Neutrino-induced quasielastic scattering

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Neutrino-induced quasielastic scattering

• Luis Alvarez-Ruso

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Neutrino-induced quasielastic scattering from a
theoretical perspective

• Luis Alvarez-Ruso

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Outline

• Motivation
• º scattering on the nucleon
• Quasielastic scattering models
• Experimental status and comparison to data
• Conclusions

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Motivation

• º Nucleus interactions (in the QE region) are
  important for
• Oscillation experiments
• º oscillations are well established )
• Goal Precise determination of oscillation
  parameters m2ij, µij,

• º are massive
• flavors are mixed

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Motivation

• º Nucleus interactions (in the QE region) are
  important for
• Oscillation experiments
• Precision measurements of m232, µ23 in º¹
  disappearance
• Understanding Eº reconstruction is critical
• Kinematical determination of Eº in a CCQE event
• Rejecting CCQE-like events relies on accurate
  knowledge of nuclear dynamics and FSI (¼, N
  propagation, ¼ absorption)

• exact only for free nucleons
• wrong for CCQE-like events

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Motivation
GENIE Eº 1 GeV

• º Nucleus interactions (in the QE region) are
  important for
• Oscillation experiments
• Precision measurements of m232, µ23 in º¹
  disappearance
• Understanding Eº reconstruction is critical
• Kinematical determination of Eº in a CCQE event
• Rejecting CCQE-like events relies on accurate
  knowledge of nuclear dynamics and FSI (¼, N
  propagation, ¼ absorption)

• exact only for free nucleons
• wrong for CCQE-like events

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Motivation

• º Nucleus interactions (in the QE region) are
  important for
• Hadronic physics
• Nucleon axial form factors
• MINERvA first precision measurement of GA at
  Q2gt1 GeV. Deviations from the dipole form?
• Strangeness content of the nucleon spin
  (isoscalar coupling GsA)
• probed in NCQE reactions
• Best experimental sensitivity in ratios
  NCQE(p)/NCQE(n) or NC(p)/CCQE
• Experiments are performed with nuclear targets )
• nuclear effects are essential for the
  interpretation of the data.

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Motivation

• º Nucleus interactions (in the QE region) are
  important for
• Nuclear physics
• Excellent testing ground for nuclear many-body
  mechanisms, nuclear structure and reaction models
• Relativistic effects
• Nuclear correlations
• Meson exchange currents (MEC)
• Nucleon and resonance spectral functions
• º-nucleus cross sections incorporate a richer
  information on nuclear structure and interactions
  than e-nucleus ones

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º scattering on the nucleon

• The (CC) elementary process
• where
• Vector form factors
• Extracted from e-p, e-d data

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º scattering on the nucleon

• At low Q2
• MV 0.71 GeV, GE/GM ¼ 1/¹p
• At high Q2

Bodek et al., EPJC 53 (2008)
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º scattering on the nucleon

• The (CC) elementary process
• where
• Axial form factors
• gA 1.267 Ã decay
• MA 1.016 0.026 GeV ( ) Bodek et
  al., EPJC 53 (2008)

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QE scattering models

• Inclusive electron-nucleus scattering (crucial
  test for any º-nucleus model)
• Relativistic Global Fermi Gas Smith, Moniz, NPB
  43 (1972) 605
• Impulse Approximation
• Fermi motion
• Pauli blocking
• Average binding energy
• Explains the main features of the inclusive cross
  sections in the QE region

Ankowski_at_NuInt09
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QE scattering models

• Inclusive electron-nucleus scattering
• Relativistic Global Fermi Gas Smith, Moniz, NPB
  43 (1972) 605
• However
• GFG overestimates the longitudinal response RL
• FG is certainly too simple to be right. Nuclear
  dynamics must be
• included in the picture Benhar_at_NuInt09

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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions of nucleons in nuclei
• The nucleon propagator can be cast as
• Sh(p) Ã hole (particle) spectral functions
  4-momentum (p) distributions of the struck
  (outgoing) nucleons
• Ã nucleon selfenergy
• Can be extended to the excitation of resonances
  in nuclei

