Produkcja pojedynczych pionów w oddziaływaniu neutrino-deuteron - re-analiza danych z eksperymentów ANL i BNL K. M. Graczyk Instytut Fizyki Teoretycznej Uniwersytet Wrocławski K.M.G, J. T. Sobczyk, Phys. Rev. D 77, (2008) K.M.G, J. T. Sobczyk, Phys. Rev. D 77, (2008) K.M.G, arXiv: D. Kiełczewska, K.M.G, P. Przewłocki, J. T. Sobczyk, in preparation

Introduction RS formalism with improvements Rarita-Schwinger formalism Re-analysis of the ANL and BNL data

Abstract (warszawa): Tematem wystąpienia będzie opis teoretyczny produkcji pojedynczych pionów w oddziaływaniu neutrino-nukleon. W szczególności omówię formalizmy stosowane w symulacjach Monte Carlo: model Reian Seghala oraz model Rarity-Schwingera. Przedstawię także wyniki re-analizy danych ANL i BNL. W analizie uwzględnione zostały efekty deuteronowe. Pokażę, że jest możliwe jednoczesne dopasowanie funkcje postaci C5A do obydwu zbiorów danych. Abstract (wrocław): Tematem wystąpienia będzie opis teoretyczny produkcji pojedynczych pionów w oddziaływaniu neutrino-nukleon. W szczególności omówię formalizmy stosowane w symulacjach Monte Carlo: model Rein-Seghal oraz formalizm Rarity-Schwingera. Przedstawię także wyniki re-analizy danych ANL i BNL. W analizie uwzględnione zostały efekty deuteronowe. Pokażę, że jest możliwe jednoczesne dopasowanie funkcje postaci C5A do obydwu zbiorów danych. Ostatnie 20 minut seminarium poświęcę na omówienie programu, za pomocą którego dokonuję analizy danych, pokaże w czasie rzeczywistym jego działanie. Opowiem także o programie root i pakiecie TMinuit.

1 production? Motivation

Physics of long baseline experiments neutrino oscillation theoretical input experiment neutrino-matter interaction weak interaction nucleon structure nucleus ----//---- new generation of neutrino oscillation experiments: T2K, NOvA -nucleus scattering: Oxygen(K2K), Carbon (MiniBooNE), Argon(ICARUS, T2K) Introduction Z or W N

J-PARC Facility Off-axis: OA2 e 700 MeV Far Detector ND280 (m) Tokai 2 Kamioka Kaon decay

Oscillation measurements: Disappearance of ν μ (Far and Near Detectors) Neutrino Energy reconstructed from QE events SPP an important background in quasi-elastic events Appearance of v e (T2K experiment) Single π 0 production an important background T2K experiment Appearance Disappearance E about 700 MeV single pions vs. long baseline experiments M. H. Ahn, Phys.Rev. D74 (2006) K2K 1 T2K ND280 Models for CC interaction NC interaction

Interactions Neutral Current Charged Current ND 280m ND? 2km Off-Axis JHF SK 295 km

Source of s Resonance and non- resonance 1 Final State Interaction re-interaction in the nucleus Coherent Pion Production neutrino interacts with nucleus without changing its quantum numbers (it is observed in small Q2 transfer, and for small scattering angles) M. Hasegawa, et al. Phys. Rev. Lett 95, (2005) K2K result Similar small MiniBooNE Nuclear corrections? An accurate -nucleon input

CC 1 production T. Kitagaki et al. Phys. Rev. D 34 (1986) 2554 Today

SPP resonance production Born graphs for CC SPP Non-resonant background Kitagaki et al.. Phys. Rev. D42, 42 (1990) Dominant (1232) contribution! Non-resonant contribution negligible!

