Observations of neutrino (flavor) oscillations have shown that neutrinos have ma

Question

Observations of neutrino (flavor) oscillations have shown that neutrinos have mass, and precisely measured the differences in their (squared) masses. [See pdg.lbl.gov.] Suppose that neutrinos come in 3 mass 21 while Amaonm What values of m1, m2 and m3 minimize the total mass: M = m1 + m2 + m3? What is the minimum M? Interestingly the next one or two generations of cosmology surveys should be able to measure even such tiny masses through their effect on the expansion history and clustering of matter!

Explanation / Answer

I have solved the problem in MATHEMATICA ..

I have taken a = m1 ; b=m2 ; c=m3

then I have minimized a+b+c for the constraints for b2 - a2 = 50 ; c2 - b2 = 3000 [Here I have changed the order by 10-6]

So , {a+b+c}min = 62.2979 x 10-3 eV/c # [order in answer will be shifted from 10-6 to 10-3 As a,b,c are not squared]

And Minimum Value of a = 0 eV/c

b = 7.07106 x 10-3 eV/c ,

c = 55.2268 x 10-3 eV/c .

The Code That I have used is..

NMinimize[{a + b + c,
b^2 - a^2 == 50 && c^2 - b^2 == 3000 && a >= 0 && b >= 0 &&
c >= 0}, {a, b, c}]

Thank you . Please hit LIKE if you are satisfied with my effort .

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