Produkcja%20pojedynczych%20pion

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Produkcja pojedynczych pionów w oddzialywaniu
neutrino-deuteron - re-analiza danych z
eksperymentów ANL i BNL

• K. M. Graczyk
• Instytut Fizyki Teoretycznej
• Uniwersytet Wroclawski

K.M.G, J. T. Sobczyk, Phys. Rev. D 77, 053001
(2008) K.M.G, J. T. Sobczyk, Phys. Rev. D 77,
053003 (2008) K.M.G, arXiv0810.1247 K.M.G , D.
Kielczewska, P. Przewlocki, J. T. Sobczyk, in
preparation
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• Introduction
• RS formalism with improvements
• Rarita-Schwinger formalism
• Re-analysis of the ANL and BNL data

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Abstract (warszawa) Tematem wystapienia bedzie
opis teoretyczny produkcji pojedynczych pionów w
oddzialywaniu neutrino-nukleon. W szczególnosci
omówie formalizmy stosowane w symulacjach Monte
Carlo model Reian Seghala oraz model
Rarity-Schwingera. Przedstawie takze wyniki
re-analizy danych ANL i BNL. W analizie
uwzglednione zostaly efekty deuteronowe. Pokaze,
ze jest mozliwe jednoczesne dopasowanie funkcje
postaci C5A do obydwu zbiorów danych. Abstract
(wroclaw) Tematem wystapienia bedzie opis
teoretyczny produkcji pojedynczych pionów w
oddzialywaniu neutrino-nukleon. W szczególnosci
omówie formalizmy stosowane w symulacjach Monte
Carlo model Rein-Seghal oraz formalizm
Rarity-Schwingera. Przedstawie takze wyniki
re-analizy danych ANL i BNL. W analizie
uwzglednione zostaly efekty deuteronowe. Pokaze,
ze jest mozliwe jednoczesne dopasowanie funkcje
postaci C5A do obydwu zbiorów danych. Ostatnie 20
minut seminarium poswiece na omówienie programu,
za pomoca którego dokonuje analizy danych, pokaze
w czasie rzeczywistym jego dzialanie. Opowiem
takze o programie root i pakiecie TMinuit.
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1p production?

• Motivation

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Introduction

• 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
• n-nucleus scattering Oxygen(K2K), Carbon
  (MiniBooNE), Argon(ICARUS, T2K)

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Tokai 2 Kamioka
Off-axis OA2
J-PARC Facility
Kaon decay
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1p Production _at_ T2K
ND280
Models for CC n interaction ? NC n interaction
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Interactions
JHF
ND 280m
ND? 2km
Off-Axis
Charged Current
Neutral Current
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Source of ps

• Resonance and non-resonance 1p
• 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)

K2K result
M. Hasegawa, et al. Phys. Rev. Lett 95, 252301
(2005)
Similar problem _at_ small Q2 _at_ MiniBooNE

• Nuclear corrections?
• An accurate n-nucleon input

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CC 1p production
Today
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SPP resonance production
Born graphs for CC SPP
Non-resonant background
Dominant D(1232) contribution! Non-resonant
contribution negligible!
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Description of 1p production

• Theory ? Monte Carlo Codes ? Experiment

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MC input

• Advanced description for SPP in neutrino-nucleon
  scattering (only in D(1232) region)
• Sato and Lee model (Phys. Rev. C67 (2003)
  065201), 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 D(1232)
  excitation
• SPP in Monte Carlo
• Rein-Sehgal Model NUANCE (MiniBooNE), NUET(K2K,
  T2K),

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Fine tuning

• Bubble chamber data

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12 ft _at_ ANL
G. M. Radecky Phys. Rev. D25 (1982) 1161

• 12 foot bubble chamber filled with deuterium and
  hydrogen _at_ Argonne National Laboratory
• S. J. Barish, Phys. Rev. D19 (1979) 2521.
• G. M. Radecky Phys. Rev. D25 (1982) 1161.
• ltEgt lt 1 GeV
• ltDfluxgt 15 (Elt1.5 GeV) and 25 (above )
• Differential cross sections in Q2
• Total cross sections
• Kinematical cuts
• 0.5 GeV lt E lt 6.0 GeV
• 0.01 GeV2 lt Q2 lt 1 GeV2
• W lt 1.4 GeV

S. J. Barish, Phys. Rev. D 16 (1977) 3103
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7-ft _at_BNL
K. Furuno NUINT02

• 7 foot bubble chamber filled with deuterium at
  Brookhaven National Laboratory.
• ltEgt 1.6 GeV
• T. Kitagaki et al. Phys. Rev. D 34 (1986) 2554.
• T. Kitagaki et al., Phys. Rev. D42 (1990) 1331.
• ltDfluxgt 10
• Kinematical cuts
• 0.5 GeV lt E lt 6.0 GeV
• Q2 lt 3 GeV2 but
• Q2 gt 0.1 ? efficiency!
• Wlt1.4 GeV
• Total cross sections
• Normalized cross sections

