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In this article, we have considered the possible signatures of radion through Bhabha scattering. The numerical results show that the total cross section with radion effects are abont 0.62-0.65 pb.
TRƯỜNG ĐẠI HỌC THỦ ĐÔ H 68 NỘI RADION EFFECTS ON BHABHA SCATTERING Ha Huy Bang, Pham Que Duong, Nguyen Thi Thu Huyen, Nguyen Thi Thuy Linh Ha Noi University of Sciences Abstract: In this article, we have considered the possible signatures of radion through Bhabha scattering The numerical results show that the total cross section with radion effects are abont 0.62-0.65 pb This could have inportant implications for radion searches and for the measurement of the cross – section of the Bhabha scattering PACS number: 12.60.Cn, 12.20.-m, 42.55.-f Keywords: Keywords radion, Bhabha scattering Email: hahuybang@hus.edu.vn Received 24 March 2019 Accepted for publication 25 May 2019 INTRODUCTION As well known, there are many convincing evidences that 80% of the matters in the universe is composed of dark matters (DM) In several extensions of the Standard Model, radion or u-boson is postulated [1-5] On the other hand, the Randall – Sundrum (RS) Model is one of the attractive condidates to solve the gauge hierarchy problem in the standard Model Many works have been done on the phenomenological aspects of radion in various colliders [6-9] As we well known, Bhabha scattering is among the key processes in particle physics Recently, the authors have presented the results of the SANC group on the complete oneloop calculation of the electroweak rediative corrections to Bhabha scattering with polarized beams [10] Very recently, we have investigated unparticle effects on Bhabha scattering [11] and on axion-like particles production in e+e- collisions [12] In this paper, we investigate virtual radion effects via Bhabha scattering TẠP CHÍ KHOA HỌC − SỐ 31/2019 69 RADION EXCHANGE AND CROSS SECTION In this cestion, we will derive a formula for the cross-section of the process presented in Figure.2, which shows on of the possible processes, where a radion may intermediate a creation of e+e- in the e+e- scattering Í´ Í Fig Feynman diagram for Bhabha scattering via radion and photon The amplitude for this process is given by M = v ( k )ieγ µ u ( k1 ) = ie ε − ie ( g µν − q µ qν / mu2 ) q −m u ( g µν − q µ qν / m ) q − mu2 u u ( p1 )i eγ ν v ( p ) (1) v ( k )γ u ( k1 )u ( p1 )γ v ( p ), µ µ From this, we get M = 16e4ε { 2( p1k1 )( p2 k2 ) + 2( p1k2 )( p2 k1 ) (q − mu2 ) − qk2 [( p1k1 )(qp2 ) + (qp1 )( p2 k1 ) − 2( p1 p2 )(qk1 )] mu2 − qk1 [ ( p1k2 )(qp2 ) + (qp1 )( p2 k2 ) − 2( p1 p2 )(qk2 )] mu2 +2 − k1k2 (qk )(qk ) 2(qp1 )(qp2 ) − ( p1 p2 )q + 2(qp1 )(qp2 ) − ( p1 p2 )q mu mu q (k1k2 ) 2(qp1 )(qp2 ) − ( p1 p2 )q } mu4 (2) In center of mass frame, four-moments of particles are defined k1 = ( E , k ), k2 = ( E , −k ), p1 = ( E , p ), p2 = ( E , − p ) and S = ( k1 + k ) = ( p1 + p2 ) = q = E Where S is the center of mass energy.The differential cross-section can be obtained as follows.Neglecting the mass of electron, we have TRƯỜNG ĐẠI HỌC THỦ ĐÔ H 70 M = 4e4ε s s + cos θ + , 2 (q − mu ) mu NỘI (3) So, the differential cross section can be obtained as follows dσ α 2ε s s = + cos θ + ’ 2 d Ω 4(q − mu ) mu (4) where Therefore, the total cross section is σ= α 2πε s s + (q − m ) mu 2 u (5) Finally, from (4) and (5) we get s + cos θ + mu dσ = σ dΩ 4 s 4π + mu (6) Numerical results and discussions Let us now turn to the numerical analysis