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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions of nucleons in nuclei
• Hole spectral function
• 80-90 of nucleons occupy shell model states
• The rest take part in the NN interactions
  (correlations) located at high momentum

Benhar et al., PRD 72 (2005) Ankwowski
Sobczyk, PRC 77 (2008)
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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions of nucleons in nuclei
• Hole spectral function
• 80-90 of nucleons occupy shell model states
• The rest take part in the NN interactions
  (correlations) located at high momentum
• Particle spectral functions
• Optical potential U V i W
• V 25 MeV Ã fitted to p-A data
• W

Benhar et al., PRD 72 (2005) Ankwowski
Sobczyk, PRC 77 (2008)

• W¾ ½ v /2
• Correlated Glauber approximation
• (straight trajectories, frozen
  spectators)
• Benhar et al., PRC 44 (1991) 2328

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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions of nucleons in nuclei Results
  Ankowski_at_NuInt09

40Ca
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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions of nucleons in nuclei Results
  Ankowski_at_NuInt09

40Ca
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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions in a Local Fermi Gas Leitner
  et al., PRC 79 (2009)
• Space-momentum correlations absent in the GFG
• OK for medium/heavy nuclei
• Microscopic many-body effects are tractable
• Can be extended to exclusive reactions (e,e N),
  (e,e ¼), etc

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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions in a Local Fermi Gas Leitner
  et al., PRC 79 (2009)
• Space-momentum correlations absent in the GFG
• OK for medium/heavy nuclei
• Microscopic many-body effects are tractable
• Can be extended to exclusive reactions (e,e N),
  (e,e ¼), etc

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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions in a Local Fermi Gas Leitner
  et al., PRC 79 (2009)
• Mean field potential
• Density and momentum dependent
• Parameters fixed in p-Nucleus scattering
  
• Nucleons acquire effective masses

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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions in a Local Fermi Gas Leitner
  et al., PRC 79 (2009)
• Hole spectral function
• The correlated part of Sh is neglected
• Particle spectral function
• Re is obtained from Im with a dispersion
  relation fixing the pole position at
• I

Gil, Nieves, Oset, NPA627 Ciofi degli Atti et
al.,PRC41
à Collisional broadening
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QE scattering models

• Inclusive electron-nucleus scattering
• Spectral functions in a Local Fermi Gas
• Results Leitner et al., PRC 79 (2009)

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QE scattering models

• Good description of the dip region requires the
  inclusions of 2p2h contributions from MEC Gil,
  Nieves, Oset, NPA627
• Important for º source of CCQE-like events

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QE scattering models

• RPA long range correlations
• In nuclei, the strength of electroweak
  couplings may change from their free nucleon
  values due to the presence of strongly
  interacting nucleons Singh, Oset, NPA 542 (1992)
  587
• For the axial coupling gA
• The quenching of gA in Gamow-Teller decay is
  well established

Â0 dipole susceptibility g Lorentz-Lorenz
factor 1/3
Ericson, Weise, Pions in Nuclei
Wilkinson, NPA 209 (1973) 470
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QE scattering models

• RPA long range correlations Nieves et. al. PRC 70
  (2004) 055503
• In particular
• ¼ spectral function changes in the nuclear medium
  ) so does

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QE scattering models

• RPA long range correlations
• RPA approach built up with single-particle states
  in a Fermi sea
• Simplified vs. some theoretical models (e.g.
  continuum RPA)
• Applies to inclusive processes not suitable for
  transitions to discrete states
• But
• Incorporates explicitly ¼ and ½ exchange and
  -hole states
• Has been successfully applied to ¼, and
  electro-nuclear reactions
• Describes correctly ¹ capture on 12C and LSND
  CCQE
• Nieves et. al. PRC 70 (2004) 055503
• Important at low Q2 for CCQE at MiniBooNE
  energies

