Axial-vector mass MA and K2K Q2 distribution

1
Axial-vector mass MA and K2K Q2 distribution

• Makoto Sakuda (Okayama)
• 22 June, 2005 _at_ NuFact05
• Outline
• 1. MA analysis with SciFi detector data
• R.Grans paper published in NuInt04
  (NPB(Proc.Suppl.)139)
• M.Hasegawa et al.(K2K), --F.Sanchezs talk
• 2. Summary
• ?Discussion Session
• Review of the method to estimate the
  quasi-elastic cross section and the axial-vector
  mass MA

2
MA analysis with K2K SciFi detector data

• Previous MA analyses generally used
• Dipole form for vector form factors
• Q2gt0.2 (GeV/c)2 to avoid the nulcear effect
• - Fermi-Gas model for nucleus (Deuteron wave
  function
• calculation for deuteron data) shows it.
• In this analysis, we studied carefully the
  following effects
• Effect of the new vector form factor
  measurements
• Effect of the energy scale (detector dep.)
  1?MA0.05.
• This may have been overlooked before.
• Effect of background shape (1p) from data
• Proton rescattering
• This is relevant to our QE/nQE separation
• Flux uncertainty and event migration

3
1. Quasi-elastic cross section nm n?m- p
and form factors
Form Factors F1V,F2V,and FA and (s-u)4MEn-Q2-Mm2

• A Q2/4M2 (4 Q2/M2)FA2 - (4 - Q2/M2)FV12
• Q2/M2(1-Q2/4M2)xFV22 4Q2/M2xReFV1FV2
• -m2/4M2 ( FV1 FV2 2 FV1 2Fp 2
  4(1t) Fp2
• B -Q2/M2ReFA(FV1 xFV2),
• C 1/4(FA2 FV12 Q2/4M2xFV22).
• Historically, we used
• Vector Form factors
• GEpD, GMpmpD, GMnmnD, GEn-mnt/(1lt)D,
• D1/(1Q2/MV2)2, MV0.843 (GeV/c2)
• mp2.792847, mn-1.913043, l5.6, t Q2/4M2
• Axial-vector form factor FA
• FA(Q2)-1.2617/(1Q2/MA2)2

4
Nucleon Form Factors

• Electromagnetic current (Jaem) and weak hadronic
  charged current (JaCCVa1i2Aa1i2) is written
  in terms of form factors

e
e
q
N
N
5
d?QE/dQ2 distribution at En 1.3 GeV
Absolute Cross-section (includes normalization)
6
Nucleon Vector Form Factors
Gourdin_at_Phys.Rep.C11(74)

• A simple dipole form
• GD (1Q2/MV2)-2, MV0.843
• was known to be good to only 10-20 level for
  vector Form Factors since 1970s. Gen looked
  finite.
• But, no one needed better accuracy than that with
  dipole forms, untill Neutrino physics need it
  recently.

7
Updated Nucleon Vector Form Factors
de Jager_at_PANIC02

• A simple dipole form
• D(1Q2/MV2)-2, MV0.843
• GMn?GMp ? GEp
• Curve Bosted, PRC51,409,95
• Curve(1a1Qa2Q2.a5Q5)-1
• E.J.Brash et al. , Phys.Rev.C65,051001(2002).
  Similar
• Neutrino cross section shape will change if we
  use these data.

Q2
8
ds/dQ2 vs. Q2 with new Vector Form Factors
GMn,GMp,GEp ,GEN
Old cross section (line) vs new (dot)
Ratio of new cross section to old cross section.
New cross section is smaller at low Q2 and larger
at higher Q2 5 overall difference in
dsQE/dQ2 Fp is lt 1 different, GEn is 2
different, both largest at low Q2 Changes MA fit
value by -0.05
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• Message from here is
• Axial vector form factor can be approximated by
  a dipole form only at 10-20 level as vector form
  factor was.
• If the accurate neutrino cross section is
  measured in 5-10 years, there is no need for MA
  in the future. We parameterize axial form
• factors in the same way.
• ?Discussion
• What formalism should be preferable?