T. Kitagaki et al. Phys. Rev. D 34 (1986) 2554
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Systematic shift (around 20 ) between total ANL
and BNL cross sections, consistent or not?
Some people claimed that there is disagreement?
M.O. Wascko, Nucl. Phys. Proc. Suppl. 159 (2006)
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Idea
Nonresonant background negligible

• D(1232) excitation induced by n-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 1p0 production in NC n-nucleon
  scattering

T. Kitagaki et al. Phys. Rev. D 34 (1986) 2554
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1p _at_ Monte Carlo

• Rein-Sehgal Model ? NUANCE ? Pawel)

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Rein and Sehgal model
FKR/Rein-Sehgal approach

• 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, 3 631 (1972) and Nuovo Cimento, 18A 385
  (1973)
• Single Pion Production in nN scattering D.Rein
  and L.M. Sehgal, Annals Phys. 133 (1981) 79,
  D.Rein, Z. Phys. C 35 (1987) 43.

• SPP in Monte Carlo
• Rein-Sehgal Model NUANCE (MiniBooNE), NUET(K2K,
  T2K),

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• Internal input
• ? 1.05 GeV2 from the Regge slope of baryon
  trajectory.
• Vector form factor
• Axial form factor
• 18 resonances with Wlt 2 GeV
• Widths masses and elasticties of resonances
  taken from PDG
• Barion wave functions Sym(SU(2)xSU(3)xO(3))
• Nonresonant contribution

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List of resonances

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Rarita Schwinger Formalism

• Form Factors

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Rarita-Schwinger Formalism
Hadronic current
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D(1232) -3/2 spin, Rarita Schwinger field
electro-weak current for N ?D(1232) transition
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Rein-Sehgal vs Rarita-Schwinger

• Some improvements

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Improvements

• Model which better fits to experimental data in
  D(1232) region
• Cross sections at small Q2 ?problem at MiniBooNE
• Previously only MA in RS model was varied.
• Charged Current and Neutral Current cross
  sections
• A proper description of vector and axial
  contribution (effective)
• We still keep only two form factors (vector and
  axial)
• Lepton mass in Charged Current nN scattering

More accurate description of 1p in NC
A phenomenological, effective input to RS
description
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FKR/RS model vs. Rarita Schwinger Formalism

• direct relation between C3V and
• GV(RS)
• _at_ Q20 original RS result is about
• 15 smaller than the same
• quantity computed from C3V(0)

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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) 014009.
• Vector Form Factors ? D(1232) Helicity Amplitudes
  --electroproduction data Tiator et al., EPJA 19
  (2004) Burkert, Li, IJMP 13 (2004)
• Axial Form Factors -gt Bubble Chambers experiments
  two different fits for ANL and BNL data

O. Lalakulich, XX Max Born Symposium, Wroclaw 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.
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F2(ep) inclusive structure function
The amplitudes are summed nonkoherently
M.Osipenko et al. CLAS Collaboration, Phys.
Rev. D67 (2003) 092001. M. Osipenko et al.,
arXiv0309052 hep-ex
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Similar Analysis for Axial Contribution
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
At RS model C5A(0) is about 1.00!!!
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Lepton Mass Effects in CC nN 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) 113004
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E700 MeV

• Pion Pole Contribution reduces cross sections
  below Q2lt0.2
• It is more important for antineutrino scattering!

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C5A axial form factor more carefully

• Re-analysis of old bubble chamber
  neutrino-deuteron scattering data

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L.Alvarez-Ruso, S.K.Singh and M.J.Vicente
Vacas, Phys. Rev. C 59 (1999) 3386

• 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

?!
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Settings

• Vector Contribution described by Lalakulich et
  al.. form factors
• C5A(Q2) will be fitted
• ANL
• ltDfluxgt 20
• Total cross sections and differential cross
  sections depending on Q2
• Kinematical cuts
• 0.5 GeV lt E lt 6.0 GeV
• 0.01 GeV2 lt Q2 lt 1 GeV2
• W lt 1.4 GeV
• BNL
• ltDfluxgt 10
• Kinematical cuts
• 0.5 GeV lt E lt 6.0 GeV
• Q2 lt 3 GeV2 but
• Q2 gt 0.1 ? efficiency!
• Wlt1.4 GeV
• Total cross sections, normalized cross sections
  depending on Q2

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Chi-2 method
Analogically the sth cross section is obtained
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Results

• Dipole and Adler parameterizations

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Dipole Parameterization
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Adler Parameterization
a-1.21, b 2 GeV2
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With deuteron structure effects
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With deuteron structure effects
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Fit uncertainties

• Cross section uncertainties

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Consistency

• parameter-goodness-of-fit

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Parameter Goodnest of Fit M. Maltoni, T.
Schwetz, Phys. Rev. D68, 033020, (2003)
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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 1p0 production
• A model independent analysis of the
  data?...................? Neural Networks?