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QE scattering models

• RPA long range correlations
• Comparison to inclusive electron-nucleus data
  LAR_at_NuInt09

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QE scattering models

• RPA long range correlations
• CCQE on 12C averaged over the MiniBooNE flux LAR
  et al., arXiv0909.5123

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QE scattering models

• RPA long range correlations
• CCQE on 12C averaged over the MiniBooNE flux LAR
  et al., arXiv0909.5123
• RPA correlations cause a reduction of ¾ at low Q2
  and forward angles

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QE scattering models

• Relativistic mean field
• Impulse Approximation
• Initial nucleon in a bound state (shell)
• ªi Dirac eq. in a mean field potential (!-¾
  model)
• Final nucleon
• PWIA
• RDWIA ªf Dirac eq. for scattering state
• Glauber
• Has been used to study 1N knockout
• Problem nucleon absorption that reduces the c.s.

Complex optical potential
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QE scattering models

• Relativistic mean field

Giusti et al., arXiv0910.1045
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QE scattering models

• Relativistic mean field
• Impulse Approximation
• Initial nucleon in a bound state (shell) no
  correlations
• ªi Dirac eq. in a mean field potential (!-¾
  model)
• Final nucleon
• PWIA
• DWIA ªf Dirac eq. for scattering states
• Glauber
• Has been used to study 1N knockout
• Problem nucleon absorption that reduces the c.s.

Complex optical potential
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QE scattering models

• Green function approach Meucci et al., PRC 67
  (2003) 054601
• QE
• The imaginary part of the optical potential is
  responsible for the redistribution of the flux
  among the different channels
• Suitable for inclusive and exclusive scattering

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QE scattering models

• Green function approach Meucci et al., PRC 67
  (2003) 054601

16O(e,e)X
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QE scattering models

• (Super)scaling Barbaro et al., arXiv0909.2602
• First kind scaling

12C
)
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QE scattering models

• (Super)scaling
• First kind scaling
• Second kind scaling
  independent of A
• First Second scaling Superscaling

à lt 0 scaling region à gt 0 scaling violation
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QE scattering models

• (Super)scaling
• Scaling violations reside mainly in the
  transverse channel

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QE scattering models

• (Super)scaling
• The experimental superscaling function (fit using
  RL data)
• Constraint for nuclear models
• Relativistic Fermi Gas
• Exact superscaling
• Wrong shape of f(Ã)

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QE scattering models

• (Super)scaling
• The experimental superscaling function (fit using
  RL data)
• Constrain for nuclear models
• Relativistic mean field describes the asymmetric
  shape of f(Ã)

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QE scattering models

• (Super)scaling
• Superscaling in the region
• Experimental superscaling function
• At à gt 0 other resonances, etc contribute

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QE scattering models

• (Super)scaling
• Superscaling Analysis SUSA
• Calculate with Relativistic Fermi Gas
• Replace fRFG ! fexp

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QE scattering models

• (Super)scaling
• Superscaling Analysis SUSA
• Calculate with Relativistic Fermi Gas
• Replace fRFG ! fexp

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QE scattering models

• (Super)scaling
• Superscaling Analysis SUSA for º-A Amaro et al.,
  PRL 98 (2007) 242501
• Calculate with Relativistic Fermi Gas
• Replace fRFG ! fexp
• SUSA 15 reduction of ¾ with respect to RFG
• Scaling approach fails at !.40 MeV, q.400 MeV
  collective effects

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Experimental status

• Data!
• CCQE, NCQE, º, anti-º
• MiniBooNE (12C), SciBooNE (16O), MINOS (Fe),
  NOMAD (12C)
• and puzzles

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Experimental status

• MiniBooNE
• Largest sample of low energy (lt Eº gt 750 MeV)
  º¹ CCQE events to date.
  Aguilar-Arevalo et. al., PRL 100 (2008) 032301
• The shape of hd¾/dcosµ¹dE¹i is accurately
  described by the Relativistic Global Fermi Gas
  Model with EB 34 MeV, pF 220 MeV
• But
• ?1.007 0.007
• MA1.35 0.17 GeV
• Large ¾ compared to GFG
  with
  MA1 GeV