We take ε = 10 −2 , mn = 10 GeV As input parameters In Fig.2 we plot the dσ with respect to cosθ As we can observer from Fig.2 the σ dΩ dσ has a minimum for cosθ = σ dΩ Fig The dσ with respect to cosθ σ dΩ TẠP CHÍ KHOA HỌC − SỐ 31/2019 Table The cosθ -1.0 dσ (×10 ) 7.959 σ dΩ 71 dσ at different cosθ σ dΩ -0.8 -0.6 -0.4 -0.2 0.0 7.958 7.957 7.957 7.956 7.956 0.2 0.4 0.6 0.8 1.0 7.956 7.957 7.957 7.958 7.959 In the figure 3, we plot the differential cross sections and the toatal cross sections as a function of s for cos θ = Fig The variation of dσ as a function of dΩ s for cos θ = As we see from the Figure that the radion effects quickly go down as s becomes larger In the following, we give the numerical values of the differential cross section with radion effects in Table Table The differential cross sections with radion effects for cos θ = at different energies s GeV 500 650 800 950 1100 1250 1400 1550 1700 1850 2000 dσ (×10 ) 5.195 5.191 5.190 5.189 5.188 5.188 5.187 5.187 5.187 5.187 5.187 σ dΩ For the next step, we give the numerical values of the total cross-sections with radion effects at different energies in Figure and Table TRƯỜNG ĐẠI HỌC THỦ ĐÔ H 72 Fig The variation of NỘI σ as a function of s So, direct computations have showed that the total cross-sections should be about 0.006-0.007 fem to barn Therefore, in the range s =500GeV to 2000GeV the total cross-sections are slightly different Table The total cross sections with radion effects at different energies s GeV σ ×103 ( fb) 500 650 800 950 1100 1250 1400 1550 1700 1850 2000 6.5266 6.5230 6.5213 6.5203 6.5197 6.5192 6.5190 6.5188 6.5186 6.5185 6.5184 CONCLUSION Our results are attractive because of possible connection to radion We hope that future experiments will confirm the existence of radion REFERENCES R.Foot, X G He (1991), Phys.Lett B 267, 509 J D Bjorken, R Essig, P Schuster, and N Toro (2009), Phys Rev D 80, 075018 Davoudiasl, H S Lee and W J Marciano (2012), Phys Rev Lett 109, 031802 M.Anelli et al [SHiP Collaboration], arXiv:1504.04956[physics.ins-det] P Ilten, Y Soreq, J Thaler, M Williams and W Xue, Phys Rev Lett 116, no 25, (2016) 251803 [arXiv:1603.08926 [help-ph]] D.V Soa, D.T.L Thuy, N.H Thao and T.D Tham, Mod Phys Lett A27 (2012) 1250126 TẠP CHÍ KHOA HỌC − SỐ 31/2019 N Desai, U Maitra and B Mukhopadhyay, ar XIV: 1307.3765 Y Ohno, ar XIV: 1402.7159 G.C Cho, Y Ohno, ar XIV: 1404.1200 73 10 Andrey Arubuzov, wt al (LL2018), proceedings of Science, POS 010 11 S.T.L Anh, H.H Bang et al (2018) , Can J Phys 96:3 268 12 S.T.L Anh, H.H Bang et al (2018), Int J Theor Phys 149 ẢNH HƯỞNG CỦA RADION LÊN TÁN XẠ BHABHA Tóm tắ tắt: Trong báo chúng tơi xem xét tín hiệu hạt radion qua tán xạ Bhabha Các kết đánh giá số tiết diện tán toàn phần với ảnh hưởng radion khoảng 0.62-0.65 pb Điều quan trọng cho việc tìm kiếm radion cho việc đo tiết diện tán xạ tán xạ Bhabha Từ khóa: khóa radion, tán xạ Bhabha ... 6.5188 6.5186 6.5185 6.5184 CONCLUSION Our results are attractive because of possible connection to radion We hope that future experiments will confirm the existence of radion REFERENCES R.Foot, X... ẢNH HƯỞNG CỦA RADION LÊN TÁN XẠ BHABHA Tóm tắ tắt: Trong báo chúng tơi xem xét tín hiệu hạt radion qua tán xạ Bhabha Các kết đánh giá số tiết diện tán toàn phần với ảnh hưởng radion khoảng 0.62-0.65... give the numerical values of the differential cross section with radion effects in Table Table The differential cross sections with radion effects for cos θ = at different energies s GeV 500 650