Quasielastic Scattering at MiniBooNE Energies

1. Quasielastic Scattering at MiniBooNE Energies L. Alvarez-Ruso1, O. Buss2, T. Leitner2, U. Mosel2 1. U. Murcia 2. U. Giessen TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAA

2. Introduction • MiniBooNEhas collected the largest sample of low energy º¹CCQE events to date. Aguilar-Arevalo et. al., PRL 100 (2008) 032301 º flux Mineral Oil: CH2 < Eº > ~ 750 MeV • CCQE is relevant for oscillation experiments • CCQE is interesting by itself: • Axial form factor of the nucleon (MA) • Nuclear correlations L. Alvarez-Ruso, Universidad de Murcia

3. Introduction • The shape of hd¾/dcosµ¹dE¹i is accurately described by a Global Fermi Gas Model Smith, Moniz, NPB 43 (1972) 605 with: EB = 34 MeV, pF = 220 MeV But • MA= 1.23 § 0.20 GeV consistent with MA= 1.2 § 0.12 GeV (K2K) higher than MA= 1.01 § 0.01 GeV ( BBBA07) MA= 1.05 § 0.08 GeV (mainly 12C, 3-100 GeV, NOMAD) L. Alvarez-Ruso, Universidad de Murcia

4. The model • Our aim: realistic description of CCQE in nuclei compare to MiniBooNEdata (modified Smith-Moniz ansatz) • Relevant hadronic degrees of freedom: ¼, N, ¢(1232) • Ingredients: • Elementary process • Fermi motion • Pauli blocking • Nuclear binding • Nucleon spectral functions • Medium polarization (RPA) and also • Non CCQE background (cannot be separated from CCQE in a model independent way) L. Alvarez-Ruso, Universidad de Murcia

5. The model • Elementary amplitude for whereand BBBA07 PCAC neutron ¯ decay Goldberger-Treiman Using PCAC and ¼-pole dominance: L. Alvarez-Ruso, Universidad de Murcia

6. The model • Local Fermi Gas • Fermi Motion of initial nucleons: • Pauli blocking of final nucleons: • Mean field potential • Density and momentum dependent • Parameters fixed in p-Nucleus scattering Teis et. al., Z. Phys. A 346 (1997) 421 • Nucleons acquire effective masses L. Alvarez-Ruso, Universidad de Murcia

7. The model • Spectral functions • The momentum distribution of a nucleon with 4-momentum p is • For final nucleons (above the Fermi sea) • is obtained from with a dispersion relation assuming that at the pole position: • For initial nucleons (holes) we take nucleon selfenergy collisional broadening GiBUU L. Alvarez-Ruso, Universidad de Murcia

8. The model • RPA nuclear 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 L. Alvarez-Ruso, Universidad de Murcia

9. The model • RPA nuclear correlations • Following Nieves et. al. PRC 70 (2004) 055503 : • In particular • ¼ spectral function changes in the nuclear medium so does L. Alvarez-Ruso, Universidad de Murcia

10. The model • RPA nuclear 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 • Can be inserted in a unified framework to study QE, 1¼, N-knockout, etc • 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 Q2 at MiniBooNE energies L. Alvarez-Ruso, Universidad de Murcia

11. The model • Non CCQE background (GiBUU transport model) • Most relevant processes: • Details in the talk by Tina Leitner (¼ less decay mode) followed by or by (¼ absorption) and then L. Alvarez-Ruso, Universidad de Murcia

12. Results • Comparison to inclusive electron scattering data • Missing strength in the deep region: more complete many-body dynamics required Gil et. al., NPA627 (1997) 543 • RPA less relevant than in the weak case L. Alvarez-Ruso, Universidad de Murcia

13. Results • Differential cross sections averaged over the MiniBooNE flux L. Alvarez-Ruso, Universidad de Murcia

14. Results • Differential cross sections averaged over the MiniBooNE flux RPA correlations cause a considerable reduction of the c.s. at low Q2and forward angles L. Alvarez-Ruso, Universidad de Murcia

15. Results • CCQE + non-CCQE background (measured quantity) L. Alvarez-Ruso, Universidad de Murcia

16. Results • 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, Universidad de Murcia

17. Results • Changing g’ = 0.5-0.7 • Leaves the shape unaltered • Smallchanges in the integrated cross sectionh¾i =3.1-3.4 £ 10-38 cm2 L. Alvarez-Ruso, Universidad de Murcia

18. Results • Changing MA The experimental shape is better described with MA=1 GeV There are large differences in the integrated cross section L. Alvarez-Ruso, Universidad de Murcia

19. Conclusions • We have developed a model for CCQE starting form a Local Fermi Gas but incorporating important many body corrections: nucleon spectral functions, medium polarization (RPA). • RPA: strong reduction at low q2 (quenching) • Good description of the shape of the MiniBooNE q2 distribution with MA=1 GeV • A larger integrated CCQE cross section would require MA>1 GeV L. Alvarez-Ruso, Universidad de Murcia

20. Conclusions • There is (nuclear) physics beyond the naive Fermi Gas Model. L. Alvarez-Ruso, Universidad de Murcia

21. Conclusions • There is (nuclear) physics beyond the naive Fermi Gas Model. L. Alvarez-Ruso, Universidad de Murcia