Description of 1 production Theory Monte Carlo Codes Experiment

MC input Advanced description for SPP in neutrino-nucleon scattering (only in (1232) region): Sato and Lee model (Phys. Rev. C67 (2003) ), electroproduction, E.Hernandez et al. (Phys. Rev. D76 (2007) 03300). Old approaches Adler model (Annals Phys. 50 (1968) 189) Foli and Narduli (Nucl. Phys. B160 (1979) 116) Rarita-Schwinger (NuWro) formalism for (1232) excitation: SPP in Monte Carlo Rein-Sehgal Model: NUANCE (MiniBooNE), NUET(K2K, T2K),

Fine tuning Bubble chamber data

12 ANL 12 foot bubble chamber filled with deuterium and Argonne National Laboratory S. J. Barish, Phys. Rev. D19 (1979) G. M. Radecky Phys. Rev. D25 (1982) < 1 GeV =15% (E<1.5 GeV) and 25% (above ) Differential cross sections in Q2 Total cross sections Kinematical cuts: 0.5 GeV < E < 6.0 GeV 0.01 GeV2 < Q2 < 1 GeV2 W < 1.4 GeV S. J. Barish, Phys. Rev. D 16 (1977) 3103 G. M. Radecky Phys. Rev. D25 (1982) 1161

7 foot bubble chamber filled with deuterium at Brookhaven National Laboratory. = 1.6 GeV T. Kitagaki et al. Phys. Rev. D 34 (1986) T. Kitagaki et al., Phys. Rev. D42 (1990) = 10% Kinematical cuts: 0.5 GeV < E < 6.0 GeV Q2 < 3 GeV2 but: Q2 > 0.1 efficiency! W<1.4 GeV Total cross sections Normalized cross sections K. Furuno NUINT02 T. Kitagaki et al. Phys. Rev. D 34 (1986) 2554

M.O. Wascko, Nucl. Phys. Proc. Suppl. 159 (2006) 50 Systematic shift (around 20% ) between total ANL and BNL cross sections, consistent or not? Some people claimed that there is disagreement?

Idea (1232) excitation induced by - nucleon interaction Simultaneous analysis of the data from two experiments: ANL and BNL Extraction of the axial contribution from bubble chamber experiments Fits either to ANL or to BNL data Input to NuWro Monte Carlo Generator New fits of cross sections and C5A with account of their uncertainties application to 1 0 production in NC -nucleon scattering Nonresonant background negligible T. Kitagaki et al. Phys. Rev. D 34 (1986) 2554

@ Monte Carlo Rein-Sehgal Model NUANCE Paweł;)

Rein and Sehgal model SPP in Monte Carlo Rein-Sehgal Model: NUANCE (MiniBooNE), NUET(K2K, T2K), FKR model – Relativistic Harmonic Oscillator Quark Model Photoproduction: R.P. Feynman, et al., Phys. Rev. D 3, 2706 (1971) Electroproduction: F. Ravndal, Phys. Rev. D 4, 1466 (1971) Neutrinoproduction: F. Ravndal, Lett. Nuovo Cimento, (1972) and Nuovo Cimento, 18A 385 (1973) Single Pion Production in N scattering: D.Rein and L.M. Sehgal, Annals Phys. 133 (1981) 79, D.Rein, Z. Phys. C 35 (1987) 43. FKR/Rein-Sehgal approach p n Nn n p Np n p lNln plNlp 0 0* 0 * 0 * * CC NC

Standard ApproachFKR/Rein-Sehgal model Elastic ep scattering and Quasi-Elastic n scattering Internal input: = 1.05 GeV2 –from the Regge slope of baryon trajectory. Vector form factor Axial form factor 18 resonances with W< 2 GeV Widths masses and elasticties of resonances: taken from PDG Barion wave functions: Sym(SU(2)xSU(3)xO(3)) Nonresonant contribution

List of resonances …+…

Rarita Schwinger Formalism Form Factors

Hadronic current Rarita-Schwinger Formalism

(1232) -3/2 spin, Rarita Schwinger field Three Vector Form Factors! Vector current Vector Current Conservation PCAC: Axial current Adler relation One axial form factor: C5A electro-weak current for N (1232) transition

Rein-Sehgal vs Rarita- Schwinger Some improvements

Improvements Model which better fits to experimental data in (1232) region Cross sections at small Q2 problem at MiniBooNE Previously only M A in RS model was varied. Charged Current and Neutral Current cross sections I. A proper description of vector and axial contribution (effective) We still keep only two form factors (vector and axial) II. Lepton mass in Charged Current N scattering ~(V-A)~(V) More accurate description of 1 in NC A phenomenological, effective input to RS description

