Several Scattering Processes In The Noncommutative Standard Model

In the recent decades, there is a big change for people’s exploration of new physics beyond the standard model. More consideration is taken from only extending the standard model in four dimensions to probing the singularity of space-times. People believe that the possible existence of extra dimension is an effective solution to overcome the hierarchy problem of standard model. At the mean time, it is founded that when the open string is fixed at D-brane and interact with NS-NS B field, the string theory at low energy limit will lead to a quantum field theory in noncommutative space-time. Black hole physics and quantum gravity also strongly suggest the existence of noncommutative space-time. By this reason, the quantum field theory in noncommutative space-time and its implication to high energy phenomenology at TeV scale become a focus in recent ten years. After some effort, people have build a noncommutative standard model(NCSM) based on Weyl-Moyal product where the gauge group is not closed in SU(3)*SU(2)*U(1) Lie algebra but in the enveloping algebra. This property is necessity for the consistence of noncommutative gauge theory under Weyl-Moyal product. On the other hand, Seiberg and Witten point out that there is a map between the field in noncommutative space and ordinary space-time. i,e. Seiberg-Witten map. Using Seiberg-Witten map, the coefficient of enveloping algebra become the function of field variable in ordinary space-time. In this sense, the infinity of field is avoid. The NCSM induce many new particle vertex beyond the ordinary Sm, such as γ-γ-γ vertex, Z-γ-γ vertex, neutrino-photon vertex etc, leading to interesting phenomenological implication.In this paper, we discuss the possibility of testing the TeV noncommutative effect at electron collision machine in the frame work of noncommutative standard model. By this time, most of the work is based on the Seiberg-Witten map by expanding to θ order or θ2order and getting the noncommutative correction of Feynman diagram up to θ or θ2order correspondingly. This method is effective for low energy processes. If We assume the non- commutative effect is located at TeV scale, however, the collision energy of LHC or ILC may access or even exceed the noncommutative scale. Then the first or second perturbative method is not accurate. To overcome this problem, we find a Seiberg-Witten map involv-ing any order of noncommutative parameter θ and apply it to the high energy collision process. We first study the Higgs production process e+e-→ZH and e+e-→HH. It is shown that the noncommutative effect have extensive impact on the cross section and angular distribution. It is noted that the the process e+e-→HH is forbid in the ordinary standard model, so any signal of the Higgs pair production has an important meaning for detecting the noncommutative space-time. For each noncommutative scle ANC, there exist a optimal collision energy where the noncommutative correction get the most. We give a linear relation between the noncommutative scle and optimal collision energy. There are also many degrees of freedom in noncommutative gauge theory. Some of them come from the solution of Seiberg-Witten map and some of them are derived from the Weyl-Moyal product of U(1) gauge theory. i.e. the hybrid gauge transformation. We study the process e+e-→μ+μ-and discuss the impact of hybrid gauge transformation. It is shown that without the hybrid gauge transformation the noncommutative effect only contribute a exp phase to the magnitude, leading to no noncommutative correction. When the hybrid gauge transformation is considered, the process get a large noncommutative correction. We cal-culate the total cross section and angular distribution at rotational reference on earth. The intrinsic Lorentz breaking effect is also discussed.