Transcript Slajd 1 - University of Wrocław

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, 053001 (2008)
K.M.G, J. T. Sobczyk, Phys. Rev. D 77, 053003 (2008)
K.M.G, arXiv:0810.1247
K.M.G , D. Kiełczewska, P. Przewłocki, J. T. Sobczyk, in preparation
 Introduction
 RS formalism with improvements
 Rarita-Schwinger formalism
 Re-analysis of the ANL and BNL data
1p production?
Motivation
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)
n
Z or W
p N
Far Detector
ND280 (m)
Off-axis: OA2
Tokai 2
Kamioka
J-PARC Facility
700 MeV
nm
ne
Kaon decay
K2K
1p Production @ T2K
single pions vs. long baseline experiments
Oscillation measurements:
 Disappearance of νμ (Far and Near Detectors)



nm
M. H. Ahn, Phys.Rev. D74 (2006) 072003
Neutrino Energy reconstructed from QE events
SPP an important background in quasi-elastic events
Appearance of ve(T2K experiment)

Single π0 production an important background
T2K experiment
E about 700 MeV
ne
n
Appearance
Disappearance
Models for CC n interaction  NC n interaction
ND280
Interactions
JHF
295 km
ND 280m
ND? 2km
Off-Axis
Charged Current
m   Ax   X i : exchangeof W

i
n m  O16  
x'
n m  A'  X 'i : exchangeof Z 0
i

Neutral Current
SK
p
p p 

i X i  ...
 N  np  ...    ...

np  ...    ...
Source of p’s
 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 @ small Q2 @ MiniBooNE
•Nuclear corrections?
•An accurate n-nucleon input
CC 1p production
n m  p  m p   p
Today
nm  n  m p 0  p
n m  n  m p   n
T. Kitagaki et al. Phys. Rev. D 34 (1986) 2554
Born graphs for CC SPP
SPP resonance production
l
n
N
*
n
l
Non-resonant
background
p
N
N
W,Z
p
N
N
N
n
l
W,Z
N
Kitagaki et al.. Phys. Rev. D42, 42 (1990)
n  p  m p   p
N
Dominant D(1232) contribution!
Non-resonant contribution negligible!
n
N
p
l
p
W,Z
N
N
Description of 1p
production
Theory  Monte Carlo Codes  Experiment
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),
Fine tuning
Bubble chamber data
12 ft @ ANL








G. M. Radecky Phys. Rev. D25 (1982) 1161
12 foot bubble chamber filled with
deuterium and hydrogen @ Argonne
National Laboratory
S. J. Barish, Phys. Rev. D19 (1979)
2521.
G. M. Radecky Phys. Rev. D25
(1982) 1161.
<E> < 1 GeV
<Dflux> =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
n  d  m   D (1232)  n
S. J. Barish, Phys. Rev. D 16 (1977) 3103
7-ft @BNL
K. Furuno NUINT02
n  d  m   D (1232)  n
 7 foot bubble chamber filled with





deuterium at Brookhaven
National Laboratory.
<E> = 1.6 GeV
T. Kitagaki et al. Phys. Rev. D 34
(1986) 2554.
T. Kitagaki et al., Phys. Rev.
D42 (1990) 1331.
<Dflux> = 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

T. Kitagaki et al. Phys. Rev. D 34 (1986) 2554
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) 50
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
n m  p  m p   p
T. Kitagaki et al. Phys. Rev. D 34 (1986) 2554
1p @ Monte Carlo
Rein-Sehgal Model  NUANCE  Paweł;)
Rein and Sehgal model
FKR/Rein-Sehgal approach


FKR model – Relativistic Harmonic Oscillator
Quark Model

SPP in Monte Carlo
 Rein-Sehgal Model:
NUANCE (MiniBooNE),
NUET(K2K, T2K),



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.
n  p l  N
qb
qa
qc
CC
l  p  p
0

 p  p
*
n  n  l  N l   
p  n
p 0  p
*
n  p n  N n   
p  n
p 0  n NC
*0
n  n n  N n   
p  p

