H3 decays into Z and A1 in the NMSSM

To solve the u problem of the Minimal Supersymmetric Standard Model (MSSM), a single field S is added to build the Next Minimal Supersymmetric Standard Model (NMSSM). Vacuum enlarged with non-zero vevs of the neutral-even CP is the combination of Hu, Hd and S.

TẠP CHÍ KHOA HỌC  SỐ 4/2016 H3 DECAYS INTO Z AND A1 IN THE NMSSM Nguyen Chinh Cuong1, Tran Trung Hieu Ha Noi National University of Education Abstract: To solve the  problem of the Minimal Supersymmetric Standard Model (MSSM), a single field S is added to build the Next Minimal Supersymmetric Standard Model (NMSSM) Vacuum enlarged with non-zero vevs of the neutral-even CP is the combination of Hu, Hd and S In the NMSSM, the higgs sector is increased to (compared with higgs in the MSSM), including three higgs – which are the even-CP h1,2,3 (mh1< mh2<  mh3), two higgs – which are odd-CP a1,2 (ma1< ma2) and a couple of charged higgs H The decay of higgs into higgs is one of the remarkable new points of the NMSSM In this paper we study the decay ofh3 into Zand a1 The decay width is calculated to one loop vertex correction The numerical calculation resultson the influence of CP violation are also given Keywords: Higgs boson, Decay, CP violation, NMSSM INTRODUCTION The simplest version of supersymmetry is the Minimal Supersymmetric Standard Model (MSSM) This version is limited by two problems: the  and the hierarchy [1,3,4,7] The simple supersymmetry, which is beyond the MSSM, is the Next Minimal Supersymmetric Standard Model (NMSSM) The special characteristic of Higgs boson in the NMSSM is the decay of Higgs into Higgs It is remarkable that the lightest state a1 of the odd-CP Higgs can play a role of a pseudo-goldstone, which has small mass and can lead to the predominated decay of the even-CP h  a1a1 [2] The even-CP Higgs and the heavy odd-CP Higgs can be generated at LEP in e e  , but they may not be discovered because the dominant h decay were not searched for There are different ways to make the mass of Higgs boson increased in the MSSM and in the beyond MSSM One simple way is to study the beyond Nhận ngày 23.04.2016, gửi phản biện duyệt đăng ngày 10.05.2015 Liên hệ tác giả: Nguyễn Chính Cƣơng ; Email: nccuong@hnue.edu.vn TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI ˆ ˆ Hˆ in the super-potential, this is the singlet of the MSSM which contains one term  SH u d term that contributes  2v sin 2 at v = 174 GeV to the squared mass of even-CP Higgs [10] and therefore, it can make the mass of Higgs boson increased over the limit of independent decay state It should be noted that this contribution is maximum with tan Thus, a condition in which the lightest odd-CP Higgs with its mass is under 2mb , the two lightest even-CP Higgs boson and the charged Higgs boson can be found in the MSSM All of them can be generated at LEP and they are now being searched for The charged Higgs makes up more than 40% in the top-quark decay at Tevatron; the products of this decay are charged Higgs and bottom-quark ( t  H b ) The decay method of charged Higgs is H   W  a1 , with a1  cc,gg The neutral Higgs sector in the NMSM includes the following states: three even - CP and two odd-CP Many analysis on Higgs sector in the NMSSM [5] have shown that, in the specific physical state of the even-CP Higgs, there is a strong mix between the doublet state and the singlet SU(2) with the reduction in the interaction of gauge boson The study on light Higgs contributes to the discovery of one or more Higgs states at LEP, at LHC [5] and at large energy accelerators The NMSSM is established from the MSSM when the MSSM is added with a gauge chiral single superfield Sˆ , which includes