The production of b1,b1 from the e e-, collision via photon, Z boson, higgs and vector unparticle exchange in the MSSM

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Despite the prediction of the Higgs boson at Large Hadron Collider (LHC) in the CERN in 2012 after it has been theorized for over 50 years, however, the Standard model (SM) still can not explain the mass of neutrinos; the hierarchy problem; the contribution of dark energy, dark matter and CP violation in cosmology.

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Nội dung Text: The production of b1,b1 from the e e-, collision via photon, Z boson, higgs and vector unparticle exchange in the MSSM

HNUE JOURNAL OF SCIENCE DOI: 10.18173/2354-1059.2018-0067 Natural Sciences 2018, Volume 63, Issue 11, pp. 34-40 This paper is available online at http://stdb.hnue.edu.vn   THE PRODUCTION OF b1 , b1 FROM THE e , e COLLISION VIA PHOTON, Z BOSON, HIGGS AND VECTOR UNPARTICLE EXCHANGE IN THE MSSM Dao Thi Le Thuy Faculty of Physics, Hanoi National University of Education Abstract. The production of b1 , b1 squarks from the e e collision via photon, Z boson,   Higgs and vector unparticle exchange when beams e , e are unpolarized and polarized are studied in detail in the Minimal Supersymmetric Standard Model (MSSM). The results show   that, the cross-section strongly depends on the polarization of e , e beams. And in the high energy region, we evaluated the exchange particles’ contributions in the cross-section of e e  b1b1 . Keywords: b1 , b1 , vector unparticle, MSSM. 1. Introduction Despite the prediction of the Higgs boson at Large Hadron Collider (LHC) in the CERN in 2012 after it has been theorized for over 50 years, however, the Standard model (SM) still can not explain the mass of neutrinos; the hierarchy problem; the contribution of dark energy, dark matter and CP violation in cosmology. Therefore the new physics beyond the SM have been studied. Such as a new physics is “unparticle” which couples to the SM sector through higher dimensional operators in low energy effective theory by Georgi [1]. The unparticle was proposed by Banks- Zaks [2], where providing a suitable number of massless fermions, theory reaches a non-trivial infrared ﬁxed point [3] and a theory can be taken in a low energy. From to now, there are many papers have studied the unparticles, such as, unparticles in CP violation [4-8], and explaining some anomalies in currents flowing in super-conductors [9-11] and the unparticles are also tried to find at the LHC [12-16]. In fact, unparticle maybe appear at TeV scale, such as in the Minimal Supersymmetric Standard Model (MSSM) [17]. We try to study the relation between the unparticle with MSSM by considering the production of squarks. Received September 11, 2018. Revised November 21, 2018. Accepted November 27, 2018. Contact Dao Thi Le Thuy, e-mail address: thuydtl@hnue.edu.vn 34
The production of b1 , b1 from the e , e collision via photon, z boson, Higgs and vector unparticle… 2. Content 2.1. Interaction Lagrangian between vector unparticle and squark In this section, we consider only the vector unparticle. We give the effective interaction  Lagrangian of vector unparticle with squark. Vector unparticle OU couplings with squarks: Lint  Fij 1UdU OU qi*  q j , (1)  where dU is the scale dimension of the unparticle operator OU , Fij is a coefficient couplings, U is induced the dimensional transmulation. The Feynman rules for the operators in Eqs. (1) are shown in Fig. 1. Fij (k1  k2 )  UdU 1 Figure 1. Feynman rules for the U (spin-1) couplings with squarks 2.2. The cross-section of the e e  b1b1 collision The pair production of squarks in e , e collision via  , Z ,U  spin1, h , H , A exchange.   0 0 0 The corresponding Feynman diagrams are shown in Fig. 2. Figure 2. The Feynman diagrams for the process e e  qi q j For unpolarized e , e beams, the matrix element for process e e  qi q j is given by: + Via  exchange: e2eq ij M   i 2 (k1  k2 )  v(p2 , s2 )  u ( p1 , s1 ) , (2) q + Via Z boson exchange: g 2Cij  q q  M Z  i (k1 -k 2 )  g    2   v(p2 , s2 ) (ve  ae )u ( p1 , s1 ) , 5 (3) 4c (qs  mZ ) 2 w 2 2  mZ  + Via vector unparticle (U–spin1) exchange: 35
