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

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.: A AAAA A A

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Outline Motivation º scattering on the nucleon Quasielastic scattering models Experimental status and comparison to data Conclusions

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Motivation º – Nucleus interactions (in the QE region) are important for: Oscillation experiments ) º oscillations are well established ) Goal: Precise determination of oscillation parameters: ¢ m 2 ij, µ ij, ± º are massive flavors are mixed

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Motivation º – Nucleus interactions (in the QE region) are important for: Oscillation experiments Precision measurements of ¢ m 23 2, µ 23 in º ¹ disappearance Understanding E º reconstruction is critical Kinematical determination of E º 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

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Motivation º – Nucleus interactions (in the QE region) are important for: Oscillation experiments Precision measurements of ¢ m 23 2, µ 23 in º ¹ disappearance Understanding E º reconstruction is critical Kinematical determination of E º 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 GENIE E º = 1 GeV

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Motivation º – Nucleus interactions (in the QE region) are important for: Hadronic physics Nucleon axial form factors MINERvA: first precision measurement of G A at Q 2 >1 GeV. Deviations from the dipole form? Strangeness content of the nucleon spin (isoscalar coupling G s A ): 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.

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 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

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 º scattering on the nucleon The (CC) elementary process: where Vector form factors: Extracted from e-p, e-d data à electric ff à magnetic ff

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 º scattering on the nucleon At low Q 2 : M V = 0.71 GeV, G E /G M ¼ 1/ ¹ p At high Q 2 : Bodek et al., EPJC 53 (2008)

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 º scattering on the nucleon The (CC) elementary process: where Axial form factors: g A = Ã ¯ decay M A = § GeV ( ) Bodek et al., EPJC 53 (2008) dipole ansatz PCAC

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 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

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Inclusive electron-nucleus scattering Relativistic Global Fermi Gas Smith, Moniz, NPB 43 (1972) 605 However GFG overestimates the longitudinal response R L FG is certainly too simple to be right. Nuclear dynamics must be included in the picture

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Inclusive electron-nucleus scattering Spectral functions of nucleons in nuclei The nucleon propagator can be cast as S h(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

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Inclusive electron-nucleus scattering Spectral functions of nucleons in nuclei Hole spectral function: % 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)

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Inclusive electron-nucleus scattering Spectral functions of nucleons in nuclei Hole spectral function: % 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) W= ¾ ½ v /2 Correlated Glauber approximation (straight trajectories, frozen spectators) Benhar et al., PRC 44 (1991) 2328

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Inclusive electron-nucleus scattering Spectral functions of nucleons in nuclei: Results 40 Ca

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Inclusive electron-nucleus scattering Spectral functions of nucleons in nuclei: Results 40 Ca

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 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 QE scattering models

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 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 QE scattering models

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 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 QE scattering models

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Inclusive electron-nucleus scattering Spectral functions in a Local Fermi Gas Leitner et al., PRC 79 (2009) Hole spectral function: The correlated part of S h is neglected Particle spectral function: Re § is obtained from Im § with a dispersion relation fixing the pole position at I QE scattering models Gil, Nieves, Oset, NPA627 Ciofi degli Atti et al.,PRC41 Ã Collisional broadening

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Inclusive electron-nucleus scattering Spectral functions in a Local Fermi Gas: Results Leitner et al., PRC 79 (2009)

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 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

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 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 g A : The quenching of g A in Gamow-Teller ¯ decay is well established  0 dipole susceptibility g Lorentz-Lorenz factor ~1/3 Ericson, Weise, Pions in Nuclei Wilkinson, NPA 209 (1973) 470

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models RPA long range correlations Nieves et. al. PRC 70 (2004) In particular ¼ spectral function changes in the nuclear medium ) so does

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 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 12 C and LSND CCQE Nieves et. al. PRC 70 (2004) Important at low Q 2 for CCQE at MiniBooNE energies

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models RPA long range correlations Comparison to inclusive electron-nucleus data

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models RPA long range correlations CCQE on 12 C averaged over the MiniBooNE flux LAR et al., arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models RPA long range correlations CCQE on 12 C averaged over the MiniBooNE flux LAR et al., arXiv: RPA correlations cause a reduction of ¾ at low Q 2 and forward angles

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Relativistic mean field Impulse Approximation Initial nucleon in a bound state (shell) ª i : Dirac eq. in a mean field potential ( ! - ¾ model) Final nucleon PWIA RDWIA: ª f : Dirac eq. for scattering state Glauber Has been used to study 1N knockout Problem: nucleon absorption that reduces the c.s. Complex optical potential

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Relativistic mean fieldRPWIARDWIARPWIARDWIA Giusti et al., arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Relativistic mean field Impulse Approximation Initial nucleon in a bound state (shell); no correlations ª i : Dirac eq. in a mean field potential ( ! - ¾ model) Final nucleon PWIA DWIA: ª f : Dirac eq. for scattering states Glauber Has been used to study 1N knockout Problem: nucleon absorption that reduces the c.s. Complex optical potential

