NuInt 09: Theory highlights Luis Alvarez-Ruso Universidade de Coimbra NuInt Series NuInt: International Workshop on Neutrino-Nucleus Interactions in the Few GeV Region NuInt 01: Tsukuba,
Download ReportTranscript NuInt 09: Theory highlights Luis Alvarez-Ruso Universidade de Coimbra NuInt Series NuInt: International Workshop on Neutrino-Nucleus Interactions in the Few GeV Region NuInt 01: Tsukuba,
NuInt 09: Theory highlights Luis Alvarez-Ruso Universidade de Coimbra NuInt Series NuInt: International Workshop on Neutrino-Nucleus Interactions in the Few GeV Region NuInt 01: Tsukuba, Japan NuInt 02: UC Irvine, USA NuInt 04: Gran Sasso Lab., Italy NuInt 05: Okayama U., Japan NuInt 06: Fermi Lab., USA L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 NuInt 09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 NuInt 09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Scientific Program Motivation Confronting theory, models and data Electron scattering and its connections to neutrino-nucleus interactions Current and future neutrino experiments Charged Current and Neutral Current quasi-elastic scattering Single pion production Deep and not-so-deep inelastic scattering The path forward: theory vs. experiments needs L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Scientific Program Motivation Confronting theory, models and data Electron scattering and its connections to neutrino-nucleus interactions Current and future neutrino experiments Charged Current and Neutral Current quasi-elastic scattering Single pion production Deep and not-so-deep inelastic scattering The path forward: theory vs. experiments needs L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Motivation º – Nucleus interactions are important for: Oscillation experiments Tanaka@NuInt09 Precision measurements of ¢m2, sin2 2µ in º¹ disappearance ) Understanding Eº reconstruction is critical Kinematical determination of Eº in a CCQE event º ¹ n ! 2mn E ¹ ¡ m2¹ ¡ m2n + m2p Eº = 2(m n ¡ E ¹ + p¹ cosµ¹ ) ¹¡ p exact only for free nucleons wrong for CCQE-like events Rejecting CCQE-like events relies on accurate knowledge of FSI (¼, N propagation, ¼ absorption) Searches for º¹ ! ºe (µ13) Electron-like backgrounds: NC ¼0 production (incoherent, coherent) Photonuclear absorption (eliminates one ° in ¼0 ! ° ° ) Photon emission in NC L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Motivation º – Nucleus interactions are important for: Astrophysics Balantekin@NuInt09 Production and detection of (low energy) solar and supernova º º reactions in supernova core collapse Nucleosynthesis (r-processes) Physics beyond standard model Deviations from universality in the Zºº and W¹º¹ vertices could be accessed in DIS experiments at TeV energies Balantekin L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Motivation º – Nucleus interactions are important for: Hadronic physics Nucleon and Nucleon-Resonance (N-¢, N-N*) axial form factors MINERvA: first precision measurement of axial nucleon ff at Q2>1 GeV. Deviations from the dipole form? Strangeness content of the nucleon spin (isoscalar coupling GsA): probed in NCQE reactions º ¹ (p; n) ! º ¹ (p; n) 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. L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Motivation º – Nucleus interactions 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 ”Neutrino cross sections incorporate a richer information on nuclear structure and interactions than electrons” Amaro@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º cross sections Tanaka@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Theoretical tools How can neutrino cross sections be calculated? At low energies Eº . 200 MeV Adapted from Balantekin@NuInt09 Effective field theory (for · 3 nucleons) Non-relativistic many-body theories: Shell model, RPA At intermediate energies 200 MeV . Eº . 