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NUCLEAR PHYSICS WITH ELECTROWEAK PROBES Carlotta Giusti

NUCLEAR PHYSICS WITH ELECTROWEAK PROBES Carlotta Giusti. XI Convegno su Problemi di Fisica Nucleare Teorica Cortona 11-14 Ottobre 2006. Fisica Teorica del Nucleo e dei Sistemi a Molti Corpi dedicato alla memoria di Adelchi Fabrocini. electron scattering. PVES. neutrino scattering. NC.

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NUCLEAR PHYSICS WITH ELECTROWEAK PROBES Carlotta Giusti

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  1. NUCLEAR PHYSICS WITH ELECTROWEAK PROBESCarlotta Giusti XI Convegno su Problemi di Fisica Nucleare Teorica Cortona 11-14 Ottobre 2006 Fisica Teorica del Nucleo e dei Sistemi a Molti Corpi dedicato alla memoria di Adelchi Fabrocini

  2. electron scattering PVES neutrino scattering NC CC

  3. electron scattering PVES neutrino scattering NC CC kinfactor

  4. electron scattering PVES neutrino scattering NC CC Lepton tensor contains lepton kinematics

  5. electron scattering PVES neutrino scattering NC CC hadron tensor

  6. nuclear response to the electroweak probe QE-peak

  7. nuclear response to the electroweak probe (e,e’) CRPA A. Botrugno and G. Co’ Nucl. Phys. A761 (2005) 200

  8. Antonio Botrugno and Giampaolo Co’: Excitation of Nuclear Giant Resonances in Neutrino Scattering Off Nuclei, Nucl. Phys. A761 (2005) 200-231 Giampaolo Co’: Nuclear Models and Neutrino-Nucleus Cross Sections, nucl-th/0601034 Giampaolo Co’: Random Phase Approximation and Neutrino-Nucleus Cross Sections, nucl-th/0605051 RandomPhase Approximation (RPA)

  9. Random Phase Approximation (RPA) RPA secular equations Input: s.p. energies and wave functions (WS potential) Veff

  10. Calculations with different Veff (0-range, finite-range) test the sensitivity of the RPA results to the residual interaction Need of an explicit treatment of degrees of freedom beyond RPA

  11. RPA quenched RPA (e,e’) spreading for different Veff reduced G. Co’ nucl-th/0605051

  12. excitation of 1+ states RPA quenched RPA 12C spreading for different Veff increased e- and  excite the same states in a different way G. Co’ nucl-th/0601034

  13. discrete excitation not negligible RPA quenched RPA 12C lower curves only excitation to the continuum upper curves include contrib. of the discrete states G. Co’ nucl-th/0605051

  14. QE region RPA 0-range RPA finite range mean field MF (Veff=0) RPA effects small G. Co’ nucl-th/0605051

  15. QE region FSI important (e,e’) MF FSI FSI folded with a Lorentz function whose parameters fixed to hadron scattering data G. Co’ nucl-th/0605051

  16. RPA effects small FSI important nuclear response dominated by one-nucleon knockout many calculations in the past for inclusive (e,e’) and exclusive (e,e’p) QE region

  17. NC and CC QE scattering NC CC

  18. NC and CC QE scattering NC CC • only N detected semi-inclusive NC and CC

  19. NC and CC QE scattering NC CC • only N detected semi-inclusive NC and CC • only final lepton detected inclusive CC

  20. Andrea Meucci, Carlotta Giusti, Franco Davide Pacati: Relativistic Approach to Neutrino-Nucleus Quasielastic Scattering, nucl-th/050147 • Andrea Meucci, Carlotta Giusti, Franco Davide Pacati: Neutrino-Nucleus Quasi-Elastic Scattering and Strange Quark Effects, Nucl. Phys. A773 (2006)250-262 • Andrea Meucci, Carlotta Giusti, Franco Davide Pacati: Relativistic Approach to Quasi-Elastic Neutrino-Nucleus Scattering, Acta Physica Polonica B37 (2006) 2279-2286 • Carlotta Giusti, Andrea Meucci, Franco Davide Pacati: Neutrino-Nucleus Quasi-elastic Scattering in a Relativistic Model, nucl-th/0607037 relativistic model, nuclear effects, FSI

