Why does electron capture produce a neutrino?
Electron capture produces an electron neutrino in order to conserve lepton numbers.
Electron capture is a process in which one of the inner electrons of an atom is captured by a proton in the nucleus, forming a neutron and emitting an electron neutrino.
You are probably familiar with conservation laws like the Law of Conservation of Energy and the Law of Conservation of Momentum. One of the rules that must be followed in nuclear reactions is the Law of Conservation of Lepton Number.
A lepton is an elementary particle with spin ½ that does not undergo strong nuclear forces. Electrons and neutrinos have spin ½ and are outside the nucleus, so they are leptons. The lepton numbers of electrons and of electron neutrinos are +1.
Protons and neutrons are held together in the nucleus by the strong nuclear force. They have lepton numbers of zero.
If the process were simply
If an electron neutrino is emitted, as in
Good presentation, very nice pictures on this website: http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/radact2.html