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Axion was postulated to explain why CP violation is not observed in strong interaction, although it should be according to the Standard Model. The CP violation in SM arises from a certain non-zero parameter related to the QCD vacuum (see instanton). It was shown in 1997 that the parameter could be driven to zero by a Higgs field. A side effect of the transformation is the introduction of a new particle - the axion. If axions do exist, they each would have a mass of around 10^{-5} ev, but there could be so many of them in the Universe, that they contribute a | |
Figure 10 Axion Detection |
large proportion of the overall mass in the form of dark matter. In the inflationary scenario, axions induce isocurvature fluctuations whereby the system remains homogeneous and constrain the allowed inflationary scale. |
The following is an attempt to clarify the rationale for the introduction of this hypothetical particle and the consequence via a simplified mathematical formulation. The problem starts from the QCD Lagrangian density L_{QCD} as shown in a "beyond the Standard Model" form below in Eq.(1). The first term is for the quarks, second term for qluons, and the third term is responsible for the expected CP violation similar to that in weak interaction. However, no strong (interaction) CP violation is observed in the very precise "neutron electric dipole moment experiment" (Figure 11). Therefore the effect must be very small or zero. One of the solutions is to add an additional field called axion with the label _{} to cancel out the CP violation term _{} as shown in Eq.(2). | |
Figure 11 CP Violation _{} |
It turns out that the cancellation process is not simply inserting a term into the formula. The axion field evolved in the very early cosmic history starting soon after the inflation period, it gradually generates an effect to cancel out the CP violation, and eventually acquires a steady mass. The sequence can be divided into three stages as shown in Figure 16,b, and described in some details below. But before proceeding further, some definition of terms and time/temperature scales are essential. The cosmic time scale is shown in Figure 12. The relevant period would be from about 10^{-37} sec in the inflation era to 10^{-5} sec at QCD phase transition when the quarks and gluons in the quark-gluon plasma combined to form hadrons. | |
Figure 12 Cosmic Time Scale [view large image] |
The relationship between time t and temperature T is established through a chain such as : t energy density T (via the Equation of State) t ~ 10^{-6}/T^{2} (in Gev) within the range of interest. |
Figure 13 Scalar Field Potential [view large image] |
BTW, the V_{eff} here represents only that part of Figure 13,b within the interval "v" (also see Figure 13a below). See "Theory of Cosmic Inflation" for derivation of the equation of motion for the field. |
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Figure 14 Types of Solution [view large image] |
Figure 15 Phase Angle |
(Stage 2) Axion Evolution : At this stage the axion field and phase angle continued on their downward slide while the mass and density moved up. A critical point was reached when the damping term 3H of the cosmic expansion is equal to the oscillating mass term in Eq.(4). Thereafter, the variables acquired an oscillating component in a state called damped-oscillation and eventually settled down into their final values. For example, the phase angle would oscillate as _{a} = _{0} e^{i(mat)}. Converting back from natural unit, the oscillating period would be about 10^{-30} sec while _{0} ~ 0 at the current epoch (Figures 13a and 16,c). | |
Figure 16 Axion Evolution [view large image] |
2016 (Figure 17,a). This numerial function enables the evaluation of V_{eff}(_{a}), which in turn allows the computation of the axion field , _{a}, and finally the evolution of the mass m_{a}(T) up to the current epoch (Figure 17b). The red line shows the range of possible axion mass : 5x10^{-5} eV < m_{a} < 1.5x10^{-3} eV, and phase angle = /f = 2.155 for making the CP violation disappeared. The number density N_{a} ~ 14x10^{12}/m^{3} would be in agreement with _{DM} = 0.23 if m_{a} = 10^{-4} eV (Figure 16,c). | ||
Figure 17 Evaluation of Axion Parameters [view large image] |
Figure 18 Dark Matter [view large image] |
Figure 18 lists the various dark matter candidates including the axion and other oddballs. Except the regular neutrinos (not the sterile type), most of them has to be discovered. See more about "Dark Matter". |