  21. RDWIA direct knockout • for a state n • the  interacts through a one-body current with one nucleon which is then emitted the remaining nucleons are spectators

  22. RDWIA for QE  scattering • jone-body nuclear weak current • n=<n|0>overlap s.p. bound state wave function •  s.p. scattering state (complex optical potential FSI) • sum over all the occupied states in the SM • sum of all one-nucleon knockout channels

  23. CC NC FSI the imaginary part of the optical potential gives an absorption that reduces the calculated cross sections RPWIA RDWIA RPWIA RDWIA FSI FSI A. Meucci, C.Giusti, F.D. Pacati, Nucl. Phys A773 (2006) 250

  24. FSI for the inclusive scattering : Green’s Function Approach (e,e’) nonrelativistic F. Capuzzi, C.Giusti, F.D. Pacati, Nucl. Phys. A 524 (1991) 281 (e,e’) relativistic A. Meucci, F. Capuzzi, C. Giusti, F.D. Pacati, PRC (2003) 67 054601 CC relativistic A. Meucci, C. Giusti, F.D. Pacati Nucl. Phys. A739 (2004) 277

  25. FSI for the inclusive scattering : Green’s Function Approach • F. Capuzzi, C. Giusti, F.D. Pacati, and D.N. Kadrev: Antisymmetrized Green’s Function Approach to (e,e’) Reactions with a Realistic Nuclear Density, Ann. Phys. 317 (2005) 492-529 • A. Meucci, C. Giusti and F.D. Pacati, Relativistic Green’s Function Approach to Parity-Violating Quasielastic Electron Scattering, Nucl. Phys. A756 (2005) 359-381 • A. Meucci, C. Giusti and F.D. Pacati, Relativistic Approach to Quasi-Elastic Neutrino-Nucleus Scattering, Acta Physica Polonica B37 (2006) 2279-2286

  26. FSI for the inclusive scattering : Green’s Function Approach • the components of the inclusive response are expressed in terms of the Green’s operators • under suitable approximations can be written in terms of the s.p. optical model Green’s functions • the explicit calculation of the Green’s function can be avoided by its spectral representation which is based on a biorthogonal expansion in terms of a non Herm opt. pot. H and H+ • matrix elements similar to RDWIA and the total flux is conserved • consistent treatment of FSI in the exclusive and in the inclusive scattering

  27. FSI flux conservation RPWIA GF rROP 1NKO GF A. Meucci, C.Giusti, F.D. Pacati, nucl-th/0501047

  28. FSI RFG, RPWIA, rROP, RMF E = 1 GeV  = 45o J.A. Caballero, J.E. Amaro, M.B. Barbaro, T.W. Donnelly, C. Maieron, and J.M. Udias PRL 95 (2005) 252502

  29. Comparison MF-RFG CC NC MF (G. Co’) RFG (M. Barbaro C. Maieron)

  30. Comparison MF-PWIA CC NC MF (G. Co’) PWIA (G. Co’)

  31. Comparison PWIA- RPWIA CC 16O NC E = 1000 MeV E = 500 MeV RPWIA (A. Meucci, C. Giusti, F.D. Pacati) NR PWIA (G. Co’)

  32. Omar Benhar, Nicola Farina, Hiroki Nakamura, Makoto Sakuda, and Ryochi Seki: Lepton-Nucleus Scattering in the Impulse Approximation Regime, hep-ph/05100259 Omar Benhar, Nicola Farina, Hiroki Nakamura, Makoto Sakuda, and Ryochi Seki: Electron and Neutrino-Nucleus Scattering in the Impulse Approximation Regime, Phys. Rev. D72 (2005) 053005 Omar Benhar: Final State Interactions in the Electroweak Nuclear Response, hep-ph/0602108 nuclear correlations FSI

