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Neutrino Interactions: Challenges in the current theoretical pictureLuis Alvarez-RusoUniversidade de Coimbra TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAA

Outline • Motivation • º-induced quasielastic scattering • Single pion production (incoherent and coherent)

Motivation • Oscillation experiments • Goal: 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

Motivation GENIE Eº = 1 GeV • Oscillation experiments • Goal: 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) • Implications for oscillation measurements: T. Leitner, Poster 56 C20 • exact only for freenucleons • wrong for CCQE-like events

Motivation • Oscillation experiments • Goal: º¹!ºe searches (µ13 & ±$CP violation) • Electron-like backgrounds: • NC¼0 production (incoherent, coherent) • Photon emission in NC (candidate for low Eº excess@MiniBoonne) Aguilar-Arevalo et al., PRL98 (2007) 231801

Motivation • Hadronic physics • Nucleon and Nucleon-Resonance (N-¢, N-N*) axial form factors • MINERvA: first precision measurement of axial nucleon ff at Q2>1 GeV. • Strangeness content of the nucleon spin (isoscalar coupling GsA): • probed in NCQE :NCQE(p)/NCQE(n) or NC(p)/CCQE • Experiments are performed with nucleartargets ) • Nuclear physics • nuclear effects are essential for the interpretation of the data. • Information about: • Nuclear correlations • Meson exchange currents • Nucleon and resonance spectral functions

Ã electric ff Ã magnetic ff º QE scattering • The (CC) elementary process: where • Vector form factors: • Extracted from e-p, e-d data

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

dipole ansatz PCAC º QE scattering • 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)

º QE scattering • The (CC) elementary process: • MA= 1.016 § 0.026 GeV ( ) Bodek et al., EPJC 53 (2008) • MA from ¼electroproduction on p: • Connected to FA 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

º QE scattering • Relativistic Global Fermi GasSmith, Moniz, NPB 43 (1972) 605 • Impulse Approximation • Fermi motion • Pauli blocking • Average bindingenergy • Explains the main features of the (e,e’)inclusive¾ in the QE region • Fails in the details (nuclear dynamics needed): talk by O. Benhar

º QE scattering Benhar et al., PRD 72 (2005) Ankowski, Sobczyk, PRC 67 (2008) Nieves et al., PRC 70 (2004) Leitner et al., PRC 79 (2009) • 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 • Better description of (e,e’)inclusive¾(O. Benhar’s talk)

º QE scattering Martinez et al., PRC 73 (2006) Budkevich, Kulagin, PRC 76 (2007) • 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 • Problem: nucleon absorption that reduces the c.s. • Can be used to study: • 1Nknockout (with only Re[Vopt]) Complex optical potential

º QE scattering • Local Fermi Gas • Space-momentum correlations absent in the GFG • Reasonable for medium/heavy nuclei • Microscopic many-body effects are tractable (calculations in infinite nuclear matter) Convolution model: Ciofi degli Atti, Simula, PRC 53 (1996)

º QE scattering Singh, Oset, NPA 542 (1992) Nieves et al., PRC 70 (2004) • RPA long range correlations • Incorporates N-hole and ¢-hole states • V: ¼, ½ exchange, Landau-Migdal parameter g’ • Describes correctly ¹ capture on 12C and LSNDCCQE • Collective effect: important at low Q2for º QE

º QE scattering • Comparison toMiniBooNE¾ • At Eº =0.8 GeV: ¾th ~ 4.5-5 < ¾MB ~ 7 £ 10-38 cm2 • CCQE models with MA~1 GeV cannot reproduce MiniBooNE¾ Source: Boyd et al., AIP Conf. Proc. 1189 Data: MiniBooNE, PRD 81, 092005 (2009) more on CCQEdata in M. Wascko’ talk

º QE scattering • Comparison toMiniBooNE¾ • Model dependence in data: • Background (CCQE-like) depends on the ¼ propagation (absorption and charge exchange) model (NUANCE) • Eº reconstruction (unfolding) Source: Boyd et al., AIP Conf. Proc. 1189 Data: MiniBooNE, PRD 81, 092005 (2009)

º QE scattering • Comparison toMiniBooNE¾ • Proposed solutions: • MA=1.35 § 0.17 GeV (RFG) MiniBooNE, PRD 81, 092005 (2010) • MA=1.37 § 0.05 GeV (RMF) Butkevich, arXiv:1006:1595 • However, MA>1 GeV is incompatible with: • data • ¼electroproduction on p (at low Q2) • NOMAD, Lyubushkin et al., EPJ C 63 (2009) 355