Katori, arXiv0909.1996
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Experimental status

• However
• The physical meaning of ? is obscure
• ?, MA values depend on the background from CC1¼
• Background subtraction depends on the ¼
  propagation (absorption and charge exchange)
  model
• NUANCE constant suppression of ¼ production
• Model dependent Eº reconstruction (unfolding)

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Experimental status

• However
• The physical meaning of ? is obscure
• ?, MA values depend on the background from CC1¼
• Background subtraction depends on the ¼
  propagation (absorption and charge exchange)
  model
• NUANCE constant suppression of ¼ production
• Model dependent Eº reconstruction (unfolding)
• Better compare to

Katori, arXiv0909.1996
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Experimental status

• NOMAD Lyubushkin et al., EPJ C 63 (2009) 355
• CCQE on 12C at high 3-100 GeV energies (DIS is
  dominant)
• No precise knowledge of the integrated º flux )
• Normalization of CCQE ¾ from processes with
  better know ¾ (DIS, IMD)
• CCQE ¾ measured from combined 2-track (¹,p) and
  1-track (¹) samples
• From measured CCQE ¾ MA 1.05 0.02(stat)
  0.06(sys) GeV
• Consistent with MA extracted from Q2 shape fit of
  2-track sample

MiniBooNE vs NOMAD Katori, arXiv0909.1996
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Interpretation

• MA gt 1 GeV?
• MA from ¼ electroproduction on p Bernard et al.,
  J Phys. G
• Using Current Algebra and PCAC
• Valid only at threshold and in the chiral limit
  (m¼ 0)
• Using models to connect with data )
• MAep 1.069 0.016 GeV Liesenfeld et al., PLB
  468 (1999) 20
• A more careful evaluation in ChPT Bernard et
  al., PRL 69 (1992) 1877
• MA MAep - MA , MA 0.055 GeV ) MA 1.014 GeV

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Interpretation

• Can nuclear effects explain the shape of the
  MiniBooNE Q2 distribution?
• Spectral functions

Benhar Meloni, arXiv0903.2329
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Interpretation

• Can nuclear effects explain the shape of the
  MiniBooNE Q2 distribution?
• Spectral functions

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Interpretation

• Can nuclear effects explain the shape of the
  MiniBooNE Q2 distribution?
• RPA
• RPA brings the shape closer to experiment keeping
  MA 1 GeV

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Interpretation

• Can CCQE nuclear models explain the size of
  MiniBooNE ¾?
• Ex. at Eº 0.8 GeV ¾th 5 lt ¾MB 7 10-38 cm2
• CCQE models with MA1 GeV cannot reproduce
  MiniBooNE ¾

Katori, arXiv0909.1996
Sobczyk_at_NuInt09
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Interpretation

• Can CCQE nuclear models explain the size of
  MiniBooNE ¾?
• Many body RPA calculation Martini et al.,
  arXiv0910.2622

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Interpretation

• Can CCQE nuclear models explain the size of
  MiniBooNE ¾?
• Many body RPA calculation Martini et al.,
  arXiv0910.2622
• Lesson Many-body dynamics beyond 1p1h is
  important
• Open questions
• Is the Q2 distribution also well described by
  CCQE2p2h?
• Role of MEC
• Is the comparison proper ?
• Comparison to inclusive data is needed
• NOMAD results?

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Conclusions

• º-A scattering in the CCQE region is relevant for
  oscillation, hadron and nuclear physics
• New data (K2K, MiniBooNE, SciBooNE, MINOS, NOMAD)
• MINERvA in the future
• A good understanding of (semi)inclusive ºA
  (together with eA) cross section in the QE and
  resonance regions is required for the (model
  dependent) separation of mechanisms only then
  more precise determinations of Eº background will
  be possible
• The physical meaning of ?, MA needs to be
  clarified
• The role nuclear effects should be established
• Theoretical progress has to be incorporated in
  the MC