  33. IA =NeN£ spectral function approach based on the nuclear many-body theory: the correlated spectral function of 16O is obtained with a local density approximation in which nuclear matter results for a wide range of density values are combined with the exp information from (e,e’p) knockout reaction statistical correlations: Pauli blocking included through a modification of the spectral function FSI: correlated Glauber approximation • eikonal approximation: the struck nucleon moves along a straight trajectory with constant velocity • frozen approximation: the spectator nucleons are seen by the struck nucleon as a collection of fixed scattering centers • the propagator of the struck nucleon in the target factorized in terms of the free space propagator and of a part related to the nuclear transparency measured in (e,e’p) • cross section in the convolution form

  34. full calc. no FSI FG Omar Benhar, Nicola Farina, Hiroki Nakamura, Makoto Sakuda, and Ryochi Seki, PRD72 (2005) 053005

  35. the failure to reproduce the data in the  region is to be mostly ascribed to the poor knowledge of the neutron structure function at low Q2 Omar Benhar, Davide Meloni: How well do we know the Nucleon Structure Functions in the  Production Region? hep-ph/0604071

  36. e + 16O ! e +X no Pauli blocking. no FSI full Omar Benhar, Nicola Farina,Hiroki Nakamura, Makoto Sakuda, and Ryochi Seki, PRD72 (2005) 053005

  37. TWO-BODY WEAK AXIAL CURRENT • B. Mosconi, P. Ricci, E. Truhlik: The Role of the Pion Pair Term in the Theory of the Weax Axial Meson Exchange Currents, Eur. Phys. J. A25 (2005) 283-291 • B. Mosconi, P. Ricci, E. Truhlik: Interactions of the Solar Neutrinos with the Deuterons, Eur. Phys. J. A27 (2006) s01 67-72 • B. Mosconi, P. Ricci, E. Truhlik: Heavy Meson Weak Axial Nuclear Exchange Currents, Nucl. Phys. A772 (2006) 81-112 Complete treatment of the two-body Weax Axial Exchange Currents (WAEC) including the heavy meson exchange contribution (--a1 meson exchange)

  38. TWO-BODY WEAK AXIAL CURRENT Partial Conservation of the Axial Current (PCAC): ma pion absorption/production amplitude

  39. TWO-BODY WEAK AXIAL CURRENT Partial Conservation of the Axial Current (PCAC): A=2 If the WAEC ‘s satisfy this condition the matrix elements of the total current satisfy PCAC

  40. TWO-BODY WEAK AXIAL CURRENT • Currents constructed from an effective Lagrangian possessing chiral symmetry and respecting VDM • Lagrangian used to construct the WAEC’s in the tree approximation: WAEC amplitudes derived as Feynman tree graphs • The relativistic amplitudes of range B (B=, , , a1) satisfy PCAC • The currents constructed from the amplitudes, in analogy with elm MEC, as the difference between the relativistic 2-body amplitude of range B and the first Born iteration of the weak axial one-nucleon current contribution to the two-nucleon scattering amplitude satisfying the Lippmann-Schwinger equation • Nonrelativistic reduction of the currents for practical calculations • Wave functions obtained solving the Schroedinger equation with OBEP CONSISTENT CALCULATIONS

  41. TWO-BODY WEAK AXIAL CURRENT Formalism applied to calculate the cross sections Important for the study of the solar neutrino oscillations and for the analysis of the results obtained in the SNO detector. For the analysis of data important to reduce the theoretical uncertainty of standard nuclear physics calculations

  42. TWO-BODY WEAK AXIAL CURRENT • Consistent calculations with OBE potentials NijmI, Nijm93 and OBEPQG • The main two-body effect comes from the  excitation • The heavy meson exchange contributions are of the same order of magnitude of the  exchange ones • In comparison with other calculations the theoretical uncertainty is reduced from 5-10% to »3%

