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Is there a value for the neutrino oscillation ratio $L/E$ (length over energy)?

Physics Asked on September 27, 2021

That ratio keeps popping up, yet I have nowhere read an estimated value…

Are scientists at least certain that high-energy neutrinos oscillate less often?

One Answer

Yes, they are "certain" to the extent scientific facts can be such: There is no plausible hint of experimental doubt, at present.

Even though there is a virtual duplicate provided in the comments, you appear to be in doubt about the neutrino oscillation formula, namely the mutation probability out of a neutrino changing its flavor, $$ P_{alpharightarrowbeta, alphaneqbeta} = sin^2(2theta)~~ sin^2 left(frac{Delta m^2 L}{4E}right), $$ in customary HEP natural units, $hbar=1=c$.

The practical usage, semi-SI units for huge distances [km], are only partially dimensionalized, $$P_{alpharightarrowbeta, alphaneqbeta} = sin^2(2theta)~~ sin^2 left( 1.27 frac{Delta m^2 L}{E} frac{rm [eV^{2}],[km]}{rm [GeV]}right). $$

Written like this, it means L should be in km, E in GeV, but Δm2 in eV2, as these are the practical units in the trenches, with the freaky numerical factor picking up the conversion slop. (A purist would invert the dimensions' fraction on the right and remove the brackets, for logical consistency, but I already described what is meant. Check the reinstated ${1over 4hbar c}= 1.27 {GeVover km~ eV^2}$.)

  • So, go to your PDG and look at "atmospheric" neutrino conversion: For Δm2 ~ 2.5 $10^{-3}$ eV2, and a 1 GeV beam, you'd need 500 km for the first outconversion maximum, etc...

Correct answer by Cosmas Zachos on September 27, 2021

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