the renormalized superfield interaction and the soft supersymmetry breaking term LSoft In the NMSSM, the terms of the super-potential ˆ , Hˆ and Sˆ (here, we follow the SLHA2 WHiggs are dependent on superfieldHiggs H d u ˆ is also written as Hˆ and Hˆ is also written as H ˆ ): regulations, however H d d u ˆ H ˆ   Sˆ  Sˆ   Sˆ WHiggs    Sˆ H u d F  with: -  (1) ,  is the non-dimension coupling Yukawa - ,  is the supersymmetry mass, - F is the square supersymmetry mass parameter From (1), Yuakawa interaction of quark and lepton superfield are added to: ˆ ˆ c +h H ˆ QU ˆ ˆ ˆc ˆ ˆ ˆc (2) WYukawa = h u H u R d d QDR + h e Hd LER ˆ U ˆ c ,D ˆ c , L, ˆ Eˆ c are the Here, the Yukawa interaction h u , h d , h e and the superfields Q, R R R matrices and vectors in the corresponding spaces The soft breaking supersymmetry sector is regulated in SLHA2: TẠP CHÍ KHOA HỌC  SỐ 4/2016 2  Lsoft  m Hu H u  m Hd H d  ms2 S  m Q2 Q  m 2U U R2 2  m 2D D 2R  m 2L L2  m 2E E 2R  (h u A u Q.H u U cR  h d A d Q.H d D cR  h e A e L.H d E cR  A  H u H dS  A S3  m 32 H u H d  m s2S2  sS  hc) (3) In the super-potential (1) we have supersymmetry parameters ,  and F (the soft 2 supersymmetry interactions break the parameters m , mS and parameter S in (3)), however, some terms are not eliminated in some different solutions for simple NMSSM with a part of invariant super-potential when     F  WNMSSM  SH u H d   S (4) 2 Then, eliminating the parameters m , mS and S in (3), combining the vevs of Sˆ in the weak sector or in the breaking supersymmetry to define  :  eff  s The matter of  (5) in MSSM has been solved then As any supersymmetry theory with invariant super-potential sector (ternary), the Lagrangians, which contain the soft supersymmetry violation conditionsspecified by (3), have one symmetry  randomly, which is corresponding to the multiplication of all chiral superfields with e2i/3 The invariant super-potential (4) is presented like invariant  The non-dimension terms in the super-potential (1) will break the symmetry  The model with super-potential (1) is the NMSSM The invariant  Higgs sector is defined by the seven parameters , ,m2Hd ,m2Hu ,mS2 ,A ,A The expression of Higgs mass matrix in the invariant  of the NMSSM shows that invariant  is obtained when: m32  mS2  S       F  (6) From the supersymmetry gauge interaction and soft supersymmetry breaking conditions, we obtain the Higgs potential: TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI VHiggs  (H u H d  H 0u H d0 )  S2  2S   F 2 2  (m 2H    S ( H 0u  H u )  (m H2    S ( H d0  H d ) 2 u d g g g 22  0*  2  2  ( Hu  Hu  Hd  Hd )  H u H d  H 0u H 0* d 2  mS2 S  (A  (H u H d  H 0u H d0 )S  A S3  m32 (H u H d  H 0u H 0d ) 2  mS S  SS  h.c (7) 2 where g1 and g2 present gauge interaction U(1) and SU(2) The Higgs doublets H and H2 can be developed in the form:  v  S  iA sin     H  cos  H1   1* , H    , S = (x + X + iY)  v  S  iA cos   H sin    2  (8) In case the CP violation is considered, the x parameter will be considered as the complex number In the year 2012, the Higgs boson was found out with the mass approximates to 125GeV In late of the year 2015, the signal of another scalar particle appeared and this is being studied in the experiment The decay of Higgs into Higgs in the NMSSM is being researched in the experiment The research on the decay of the new particles in the model will bring us the hope of finding out these particles as well as verifying the correctness of the model [8] In this paper, we have studied the decay h3 Z + a1 and calculated the decay width of this process to one loop vertex correction The numerical calculation results are also presented in charts to evaluate the influence of CP