º QE scattering • Comparison toMiniBooNE¾ • Many body, RPA, calculation Martini et al., PRC 80 (2009) • Lesson: Many-body dynamics beyond 1p1h is important

º QE scattering • Comparison toMiniBooNE¾ • Models should be compared to <d2¾/dT¹ dcosµ¹>… • … preferably to CCQE + CCQE-like • Inclusive data are desirable MiniBooNE, PRD 81 (2010)

1¼ production • Reactions • Incoherent: • Coherent: • CC • NC

1¼ production • Elementary process: • Dominated by resonance production • At Eº ~ 1 GeV: ¢(1232) • N-¢ transition current: • Form factors , Helicity amplitudes

1¼ production • Elementary process: • Dominated by resonance production • Rein-Sehgal model: Rein-Sehgal, Ann. Phys. 133 (1981) 79. • Used by almost all MC generators • Relativistic quark model of Feynman-Kislinger-Ravndal with SU(6) spin-flavor symmetry • Helicity amplitudes for 18 baryon resonances • Lepton mass = 0 • Corrections: • Poor description of ¼ electroproduction data on p Kuzmin et al., Mod. Phys. Lett. A19 (2004) Berger, Sehgal, PRD 76 (2007) Graczyk, Sobczyk, PRD 77 (2008)

1¼ production • Elementary process: • Dominated by resonance production • Rein-Sehgal model: • Used by almost all MC generators • Relativistic quark model of Feynmann-Kislinger-Ravndal with SU(6) spin-flavor symmetry • Helicity amplitudes for 18 baryon resonances • Lepton mass = 0 • Corrections: • Poor description of ¼ electroproduction data on p Leitner et al., POS NUFACT08 Kuzmin et al., Mod. Phys. Lett. A19 (2004) Graczyk, Sobczyk, PRD 77 (2008) Berger, Sehgal, PRD 76 (2007)

1¼ production • N-¢ transition current • Unitary isobar model MAIDhas been used to extract N-R helicity amplitudes (A1/2, A3/2, S1/2) from world data on ¼ photo- and electro-production for all 4 star resonances with W<2 GeV Drechsel, Kamalov, Tiator, EPJA 34 (2007) 69

1¼ production • N-¢ transition current • N-¢(1232) helicity amplitudes from MAID • N-¢(1232)is not a pureM1 transition , A3/23 A1/2 , S1/2 0

1¼ production • N-¢ transition current • Axial form factors PCAC Adler model

1¼ production • N-¢axial form factors: determination of CA5(0) and MA ¢ • From ANL and BNL data on • with large normalization (flux) uncertainties • Graczyk et al., PRD 80 (2009) • Deuteron effects • Non-resonant background absent • CA5(0)=1.19 § 0.08, MA ¢= 0.94 § 0.03 GeV • Hernandez et al., PRD 81 (2010) • Deuteron effects • Non-resonant background fixed by chiral symmetry • CA5(0)=1.00 § 0.11, MA ¢= 0.93 § 0.07 GeV • 20 % reduction of the GT relation off diagonal GT relation

1¼ production • Incoherent 1¼production in nuclei • Large number of excited states )semiclassical treatment • ¼propagation (scattering, charge exchange), absorption (FSI) • Most models cannot calculate this reaction channel. Exceptions: • MC generators: NUANCE, NEUT, GENIE, NuWro • Cascade: Ahmad et al., PRD 74 (2006) • Transport: GiBUU

1¼ production • Incoherent 1¼production in nuclei (FSI) • NuWro Poster 75 (B04), J. Sobczyk • Intranuclear cascade • ¼propagation: empirical ¼-N vacuum ¾ • ¼absorption: ¼-A absorption data • Ahmad et al., PRD 74 (2006) • Cascade (~NuWro) • In-medium modification of ¢ spectral f. (only in the production mech.) • GiBUU • Transport: ne approach for eA, ºA, pA, ¼A reactions • ¼, N but also ¢ are propagated • Main absorption mech.: ¢N!N N, ¼N N!N N

1¼ production • GiBUULeitner et al., PRC 73 (2006) • Effects of FSI on pion kinetic energy spectra • strong absorption in Δ region • side-feeding from dominant ¼+ into ¼0 channel • secondary pions through FSI of initial QE protons

