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The XXII International Workshop High Energy Physics an d Quantum Field Theory

Higgs b osons in NMSSM with CP-violation
Albina V. Gurskaya Samara State University, Russia

Samara, 2015


The CP-violation problem
[1] Christenson J. H. Evidence for the 2p decay of the K0 2 meson / J. H. Christenson, J.W. Cronin, V.L. Fitch, R. Turlay // Phys. Rev. Lett. - 1964. - V.13. - P.138-140. [2] Sakharov A.D. Violation of CP invariance, C-asymmetry and baryon asymmetry of the Universe // Pisma v ZhETF [ Letters to the Journal of Experimental and Theoretical Physics ], 1967, Vol. 5, Issue 1, pp. 32­35. [in Russian]

The Sakharov conditions for baryon asymmetry: the violation of baryon numb er; C-violation and CP-violation; the deviation from thermo dynamic.

Higgs b osons in NMSSM with CP-violation

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The CP-violation problem
[3] Kobayashi M., Maskawa T. CP Violation in the Renormalizable Theory of Weak Interaction // Prog. Theor. Phys.­1973.­V. 49.­ P. 652-657.

Matrix CKM:

^ VC

KM

C 12 C 13 = -S12 C23 - C12 S23 S13 ei S12 S23 - C12 C23 S13 ei where C
ij

V ud = Vcd Vtd



V us Vcs Vts

S12 C13 C12 C23 - S12 S23 S13 ei -S23 C12 - S12 C23 S13 ei

V ub Vcb = Vtb

S13 ei S23 C13 , C 23 C 13

= cos ij , Sij = sin ij , -complex phase.

[4] Gavela M.B. Standard model CP-violation and baryon asymmetry (II). Finite temperature / M.B. Gavela [et al.] // Nucl.Phys.B. - 1994. - V.430. - P.382-426. Matrix CKM is not enough to describe the baryon asymmetry!

Higgs b osons in NMSSM with CP-violation

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The CP-violation problem CP-violation in the lepton sector:
[5] Connecting Leptonic CP Violation, Lightest Neutrino Mass and Baryon Asymmetry Through Type II Seesaw // Int. J. Mod. Phys. A ­ 2015. ­ V. [6] Petcov S.T. Leptonic CP violation and leptogenesis // Int. J. Mod. Phys.A ­ 2014.­ V.30.­19P. ... etc. CP-violation in the extended Higgs sector: [7] Pilaftsis A., WagnerC.E.M. Higgs Bosons in the Minimal Sup ersyminetry Standard Model with Explicit CP Violation // Nucl. Phys. B. 1999. V. 553. P. 3-42. [8] Choi S. K, Lee J.S. Decays of the MSSM Higgs Bosons with Explicit CP-Violation // Phys. Rev. D. 2000. V. Gl. P. 015003. [9] Carena M. et al Higgs-Boson Pole Masses in the MSSM with Explicit CP Violation // NucL Phys. B. 2002. 625. P. 345-371.

Higgs b osons in NMSSM with CP-violation

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The CP-violation problem CP-violation in the extended Higgs sector:
[10] Akhmetzyanova E.N., Dolgopolov M.V., Dubinin M.N. Higgs Bosons in the Two-Doublet Model with CP Violation // Phys.Rev.D. V.71. N7. 2005. P.075008 [11] Akhmetzyanova E.N., Dolgopolov M.V., Dubinin M.N., Smirnov I.A., Shcherbakova E. S. Supersymmetric model with violation of CP invariance. 1. The decays of the Higgs boson h g g h // Vestnik SamGU, 2003. N 2(28). .122-136.

Fig.1. The dep endence of the decay widths from tan [11].

[12] Akhmetzyanova E. N., Dolgopolov M. V., Dubinin M. N. Supersymmetric model with violation of CP invariance. 3. The violation of CP invariance in the Higgs sector // Vestnik SamGU, 2003. N 4(30). P. 147-179. ... etc.