5 GeV (Relativistic) Fermi gas (for medium to heavy nuclei) Hadron spectral functions functions (N, ¼, ¢(1232), N*) (Super)scaling At high energies Eº & 5 GeV Quark-hadron duality Parton distribution functions (PDF) Perturbative QCD and DGLAP The regions of validity are not well established (!, q) ( better variables L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering 1. These techniques have been applied to electron-nucleus reactions lepton How can neutrino cross sections be calculated? At low energies Eº . 200 MeV Effective field theory (for · 3 nucleons) Non-relativistic many-body theories: Shell model, RPA At intermediate energies 200 MeV . Eº . 5 GeV (Relativistic) Fermi gas (for medium to heavy nuclei) Hadron spectral functions functions (N, ¼, ¢(1232), N*) (Super)scaling At high energies Eº & 5 GeV Quark-hadron duality Parton distribution functions (PDF) Perturbative QCD and DGLAP The regions of validity are not well established (!, q), (x,Q2) ( better variables L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering 1. These techniques have been applied to electron-nucleus reactions 2. Large set of inclusive electron-nucleus scattering data SLAC, MIT/Bates, ELSA, MAMI, JLab Several targets: A=1-208 Different kinematics (!, q) ) crucial test for any º-nucleus model L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering 3. Nucleon, N-¢, N-N* e.m. form factors are extracted from e-p, e-d data For the nucleon ¡ ¹ = ° ¹ F1N (q2 ) + i 2m N ¾¹ º qº F2N (q2 ) V For º scattering one needs F12 p n = F12 ¡ F12 q2 GE = F1 + F2 à electric ff 2mN GM = F1 + F2 à magnetic ff GE and GM exhibit different q2 dependence ) BBBA parametrization The study of nucleon electric form factors at large Q2 (5.2-8.5 GeV2) continues at JLab with the recoil polarization method (Rosenbluth separation technique does not work) Brash@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering 3. Nucleon, N-¢, N-N* e.m. form factors are extracted from e-p, e-d data For N-Resonance transitions Unitary isobar model MAID has been used to extract N-R helicity amplitudes (A1/2, A3/2, S1/2) from world data on ¼ photo- and electroproduction for all 4 star resonances with W<2 GeV Drechsel, Kamalov, Tiator, EPJA 34 (2007) 69 q A 1=2 = A 3=2 = S1=2 = ¯+ ¹ ¯ ® ¯ ¯ R; J z = 1=2 ² ¹ J EM N ; J z = ¡ 1=2 ³ q ¯+ ¹ ¯ ® 2¼® ¯ ¯ R; J z = 3=2 ² ¹ J EM N ; J z = 1=2 ³ kR q ¯0 ¹ ¯ ® 2¼® pj q j ¡ R; J z = 1=2 ¯² ¹ J EM ¯N ; J z = 1=2 ³ kR 2 2¼® kR - Q Helicity amplitudes ) Vector form factors MAID also contains non-resonant ¼ production L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering 3. Nucleon, N-¢, N-N* e.m. form factors are extracted from e-p, e-d data For the N-Resonance transitions Example N-¢(1232) N-¢(1232) is not a pure M1 transition , A3/2 3 A1/2 , S1/2 0 Consequence for º scattering: L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering 3. Nucleon, N-¢, N-N* e.m. form factors are extracted from e-p, e-d data For the N-Resonance transitions Example N-¢(1232) Consequence for º scattering: N-¢ axial ff should be refitted L. Alvarez-Ruso, Universidade de Coimbra Leitner@NuInt09 NuFact 09 Electron scattering Inclusive electron-nucleus scattering at intermediate energies Relativistic Global Fermi Gas Smith, Moniz, NPB 43 (1972) 605 Impulse Approximation f (~ r;p ~) = £ (pF ¡ j~ pj) Fermi motion Pauli blocking PPauli = 1 ¡ q £ (pF ¡ j~ pj) Average binding energy E = p ~2 + m2N ¡ ² B Explains the main features of the inclusive cross sections in the QE region Ankowski@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Inclusive electron-nucleus scattering at intermediate energies 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@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Inclusive electron-nucleus scattering at intermediate energies Spectral functions of nucleons in nuclei The nucleon propagator can be cast as Z G(p) = Sh (! ; p ~) d! 0 + p ¡ ! ¡ i´ Z Sp (! ; p ~) d! 0 p ¡ ! ¡ i´ Sh(p) à hole (particle) spectral functions: 4-momentum (p) distributions of the struck (outgoing) nucleons 1 Im§ (p) Sp;h (p) = ¡ ¼[p2 ¡ M 2 ¡ Re§ (p)]2 + [Im§ (p)]2 § à nucleon selfenergy Can be extended to the excitation of resonances in nuclei L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Inclusive