M2 h(z )
Split NMSSM

1 gu ~ 2

h(z ) µ(z ) ~

,

(9)
10 / 15


EDM constraints
There are three terms which contribute to EDM of fermion df = d where dfH , d
HZ f H f

+ dfHZ + d

WW f

,

and dfWW are the partial EDMs related to the exchange
-

of H , HZ 0 and W + W

bosons in chargino-neutralino sector.

The most stringent upper limit on EDM of the electron |de /e | < 8.7 · 10-29 cm was obtained by ACME collaboration at 90% CL (Baron et al. 2013). The current bound on neutron's EDM is |dn /e | < 3.0 · 10- CL ( Baker et al. 2006).
26

cm at 90 %

Kirpichnikov D.V. (INR RAS)

Split NMSSM

11 / 15


1e-25

1e-25

1e-26 |dn/e| |dn/e| 1e-27

1e-26

1e-27

1e-28 110

115

120

125

130 135 m+, GeV

140

145

150

1e-28 110

115

120 125 m+, GeV

130

135

The numerical results for neutron EDM. One can see that predictions for the neutron EDMs satisfy the current experimental bound |dn /e | < 3.0 · 10-26 cm. Scanning over the region 0 < M1 , M2 < 1000GeV.
Kirpichnikov D.V. (INR RAS) Split NMSSM 12 / 15


1e-27

1e-27

|de/e|

1e-28

|de/e| 1e-28 1e-29 110 115 120 125 130 135 m+, GeV 140 145 150 1e-29 110

115

120 125 m+, GeV

130

135

The EDM of electron versus experimental bound is |de /e | m+ = 140 GeV and m+ 1 1 limits on chargino-neutralino squarks.

the lightest chargino mass m+ . Current 1 < 8.7 · 10-29 cm. Predicted chargino masses, 132.5 GeV, in agreement with CMS and ATLAS production at LHC without light sleptons and

Right pane: MS = 4.0 TeV, tan = 6.59, = 0.4, k = -0.5, Left panel: MS = 4.72 TeV, tan = 4.91, = 0.4, k = -0.5.
Kirpichnikov D.V. (INR RAS) Split NMSSM 13 / 15


Summary
Successful baryogenesis is considered in Split NMSSM for Higgs favored (mH = 125 GeV) parameter space. Light charginos are predicted, m+ = 140 GeV and 1 m+ = 132.5 GeV, from the experimental bound on electron EDM, 1 |de /e | < 8.7 · 10-29 cm. TeV split scale and large tan are reqiured, MS = 4 TeV and tan = 7, to explain the observed asymmetry between baryon and antibaryon in the Universe. Very narrow region in parameter space of Split NMSSM can be probed in pp collision at LHC 14.

Kirpichnikov D.V. (INR RAS)

Split NMSSM

14 / 15


Thank You!

Kirpichnikov D.V. (INR RAS)

Split NMSSM

15 / 15