violation on the decay width and the lifetime of h3 THE DECAYh3 Za1 The amplitude which is calculated to one loop vertex correction has the following result: M = M00 + M1 + M2 + M3 + M4 In which:  From the diagram (a) we have: M 00  A1  k1  k    k   (9) TẠP CHÍ KHOA HỌC  SỐ 4/2016 Figure Feyman diagram for correction SUSY – QCD in decay h (k1 )  a1 (k )  Z(k ) (a) Tree level ; (b), (c), (d) and (e) Oneloop vertex correction  From the diagram (b) we obtain:  (m  ma2 )  B 02  B13  B 03  B 02  B13  B03       k    (m  m )(2m  m )  2m  m  2m C 01  a1 Z h3 h3 Z ha      2 2 2   B12 A1  (k3 )   2(mZ  mha  ma1 )C 01  (4mha  2ma1  mh3 )C11  k2  M1 =    mZ2 32    B12  (m  ma2 )(2mZ2  mh2 )C 01  ( m  ma2 ) B12   ha     2 2 2  (mha  ma1 )(2mZ  mh3 )C 21  A01  (2mZ  mh3 ) B11   k    2 2     2(m  ma )C11  2m  mh C 21 ha         + From the diagram (c) we obtain:     B02  B12   C 02  C12  m  m  k   a h3  3   A1 B1M 0  (k3 )    M2    mZ  C 02  C12   k2  2 mZ 16     mZ2  C 02  C 22   ma2  mh23 C 22  k1        From the diagram (d) we obtain:  10 TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI       m  m  m B 03  m  m  m B 05  m  B 04  B14    h a1 Z a h3 Z  Z      k3  2 2 2 2  C 03  C 13 m m  m  m  m  m  m m  m     Z Z a h3 h a1  a h a1    A1   (k3 )    2   M3  2 B13 mh  ma1  mZ  k2  mZ 16       B15  2C 23 m  m  m  2m    Z a h a1       2 2   2C 23 ma  mh3 mh  ma1     k  2 2     ma  mh3 mh  ma1                       From the diagram (e) we obtain: M4  and:   A1  iA1E1  (k3 )k g U aS1UP1  U aS2UP2  ,  cos W 16 B1   B04  B14 igmZ cos U aS1  sin U aS2  ,  cos W  g  g ,2 U aS1U bS1U P1U P1  U aS2U bS2U P2U P2  1   i   g  g ,2     U aS1U bS1U P2U P2  U aS2U bS2U P1U P1   2ik 2U aS3U bS3U P3U P3 4  E1  i  i U aS1U bS1U P3U P3  U aS3U bS3U P1U P1  U aS2U bS2U P3U P3  U aS3U bS3U P2U P2  U aS1U bS2  U aS2U bS1 U P3U P3  U aS3U bS3 U P1U P2  U P2U P1      i k  U aS1U bS3U P2U P3  U aS3U bS1U P2U P3  U aS1U bS3U P3U P2  U aS3U bS1U P3U P2   S S P P  S S P P S S P P S S P P  U a 2U b 3U  1U   U a 3U b 2U  1U   U a 2U b3U  3U   U a 3U b 2U  3U   g  g ,2 v1U aS1U P1U P1  v2U aS2U P2U P2   2  g  g ,2   i  2   v1U aS1U P2U P2  v2U aS2U P1U P1   2  M  i  2i   kv1   v2 U aS2U P3U P3  2i   kv2   2v1 U aS1U P3U P3    2i xU aS3 U P1U P1  U P2U P2   i 2k x  2kAk U aS3U P3U P3  2i kU aS3 v1 U P2U P3  U P3U P2   v2 U P1U P3  U P3U P1   A   i  2 kx    A   i  2 kx     S P P P P S P P P P  U a1 U  2U   U  3U    U a U  1U   U  3U      S P P P P  U a U  1U   U  2U    TẠP CHÍ KHOA HỌC  SỐ 4/2016 11 And the Pasarino – Velmanfunctions: A01  A0  mZ2  ,  m   ,m ,  B01; B11  B0;1 mh23 , mZ2 , mZ2 , B02; B12  B0;1 mZ2 , mh2 , mZ2 , B03; B13  B0;1 B04; B14  B0;1 mZ2 , mh2 , ma2 , a1 , mh2  Z    B05; B15  B0;1 mh23 , ma2 , mZ2 ,   C 01; C11; C 21  C0;11;12 ma21 , mh23 , mZ2 , mh2a , mZ2 , mZ2 ,  m , m , m  ,m , C 02; C12; C 22  C0;11;12 mZ2 , mh23 , ma21 , mh2a , mZ2 , ma2 , C 03; C13; C 23  C0;11;12 Z h3 a1 , mh2 , ma2 Z The decay width which is calculated to one loop vertex correction has the following result: (h3  Za1 )   M  mh23 , mZ2 , ma21  16m  h3 (10) with:    +  m2h3 ,m2Z ,ma21  m 4h3  m 4Z  ma41  2m 2h3 m 2Z  2m 2Z m 2a1  2m 2h3 m 2a1  1/2 +  = 1; 2; and = 1; NUMERICALRESULTS To study the influence of the mass ma1 on the decay process h3Za1, we have used two set of parameters [5, 6, 8, 9] for programming numerical calculation  The 1st parameter set: λ = 0,8; x = 200.ei; k = 0,1; mh3 = 498GeV; tanβ = 3; sin α = 0,58; Ak = 6; Aλ = 486; ma1 = 79.3GeV From the results obtained, we have found that the influence of  on the decay h3Za1is relatively significant (Fig and Fig.3) 12 TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI Figure The influence of  on the decay Figure The influence