P461 - particles VIII1 Neutrino Physics Three “active” neutrino flavors (from Z width measurements). Mass limit from beta decay Probably have non-zero masses as they oscillate Only have weak interactions and can be either charged or neutral currents W Z n p n,p,e charge neutral

P461 - particles VIII2 Neutrino Cross Sections Use Fermi Golden Rule M (matrix element) has weak interaction physics…W, Z exchange ~ constant at modest neutrino energies. Same G factor as beta decay cross section depends on phase space and spin terms. Look at phase space first for charged current. Momentum conservation integrates out one particle

P461 - particles VIII3 Neutrino Cross Sections II Look in center-of-momentum frame s is an invariant and can also determine in the lab frame cross section grows with phase space (either neutrino energy or target mass)

P461 - particles VIII4 Neutral Currents The detection of some reactions proved that neutral current (and the Z) exist the cross section depends on the different couplings at each vertex and measure the weak mixing angle about 40% of the charged current cross section due to Z-e-e coupling compared to W-e-nu coupling

P461 - particles VIII5 Neutrino Oscillations Different eigenstates for weak and mass can mix with a CKM-like 3x3 matrix with (probably) different angles and phases then quarks. The neutrino lifetime is ~infinite and so mix due to having mass and mass differences (like KL and KS) example. Assume just 2 generations (1 angle) assume that at t=0 100% muon-type

P461 - particles VIII6 Neutrino Oscillations II Can now look at the time evolution from the Scrod. Eq. And assuming that the energy is much larger than the mass probability of e/mu type vs time (or length L the neutrino has traveled) is then where we now put back in the missing constants and use a trig identities

P461 - particles VIII7 Neutrino Oscillations III Oscillation depends on mixing angle and mass difference (but need non-zero mass or no time propagation) so some muon-type neutrinos are converetd to electron type. Rate depends on neutrino energy and distance neutrino travels L/E go to 3 neutrino types and will have terms with more than one mixing angle. Plus neutrinos can oscillate into either of the other two (or to a fourth “sterile” type of neutrino which has different couplings to the W/Z than the known 3 types)

P461 - particles VIII8 Detecting Neutrino Oscillations Disappearance: flux reduction larger L/E Solar Neutrinos. Measure rate for both electron neutrinos and all neutrinos (using neutral current). Low energies (for MeV) cause experimental thresholds for some techniques. Compare to solar models. Atmospheric neutrinos. Measure rate as a function of energy and length (from angle) also electron or muon neutrinos produced at reactors or accelerators. Compare flux near production to far away L/E >> 1

P461 - particles VIII9 Detecting Neutrino Oscillations Appearance: start with one flavor detect another Ideal. Tag nu production by detecting the lepton. Then detect neutrino interaction. Poor rates (considered pi/K beams and muon storage rings) Real. Tau neutrino very difficult to detact sources of pure electon neutrinos (reactors) are below muon/tau threshold ---> use mostly muon neutrino beam can measure neutrino energy in detector (if above 1 GeV. Below hurt by Fermi gas effects). Can usually separate electron from muon events with a very good ~100% active detector