Higgs b osons in NMSSM with CP-violation

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Mo dels with the extended Higgs sector
sup erfield quarks/ squarks leptons/ sleptons gauge b osons / gaugino Higgs/ higgsino, S field/ singlino ^ Q ^ U ^ D ^ L ^ E ^ G ^ W ^ B ^ H ^ H
1

Q=

SM field U D

s pi n
1 2 L 1 2 1 2 1 2 1 2

2

U R D R L L ER Ga µ W ±, W 0 B0 0 H1 H1 = - H1 + H2 H2 = 0 H2 S

1 1 1 0 0 0

sup erpartner ~ U ~ D L ~ U R ~ D R ~ L L ~ ER ~ Ga µ ~ ~ W ±, W 0 ~ B0 ~0 H1 ~ H1 = ~ - H1 ~+ H2 ~ H2 = ~ H0 ~ Q=
2

s pi n 0 0 0 0 0
1 2 1 2 1 2 1 2 1 2 1 2

^ S

~ S

models physical Higgs states

2HDM 2 neutral CP-even 1 neutral CP-odd 2 charged

MSSM 2 neutral CP-even 1 neutral CP-odd 2 charged

NMSSM 3 neutral CP-even 2 neutral CP-odd 2 charged
6

Higgs b osons in NMSSM with CP-violation


The NMSSM Fields can be parameterized: 1 =
1 2

( 1 + h 1 + i a1 ) - 1 S=

, 2 = e

i

1 2

+ 2 ( 2 + h 2 + i a2 )

, (1)

1 e i 2

( 3 + h 3 + i a3 )

U ( 1 , 2 , S ) = - µ2 ( 1 ) - µ2 ( 2 ) - µ2 ( S S ) + 3 2 1 2 1 + 1 2 ( 1 1 )2 + ( 2 2 ) 2 + 3 ( 1 1 ) ( 2 2 ) + 4 ( 2 ) ( 1 ) + 1 2 2 2 5 + ( 2 )( 2 ) + 5 ( 1 )( 1 )+ 1 1 2 2 2 2

+6 ( 2 )( 1 ) + (2 1 )( 1 ) + 7 ( 2 )( 2 ) + 7 ( 1 )( 2 )+ 6 1 1 1 1 2 2 2

+k1 ( 1 )(S S ) + k2 ( 2 )(S S ) + k3 ( 2 )(S S ) + k3 ( 1 )(S S )+ 1 2 1 2 +k4 (S S )2 + k5 ( 2 )S + k5 ( 1 )S + k6 S 3 + k6 (S ) 1 2
Higgs b osons in NMSSM with CP-violation

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Lo cal minimum conditions of the Higgs p otential We should calculate: 2 2 µ 1 , µ 2 , µ 22 . 1
2 µ1 = U v1

= 0,

U v2

= 0,

U v3

= 0 and obtain equations for:

12 v 1 cos2 + v 2 (3 + 4 + Re5 )sin 2 + v 2 sin (3Re6 cos + Re7 tan ) + 2 1 1 1 2 + k1 v3 + ( Rek3 v3 + Rek5 )v3 tan , 2 2 2 12 2 2 2 µ2 = v 2 sin + v (3 + 4 + Re5 )cos 2 + v 2 cos (3Re7 sin + Re6 cot ) + 2 1 1 1 2 + k2 v3 + ( Rek3 v3 + Rek5 )v3 cot , 2 2 2
2 µ3 =

v2 2

k1 cos2 + k2 sin2 + (Rek3 +
1

1 2v
3

23 Rek5 ) sin 2 +Rek4 v3 + Rek6 v3 . 2

2 2 where v 2 = v1 + v2 , tan = v2 /v

Higgs b osons in NMSSM with CP-violation

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If CP invariance is violated, we must eigenvalues do not have a definite CP m 11 m 12 m 21 m 22 M 2 = m 31 m 32 m 41 m 42 m 51 m 52

consider the matrix 55 for which the -parity. m 13 m 14 m 15 m 23 m 24 m 25 m 33 m 34 m 35 , (2) m 43 m 44 m 45 m 53 m 54 m 55

