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Feynman Rules for Neutrinos and New Neutralinos in the BLMSSM*

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Feynman Rules for Neutrinos and New Neutralinos in the BLMSSM* Chinese Physics C Vol. 40, No. 9 (2016) 093103 Feynman rules for neutrinos and new neutralinos in the BLMSSM * Xing-Xing Dong(Â33)1;1) Shu-Min Zhao(ëä¬)1;2) Hai-Bin Zhang(Ü°R)1 Fang Wang()3 Tai-Fu Feng(¾F)1;2 1Department of Physics and Technology, Hebei University, Baoding 071002, China 2State Key Laboratory of Theoretical Physics (KLTP), Institute of Theoretical Physics, Chinese Academy of Sciences, 100190 Beijing, China 3Department of Electronic and Information Engineering, Hebei University, Baoding 071002, China Abstract: In a supersymmetric extension of the Standard Model where baryon and lepton numbers are local gauge symmetries (BLMSSM), we deduce the Feynman rules for neutrinos and new neutralinos. We briefly introduce the mass matrices for the particles and the related couplings in this work, which are very useful to research the neutrinos and new neutralinos. Keywords: supersymmetry, Feynman rules, mass matrices PACS: 13.15.+g, 12.60.-y DOI: 10.1088/1674-1137/40/9/093103 1 Introduction explain the discovery from neutrino oscillations. There- fore, theoretical physicists have extended the MSSM to In quantum field theory, the Standard Model (SM) account for the light neutrino masses and mixings. is a theory concerning the electromagnetic weak and As an extension of the MSSM which considers the strong interactions. Though the lightest CP-even Higgs local gauged baryon (B) and lepton (L) symmetries, the (mh0 126 GeV) was detected by the LHC, the SM is BLMSSM is spontaneously broken at the TeV scale [17{ unable'to explain some phenomena and falls short of be- 20]. In the BLMSSM, the lepton number is broken in ing a complete theory of fundamental interactions. In an even number while baryon number can be changed the neutrino sector, the observations of solar and atmo- by baryon number violating operators through one unit. spheric neutrino oscillations [1{4] are not incorporated The BLMSSM can not only account for the asymme- in the SM, which provides clear evidence for physics be- try of matter-antimatter in the universe but also explain yond the SM. Furthermore, the authors think that a well- the data from neutrino oscillation experiments [21{23]. motivated dark matter candidate emerges from the neu- Compared with the MSSM, the BLMSSM includes many trino sector [5{7]. new fields such as new quarks, new leptons, new Higgs, Physics beyond the SM has drawn physicists' atten- and the superfields X^ and X^0 [24{26]. In this work, we tion for a long time. One of the most appealing theories mainly study the Feynman rules for the neutrino and to describe physics at the TeV scale is the minimal super- new neutralinos in the BLMSSM. symmetric extension of the Standard Model (MSSM) [8{ In the BLMSSM, the light neutrinos get mass from 11]. The MSSM includes necessary additional new par- the seesaw mechanism, and proton decay is forbid- ticles that are superparters of those in the SM. The den [17{20]. Therefore, it is not necessary to build a large right-handed neutrino superfields can extend the next-to- desert between the electroweak scale and grand unified minimal supersymmetric standard model (NMSSM), and scale. This is the main motivation for the BLMSSM. these superfields only couple with the singlet Higgs [12{ Many possible signals of the MSSM at the LHC have 15]. In R-parity [16] conserved MSSM, the left-handed been studied by the experiments. However, with the light neutrinos are still massless, leading to a failure to broken B and L symmetries, the predictions and bounds Received 19 February 2016, Revised 16 May 2016 ∗ Supported by Major Project of NNSFC (11535002) and NNSFC (11275036), Natural Science Foundation of Hebei Province (A2016201010), and Foundation of Hebei Province (BR2-201), and the Natural Science Fund of Hebei University (2011JQ05, 2012-242), Hebei Key Lab of Optic-Electronic Information and Materials, Midwest