electron-nucleus scattering at intermediate energies Spectral functions of nucleons in nuclei Hole spectral function: Ankowski,Benhar@NuInt09 80-90 % of nucleons occupy shell model states The rest take part in the NN interactions (correlations); located at high momentum n(~ p) = R d! Sh (! ; p ~) Meloni@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Inclusive electron-nucleus scattering at intermediate energies Spectral functions of nucleons in nuclei Hole spectral function: Ankowski,Benhar@NuInt09 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 Glauber approximation (straight trajectories, frozen spectators) L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Inclusive electron-nucleus scattering at intermediate energies Spectral functions of nucleons in nuclei: Results Ankowski@NuInt09 40Ca L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Inclusive electron-nucleus scattering at intermediate energies Spectral functions of nucleons in nuclei: Results Ankowski@NuInt09 40Ca L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Inclusive electron-nucleus scattering at intermediate energies Spectral functions in a Local Fermi Gas LAR,Leitner@NuInt09 pF (r ) = [ 32 ¼2 ½(r )]1=3 OK for medium/heavy nuclei Microscopic many-body effects are tractable Can be extended to exclusive reactions: (e,e’ N), (e,e’ ¼), etc Hole spectral function: Im§ ¼ 0 2 r;p ~) Sh (p) ! ±(p2 ¡ M e® ) M e® = M + U(~ The correlated part of SL is neglected Particle spectral functions Im§ = ¡ p Density and momentum à dependent mean field potential Gil, Nieves, Oset, NPA627 Ciofi degli Atti et al.,PRC41 (p2 )¡ coll (p; r ) ; ¡ coll = h¾N N vrel i à Collisional broadening GiBUU Re§ is obtained from Im§ with a dispersion relation L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Inclusive electron-nucleus scattering at intermediate energies Spectral functions in a Local Fermi Gas: Results L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering 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 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Relativistic mean field Giusti,Udias@NuInt09 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 Complex optical potential Glauber Has been used to study 1N knockout Problem: nucleon absorption that reduces the c.s. L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Relativistic mean field RPWIA RDWIA RPWIA RDWIA Giusti@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Relativistic mean field Giusti,Udias@NuInt09 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 Complex optical potential Glauber Has been used to study 1N knockout Problem: nucleon absorption that reduces the c.s. Problem: hard to include resonance excitation… Gent: ¢(1232) in PWIA L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Green function approach Giusti@NuInt09 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 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Green function approach Giusti@NuInt09 16O(e,e’)X L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering Green function approach Giusti@NuInt09 Problem: RT is underestimated (lack of more complicated effects: MEC) 12C(e,e’)X Meucci et al., PRC 67 (2003) L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering (Super)scaling Barbaro,Amaro,Udias,Giusti@NuInt09 F (! ; j~ qj) = d¾ d- d! Z ¾ep + N ¾en First kind scaling: F = F (Ã0(! ; j~ qj)) 12C ) L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering (Super)scaling Barbaro,Amaro,Udias,Giusti@NuInt09 F (! ; j~ qj) = d¾ d- d! Z ¾ep + N ¾en First kind scaling: F = F (Ã0(! ; j~ qj)) Second kind scaling: f (Ã0) = pF F (Ã0) independent of A First + Second scaling = Superscaling Ã’ < 1 scaling region Ã’ > 1 scaling violation L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering (Super)scaling Barbaro,Amaro,Udias,Giusti@NuInt09 Scaling violations reside mainly in the transverse channel L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering (Super)scaling Barbaro,Amaro,Udias,Giusti@NuInt09 The experimental