  43. Need of reliable calculations of -nucleus cross sections Analogies between -nucleus and e--nucleus scattering where a large amount of data is available Isit possible to extract model independent -nucleus cross sections from e—-nucleus experimental cross sections? Instead of using a specific model nuclear model one can exploit the scaling properties of (e,e’) data and nextract a scaling function from (e,e’) n invert the procedure to predict (,l) cross sections SCALING APPROACH J.E. Amaro, M.B. Barbaro, J.A. Caballero, T.W. Donnelly, A. Molinari and I. Sick PRC71 (2005) 015501

  44. SCALING APPROACH • J.E. Amaro M.B. Barbaro, J.A. Caballero, T.W. Donnelly, A. Molinari and I. Sick: Using Electron Scattering Superscaling to Predict Charge Changing Neutrino Cross Sections in Nuclei, PRC 71 (2005) 015501 • J.E. Amaro M.B. Barbaro, J.A. Caballero, T.W. Donnelly, C. Maieron: Semi-Relativistic Description of Quasielastic Neutrino Reactions and Superscaling in a Continuum Shell Model, PRC 71 (2005) 065501 A 27 • J.A. Caballero,J.E. Amaro M.B. Barbaro, T.W. Donnelly, C. Maieron, J.M. Udias: Superscaling in Charged Current Neutrino Quasielastic Scattering in the Relativistic Impulse Approximation, PRL 95 (2005) 252502 • M.B. Barbaro, J.E. Amaro, J.A. Caballero, T.W. Donnelly, A. Molinari, I. Sick: Superscaling and Charge Changing Neutrino Cross Sections, Nucl. Phys. Proc. Suppl., 155 (2006) 257-259 • Maria B. Barbaro: Superscaling in Electron and Neutrino-Nucleus Scattering, nucl-th/0602011 • J.E. Amaro M.B. Barbaro, J.A. Caballero, T.W. Donnelly, Superscaling and Neutral Current Quasielastic Neutrino-Nucleus Scattering. PRC 73 (2006) 035503 • M.B. Barbaro, J.E. Amaro, J.A. Caballero, T.W. Donnelly; Superscaling in Lepton-Nucleus Scattering, nucl-th/0609057 • A.N. Antonov, M.V. Ivanov, M.K. Gaidarov, E. Moya de Guerra, J.A. Caballero, M.B. Barbaro, J.M. Udias, P. Sarriguren: Superscaling Analysis of Inclusive Electron Scattering and its Extension to Charge-Changing Neutrino-Nucleus Cross Sctions beyond the Relativistic Fermi Gas Approach, nucl-th/0609056

  45. SCALING APPROACH The method relies on the scaling properties of the electron scattering data At sufficiently high q the scaling function depends only upon one kinematical variable (scaling variable) (SCALING OF I KIND) is the same for all nuclei (SCALING OF II KIND) I+II SUPERSCALING

  46. Scaling variable (QE) + (-) for  lower (higher) than the QEP, where =0 • Reasonable scaling of I kind at the left of QEP • Excellent scaling of II kind in the same region • Breaking of scaling particularly of I kind at the right of QEP (effects beyond IA) • The L contribution superscales fQE can be extracted from the data and used to calculate -nucleus CC cross section

  47. Experimental QE superscaling function M.B. Barbaro,J.E. Amaro, J.A. Caballero, T.W. Donnelly, A. Molinari, and I. Sick, Nucl. Phys Proc. Suppl 155 (2006) 257

  48. Experimental QE superscaling function M.B. Barbaro,J.E. Amaro, J.A. Caballero, T.W. Donnelly, A. Molinari, and I. Sick, Nucl. Phys Proc. Suppl 155 (2006) 257

  49. Scaling analysis extended to the -peak region The  contribution isolated in the data by subtracting from the total exp c.s. the QE scaling contribution Analysis done with a new scaling variable • Superscaling at the left of the  peak • Breaking of scaling at the right of the peak (other resonances and tail of DIP)

  50. Experimental  superscaling function M.B. Barbaro,J.E. Amaro, J.A. Caballero, T.W. Donnelly, A. Molinari, and I. Sick, Nucl. Phys Proc. Suppl 155 (2006) 257

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