of  on the lifetime of width of the decay h3Za1 h3of the decay h3Za1 Specifically, the influence of on the decay width and on the lifetime of h3 in the decay h3Za1is relatively significant When runs from 0.0to0.1Rad, it can influenceabout 30% onthe decay width and about 30% on the lifetime of h3 With the 1st parameter set, we have obtained the results of the decay width h3Za1at about 5.1010 – 7.5.1010 (1/s) and forthe lifetime of h3 at about1.4.10-11–1.9.10-11 (s)  The 2nd parameter set: λ = 0.8; x = 200ei; k = 0.1; mh3 = 498GeV; tanβ = 10; sinα = - 0.726; Ak = 7; Aλ = 492; ma1 = 79.3GeV We have obtained the results as in Fig and Fig Figure The influence of  on the decay Figure The influence of  on the lifetime of width of the decay h3Za1 h3of the decay h3Za1 TẠP CHÍ KHOA HỌC  SỐ 4/2016 13 From the results in the graphs for the 2nd parameter set, we can see that the contribution ofin this case is insignificant With this parameter set, we have obtained the value of the decay width h3Za1at about 1.356.1010 (1/s)and for the lifetime of h3 at about 7.368.10-11 (s) CONCLUSIONS In the NMSSM, a single superfield is added with complex scalar field components, this leads to the appearance of seven Higgs in the NMSSM (including three even-CP Higgs h1,2,3 (mh1< mh2< mh3), two odd-CP Higgs a1,2 (ma1< ma2) and a pair of charged Higgs H  ) The influence of CP violation on the decay width and the life time of h3 is relatively significant in case the 1st set of parameter is used (the results can be changed up to 30%) The numerical calculation results have shown that the lifetime of h3 is relatively small and the decay with is relatively large (10101/s) From these results, we need to pay attention to the above two elementsin studying theories as well as to the decay experiments of h3.These results bring us the hope that we can find the other Higgsbosons soon REFERENCES 10 Radovan Demi‟senk and John F Gunion, hep-ph/0811.3537 M.M Almarashi anh S.moretti, hep-ph/1109.1735 M.M Almarashi anh S.moretti, hep-ph/1105.4191 H E Haber and G.L Kane.Phys Rep 117 (1985) 75 Ulrich Ellwanger, hep-ph/1108.0157 U Ellwanger, C Hugonie and A M Teixeira, Phys Rept 496 (2010) W Bernrenther and M Suzuki, Rev Mod Phys 63 (1991) 3-13 N C Cuong, P X Hung, L H Thang (2016), Scientific Journal of HMU, 2, 22-30 Radovan Dermisek (2010), hep-ph/1012.3487vl A Barlt, et al., Phys Lett.B419 (1998) 243 14 TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI PHÂN RÃ H3 THÀNH Z VÀ A1 TRONG NMSSM Tóm tắt: Để giải vấn đề  mơ hình chuẩn siêu đối xứng tối thiểu (MSSM), trường đơn S đưa vào xây dựng mơ hình chuẩn siêu đối xứng gần tối thiểu (NMSSM) Chân không mở rộng với giá trị kỳ vọng không suy biến hạt trung hòa CP chẵn Hu, Hd S Trong NMSSM có boson Higgs (cịn MSSM có boson Higgs), với ba Higgs vô hướng - CP chẵn1,2,3 (mh1< mh2< mh3) hai Higgs giả vô hướng - CP lẻ a1,2 (ma1< ma2) cặp Higgs mang điện H  Phân rã Higgs thành Higgs điểm đáng ý NMSSM Trong báo nghiên cứu phân rã h3 Z a1 Độ rộng phân rã tính tới hiệu chỉnh đỉnh vịng Các kết tính số ảnh hưởng vi phạm CP đưa Từ khóa: Higgs boson, phân rã, vi phạm CP, NMSSM ... Figure The influence of  on the decay Figure The influence of  on the lifetime of width of the decay h3? ??Za1 h3of the decay h3? ??Za1 Specifically, the influence of on the decay width and on the. .. correction has the following result:  (h3  Za1 )   M  mh23 , mZ2 , ma21  16m  h3 (10) with:    +  m 2h3 ,m 2Z ,ma21  m 4h3  m 4Z  ma41  2m 2h3 m 2Z  2m 2Z m 2a1  2m 2h3 m 2a1  1/2 +... 125GeV In late of the year 2015, the signal of another scalar particle appeared and this is being studied in the experiment The decay of Higgs into Higgs in the NMSSM is being researched in the