Higgs b osons in NMSSM with CP-violation

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m

11

=

v2 ( 1 c o s 4 + 2 s in 4 + 2 ( 3 + 4 + R e 5 ) c o s 2 s in 2 + 2 +4Re6 cos3 sin + 4Re7 cos sin3 ), 1 ( 3 v 2 ( I m 5 s in 2 + I m 6 ( 1 + c o s 2 ) + I m 7 ( 1 - c o s 2 ) ) 4 -2v3 (v3 I mk3 + 2I mk5 )),

m

12

=

m

13

=

12 v (-1 (sin 2 +sin 4 )+2 (sin 2 -sin 4 )+2(3 +4 +Re5 ) sin 4 + 8 +4(Re6 (cos 2 + cos 4 ) + Re7 (cos 2 - cos 4 )), 1 = v (v3 (k1 cos2 + k2 sin2 ) + (v3 Rek3 + Rek5 ) sin 2 ), 2 1 m15 = v (v3 I mk3 - I mk5 ) sin 2 , 2 12 = - v ( 2 R e 5 s in 2 + R e 6 ( 1 + c o s 2 ) + R e 7 ( 1 - c o s 2 ) ) + 8 + 2v3 (v3 Rek3 + 2Rek5 ) csc sec ,
14

m

m

22

Higgs b osons in NMSSM with CP-violation

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m m
33

24

12 v ( I m 5 c o s 2 + ( I m 7 - I m 6 ) s in 2 ) , 2 1 1 = -v (v3 I mk3 + I mk5 ), m25 = v (v3 Rek3 - Rek5 ), 2 2 m
23

=

=

1 v 2 ( 1 ( 1 - c o s 4 ) + 2 ( 1 - c o s 4 ) + 2 ( 3 + 4 + R e 5 ) ( c o s 4 - 1 ) - 16 -(.4(Re6 (cot + sin 4 ) + Re7 (tan - sin 4 )) -4v3 Rek3 v3 + 2R ek
5

csc sec ),
5

m

34

=

1 1 v v3 (k2 - k1 ) sin 2 + 2 v3 Rek3 + Rek 2 2 m
35

co s 2 ,

1 = v cos 2 v3 I mk3 - I mk5 , 2

m

55

v2 Rek5 sin cos + 3v3 Rek6 , v3 m45 = v 2 I mk3 sin cos - 3 2v3 I mk6 , 2 1 (v 2 (4Rek3 v3 + 2Rek5 ) sin cos + 9 2v3 Rek6 ). =- 4v3 m
44

1 2 = v3 k4 - 22

Higgs b osons in NMSSM with CP-violation

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Free parameters 1.0 < tg 60, M1 = M2 , 100 M2 2000 , 0 .0 0 0 1 0 .7 , 0 0 .6 5 . 0 A 1000 , -100 A -10
2 2 g1 + g2 , 8 2 2 g2 - g1 , 4 2 g2 . 2

1 = 2 =

3 =

4 = -

(3)

k1 = | | 2 , k2 = | | 2 , k3 = k , k4 = | k | 2 , k5 = A , k6 =

1 kA 3

k

Higgs b osons in NMSSM with CP-violation

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NMSSM parametrs for Higgs b osons scenario CP invariance Parameters of model \ tg A , GeV A , GeV m m
h1 h2 a1

CP violation 3 0 .3 5 0 .3 6 14 1000 -100 125 142 395 103 4 0 .1 4 0 .4 7 50 100 -100 46 125 424 38

1 0 .0 0 2 0 .6 5 9 .5 3 -100 125 127 121 34

2 0 .0 1 0 .6 5 1 .7 5 115 -100 127 848 125 33

\m \m \m
0 1

H1 H2

, GeV , GeV , GeV

m

H3

m

, GeV

Higgs b osons in NMSSM with CP-violation

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Thank you for your attention!

Higgs b osons in NMSSM with CP-violation

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