Axion production in unpolarized and polarized γe− collision

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.

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JOURNAL OF SCIENCE OF HNUE Interdisciplinary Science, 2013, Vol. 58, No. 5, pp. 11-16 This paper is available online at 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: ∣∣Ms∣∣2 = 2e2m2e λ2as (s−m2a)(1 + cos θ), (2.1) for s-channel. ∣∣Mu∣∣2 = e2m2e λ2a 8s (s−m2a)(1 + cos θ) , (2.2) for u-channel. ∣∣Mt∣∣2 = 8e2 λ2γ(s−m2a)(1− cos θ) {4s2 + (s−m2a)2(1 + cos θ)2}, (2.3) for t-channel, with λγ = 4πfa αgaγ . MsM + u = 4e2m2e λ2as(1 + cos θ) [(s−m2a)(1− cos θ)− 2s], (2.4) 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, ∣∣MsRL∣∣2 = e2m2e λ2as (s−m2a)(1 + cos θ), (2.5) 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, ∣∣MsLR∣∣2 = e2m2e λ2as (s−m2a)(1 + cos θ), (2.6) for s-channel. - 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, ∣∣MuRL∣∣2 = e2m2e λ2a 4s (s−m2a)(1 + cos θ) , (2.7) for u-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, ∣∣MuLR∣∣2 = e2m2e λ2a 4s (s−m2a)(1 + cos θ) , (2.8) for u-channel. - When the beam of e− in the initial state, the finial state is right polarized, we have, ∣∣MtRR∣∣2 = 4e2 λ2γ(s−m2a)(1− cos θ) {4s2 + (s−m2a)2(1 + cos θ)2}, (2.9) for t-channel. - When the beam of e− in the initial state, the finial state is left polarized, we have, ∣∣MtLL∣∣2 = 4e2 λ2γ(s−m2a)(1− cos θ) {4s2 + (s−m2a)2(1 + cos θ)2}, (2.10) 13 Dang Thi Le Thuy and Le Nhu Thuc for t-channel. - For interference between the s-channel and u-channel when the beam of e− is polarized, we have: MsLRM + uLR = MsRLM + uRL = 2e2m2e λ2as(1 + cos θ) [(s−m2a)(1− cos θ)− 2s] (2.11) The straightforward calculation yields the following differential cross section (DCS) and total cross section (TCS) in the center-of-mass frame. In our calculation, we choose: me = 5, 1.10 −4GeV , λa = 247GeV , α = 1 137 , ma = 6.10 −10GeV , fa = 10 10GeV , gaγ = 0, 36 (DFSZ model), we have: - When the evaluation of the cross section depends on the polarization factor, we evaluate the DCS depending on cos θ (Figure 2) where TCS depends on the center of mass energy (Figure 3). Figure 2. The DCS as a function of cosθ Figure 2 shows that the DCS depends strongly on cos θ and the DCS’s reduce with an increasing value of cos θ, the DCS quickly reduse when the value of cos θ is in the range of -1 to -0.9 and the DCS slowly reduse when the value of cos θ is in the range of -0.9 to 1. For P1 = P2 = 0 (line 1), it is the case of the beam of e − becoming unpolarized. For P1 = −1, P2 = 1 or P1 = 1, P2 = −1 (line 2), the DCS is bigger than in the case of unpolarization. For P1 = P2 = 1 or P1 = P2 = −1 (line 4), the contribution of t-channel scattering is mainly in the collision process. However, this contribution is very small (about 10−9 times) compared to the contribution of the s-channel and u-channel when P1 = 1, P2 = −1 or P1 = −1, P2 = 1. From Figure 3, for P1 = P2 = 1 (line 4), the TCS does not change. In other cases, when the center of mass energy increases, then the TCS decreases. 14 Axion production in unpolarized and polarized γe− collision Figure 3. The TCS as a function of √ s Figure 4. The TCS as a function of the polarization factor of e− - An evaluation of the total cross section depends on the polarization factor, and we note that P1 is the polarization factor of the beam in the initial state and P2 is the polarization factor of the beam in the finial state. From Figure 4, we can see that the TCS reaches a maximum value when P1 = −1, P2 = 1 or P1 = 1, P2 = −1. In this state, the beams of are fully polarized. In addition, the TCS is equal to zero when P1 = −1, P2 = −1 or P1 = 1, P2 = 1. 