Standard Model and Beyond · Problem 7.3

Elastic neutrino-electron scattering is a clean probe of the weak interaction because the kinematics are completely determined by energy and momentum conservation. The key is to express the Mandelstam variables ($s$, $t$, $u$) and the inelasticity parameter $y$ (the fraction of energy transferred to the electron) in terms of measurable quantities, then use kinematic constraints to find what range of $y$ values are physically allowed. Working through the algebra of four-momentum conservation will show how the limits emerge naturally from requiring $t$ and $u$ to stay within physical bounds.

Elastic neutrino-electron scattering is a clean probe of the weak interaction because the kinematics are completely determined by energy and momentum conservation. The key is to express the Mandelstam variables ($s$, $t$, $u$) and the inelasticity parameter $y$ (the fraction of energy transferred to the electron) in terms of measurable quantities, then use kinematic constraints to find what range of $y$ values are physically allowed. Working through the algebra of four-momentum conservation will show how the limits emerge naturally from requiring $t$ and $u$ to stay within physical bounds.