In this work, we study the possible dark photon signatures through Bhabha scattering. The numerical results show that the total cross sections with dark photon effects are about 0.006 – 0.007 femtobarn. This could have important implications for dark photon searches.
Scientific Journal − No27/2018 57 DARK PHOTON EFFECTS ON BHABHA SCATTERINGS Ha Huy Bang, Ngan Van Thap, Sa Thi Lan Anh, Truong Minh Anh University of sciences - Hanoi National University Abstract: In this work, we study the possible dark photon signatures through Bhabha scattering The numerical results show that the total cross sections with dark photon effects are about 0.006 – 0.007 femtobarn This could have important implications for dark photon searches Keywords: Dark photon, effect, cross-section Email: hahuybang@hus.edu.vn Received 12 November 2018 Accepted for publication 15 December 2018 INTRODUCTION As well known, astrophysical observations have shown that Dark Matter (DM) exists in our universe In several extensions of the standard Model, dark photon or u-boson is postulated [1-5] Searching for the new physics effects, the e+e- linear colliders have an exceptional advantageous for its appealing clean background, and the possibility for the options of e D, and DD colliders based on it Especially, very recently, we have investigated unparticle effects on Bhabha scattering [6] and on axion-like particles production in e+e- collisions [7] Remarkably, the production and decays of dark photon at e+e- colliders have been discussed in Ref [8] and a new way to search for narrow resonances, and specifically dark photon, coupled to e+e- pairs have been suggested in Ref [9] In this paper we investigate dark photon effects on Bhabha scatterings THE CROSS SECTIONS This process is described by the Feynman diagram presented in Fig.1 The amplitude for this process is given by M = v ( k )ieγ µ u ( k1 ) = ie ε − ie ( g µν − q µ qν / mu2 ) ( g µν − q µ qν / mu2 ) q − mu2 q − mu2 µ u ( p1 ) ieγ ν v ( p ) (1) µ v ( k )γ u ( k1 )u ( p1 )γ v ( p ), Ha Noi Metroplolitan University 58 E2 E2 E E Fig.1: Feynman diagram for Bhabha scattering via dark photon and photon From this, we get M = +2 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 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 M = 4e 4ε s s + cos θ + , 2 (q − mu ) mu (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) Therefore, the total cross section is σ= α 2πε s s + (q − m ) mu 2 u (5) Scientific Journal − No27/2018 59 Finally, from (4) and (5) we get s 1 + 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 cos θ As we can observer from Fig.2 the σ dΩ dσ has a minimum for cos θ = σ dΩ Fig.2: The dσ with respect to cos θ σ dΩ Table 1: The cos θ -1.0 -0.8 dσ (×10 ) σ dΩ 7.959 7.958 -0.6 dσ at different cos θ σ dΩ -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 7.957 7.957 7.956 7.956 7.956 7.957 7.957 7.958 7.959 Ha Noi Metroplolitan University 60 In the Fig.3, we plot the differential cross sections and the toatal cross sections as a function of s for cos θ = Fig.3: The variation of dσ as a function of dΩ s for cos θ = As we see from the Fig.3 that the dark photon effects quickly go down as s becomes larger In the following, we give the numerical values of the differential cross section with dark photon effects in Table Table 2: The differential cross sections with dark photon effects for cos θ = at different energies 1850 2000 dσ (×102 ) 5.195 5.191 5.190 5.189 5.188 5.188 5.187 5.187 5.187 5.187 σ dΩ 5.187 s GeV 500 650 800 950 1100 1250 1400 1550 1700 For the next step, we give the numerical values of the total cross-sections with dark photon effects at different energies in Fig.4 and Table So, direct computations have showed that the total cross-sections should be about 0.006-0.007 fem to barn Therefore, in the range different s =500GeV to 2000GeV the total cross-sections are slightly Scientific Journal − No27/2018 61 Fig.4: The variation of σ as a function of s Table 3: The total cross sections with dark photon 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 Our results are attractive because of possible connection to dark photon We hope that future experiments will confirm the existence of dark photon REFERENCES L.B.Okun, Zh Eksp Teor Fiz 83,892 (1982) [JETP 56,502 (1982)]; 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Our results are attractive because of possible connection to dark photon We hope that future experiments will confirm the existence of dark photon REFERENCES L.B.Okun, Zh Eksp Teor Fiz 83,892