1¼ production • Comparison to the ¾(CC¼+)/¾(CCQE-like) ratio at MiniBooNE Athar et al. GiBUU NuWro

1¼ production • NC ¼0 production at MiniBooNE • Good description of shape • Integrated ¾ : factor 2 smaller GiBUU vs MiniBooNE T. Leitner, PhD Thesis

1¼ production • Coherent pion production • CC • NC • Takes place at low q2 • Very small cross section but relativelylarger than in coherent ¼ production with photons or electrons • At q2» 0 the axial current is not suppressed while the vector is • Models: • PCAC • Microscopic NEUT Hiraide@NuInt09

1¼ production • Coherent pion production • PCAC models: Rein-Sehgal model NPB 223 (83) 29 • In the q2=0 limit, PCAC is used to relate ºinduced coherent pion production to ¼Aelastic scattering • Continuation to q2 0: (1-q2/1 GeV2)-2 factor • Describes ¼A in terms of ¼N scattering • Subtracts the spurious initial ¼ distortion present in ¼Abut not in coherent pion production Problems: Hernandez et al., PRD 80 (2009) 013003 • q2=0 limit neglects important angular dependence at low energies • The ¼A elastic description is not realistic

1¼ production • Coherent pion production • PCAC:Paschos & Schalla, PRD 80 (2009), Berger & Sehgal, PRD 76 (2007),79 (2009) • In the q2=0 limit, PCAC is used to relate ºinduced coherent pion production to ¼Aelastic scattering • Extrapolate to q2 0 • Directly use¼A cross section)spurious initial ¼ distortion present in ¼Abut not in coherent ¼ production is not subtracted • Smaller ¾ than RS • Problems of PCAC models: less relevant as the energy increases • NOMAD: ¾=72.6 § 8.1(stat) § 6.9(syst) £ 10-40 cm2 • Consistent with RS: ¾¼ 78 £10-40 cm2 • see L. Camilleri’s talk

1¼ production • Coherent pion production • Microscopic models: • ¢ excitation is dominant • ¢ properties change in the nuclear medium • ¼distortion: DWIA with optical potential based on ¢-hole model Singh et al., PRL 96 (2006) LAR et al, PRC 76 (2007) Amaro et al., PRD 79 (2009) Nakamura et al., PRC 81 (2010)

1¼ production • Coherent pion production • Microscopic models Amaro et al., PRD 79 (2009) • Medium effects reduce considerably de cross section • Pion distortion shifts down the peak

1¼ production • Coherent pion production • Microscopic models: • ¢ excitation is dominant • ¢ properties change in the nuclear medium • ¼distortion: DWIA with optical potential based on ¢-hole model • Treatment is consistent with incoherent ¼ production • Valid only at low energies Singh et al., PRL 96 (2006) LAR et al, PRC 76 (2007) Amaro et al., PRD 79 (2009) Nakamura et al., PRC 81 (2010)

1¼ production • Coherent pion production • Comparison to MiniBooNENC ¼0: • 35 % reduction inRS model • Data seem to prefer a CA5(0)~1.2 (in agreement with the GT relation) rather than a smaller one. • But a subtraction of a large incoherent¼0background is performed • Anderson@NuInt09

1¼ production • Coherent pion production • Comparison to SciBooNE: arXiv:1005.0059 • NC ¼0¾ compatible with RS • CC¼+/NC¼0=0.14+0.30-0.28 • Theoretical models predict CC¼+/NC¼0» 1-2 ! • But a subtraction of a large incoherent¼background is performed

Conclusions • Road map: • Understand the measurements • Explain (not fit) data • Implement better models in MC

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º QE scattering • Relativistic Global Fermi GasSmith, Moniz, NPB 43 (1972) 605 • Explains the main features of the (e,e’)inclusive c. s. in the QE region Ankowski@NuInt09

Electron scattering Inclusive electron-nucleus scattering at intermediate energies • Spectral functions of nucleons in nuclei: Results Ankowski@NuInt09 40Ca

º QE scattering • But RPA correlations cause a considerable reduction of the c.s. at low Q2

1¼ production • Elementary process • Sato & Lee model Nacamura@NuInt09 • Dynamical model for ¼ production with °, e, º • Starting with an effective H: ¼N, ¢N ) • T-matrix obtained from coupled channel Lippman-Schwinger eq. • Good agreement with data • Bare ¢N renormalized by meson clouds (30 %): reconciles the empirical value with quark model results

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