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Neutrino-induced quasielastic scattering

Neutrino-induced quasielastic scattering. Luis Alvarez-Ruso. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A. Neutrino-induced quasielastic scattering from a theoretical perspective. Luis Alvarez-Ruso. TexPoint fonts used in EMF.

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Neutrino-induced quasielastic scattering

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  1. Neutrino-induced quasielastic scattering Luis Alvarez-Ruso TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAA

  2. Neutrino-induced quasielastic scattering from a theoretical perspective Luis Alvarez-Ruso TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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

  4. 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, ± • ºare massive • flavors are mixed

  5. 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 freenucleons • wrong for CCQE-like events

  6. 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 freenucleons • wrong for CCQE-like events

  7. Motivation º – Nucleus interactions (in the QE region) are important for: • Hadronic physics • Nucleon axial form factors • MINERvA: first precision measurement of GA at Q2>1 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 nucleartargets ) nuclear effects are essential for the interpretation of the data.

  8. 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

  9. à electric ff à magnetic ff º scattering on the nucleon • The (CC) elementary process: where • Vector form factors: • Extracted from e-p, e-d data

  10. º scattering on the nucleon • At low Q2: • MV = 0.71 GeV, GE/GM¼ 1/¹p • At high Q2: Bodek et al., EPJC 53 (2008)

  11. dipole ansatz PCAC º scattering on the nucleon • The (CC) elementary process: where • Axial form factors: • gA = 1.267 ï decay • MA= 1.016 § 0.026 GeV ( ) Bodek et al., EPJC 53 (2008)

  12. QE scattering models Inclusive electron-nucleus scattering (crucial test for any º-nucleus model) • Relativistic Global Fermi GasSmith, Moniz, NPB 43 (1972) 605 • Impulse Approximation • Fermi motion • Pauli blocking • Average bindingenergy • Explains the main features of the inclusive cross sections in the QE region Ankowski@NuInt09

  13. QE scattering models Inclusive electron-nucleus scattering • Relativistic Global Fermi GasSmith, 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@NuInt09

  14. QE scattering models Inclusive electron-nucleus scattering • Spectral functions of nucleons in nuclei • The nucleon propagator can be cast as • Sh(p)Ãhole (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

  15. Meloni@NuInt09 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)

  16. 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 MeVÃfitted to p-A data • W: Benhar et al., PRD 72 (2005) Ankwowski & Sobczyk, PRC 77 (2008) • W=¾½ v /2 • Correlated Glauberapproximation • (straight trajectories, frozen spectators) • Benhar et al., PRC 44 (1991) 2328

  17. QE scattering models Inclusive electron-nucleus scattering • Spectral functions of nucleons in nuclei: Results Ankowski@NuInt09 40Ca

  18. QE scattering models Inclusive electron-nucleus scattering • Spectral functions of nucleons in nuclei: Results Ankowski@NuInt09 40Ca

  19. QE scattering models Inclusive electron-nucleus scattering • Spectral functions in a LocalFermi GasLeitner 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

  20. QE scattering models Inclusive electron-nucleus scattering • Spectral functions in a LocalFermi GasLeitner 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

  21. QE scattering models Inclusive electron-nucleus scattering • Spectral functions in a LocalFermi GasLeitner et al., PRC 79 (2009) • Mean field potential • Density and momentum dependent • Parameters fixed in p-Nucleus scattering • Nucleons acquire effective masses

  22. QE scattering models Inclusive electron-nucleus scattering • Spectral functions in a LocalFermi GasLeitner et al., PRC 79 (2009) • Hole spectral function: • The correlated part of Shis 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 ÃCollisional broadening

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

  24. 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

  25. 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

  26. 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

  27. 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 Q2for CCQE at MiniBooNE energies

  28. QE scattering models • RPA long range correlations • Comparison to inclusive electron-nucleus data LAR@NuInt09

  29. QE scattering models • RPA long range correlations • CCQE on 12C averaged over the MiniBooNE flux LAR et al., arXiv:0909.5123

  30. QE scattering models • RPA long range correlations • CCQE on 12C averaged over the MiniBooNE flux LAR et al., arXiv:0909.5123 • RPA correlations cause a reduction of ¾ at low Q2and forward angles

  31. QE scattering models • Relativistic mean field • Impulse Approximation • Initialnucleon in a bound state (shell) • ªi : Dirac eq. in a mean field potential (!-¾ model) • Finalnucleon • PWIA • RDWIA: ªf : Dirac eq. for scattering state • Glauber • Has been used to study 1Nknockout • Problem: nucleon absorption that reduces the c.s. Complex optical potential

  32. RPWIA RDWIA RPWIA RDWIA QE scattering models • Relativistic mean field Giusti et al., arXiv:0910.1045

  33. QE scattering models • Relativistic mean field • Impulse Approximation • Initialnucleon in a bound state (shell); no correlations • ªi : Dirac eq. in a mean field potential (!-¾ model) • Finalnucleon • PWIA • DWIA: ªf : Dirac eq. for scattering states • Glauber • Has been used to study 1Nknockout • Problem: nucleon absorption that reduces the c.s. Complex optical potential

  34. 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

  35. QE scattering models • Green function approach Meucci et al., PRC 67 (2003) 054601 16O(e,e’)X

  36. QE scattering models • (Super)scaling Barbaro et al., arXiv:0909.2602 • First kind scaling: 12C )

  37. QE scattering models • (Super)scaling • First kind scaling: • Second kind scaling: independent of A • First + Second scaling = Superscaling Ã’ < 0 scaling region Ã’ > 0 scaling violation

  38. QE scattering models • (Super)scaling • Scaling violations reside mainly in the transverse channel

  39. QE scattering models • (Super)scaling • The experimental superscaling function (fit using RLdata) • Constraint for nuclear models • Relativistic Fermi Gas • Exact superscaling • Wrong shape of f(Ã’)

  40. QE scattering models • (Super)scaling • The experimental superscaling function (fit using RLdata) • Constrain for nuclear models • Relativistic mean field describes the asymmetric shape of f(Ã’)

  41. QE scattering models • (Super)scaling • Superscaling in the ¢ region • Experimental superscaling function • At Ã’¢ > 0 other resonances, etc contribute

  42. QE scattering models • (Super)scaling • Superscaling Analysis SUSA • Calculate with Relativistic Fermi Gas • Replace fRFG! fexp

  43. QE scattering models • (Super)scaling • Superscaling Analysis SUSA • Calculate with Relativistic Fermi Gas • Replace fRFG! fexp

  44. 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

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

  46. Experimental status • MiniBooNE • Largest sample of low energy (< Eº > ~ 750 MeV) º¹CCQE 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 • ϰ=1.007 § 0.007 • MA=1.35 § 0.17 GeV • Large ¾ compared to GFG with MA=1 GeV Katori, arXiv:0909.1996

  47. Experimental status However: • The physical meaning of ϰ is obscure • ϰ, 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)

  48. Experimental status However: • The physical meaning of ϰ is obscure • ϰ, 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, arXiv:0909.1996

  49. Experimental status • NOMAD Lyubushkin et al., EPJ C 63 (2009) 355 • CCQE on 12Cat high 3-100 GeV energies(DIS is dominant) • No precise knowledge of the integrated º flux ) • Normalization of CCQE¾ from processes with better know ¾ (DIS, IMD) • CCQE¾ measured from combined 2-track (¹,p) and 1-track (¹) samples • From measured CCQE¾ : 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, arXiv:0909.1996

  50. Interpretation • MA > 1 GeV? • MA from ¼electroproduction 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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