# 4.2. Two-flavor and Three-flavor¶

Some times we use two flavor to demonstrate the three flavor oscillations. Can we actually do this and how exactly? The answer depends on the specific problem. In general we have several factors to consider.

## 4.2.1. Oscillation Scales¶

For three flavor vacuum oscillations, we have at least two most important energy scales, since we have three mass states. Two energy scales leads to two different oscillation frequencies. More over, we know that $$\Delta m_{12}^2$$ is much smaller than $$\Delta m_{13}^2$$, the corresponding oscillation length scales will be very different.

## 4.2.2. Refs & Notes¶

Several papers:

1. Lim, C. S., Ogure, K., & Tsujimoto, H. (2003). How precisely can we reduce the three-flavor neutrino oscillation to the two-flavor one only from $$\delta m_{12}^2/\delta m_{13}^2 \lesssim 1/15$$. Physical Review D, 67(3), 033007. doi:10.1103/PhysRevD.67.033007

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