*


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
Elastic ep scattering and Quasi-Elastic nn scattering
Standard Approach
FKR/Rein-Sehgal model
List of
resonances
…+…
Rarita Schwinger
Formalism
Form Factors
Rarita-Schwinger Formalism
n  p  m   D (1232)
Hadronic current
D(1232) -3/2 spin, Rarita Schwinger field
electro-weak current for N D(1232) transition
Vector current
Vector Current Conservation
Three Vector Form Factors!
Axial current
Adler relation
One axial form factor: C5A
g D fp
 1.2
3
M2
C6A (Q 2 )  2
C A (Q 2 )
2 5
mp  Q
C5A (0) 
PCAC:
Rein-Sehgal vs RaritaSchwinger
Some improvements
Improvements




I.

II.
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)
GVRS
GARS
We still keep only two
form factors (vector and
axial)
Lepton mass in Charged
Current nN scattering
More accurate description of 1p in NC
~(V-A)
GARS
A phenomenological, effective input to RS description
~(V)
GVRS
FKR/RS model vs. Rarita Schwinger Formalism
C5V  0
M V
V
C4   C3
W
Quark model suggested solution
•direct relation between C3V and
GV(RS)
•@ 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) 014009.
 Vector Form Factors 
D(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
e  p  e  D (1232 )
n  p  m   D  (1232 )
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
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., arXiv:0309052 [hep-ex]
Similar Analysis for Axial Contribution
Lattice calculations
C. Alexandrou et al..
two different fits:
Adler relations (S.L. Adler, Ann. Phys. 50 (1968) 189)
For small Q2 there is small difference between both fits
Our choice
At RS model C5A(0) is about 1.00!!!
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
E=700 MeV
n  n  m  p p 0
n  p  m  n p 0
n  n  m  p p 0
n  p  m  n p 0
Normalized to the area
•Pion Pole Contribution reduces cross sections below Q2<0.2
•It is more important for antineutrino scattering!
C5A axial form factor
more carefully
Re-analysis of old bubble chamber
neutrino-deuteron scattering data
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
Used in this analysis
?!
Settings



Vector Contribution described by Lalakulich et al.. form factors
C5A(Q2) will be fitted
ANL



<Dflux> = 20%
Total cross sections and differential cross sections depending on Q2
Kinematical cuts:






BNL
<Dflux> = 10%
Kinematical cuts:


0.5 GeV < E < 6.0 GeV
Q2 < 3 GeV2 but:



0.5 GeV < E < 6.0 GeV
0.01 GeV2 < Q2 < 1 GeV2
W < 1.4 GeV
Q2 > 0.1  efficiency!
W<1.4 GeV
Total cross sections, normalized cross sections depending on Q2
Chi-2 method
Total # sections
normalization
Analogically the sth cross section is obtained
Flux uncertainty
Results
Dipole and Adler parameterizations
Dipole Parameterization
M2 A 
C5A (0)
2

Q 
C5A (Q 2 )  C5A (0)1  2 
 MA 
M A  pBNL
M A  p ANL
C5A (0)  pBNL
C5A (0)  pANL
pANL  pBNL
Dipole axial mass
0.94 GeV
Adler Parameterization

aQ2  Q 2 
A
2
A
1  2 
C5 (Q )  C5 (0)1 
2 
 b  Q  M A 
2
a=-1.21, b= 2 GeV2

Q2 
A
2
A
C5 (Q )  C5 (0)1  2 
 MA 
2
About 10% of difference
between ANL and BNL
10% of deuteron structure
effects

aQ2 
Q2 



C (Q )  C (0)1 
1

2 
2 
b

Q
M


A 
A
5
2
2
A
5
•ANL
•Deuteron structure
effects seems to more
important
•BNL
•Cut in Q2
•Higher E beam energy
With deuteron structure effects
4%
With deuteron structure effects
Fit uncertainties
Cross section uncertainties
Consistency
parameter-goodness-of-fit
2
2
2
2
 2   ANL
  BNL
  ANL


, min
BNL , max  0.2
NDF  3  3  4  2
PGOF  0.90
Parameter Goodnest of Fit: M. Maltoni, T. Schwetz, Phys. Rev. D68, 033020, (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 1p0 production
 A model independent analysis of the
data?................... Neural Networks?