superscaling function (fit using RL data) Constrain for nuclear models Relativistic Fermi Gas Exact superscaling Wrong shape of f(Ã’) L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering (Super)scaling Barbaro,Amaro,Udias,Giusti@NuInt09 The experimental superscaling function (fit using RL data) Constrain for nuclear models Relativistic mean field describes the asymmetric shape of f(Ã’) L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering (Super)scaling Barbaro,Amaro,Udias,Giusti@NuInt09 Superscaling in the ¢ region Experimental superscaling function At Ã’¢ > 1 other resonances, etc contribute L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering (Super)scaling Barbaro,Amaro,Udias,Giusti@NuInt09 Superscaling Analysis SUSA Calculate with Relativistic Fermi Gas Replace fRFG ! fexp L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering (Super)scaling Barbaro,Amaro,Udias,Giusti@NuInt09 Superscaling Analysis SUSA Calculate with Relativistic Fermi Gas Replace fRFG ! fexp L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Electron scattering (Super)scaling Barbaro,Amaro,Udias,Giusti@NuInt09 Superscaling Analysis SUSA for º-A 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 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering The (CC) elementary process: º ¹ (k) n(p) ! ¹ ¡ (k0) p(p0) GF cosµC ® p M = l J® 2 where l ® = u ¹ (k0)° ®(1 ¡ ° 5 )u(k) £ J® = u ¹ (p ) ° ®F1V + 0 i 2M µ Form factors: FA (Q ) = gA 2 dipole ansatz ¯ ¾®¯ q F2V 2 Q 1+ M A2 ¶¡ + ° ¹ ° 5 FA + 2 q¹ M ¤ ° 5 FP u(p) 2M 2 2 ; FP (Q ) = 2 F (Q ) A 2 Q + m¼ 2 PCAC gA = 1.26 à ¯ decay L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering The (CC) elementary process: µ ¶¡ 2 2 Q FA (Q2 ) = gA 1 + M A2 º ¹ (k) n(p) ! ¹ ¡ (k0) p(p0) MA: MA= 1.026 § 0.021 (world average from º scattering) MA= 1.069 § 0.016 (¼ electroproduction close to threshold) At low q2, this difference can be understood with ÂPT: µ FA (q2 ) = gA ¶ 1 2 2 12 2 1 + hr A i q + ¢¢¢ ) hr A i = 6 MA 2 µ hr A2 i e = hr A2 i º ¶ 3 12 + 1 ¡ 2 ) ¢ M A = 0:055 GeV 64f ¼ ¼ L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering Data! CCQE, NCQE, º, anti-º MiniBooNE (12C), SciBooNE (16O), MINOS (Fe), NOMAD (12C) and puzzles… L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering MiniBooNE: largest sample of low energy º¹ CCQE events to date. Aguilar-Arevalo et. al., PRL 100 (2008) 032301 The shape of hd¾/dcosµ¹dE¹i is accurately described by the Relativistic Fermi Gas Model with: EB = 34 MeV, pF = 220 MeV µq ¶ But E pmi n = · M 2 + p2F ¡ ! + E B ; · = 1:019 § 0:011 MA = 1.23 § 0.20 GeV Convenient parametrization of CCQE data L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering However: The physical meaning of ϰ is obscure MA > 1 GeV ϰ, MA values depend on the background from CC1¼ New analysis using different CC1¼ gets: MA=1.35 § 0.17 GeV, ϰ=1.007 § 0.007 L. Alvarez-Ruso, Universidade de Coimbra Katori@NuInt09 NuFact 09 º QE scattering Spectral functions do not explain the shape of the Q2 distribution Meloni,LAR@NuInt09 Meloni@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering RPA long range correlations LAR@NuInt09 “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 : (gA ) e® 1 = gA 1 + g0Â0 Â0 dipole susceptibility g’ Lorentz-Lorenz factor ~1/3 Ericson, Weise, Pions in Nuclei The quenching of gA in Gamow-Teller ¯ decay is well established (gA ) e® » 0:9 gA Wilkinson, NPA 209 (1973) 470 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering RPA long range correlations LAR@NuInt09 Following Nieves et. al. PRC 70 (2004) 055503 : VN N = ~ ¿1~ ¿2 ¾1i ¾2j [^ qi q ^j VL (q) + (±i j ¡ q ^i q ^j )VT (q)] + g~ ¾1~ ¾2 + f 0~ ¿1~ ¿2 + f I 1 I 2 In particular ( µ ) ¶ 2 2 2 2 2 fNN¼ ¤ ¼ ¡ m¼ q ~ 0 VL = + g m2¼ ¤ 2¼ ¡ q2 q2 ¡ m2¼ ¼ spectral function changes in the nuclear medium ) so does J ®A L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering RPA long range correlations LAR@NuInt09 Following Nieves et. al. PRC 70 (2004) 055503 : Describes correctly ¹ capture on 12C and LSND CCQE VN N = ~ ¿1~ ¿2 ¾1i ¾2j [^ qi q ^j VL (q) + (±i j ¡ q ^i q ^j )VT (q)] + g~ ¾1~ ¾2 + f 0~ ¿1~ ¿2 + f I 1 I 2 In particular ( µ ) ¶ 2 2 2 2 2 fNN¼ ¤ ¼ ¡ m¼ q ~ 0 VL = + g m2¼ ¤ 2¼ ¡ q2 q2 ¡ m2¼ ¼ spectral function changes in the nuclear medium ) so does J ®A L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering Comparison to the modified Smith-Moniz ansatz (shape) All curves are normalized to the same area The effect of RPA brings the shape of the Q2 distribution closer to experiment keeping MA = 1 GeV L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering But RPA correlations cause a considerable reduction of the c.s. at low Q2 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering CCQE c.s. from MiniBooNE Katori@NuInt09 ¾ considerably larger than the RFG prediction with MA=1 GeV L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 º QE scattering CCQE c.s. from MiniBooNE Katori@NuInt09 c.s considerably larger than the RFG prediction with MA=1 GeV Possible issues: Flux Background substraction: 1¼, 2p2h, MEC Inclusive (model independent) data are desirable L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Reactions Incoherent: Coherent: CC º l NC º º l A ! l ¼X A ! l ¡ ¼+ A A ! º ¼0 A New data: SciBooNE: ¾(NC¼0)/¾(CC) MiniBooNE: NC¼0 normalized differential c.s. d¾/dp¼, d¾/dcosµ¼ CC¼+ ratio ¾(CC¼+)/¾(CCQE) arXiv:0904.3159 absolute c.s., d¾/dq2 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Elementary processes (on nucleons) Hernandez@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Elementary process (on nucleons) largest Hernandez@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production N-¢ transition current "à ¹¹ J¹ = à C3V ¯¹ C4V ¯¹ C5V ¯¹ ¯ ¹ 0 ¯ 0 ¹ ¯ p¹ ) (g = q¡ q ° ) + ( g q ¢p ¡ q p ) + ( g q ¢p ¡ q M M2 M2 C3A ¯¹ C4A ¯¹ C6A ¯ ¹ ¯ ¹ 0 ¯ 0 ¹ A ¯¹ + (g = q¡ q ° ) + ( g q ¢p ¡ q p ) + C 5 g + q q M M2 M2 M2 A A C6 = C5 2 à PCAC 2 m¼ ¡ q 1 A C4A = ¡ C5A C3 = 0 à Adler model 4 µ 2 q C5A = C5A (0) 1 ¡ 3M A2 ¢ ¶¡ 1µ C5A(0), MA¢: fitted to ANL data on L. Alvarez-Ruso, Universidade de Coimbra 2 q 1¡ M A2 ¢ ¶¡ ! °5 # u 2 º ¹ d ! ¹ ¡ ¼+ pp NuFact 09 1¼ production N-¢ transition current C5A (0) , MA¢: fitted to ANL data on M A ¢ = 0:985§ 0:082 GeV C5A (0) L. Alvarez-Ruso, Universidade de Coimbra º ¹ d ! ¹ ¡ ¼+ pp = 0:867 § 0:075 < g¢ N ¼f ¼ p ¼ 1:2 à off diag. GT relation 6M NuFact 09 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 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Incoherent 1¼ production in nuclei Large number of excited states ) semiclassical treatment ¼ propagation (scattering, charge exchange), absorption (FSI) Most models cannot calculate this reaction channels. Exceptions: MC generators: NUANCE, NEUT, GENIE Cascade: Ahmad, Athar, Singh, PRD 74 (2006) Transport: GiBUU L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production GiBUU Leitner@NuInt09 Boltzmann-Uehling-Uhlenberg transport model in coupled channels One approach for eA, ºA, pA, ¼A reactions Includes 61 baryons and 21 mesons (most relevant for us: ¢, N, ¼) Elastic and inelastic scattering (NN, N¢, NN ! NN¼,…) L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production GiBUU Leitner@NuInt09 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 º¹ + 56 F e ! ¹ ¡ ¼X E º = 1 GeV L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production GiBUU Leitner@NuInt09 Comparison to the ¾(CC¼+)/¾(CCQE) ratio at MiniBooNE L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production GiBUU Leitner@NuInt09 Comparison to the ¾(CC¼+)/¾(CCQE) ratio at MiniBooNE Possible issues: Insufficient non-resonant background for the elementary reaction Problems in Eº reconstruction L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Coherent pion production CC º l A ! l ¡ ¼+ A NC º A ! º ¼0 A NEUT Hiraide@NuInt09 Takes place at low q2 Very small cross section but relatively larger than in coherent ¼ production with photons or electrons At q2 » 0 the axial current is not suppressed while the vector is L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Coherent pion production Rein-Sehgal