12004, TorinoAram Kotzinian Neutrino Scattering Neutrino interactions Neutrino-electron scattering Neutrino-nucleon quasi-elastic scattering Neutrino-nucleon deep inelastic scattering Variables Charged current Quark content of nucleons Sum rules Neutral current

22004, TorinoAram Kotzinian Neutrino-electron scattering Neutrino-electron scattering o Tree level Feynman diagrams: o Effective Hamiltonian: (through a Fierz transformation)

32004, TorinoAram Kotzinian o Only charged current: Inelasticity variable (0<y<1) Total cross-section: (cross-section proportional to energy!)

42004, TorinoAram Kotzinian o Only neutral current:

52004, TorinoAram Kotzinian o Only neutral current (total cross-section):  Can obtain value of sin 2  W from neutrino electron scattering (CHARM II):

62004, TorinoAram Kotzinian o Back to (charged and neutral currents) Then: This cross-section is a consequence of the interference of the charged and neutral current diagrams.

72004, TorinoAram Kotzinian o Neutrino pair production: Then: Contribution from both W and Z graphs. o Only neutral current contribution to:

82004, TorinoAram Kotzinian Neutrino-electron scattering o Summary neutrino electron scattering processes: ProcessTotal cross-section

92004, TorinoAram Kotzinian Neutrino-nucleon quasi-elastic scattering Quasi-elastic neutrino-nucleon scattering reactions (small q 2 ):

102004, TorinoAram Kotzinian Neutrino-nucleon quasi-elastic scattering For low energy neutrinos (E <<m N ): o Form factors introduced since proton, neutron not elementary. o Depend on vector and axial weak charges of the proton and neutron. o Two hypotheses: - Conservation of Vector Current (CVC): - Partial conservation of Axial Current (PCAC):

112004, TorinoAram Kotzinian Inelastic neutrino-nucleon scattering Since parity is not conserved in weak interactions, there are more structure functions for weak processes, like neutrino scattering, than for electromagnetic processes, like electron scattering. Again the variables x = Q 2 /2M and y = /E can be used. Parton model is used to make predictions for deep inelastic neutrino-nucleon scattering. Neutrino beams from pion and kaon decays, dominated by muon neutrinos are used to study this process.

122004, TorinoAram Kotzinian Weak structure functions General form for the neutrino-nucleon deep inelastic scattering cross-section, neglecting lepton masses and corrections of the order of M/E: The functions F 1, F 2 and F 3 are the functions of Q 2 and. In the scaling limit they are the functions of x only.

132004, TorinoAram Kotzinian Scaling behaviour Compilation of the data on structure functions in deep inelastic neutrino scattering (1983)

142004, TorinoAram Kotzinian Neutrino proton CC scattering: = number of u-quarks in proton between x and x+dx Some of the quarks are from sea: For proton (uud): o Scattering off quarks:

152004, TorinoAram Kotzinian Scattering off proton: o Structure functions: Callan-Gross relationship: o Neutron (isospin symmetry):

162004, TorinoAram Kotzinian Scattering off isoscalar target (equal number neutrons and protons): o Total cross-section:

172004, TorinoAram Kotzinian

182004, TorinoAram Kotzinian Rise of mean q 2 with energy Mean q 2 was found to be linear function in neutrino (antineutrino) energy.

192004, TorinoAram Kotzinian Quark content of nucleons from CC cross-sections Define: Experimental values from y distribution of cross-sections yields: If o Quarks and antiquarks carry 49% of proton momentum, valence quarks only 33% and sea quarks only 16%.

202004, TorinoAram Kotzinian Some details Note that for right-handed incident anti-neutrinos the e term changes sign. Note also that the e term is orthogonal to the asymmetric hadronic term that is proportional to since q = l – l’ and gives zero when dotted into where both signs for the last term appear in the literature.

212004, TorinoAram Kotzinian To obtain these expressions we have used

222004, TorinoAram Kotzinian Finally we can put the pieces together to obtain the corresponding cross sections(in the limit ) We recognize this to be similar to the EM result but with replacements, an extra factor of 4 and the (new) term.

232004, TorinoAram Kotzinian We now consider the scaling limit Substituting in terms of the scaling variables we find the result

242004, TorinoAram Kotzinian For scattering on structureless fermions/antifermions (e.g., point particle quarks) we have Thus measures the difference between quarks and antiquarks.

252004, TorinoAram Kotzinian For elastic neutrino scattering from quark and antiquark we have: and Working the details out explicitly in terms of the parton momentum and mass, we find Thus for pointlike quarks we have

262004, TorinoAram Kotzinian Gross-Llewellyn-Smith (2 names) sum rule In terms of the parton distributions in the proton we have Thus we have and hence