Dao Thi Le Thuy 1 Ad (q 2 )d Fij  U 2 q q    MU  spin1      (k1 -k 2 ) v(p2 , s2 ) (1   )u ( p1 , s1 ) , 5  g U (4) U2( dU 1) 2sin dU   mZ 2  + Via Higgs h0 , H 0 and A0 exchange: ihe sin  (G1 ) M h0  v ( p2 , s2 )u ( p1 , s1 ) , (5) 2(q 2  mh20 ) ihe cos (G2 ) M H0  v ( p2 , s2 )u ( p1 , s1 ) , (6) 2(q 2  mH2 0 ) ihe cos (G3 ) M A0  v ( p2 , s2 ) 5u ( p1 , s1 ) , (7) 2(q  m ) 2 2 A0 Similar, for polarized e , e beams, we get + Via  exchange: e2eq ij M  LL  i 2 (k1  k2 )  v(p2 , s2 )(1   5 )  u ( p1 , s1 ) , (8) 2q e2eq ij M  RR  i 2 (k1  k2 )  v(p2 , s2 )(1   5 )  u ( p1 , s1 ) , (9) 2q + Via Z boson exchange: g 2Cij (ve  ae )  q q  M ZLL  i (k1 -k 2 )  g    2   v(p2 , s2 ) (1   )u( p1 , s1 ) , 5 (10) 8c (qs  mZ ) 2 w 2  2 mZ  g 2Cij (ve  ae )  q q  M ZRR  i (k1 -k 2 )  g    2   v(p2 , s2 ) (1   )u( p1 , s1 ) , 5 (11) 8c (qs  mZ ) 2 w 2  2 mZ  + Via vector unparticle (U–spin1) exchange: 1 Ad (q 2 )d Fij  U 2 q q    M (U  spin1) RR     g    (k1 -k 2 ) v(p2 , s2 ) (1   )u ( p1 , s1 ) , U 5 (12)  2( dU 1) U 4sin dU   mZ 2  + Via Higgs h0 , H 0 and A0 exchange: ihe sin  (G1 ) M h0 LR  v ( p2 , s2 )(1   5 )u ( p1 , s1 ) , (13) 2 2(q  m ) 2 2 h0 ihe sin  (G1 ) M h0 RL  v ( p2 , s2 )(1   5 )u ( p1 , s1 ) , (14) 2 2(q  m ) 2 2 h0 36
The production of b1 , b1 from the e , e collision via photon, z boson, Higgs and vector unparticle… ihe cos (G2 ) M H 0 LR  v ( p2 , s2 )(1   5 )u ( p1 , s1 ) , (15) 2 2(q  m ) 2 2 H0 ihe cos (G2 ) M H 0 RL  v ( p2 , s2 )(1   5 )u ( p1 , s1 ) , (16) 2 2(q  m ) 2 2 H0 ihe cos (G3 ) M A0 LR  v ( p2 , s2 )(1   5 )u ( p1 , s1 ) , (17) 2(q  m ) 2 2 A0 ihe cos (G3 ) M A0 RL  v ( p2 , s2 )(1   5 )u ( p1 , s1 ) , (18) 2(q  m ) 2 2 A0 In this section, we discuss the pair production of squarks (b1 , b1 ) in e e collision. The cross – section for process e e  b1b1 is given by d 1 k 2  M fi S . (19) d  64 s p 2 where s is the center-of-mass energy, M fi is the matrix element, d   d (cos )d ;   0,   ;  0, 2  . We choose mb  157GeV ; mh0  125GeV ; mH 0  162GeV GeV; mA0  150GeV ; 1 U  1000GeV ; dU  1, 7 ; 1  1 . At s  3000GeV , Figure 3 shows the (b1 , b1 ) production differential cross section (DCS) as a function of cos  . a) b) Figure 3. The differential cross – section as a function of cos  when e , e beams are unpolarized We see that, the DCS has its minimum value at cos   1 and maximum value at cos  0 . Therefore, the advantageous direction to collect (b1 , b1 ) is perpendicular direction to the e , e beams. The s dependence of the e e  b1b1 cross section is shown in Figure 4. 37
Dao Thi Le Thuy a) b)   Figure 4. The cross – section as a function of s when e , e beams are unpolarized s  500GeV . The maximum value is In Figure 4, the cross section has maximum value at 3 about 4,5 10 pbar . The cross section decreases while s increases from 500GeV to 3000GeV . In Figure 3.3b, when s  320GeV ,  / F11 is about zero.  / F11 2 2 increases while s increases from 320GeV to 3000GeV . Next, we turn to the effects of polarization. Specifically, we calculated the differential cross-sections and the total cross-sections in case of both e  and e  beams are polarized. Here, we evaluated the cross section in case of the exchange contribution of U  spin1 and exchange contribution of photon is the same level. The results are shown in Figure 5 and Figure 6. a) b) c) d) Figure 5. The differential cross – section as a function of cos  when e , e beams are polarized 38
