Deflection of massive neutrinos by gravitational fields

Conclusions

The angular deflection undergone by massive neutrinos near astrophysical objects is described by formula (11).

This result led us to two main conclusions:

• a) that ultrarelativistic neutrinos are deflected almost as massless particles; more precisely for$\gamma _\infty \equiv 1/\sqrt {1 - \beta _\infty ^2 } \gg 1$, one has

  $$\Delta \varphi \equiv \frac{{4m}}{b}\frac{{\left( {1 - 1/2\gamma _\infty ^2 } \right)}}{{\left( {1 - 1/\gamma _\infty ^2 } \right)}} \simeq \frac{{4m}}{b}\left( {1 + \frac{1}{{2\gamma _\infty ^2 }}} \right)$$

  (1)

  ,i.e. a deviation from 4m/b by a small factor:$1/2\gamma _\infty ^2 \left( {1/2\gamma _\infty ^2 \ll 1} \right)$;

• b) that nonrelativistic neutrinos (as the slow cosmological ones) suffer large deflection because of the factor$\beta _\infty ^2$ at denominator at formula (11); therefore, even for large impact parameterb, slow neutrinos could be deflected and could transfer their momentum to the gravitating objects.

This effect has relevant consequences in astrophysical problems (5).