FKR/RS model vs. Rarita Schwinger Formalism Quark model suggested solution direct relation between C3V and Q2=0 original RS result is about 15 % smaller than the same quantity computed from C3V(0)

Vector Form Factors P.Schreiner and F.Von Hippel, Nucl. Phys. B58 (1973) 333. L. Alvarez-Ruso, S. K. Singh and M. J. Vincente Vascas, Phys. Rev. 57 (1998) 2693 O.Lalakulich, E.Paschos and G.Piranishvili, Phys. Rev. D74 (2006) Vector Form Factors (1232) Helicity Amplitudes - -electroproduction data: Tiator et al., EPJA 19 (2004); Burkert, Li, IJMP 13 (2004) Axial Form Factors -> Bubble Chambers experiments two different fits for ANL and BNL data O. Lalakulich, XX Max Born Symposium, Wrocław 2005 Agrees with MAID predictions! D.Drechsel, O.Hanstein, S. Kamalov, and L.Tiator, A unitary isobar model for pion photo- and electroproduction on the proton up to 1-GeV, Nucl. Phys. A645 (1999) 145.

Since

M.Osipenko et al. [CLAS Collaboration], Phys. Rev. D67 (2003) M. Osipenko et al., arXiv: [hep-ex] F2(ep) inclusive structure function The amplitudes are summed nonkoherently

Adler relations (S.L. Adler, Ann. Phys. 50 (1968) 189) two different fits: For small Q2 there is small difference between both fits Our choice Lattice calculations C. Alexandrou et al.. Similar Analysis for Axial Contribution At RS model C5A(0) is about 1.00!!!

Lepton Mass Effects in CC N scattering Nonzero lepton mass effects – small Q2 region Rein-Seghal model: lepton mass was neglected MC generators Lepton mass in kinematics Pion Pole contribution from the PCAC argument C.Berger and L.Sehgal, Lepton Mass Effects in Single Pion Production by Neutrinos, Phys. Rev. D76 (2007)

Pion Pole Contribution reduces cross sections below Q2<0.2 It is more important for antineutrino scattering! E=700 MeV Normalized to the area

C5A axial form factor more carefully Re-analysis of old bubble chamber neutrino-deuteron scattering data

NN potentials Hulthen, L. Hulthen and M. Sugawara, Handbuch der Physik Bonn, R. Machleidt, K. Holinde and C. Elster, Phys. Rept. 149 (1987) 1 Paris: M. Lacombe, B. Loiseau, R. Vinh Mau, J. Cote, P. Pires and R. de Tourreil, Phys. Lett. B 101 (1981) 139 Used in this analysis L.Alvarez-Ruso, S.K.Singh and M.J.Vicente Vacas, Phys. Rev. C 59 (1999) 3386 ?!

Settings Vector Contribution described by Lalakulich et al.. form factors C5A(Q2) will be fitted ANL = 20% Total cross sections and differential cross sections depending on Q2 Kinematical cuts: 0.5 GeV < E < 6.0 GeV 0.01 GeV2 < Q2 < 1 GeV2 W < 1.4 GeV BNL = 10% Kinematical cuts: 0.5 GeV < E < 6.0 GeV Q2 < 3 GeV2 but: Q2 > 0.1 efficiency! W<1.4 GeV Total cross sections, normalized cross sections depending on Q2

Flux uncertainty normalization Analogically the th cross section is obtained Chi-2 method Total # sections

Results Dipole and Adler parameterizations

Dipole axial mass 0.94 GeV Dipole Parameterization

a=-1.21, b= 2 GeV 2 Adler Parameterization

About 10% of difference between ANL and BNL 10% of deuteron structure effects ANL Deuteron structure effects seems to more important BNL Cut in Q2 Higher E beam energy

4% With deuteron structure effects

Fit uncertainties Cross section uncertainties

Consistency parameter-goodness-of-fit

Parameter Goodnest of Fit: M. Maltoni, T. Schwetz, Phys. Rev. D68, , (2003)

Summary and Future Improvements of the RS model Corrections to the Vector and Axial contributions Lepton mass effects Easy to implement to MC ANL and BNL data are consistent The fits have large uncertainties Both analysis are consistent The analysis of uncertainties of cross sections (due to data) for 1 0 production A model independent analysis of the data? Neural Networks?