### Oscillation of neutrino in a vacuum with mixing flavor

*Bibek Koirala, Saddam Husain Dhobi, Prakash Subedi, Milan Gurung, Kumar Teemilsina, Sharad Kumar Oli*

#### Abstract

We developed multiple equations to observe the two and three flavors of neutrino oscillation with the mixing angle based on L/E=0.1 to 0.9 in this study. In different settings, the nature of the neutrino oscillation probability was discovered to be varied in different equations. The observation indicates increasing likelihood in one equation and decreasing probability in the other equations in two flavor oscillation neutrinos. To characterize the probability of neutrino oscillation, we use four distinct angles: 5degree, 10 degree, 15degree , and 20degree . The probability of neutrino oscillation was determined to be highest at an angle of 15 degrees. However, with increasing mixing angles, the likelihood of oscillation increases on the basis of created equation (25) and decreases on the basis of equations (26) and (27) in the three-flavor neutrino oscillation. From generated equations (25) and (26) the maximum neutrino oscillation of probability is discovered at an angle of 15degree , however, from equation (27), the maximum probability is observed at 5degree . The greatest neutrino oscillation is found to be 0.9999 and the minimum is zero in all of these two and three flavors of oscillation.

#### Keywords

Neutrino; Neutrino oscillation; flavor; mixed angle

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