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Green function approach Meucci et al., PRC 67 (2003) 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 Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models Green function approach Meucci et al., PRC 67 (2003) O(e,e)X

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models (Super)scaling Barbaro et al., arXiv: First kind scaling: ) 12 C

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models (Super)scaling First kind scaling: Second kind scaling: independent of A First + Second scaling = Superscaling à < 0 scaling region à > 0 scaling violation

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models (Super)scaling Scaling violations reside mainly in the transverse channel

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models (Super)scaling The experimental superscaling function (fit using R L data) Constraint for nuclear models Relativistic Fermi Gas Exact superscaling Wrong shape of f( Ã )

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models (Super)scaling The experimental superscaling function (fit using R L data) Constrain for nuclear models Relativistic mean field describes the asymmetric shape of f( Ã )

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models (Super)scaling Superscaling in the ¢ region Experimental superscaling function At à ¢ > 0 other resonances, etc contribute

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models (Super)scaling Superscaling Analysis SUSA Calculate with Relativistic Fermi Gas Replace f RFG ! f exp

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models (Super)scaling Superscaling Analysis SUSA Calculate with Relativistic Fermi Gas Replace f RFG ! f exp

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 QE scattering models (Super)scaling Superscaling Analysis SUSA for º -A Amaro et al., PRL 98 (2007) Calculate with Relativistic Fermi Gas Replace f RFG ! f exp SUSA: ~ 15 % reduction of ¾ with respect to RFG Scaling approach fails at !. 40 MeV, |q|. 400 MeV: collective effects

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Experimental status Data! CCQE, NCQE, º, anti- º MiniBooNE ( 12 C), SciBooNE ( 16 O), MINOS (Fe), NOMAD ( 12 C) and puzzles…

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Experimental status MiniBooNE Largest sample of low energy ( ~ 750 MeV ) º ¹ CCQE events to date. Aguilar-Arevalo et. al., PRL 100 (2008) The shape of h d ¾ /dcos µ ¹ dE ¹ i is accurately described by the Relativistic Global Fermi Gas Model with: E B = 34 MeV, p F = 220 MeV But ϰ =1.007 § M A =1.35 § 0.17 GeV Large ¾ compared to GFG with M A =1 GeV Katori, arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Experimental status However: The physical meaning of ϰ is obscure ϰ, M A values depend on the background from CC1 ¼ Background subtraction depends on the ¼ propagation (absorption and charge exchange) model NUANCE: constant suppression of ¼ production Model dependent E º reconstruction (unfolding)

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Experimental status However: The physical meaning of ϰ is obscure ϰ, M A values depend on the background from CC1 ¼ Background subtraction depends on the ¼ propagation (absorption and charge exchange) model NUANCE: constant suppression of ¼ production Model dependent E º reconstruction (unfolding) Better compare to: Katori, arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Experimental status NOMAD Lyubushkin et al., EPJ C 63 (2009) 355 CCQE on 12 C at high 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 : M A = 1.05 § 0.02(stat) § 0.06(sys) GeV Consistent with M A extracted from Q 2 shape fit of 2-track sample MiniBooNE vs NOMAD Katori, arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Interpretation M A > 1 GeV? M A 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 (m ¼ =0) Using models to connect with data ) M A ep = § GeV Liesenfeld et al., PLB 468 (1999) 20 A more careful evaluation in ChPT Bernard et al., PRL 69 (1992) 1877 M A = M A ep - ¢ M A, ¢ M A =0.055 GeV ) M A = GeV

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Interpretation Can nuclear effects explain the shape of the MiniBooNE Q 2 distribution? Spectral functions: Benhar & Meloni, arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Interpretation Can nuclear effects explain the shape of the MiniBooNE Q 2 distribution? Spectral functions: LAR, Leitner, Buss, Mosel, arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Interpretation Can nuclear effects explain the shape of the MiniBooNE Q 2 distribution? RPA: RPA brings the shape closer to experiment keeping M A = 1 GeV LAR, Leitner, Buss, Mosel, arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Can CCQE nuclear models explain the size of MiniBooNE ¾ ? Ex. at E º =0.8 GeV: ¾ th ~ 5 < ¾ MB ~ 7 £ cm 2 CCQE models with M A ~1 GeV cannot reproduce MiniBooNE ¾ Interpretation Katori, arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Interpretation Can CCQE nuclear models explain the size of MiniBooNE ¾ ? Many body RPA calculation Martini et al., arXiv:

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 Interpretation Can CCQE nuclear models explain the size of MiniBooNE ¾ ? Many body RPA calculation Martini et al., arXiv: Lesson: Many-body dynamics beyond 1p1h is important Open questions: Is the Q 2 distribution also well described by CCQE+2p2h? Role of MEC Is the comparison proper ? Comparison to inclusive data is needed NOMAD results?

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09 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 º A (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 E º background will be possible The physical meaning of ϰ, M A needs to be clarified The role nuclear effects should be established Theoretical progress has to be incorporated in the MC