Neutrino%20Scattering

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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

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Neutrino-electron scattering

• Tree level Feynman diagrams

• Effective Hamiltonian

• (through a Fierz transformation)

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• Only charged current

• Inelasticity variable (0ltylt1)

• Total cross-section

• (cross-section proportional to energy!)

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• Only neutral current

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• Only neutral current (total cross-section)

• Can obtain value of sin2qW from neutrino electron
  scattering (CHARM II)

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• Back to
  (charged and neutral currents)

• Then

• This cross-section is a consequence of the
  interference of the charged and neutral current
  diagrams.

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• Neutrino pair production

• Contribution from both W and Z graphs.

• Then

• Only neutral current contribution to

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Neutrino-electron scattering

• Summary neutrino electron scattering processes

Process Total cross-section







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Neutrino-nucleon quasi-elastic scattering

• Quasi-elastic neutrino-nucleon scattering
  reactions (small q2)

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Neutrino-nucleon quasi-elastic scattering

• Form factors introduced since proton, neutron not
  elementary.
• Depend on vector and axial weak charges of the
  proton and neutron.
• Two hypotheses
• Conservation of Vector Current (CVC)
• Partial conservation of Axial Current (PCAC)

• For low energy neutrinos (EnltltmN)

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Inelastic neutrino-nucleon scattering

• 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.

• 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 Q2/2M? and y ? /E can
  be used.

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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 F1 , F2 and F3 are the functions
of Q2 and ? . In the scaling limit they are the
functions of x only.
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Scaling behaviour

• Compilation of the data on structure functions in
  deep inelastic neutrino scattering (1983)

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• Neutrino proton CC scattering
• number of u-quarks in proton
  between x and xdx
• Some of the quarks are from sea
• For proton (uud)

• Scattering off quarks

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• Scattering off proton

• Structure functions
• Callan-Gross relationship

• Neutron (isospin symmetry)

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• Scattering off isoscalar target (equal number
  neutrons and protons)

• Total cross-section

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Rise of mean q2 with energy
Mean q2 was found to be linear function in
neutrino (antineutrino) energy.
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• Quark content of nucleons from CC cross-sections
• Define
• Experimental values from y distribution of
  cross-sections yields
• If

• Quarks and antiquarks carry 49 of proton
  momentum, valence quarks only 33 and sea quarks
  only 16.

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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.
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To obtain these expressions we have used
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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.
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We now consider the scaling limit
Substituting in terms of the scaling variables
we find the result
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For scattering on structureless
fermions/antifermions (e.g., point particle
quarks) we have
Thus measures the difference between quarks
and antiquarks.
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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
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Gross-Llewellyn-Smith (2 names) sum rule
In terms of the parton distributions in the
proton we have
Thus we have
and hence