10
2.Reconstruction of Quasi-Elastic Neutrino
Interactions from measured lepton angle and
lepton momentum
q
Axial vector form factor depends on MA and Q2
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Scintillating Fiber (SciFi) detector -a
Fine-grain detector with water target -It has
operated since 1999 till the end of 2003 and
measured flux
To Muon Range Detector
Muon in the Muon Range Detector must have pmuon
gt 600 MeV/c
Recoil proton threshold is three layers in SciFi
pproton gt 600 MeV/c
1-track events with muon only 2-track events with
muon plus either proton or pion
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Typical two-track event showing the muon and
second track
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Dq distribution of 2 track events QE and nonQE
?? n -gt ?-p
use the location of proton track to separate
events into three subsamples 1-track (no
proton) 60 QE 2-track QE enhanced 60
QE 2-track nQE 85 nonQE, 15 QE
nonQE
QE
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Basic Distributions, Pm, qm for Scifi Detector
Overall agreement is good
Pm
qm
Muon momentum
Muon angle
One-track events (60 QE)
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Reconstructed Q2 distribution in SciFi
detector Make DIS correction (Bodek/Yang) and
reduced Coherent Pion production (Marteau)
2 track non-QE
1 track sample
2 track QE enhanced
Q2 (GeV/c)2
Q2 (GeV/c)2
Q2 (GeV/c)2
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Fit only Q2 gt 0.2 region
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Uncertainty in QE cross section due to Pauli
Blocking in the Q2 lt 0.2 region a Fermi-gas
model with different Fermi-momenta kf
18
Preliminary MA fit with K2K-I and K2K-IIa
data MA 1.18 /- 0.03 stat /- 0.12
syst Bodek/Yang DIS correction and Marteau
Coherent Pi cross-section
Reconstructed Q2
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Systematic Errors in combined fit
Flux and Normalization 0.08 Energy
scale 0.04 LG density 0.02 Escale/LG
correlation 0.04 Escale-MA correlation 0.03 MA
-1pi 0.03 nQE/QE
0.03 Statistics 0.03 Total error 0.12
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MA vs Q2 cut value -- We use data for Q2gt0.2
At low Q2 there are large nuclear effects (Pauli
blocking) also uncertainty in coherent pion and
multi-pion interactions.
Zero Coherent pion Lowers MA by
0.10 ?better Pauli Blocking 0.10 effect
at Q2min0.0
K2K-I data, MA-1p 1.1
Standard Cut
statistical errors and energy spectrum uncertaint
y
Result is stable and consistent with MA1.06 for
cuts above Q2 0.2 But statistical errors
dominate for high Q2 cuts This is the standard
cut used by almost all the experiments.
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MA for different energy ranges
The MA fit can be peformed separately for each
energy range. They are consistent each other
within 2s errors QE cross sections are
consistent with MA1.06 (GeV/c2) at each energy.
1.06
Q2 cut 0.2
statistical errors only

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Comparison of MA obtained by other experiments
total error
stat error
(H2O) This experiment
1.06 /- 0.03 stat /- 0.14 syst.
Dipole Form Factors Q2min. 0.2 (GeV/c)2
Deuterium
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Conclusions

• We present the preliminary analysis of MAQE with
  SciFi detector (1999-2003)
• MA 1.18 /- 0.03 stat. /- 0.12 syst.
• Here, we use Fermi Gas modl, the dipole form
  (MV0.843) for vector form factors,
• and only data with Q2 gt 0.2.
• We will give two values of MA, one with old
  vector form factors in order to compare
• with the old MA measurements, and the other with
  new vector form factors.
• MA becomes smaller by 0.05-0.07.
• ----------------------------------------------
• Personal comment
• In the near future, we need better
  parametrization for the quasi-elastic cross
  sections
• (single pion production) and better theoretical
  calculations over the entire
• q2 region, if we want to obtain the accuracy at
  a few level.
• Bodek?Vector form factors and nuclear effect will
  be measured. eC?eX.
• June 25 (WG2)
• Benhar, Varverde,Barbaro?Better calculation over
  the entire q2 region.
• ?Benhar et.al,hep-ph/0506116, to appear in PRD.

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Benhar et al., hep-ph/0506116, PRD,-Comparison
of FG, SP, SPFSI validated by electron
scattering data
FG
SP
SPFSI
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Combined fit with the K2K-I data
Q2 distribution, all energy bins combined, no
Coherent Pion in MC Green shows the QE fraction
Slide 4a
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Combined fit with the K2K-IIa data
Q2 distribution, all energy bins combined, no
Coherent Pion in MC Green shows the QE fraction
Slide 4b
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Pauli Bloching effect
Nuclear effects are large in the low Q2 region,
where the cross section is large.
En1.3 GeV,kF220 MeV/c
ds/dQ2
n
m-
Quasi-elastic
q
W/o Pauli effect
n p
P p
W/ Pauli effect
Total 8
0.5 1.0
ds/dQ2
If P ltkF , suppressed.
D production
n
m-
10-15 suppression At low Q2 Total 3 reduction
p
q
D
P p
P p
W
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Charged-Current Quasi-elastic Scattering

• This is the simplest and the most important
  reaction. Calculation by Ch.L.Smith et al. with
  MA1.0.

• _
  
• s(nm p?m n)

s(nm n?m- p)
1.0
1x10-38?1.0 (cm2)
Pauli effect 8
0.1
1.0
10.
50.
0.
10.
1.
0.1
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Single Pion Production Cross Section

• Prediction Rein-Sehgal MA1.2 GeV/c2

MS_at_nuint01
1x10-38?1.0 (cm2) 0.0