Neutrino Cross Section Calculations

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Neutrino Cross Section Calculations

• (Status Report)
• Emmanuel A. Paschos
• University of Dortmund
• March 21st, 2007

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Main Properties

• Neutrinos are important because they have only
  weak and gravitational interactions
• They provided the first evidence for physics
  beyond the standard model
• There are expectations that they have important
  consequences, but we do not know yet what the
  exact implications are

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A LOOK AT HISTORYL. Michel 1966

• TABLE 1
• Problems of the Weak Interactions
• G0.72x10-5 Mp-2 0.83x10-5 GeV-2
• todays value (1.16632-0.00004)x10-5
  GeV-2
• structure at small distances Ws or what ?
  discovered
• Cabibbo angle sin? 0.21
  now CKM Matrix
• ?I 1/2
  partly understood
• no neutral leptonic currents ?
  discovered
• why two kinds of leptons separately conserved ?
• µ-e symmetry, but µ-e mass difference ? µ-e-t
  symmetry
• CP- violation
  e, e, B-mesons
• --------------------
  -------
• V-A nature, P and C violation and two component
  neutrinos
• seem well understood

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• The mixing of neutrinos implies mass differences.
• The small masses suggest a high mass scale a
  popular realization is the see-saw mechanism.
• Since the elements in the mass matrix are not
  equal ? there is a symmetry that is broken
• 1) if Global Goldstone bosons
• 2) if Local additional Higgs
  particles.
• To answer many of the questions we need precise
• determination of the cross sections.

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Neutrinos have Masses

• A mass like MMRNRC(bar)NR is called Majorana
  Mass and creates a Majorana
• mass state ? 1/v2 (NRCNR )
• Two kinds of mass terms
• ? Dirac ?L(bar)NR
• ? Majorana NRC(bar)NR
• We wish to know the masses, mixings and
  phases of neutrinos , as well as other particles
  that are associated with them (Goldstone or
  pseudo-Goldstone mesons).

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• Cross sections at medium and higher energies have
  been studied for a long time. At the time of the
  discovery of neutral currents several reactions
  could have been more accurately
  determined.....there are new efforts to measure
  them accurately, because we need them for
  oscillation experiments.

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Contents

• Overview of the cross sections
• ? and higher resonances (work with
• J-Y. Yu, O. Lalakulich, M. Sakuda,EAP)
• Quasi elastic ( A. Bodek et al.)
• Coherent pion production(A. Kartavtsev, G
  .Gounaris, EAP)
• Importance of the results
• Summary

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Anatomy of cross sections

• s,qe 0.50x10-38 cm2
• s (?) 0.60 x10-38 cm2
• s(coh,p) (1.0 to 3.0)x10-40 cm2
• s,dis 0.65x10-38 E,? (Gev) cm2
• for E,? 10 GeV 6.5x10-38 cm2

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Aims

• Determine the ?-peak in various channels
  (accuracy of 10)
• Observe ds/dQ2 , s(Ev)
• Observe several channels, perhaps one of the next
  resonanances
• Nuclear effects for various Nuclei
• With accurate vector couplings we can check the
  axial couplings CA6(Q2)

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More recent Work

• Leitner, Alvarez-Ruso and Mosel
• Nucl-th/0606058
• Hernandez,Nieves and Velverde
• hep-th/0701149
• Sato, Lee and Sakuda,...
• ..........

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Part II

• Jµ(k,k)Co eµ(long) S C? eµ(?)
• eµ(long) 1/vQ2(qo,0,0,q3) i
• eµ(?) 1/vQ2(q3,0,0,qo) ,
  for ? 0
• 1/v2(0,1,i,0),
  ?1
• 1/v2(0,1, -i,0)
  ? -1
• ---- eµ(?) qµ 0 or for neutral current Jµqµ 0

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Aims

• estimate to better than 5 accuracy
• measure Q2 dependence Adler Test
• measure s(Ev)
• use results to estimate background for ?eN ? e-X
  oscillation studies

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Relevance for other topics

• ? Precise values of cross sections are needed in
  LBL in order to determine ?m2 and mixings angles
  ?13 especially
• In MINOS, Icarus and OPERA the signal is
  excess of events in
• vµ?ve CC reactions good knowledge of reactions
  is necessary.
• Exper. in accelerators complementary to double
  CHOOZ
• (Huber, Kopp, Lindner, Rolinec, Rodejohann and
  Winter ...)
• ? The mixing and oscillations are important for
  CP violation.
• ? Relevant for Leptogenesis which is a good
  candidate for Baryon Asymmetry in Universe.....
• ? If there are additional scalar particles, do
  they have observable consequences?

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Summary

• There is considerable improvement in the
  estimates of cross sections aiming for an
  accuracy of 5 to 15, depending on the reaction.
• We are interested on the dynamics of the
  reactions as well as their importance for
  properties of the neutrinos (Oscillations).

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