Universities Comprehensive Strength Promotion Project 1) E-mail: [email protected] 2) E-mail: [email protected] Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd 093103-1 Chinese Physics C Vol. 40, No. 9 (2016) 093103 = λ Q^ Q^c Φ^ +λ U^ cU^ '^ +λ D^ cD^ '^ for the collider experiments should be changed. From WB Q 4 5 B U 4 5 B D 4 5 B ^ ^ ^ ^ c ^ ^ ^ c the decays of right handed neutrinos [19, 20, 27], we +µBΦB'^B +Yu4 Q4HuU4 +Yd4 Q4HdD4 can look for lepton number violation at the LHC. Sim- ^c ^ ^ ^c ^ ^ +Yu5 Q HdU5 +Yd5 Q HuD5; ilarly from the decays of squarks and gauginos, we can 5 5 also detect baryon number violation at the LHC. For ex- ample, the channels with multi-tops and multi-bottoms ^ ^ ^c ^ ^ ^ c ^c ^ ^ L = Ye4 L4HdE4 +Yν4 L4HuN4 +Ye5 L5HuE5 may be caused by the baryon number violating decays W ^c ^ ^ ^ ^ ^ c ^ c ^ c of gluinos [19, 20]. +Yν5 L5HdN5 +Yν LHuN +λNc N N '^L After this introduction, we briefly summarize the +µLΦ^L'^L; main contents of the BLMSSM in Section 2. The mass ^ ^c ^ ^ c ^ ^ 0 matrices for the particles are collected in Section 3. Sec- X = λ1QQ5X +λ2U U5X W tions 4 and 5 are respectively devoted to the related cou- c 0 0 +λ3D^ D^ 5X^ +µX X^X^ : (2) plings of neutralinos and neutrinos beyond the MSSM. We give some discussion and conclusions in Section 6. The soft breaking terms soft of the BLMSSM are generally shown as [17, 18, 28L] MSSM 2 c∗ c 2 y 2 Main content of the BLMSSM = (mνc ) N~ N~ m Q~ Q~ Lsoft Lsoft − ~ IJ I J − Q~4 4 4 m2 U~ c∗U~ c m2 D~ c∗D~ c m2 Q~cyQ~c Extending the MSSM with local gauged baryon (B) − U~4 4 4 − D~ 4 4 4 − Q~5 5 5 2 ~ ∗ ~ 2 ~ ∗ ~ 2 ~y ~ and lepton (L) numbers, one obtains the BLMSSM, m ~ U U5 m ~ D D5 m~ L L4 − U5 5 − D5 5 − L4 4 and at the TeV scale the local gauge symmetries m2 N~ c∗N~ c m2 E~c∗E~c m2 L~cyL~c are spontaneously broken. In this section, we briefly − ν~4 4 4 − e~4 4 4 − L~5 5 5 2 ~ ∗ ~ 2 ~∗ ~ 2 ∗ review some features of the BLMSSM. SU(3) mν~5 N5 N5 me~5 E5 E5 mΦB ΦBΦB C − − − SU(2) U(1) U(1) U(1) [19, 20] is the basic⊗ 2 ∗ 2 ∗ 2 ∗ L Y B L m'B 'B'B mΦL ΦLΦL m'L 'L'L gauge symmetry⊗ ⊗of the BLMSSM.⊗ The exotic leptons − − − c c mBλBλB +mLλLλL +h:c: L4 (1;2; 1=2;0;L4), E4 (1;1;1;0; L4), N4 − ∼ − c ∼ − ∼ (1;1;0;0; L4), L5 (1;2;1=2;0; (3 + L4)), E5 (1;1 ~ ~ c ~ ~ c − ∼ − ∼ − + Au4 Yu4 Q4HuU4 +Ad4 Yd4 Q4HdD4 1b;0;3 + L4), N5 (1;1;b0;0;3 + L4) and the exoticb ∼ c n ~c ~ ~c ~ quarks Q (3b;2;1=6;B ;0), U (3;1; 2=b3; B ;0), +Au5 Yu5 Q5HdU5 +Ad5 Yd5 Q5HuD5 4 ∼ 4 4 ∼ − − 4 Dc (3;1;1=3b; B ;0), Qc (3;2; 1=6; (1 + B );0), +A λ Q~ Q~cΦ +A λ U~ cU~ ' 4 ∼ − 4 5 ∼ − − 4 BQ Q 4 5 B BU U 4 5 B U (3;b1;2=3;1 + B ;0), D b(3;1 1=3;1 + B ;0) are c 5 4 5 4 +A λ D~ D~ ' +B µ Φ ' +h:c: inbtro∼duced to cancel L andb ∼B anomalies− respectively. BD D 4 5 B B B B B o Theb exotic Higgs superfieldsb ΦL (1;1;0;0; 2), 'L ~ ~c ~ ~ c ∼ − ∼ + Ae4 Ye4 L4HdE4 +Aν4 Yν4 L4HuN4 (1;1;0;0;2) and ΦB (1;1;0;1;0), 'B (1;1;0; 1;0) ∼ ∼ − n ~c ~ ~c ~ are introduced respectively to bbreak lepton numberband +Ae5 Ye5 L5HuE5 +Aν5 Yν5 L5HdN5 ~ ~ c ~ c ~ c baryon number spbontaneously. The exoticb Higgs super- +AνYνLHuN +Aνc λνc N N 'L fields Φ , ' and Φ , ' acquire nonzero vacuum expec- L L B B +B µ Φ ' +h:c: tation values (VEVs), then the exotic leptons and exotic L L L L quarksbobtain masses.b The model also includes the su- ~ ~c o ~ c ~ 0 b b 0 + A1λ1QQ5X +A2λ2U U5X perfields X (1;1;0;2=3+B4;0) and X (1;1;0; (2=3+ ∼ ∼ − n c 0 0 B4);0) to make heavy exotic quarks unstable. Further- +A3λ3D~ D~ 5X +BX µX XX +h:c: ; (3) more, theblightest mass eigenstate canb be a dark matter 0 o candidate, while X and X mix together. Anomaly can- where MSSM represent the soft breaking terms of MSSM, Lsoft cellation requires the emergence of new families. How- and λB and λL are the gauginos of U(1)B and U(1)L, re- ever there is no flabvour violationb at tree level since they spectively. The SU(2)L doublets Hu; Hd and SU(2)L do not mix with the SM fermions and there are no Lan- singlets ΦB; 'B; ΦL; 'L acquire the nonzero VEVs υu; υd dau poles at the low scale due to the new families.
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