The production of b1 , b1 from the e , e collision via photon, z boson, Higgs and vector unparticle… a) b) c) d) Figure 6. The cross – section as a function of s   when e , e beams are polarized In Figure 5, we ploted the DCS as a function of cos  at s  3000GeV for right-      polarized e and e beams; left-polarized e and e beams; right-polarized e beam and left-   polarized e  beam. Figure 5a shows the DCS for both the e , e beams are right-polarized has  largest value. In case of a right-polarized e beam, a left-polarized e  beam and backwards (Figure 6d), the DCS don’t depend on cos  and it’s value is very small. So that, the cross- section is largest for the vector unparticle exchange contributions and is smallest for the Higgs exchange contributions. The s dependence of  (e e  b1b1 ) is shown in Figure 6 for polarized e , e beams. In the high energy region, the Figure 6a shows that the cross section increases when s increases   for right-polarized e and e beams. In Figure 6b-d, the cross section decreases when s     increases for left-polarized e , e beams; right-polarized e beam and left-polarized e beam. 3. Conclusions In this paper, we calculated the cross section of the process e e  b1b1 for unpolarized and  polarized e , e  beams. The results shows that, the advantageous direction to collect (b1 , b1 ) are perpendicular direction to the e , e beams. In the high energy region, the cross section increases 39
Dao Thi Le Thuy when s increases for right-polarized e  and e  beams; the cross section decreases when s   increases for left-polarized e , e  beams; right-polarized e beam and left-polarized e  beam. The cross-section is largest for the vector unparticle exchange contributions and is smallest for the Higgs exchange contributions. REFERENCES [1] H. Georgi, 2007. Unparticle Physics, Phys. Rev. Lett. 98, 221601. [2] T. Banks and A. Zaks, 1982. On the phase structure of vector-like gauge theories with massless fermions, Nucl. Phys. B 196, 189. [3] V. Barger, Y. Gao, W.Y. Keung, D. Marfatia and V. N. Senguz, 2008. Unparticle physics with broken scale invarance, Phys.Lett.B661, pp.276-286. [4] C. H. Chen and C. Q. Geng, 2007. Unparticle physics effects on direct CP violation, Phys. Rev. D 76, 115003. [5] C.S. Huang, and X.H. Wu, 2008. Direct CP violation of B  lv in unparticle physics, Phys. Rev. D 77, 075014. [6] R. Zwicky, 2008. Unparticles and CP -violation", Journal of Physics: Conference Series 110 , 072050. [7] M. Ettefaghi, R. Moazzemi, and M. Rousta, 2017. Constraining unparticle physics from CP violation in Cabibbo-favored decays of D mesons, Phys. Rev. D95, 095027. [8] H. Bagheri, M. Ettefaghi, and R. Moazzemi, 2017. On the difference of time-integrated CP asymmetries in D0  K  K  and D0     decays: unparticle physics contribution, Phys. Lett, B771, 309-312. [9] J. P. F. LeBlanc and A. G. Grushin, 2015. Unparticle mediated superconductivity, New J. Phys. 17, 033039. [10] P. W. Phillips, B. W. Langley, J. A. Hutasoit, 2013. Un-Fermi Liquids: Unparticles in Strongly Correlated Electron Matter, Phys. Rev. B vol. 88, 115129. [11] K. Limtragool, P. Phillips, 2015. Power-law Optical Conductivity from Unparticles: Application to the Cuprates, Phys. Rev. B 92, 155128. [12] CMS Collaboration, 2015. Search for dark matter, extra dimensions, and unparticles in monojet events in proton-proton collisions at s  8TeV , Eur. Phys. J. C75, 235. [13] CMS Collaboration, 2016. Search for dark matter and unparticles produced in association with a Z boson in proton - proton collisions at s  8TeV , Phys. Rev. D93, 052011. [14] CMS Collaboration, 2017. Search for dark matter and unparticles in events with a Z boson and missing transverse momentum in proton-proton collisions at s  13TeV , JHEP 03, 061, [arxiv: 1701.02042]. [15] J. R. Mureika, 2008. Unparticle-enhanced black holes at the LHC, Phys. Lett. B660, pp. 561–566. [16] T.M. Aliev, S. Bilmis, M. Solmaz, and I. Turan, 2017. Scalar Unparticle Signals at the LHC, Phys. Rev.D95, 095005. [17] H. Zhang, C. S. Li and Z. Li, 2007. Unparticle physics and Supersymmetry phenomenoly, Phys. Rev. D 76, 116003. 40