Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2006-12-22
Physics
High Energy Physics
High Energy Physics - Phenomenology
25 pages
Scientific paper
Kinematical aspects of pion decay $\pi \to \mu \nu$ is studied, with neutrino mixing taken into account. An attempt is made to derive the transition probability for such a sequence of processes: a $\pi^+$ produced at $(\vec{x}_{\pi},t_{\pi})$ with momentum $\vec{p}_{\pi}$ decays into a $\mu^+$ and a $\nu_{\mu}$ somewhere in space-time and then the $\mu^+$ is detected at $(\vec{x}_{\mu},t_{\mu})$ with momentum $\vec{p}_{\mu}$ and a $\nu_{\alpha}$ (a neutrino with flavor $\alpha = e$, $\mu$, $...$) is detected at $(\vec{x}_{\nu},t_{\nu})$ with momentum $\vec{p}_{\nu}$. It is shown that (1) if all the particles involved are treated as plane-waves, the energy-momentum conservation would eliminate the neutrino oscillating terms, leaving each mass-eigenstate to contribute separately to the transition probability; (2) if one treats all the particles involved as wave-packets, the neutrino oscillating terms would appear and would be multiplied by two suppression factors, which result from distinction in velocity and in energy between the two interfering neutrino mass-eigenstates. An approximate treatment which takes account of the two complementary features, each of the particles involved propagates along its classical trajectory on the one hand and energies and momenta of the particles involved are conserved during the decay on the other hand, is proposed and similarity and difference between our approach and that of Dolgov et al. are discussed.
Fuji Chikara
Matsuura Yasumasa
Shibuya Toshihiro
Tsai Shang-Yuu
No associations
LandOfFree
A Wave-Packet View of Neutrino Oscillation and Pion Decay does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Wave-Packet View of Neutrino Oscillation and Pion Decay, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Wave-Packet View of Neutrino Oscillation and Pion Decay will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-531231