model NPB 223 (83) 29 In the q2=0 limit, PCAC is used to relate º induced coherent pion production to ¼A elastic 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 ¼A but not in coherent pion production Problems: q2=0 limit neglects important angular dependence at low energies “below 1 GeV and lighter nuclei (…) the nuclear form factor is not enough forward peaked to render the finite t-dependence of the pion-nucleon cross section negligible” Nieves@NuInt09 The ¼A elastic description is not realistic L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Coherent pion production Rein-Sehgal model NPB 223 (83) 29 In the q2=0 limit, PCAC is used to relate º induced coherent pion production to ¼A elastic scattering Continuation to q2 0: (1-q2/1 GeV2)-2 factor Describes ¼A in terms of ¼N scattering Subtracts the spurious initial pion distortion present in ¼A but not in coherent pion production Problems: q2=0 limit neglects important angular dependence at low energies “below 1 GeV and lighter nuclei (…) the nuclear form factor is not enough forward peaked to render the finite t-dependence of the pion-nucleon cross section negligible” Nieves@NuInt09 The ¼A elastic description is not realistic L. Alvarez-Ruso, Universidade de Coimbra Nieves@NuInt09 NuFact 09 1¼ production Coherent pion production Rein-Sehgal model NPB 223 (83) 29 RS model should not be used in the analysis of º experiments at low energies Ruled out by data: Rein-Sehgal w/ lepton mass correction (Our default model) SciBooNE 90% C.L. Alvarez-Ruso et al. Kartavtsev et al. Hiraide@NuInt09 L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Coherent pion production PCAC models Paschos,Berger@NuInt09 In the q2=0 limit, PCAC is used to relate º induced coherent pion production to ¼A elastic scattering Extrapolate to q2 0 Directly use ¼A cross section ) the spurious initial pion distortion present in ¼A but not in coherent pion production is not substracted Smaller c.s. than RS L. Alvarez-Ruso, Universidade de Coimbra Paschos@NuInt09 NuFact 09 1¼ production Coherent pion production Microscopic model Hernandez@NuInt09 ¢ excitation is dominant ¢ properties change in the nuclear medium Pion distortion: e¡ ³ ip ~¼ ¢~ r ! Á¤out (~ p¼; ~ r) ´ ^opt Á¤out = 0 ¡ r~ 2 ¡ p ~2¼ + 2! ¼V ^opt (r ) à V Optical potential in the ¢-hole model Nonlocality for the pion momentum: p ~¼e¡ L. Alvarez-Ruso, Universidade de Coimbra ip ~¼ ¢~ r ! i r~ Á¤out (~ p¼; ~ r) NuFact 09 1¼ production Coherent pion production Microscopic model Hernandez@NuInt09 Medium effects reduce considerably de cross section Pion distortion shifts down the peak L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Coherent pion production Microscopic model Hernandez@NuInt09 £ A ¤2 l¾» C5 (0) Comparison to MiniBooNE data Anderson@NuInt09 Data seem to prefer C5A (0) » 1:2 in agreement with the GT relation, but the subtraction of a large incoherent ¼0 background is performed L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 1¼ production Coherent pion production Microscopic model Hernandez@NuInt09 Caveats: The validity of the model is restricted to the kinematic region where the ¢(1232) is dominant Nonlocalities in the ¢ propagation can be important Nakamura@NuInt09 PWIA calculation with bound state spinors in a mean field vs. free nucleons in a Local Fermi Gas Leitner et al., PRC 79 (2009) L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Conclusions Excellent time for theoretical ºA studies New inclusive and exclusive 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 and NC¼0 background will be possible The physical meaning of ϰ, MA needs to be clarified The role of FSI in ¼ production in nuclei should be established Understand the validity of the approximations used in coherent pion production calculations Theoretical progress has to be incorporated in the MC New measurements of the º c.s. on the nucleon would help… L. Alvarez-Ruso, Universidade de Coimbra NuFact 09 Conclusions Thanks to all NuInt09 participants L. Alvarez-Ruso, Universidade de Coimbra NuFact 09