15 Dang Thi Le Thuy and Le Nhu Thuc 3. Conclusion In this paper, we have calculated the production of axion in unpolarized and polarized γe− collision. The results show that, cross sections depend strongly on the polarization factors of e− beams (P1, P2) and have a value that is much smaller than the production of axion in γµ− collision. However, the cross sections for the axion production at high energy are very small, much below neutrino production cross section, so that the direct production of dark matter particles is in general not expected to lead to easily observable signals in γe− and γµ− collision. Acknowledgment. The work is supported in part by the Science and Technology Foundation of the Hanoi National University of Education (HNUE) under grant No. SPHN-12-216. REFERENCES [1] Aune.S, et al., 2009. Nucl. Instrum. Meth. A604, p. 15. [2] Babu.K.S, Gogoladze.I and Wang.K, 2003. Phys. Lett. B560, p. 214. [3] Hagman.C, Sikivie.P, Sullivan.N.S and Tanner.D.B, 1990. Phys. Rev. D42, p. 1297. [4] Kim.I. E, 1984. Phys. Lett. B136, p. 387. [5] Kim.J.E, 1987. Phys. Rep. 150, p. 1. [6] Long.H.N, Soa.D.V and Tuan. A. Tran, 1995. Phys. Lett. B357, p. 469. [7] Long.H.N and Lan.N.Q, 2003. Europhys. Lett. 64, p. 571. [8] Peccei.R.D and Quinn. H. R, 1977. Phys. Rev. 38, p. 1440. [9] Primakoff.H, 1951. Phys. Rev. 81, p. 899. [10] Sikivie.P, 1985. Phys. Rev. D32, p. 2988. [11] Soa. D.V, Thuy.D.T.L, Thao.N.H and Tham.T.D, 2012. Mod. Phys. Lett A. 27, No. 23, p. 1250126. [12] Raffelt.G.G, 1990. Phys. Rep. 198, p. 1. [13] Turner.M.S, 1990. Phys. Rep. 197, p. 67. [14] VysotskyM.I and Voloshin.M.B, 1986. Yad. Fiz. Rev. 44, p. 845. 16 JOURNAL OF SCIENCE OF HNUE Interdisciplinary Science, 2013, Vol. 58, No. 5, pp. 17-21 This paper is available online at DOPANT EFFECT OF Y ON OPTICAL PROPERTIES OF ZnWO4 CERAMICS Nguyen Manh An Faculty of Physics, Hong Duc University Abstract. We investigate the effect of the rare earth ion, Y on the structure, absorption and Raman spectroscopy of ZnWO4 ceramics. In the XRD patterns of Ce doped ZnWO4, some foreign peaks were found and an anormalous change in cell parameter appeared around x = 0.15. This indicates that the Ce ion has an effect on the structure of ZnWO4 and suggests a solubility limit of Ce in ZnWO4 ceramics. In addition, we also calculated the Raman active modes by using group theory and we received 18 modes in Raman active and 16 modes in IR active. The absorption measurement indicates the band gap of ZnWO4 decreases with increasing Y content. The reasons for the above changes are discussed in this presentation. Keywords: Effect, Y, structure, absorption, Raman spectroscopy, ZnWO4 ceramics. 1. Introduction Tungstate crystals are perspective scintillating materials for x-ray detectors’ γ-ray medical tomographs. In particular, the ZnWO4 crystal is a well-known scintillator emitting light at 480 nm under UV, X-ray and γ-ray excitation. An important parameter of scintillating material is light emission efficiency and that depends on the transparency of the host crystal in the visible spectral region. Parasite absorption is usually caused by various defects of the lattice. Therefore, investigating the nature of defects responsible for absorption in the ZnWO4 is needed in order to solve material science problems. Doping of rare-earth ions into ZnWO4 lattice are expected to influence its chemical and physical properties. However few studies have been reported on doped-ZnWO4 compared to that of other inorganic compounds [1, 2]. Furthermore, the doping causes a disorder in structure. The disorder in doped rare earth ZnWO4 ceramics is expected to vary strongly depending on the doping level and temperature. The dynamic disorder is directly related to electronic processes and localization in the insulating phase of this material. Therefore, monitoring the disorder is of significant interest in order to understand the interplay of structural and optical properties. Raman spectroscopy is an efficient tool for the study of structural Received April 17, 2013. Accepted June 2, 2013. Contact Nguyen Manh An, e-mail address: nguyenmanhan@hdu.edu.vn 17