Axion production in unpolarized and polarized ye− collision

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Axion production ina Axion production in unpolarized and polarized ye− collision are considered in detail using the Feynman diagram method. The cross-sections are presented and numerical evaluations are given. The results show that the axion can be dark matter of the universe. Some estimates for experimental conditions are given from our results. unpolarized and polarized ye− collision

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Nội dung Text: Axion production in unpolarized and polarized ye− collision

JOURNAL OF SCIENCE OF HNUE Interdisciplinary Science, 2013, Vol. 58, No. 5, pp. 11-16 This paper is available online at http://stdb.hnue.edu.vn AXION PRODUCTION IN UNPOLARIZED AND POLARIZED γe− COLLISION Dao Thi Le Thuy and Le Nhu Thuc Faculty of Physics, Hanoi National University of Education Abstract. Axion production in unpolarized and polarized γe− collision are considered in detail using the Feynman diagram method. The cross-sections are presented and numerical evaluations are given. The results show that the axion can be dark matter of the universe. Some estimates for experimental conditions are given from our results. Keywords: Axion, axino, DCS, TCS. 1. Introduction The strong CP problem is a big, unexplained mistery in the Standard Model of particle physics. Among the various candidate solutions that have been proposed thus far, the Peccei-Quinn mechanism is the most attractive candidate as a solution of the strong CP problem where the CP-violating phase θ (θ 6 10−9 ) is explained by the existence of a new pseudo-scalar field called the axion [8]. At present, axion mass is constrained by laboratory [5], astrophysical and cosmological considerations [12, 13] to between 10−6 eV and 10−3 eV. If the axion has a mass near the low limit of order 10−5 eV, it is a good candidate for the dark matter of the universe. In addition, an axino (the fermionic partner of the axion) naturally appears in SUSY models [4] which acquires a mass from three-loop Feynman diagrams in a typical range of between a few eV to a maximum of 1 keV [14]. Candidates for dark matter can appear in different models, such as the 3-3-1 models [7] or in supersymmetric and superstring theories [2]. Light particles with a two photon interaction can be transformed into photons in an external electric or magnetic field by an effect first discussed by Primakoff [9]. This effect is the basis of Sikivie’s methods for the detection of axions in a resonant cavity [10]. Various terrestrial experiments to detect invisible axions by making use of their coupling to photons have been proposed [6] and results from such experiments have appeared recently [3]. The experiment CAST [1] at CERN searches Received January 15, 2013. Accepted May 24, 2013. Contact Le Nhu Thuc, e-mail address: thucln@hnue.edu.vn 11
Dang Thi Le Thuy and Le Nhu Thuc for axions from the sun or other sources in the universe. Recently, several authors have analyzed the potential of CLIC (Compact Linear Collider) based on the γe− collisions to search for radion in the Randall-Sundrum (RS) model and the result shows that the cross-section of radions may give observable values at moderately high energies [11]. In this paper, we consider axion production in polarized and unpolarized γe− collision using the Feynman method. The polarization of electron and positron beams at the colliders gives a very effective means to control the effect of the MS processes for experimental analyses. Beam polarization is also an indispensable tool used to identify and study new particles and their interactions. 2. Axion production γe− collision The Feynman diagrams for the collision process γe− through the s, t, u - channel are drawn as Figure 1. From that, we get the following expression for the matrix element for the production axion in a γe− collision when the beam of e− causes either polarization and unpolarization. Figure 1. Feynman diagram of γe− collision When the beam of e− is not polarized, we can use the Feynman rules to make calculations and obtain the square of the scattering amplitude as follows:
2 2e2 m2e
Ms
= 2 (s − m2a )(1 + cos θ), (2.1) λa s for s-channel.
2 e2 m2e 8s
Mu
= , (2.2) 2 2 λa (s − ma )(1 + cos θ) for u-channel.
2 8e2
Mt
= {4s2 + (s − m2a )2 (1 + cos θ)2 }, (2.3) λ2γ (s − m2a )(1 − cos θ) 4πfa for t-channel, with λγ = . αgaγ 4e2 m2e Ms Mu+ = 2 [(s − m2a )(1 − cos θ) − 2s], (2.4) λa s(1 + cos θ) 12
Axion production in unpolarized and polarized γe− collision for interfering between s-channel and u-channel; for interfering between s-channel and t-channel; interfering between u-channel and t-channel, not give us the results. When the beam of e− is polarized, we have the square of the scattering amplitude as follows: - When the beam of e− in the initial state is left polarized and the beam of e− in the finial state is right polarized, we have, 2 2
MsRL
2 = e me (s − m2a )(1 + cos θ),
(2.5) λ2a s for s-channel. - When the beam of e− in the initial state is right polarized and the beam of e− in the finial state is left polarized, we have, 2 2
MsLR