Dark photon effects on Bhabha scatterings

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.

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:

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:

Keywords: Dark photon, effect, cross-section

Email: hahuybang@hus.edu.vn

Received 12 November 2018

Accepted for publication 15 December 2018

1 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

2 THE CROSS SECTIONS

This process is described by the Feynman diagram presented in Fig.1

The amplitude for this process is given by

2

2

( )

u u

u

u

M u k ie g q q m u p i v p

q

v k

m

g q q m

−

=

−

=

Fig.1: Feynman diagram for Bhabha scattering via dark photon and photon

From this, we get

16

e M

ε

=

2

u

qk

p k qp qp p k p p qk m

1

u

qk

m

( )( )

qp qp p p q qp qp p p q

2

2

1 2

4

u

q k k

−  − } (2)

In center of mass frame, four-moments of particles are defined

S = k +k = p + p =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

4 4 2

M

ε

θ

So, the differential cross section can be obtained as follows

2 4

2

θ

Therefore, the total cross section is

4

α πε

E2

E

E2

E

Finally, from (4) and (5) we get

2 2

2

1 cos 4 4 3

u

u

s m d

m

θ σ

σ

π

=

+

(6)

Numerical results and discussions

Let us now turn to the numerical analysis We takeε 10 ,− 2 m n 10

As input parameters

In Fig.2 we plot the d

d

σ

σ Ωwith respect to cosθ As we can observer from Fig.2 the

d

d

σ

σ Ωhas a minimum for cosθ =0

Fig.2:

Fig.2: The d

d

σ

σ Ωwith respect to cosθ

Table 1:

Table 1: The d

d

σ

σ Ω at different cosθ

cosθ -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

2

( 10 )

d

d

σ

σ Ω × 7.959 7.958 7.957 7.957 7.956 7.956 7.956 7.957 7.957 7.958 7.959

In the Fig.3, we plot the differential cross sections and the toatal cross sections as a function of sfor cosθ =1

Fig.3:

Fig.3: The variation of d

d

σ

Ωas a function of s for cosθ =1

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 2

Table 2:

Table 2: The differential cross sections with dark photon effects for cosθ=1at different energies

sGeV 500 650 800 950 1100 1250 1400 1550 1700 1850 2000

2

( 10 )

d

d

σ

σ Ω × 5.195 5.191 5.190 5.189 5.188 5.188 5.187 5.187 5.187 5.187 5.187

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 3

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

Fig.4: The variation of σ as a function of s

Table 3: The total cross sections with dark photon effects at different energies

sGeV 500 650 800 950 1100 1250 1400 1550 1700 1850 2000 3

σ× 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

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2 R.Foot and X G He, Phys.Lett B 267,509 (1991)

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5 P Ilten, Y Soreq, J Thaler, M Williams and W Xue, Phys Rev Lett 116, no 25, 251803 (2016) [arXiv:1603.08926 [help-ph]]

6 S.T.L.Anh et al., Can J Phys 96:3 268 (2018)

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TÁC ĐỘNG CỦA PHOTON TỐI LÊN TÁN XẠ BHABHA

Tóm t ắắắắt: t: t: Trong công trình này, chúng tôi nghiên c ứu các tín hiệu photon tối qua tán xạ Bhabha Các kết quả tính số chỉ ra rằng các tiết diện tán xạ toàn phần là khoảng từ 0.006 đến 0.007fb Điều này có thể là sự gợi ý quan trọng cho việc tìm kiếm vật chất tối

T ừ ừừ ừ khóa: khóa: khóa: V ật chất tối, tác động, tiết diện toàn phần