1. Axial-vector mass MA and K2K Q2 distribution
Makoto Sakuda (Okayama)
22 June, NuFact05
Outline
1. MA analysis with SciFi detector data
R.Gran’s paper published in NuInt04 (NPB(Proc.Suppl.)139)
M.Hasegawa et al.(K2K), --F.Sanchez’s talk
2. Summary
Discussion Session
Review of the method to estimate the quasi-elastic cross section and the axial-vector mass MA
22 June 2005

2. MA analysis with K2K SciFi detector data
Previous MA analyses generally used
Dipole form for vector form factors
Q2>0.2 (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%~MA±0.05.
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
22 June 2005

3. and form factors 1. Quasi-elastic cross section nm nm- p
Form Factors F1V,F2V,and FA and (s-u)=4MEn-Q2-Mm2
A = Q2/4M2 [(4 + Q2/M2)|FA|2 - (4 - Q2/M2)|FV1|2
+ Q2/M2(1-Q2/4M2)|xFV2|2+ 4Q2/M2xReFV*1FV2
　　 -m2/4M2 (| FV1 + FV2 |2 + | FV1 +2Fp |2 –4(1+t) |Fp|2]
B = -Q2/M2ReF*A(FV１ + xFV２),
C = 1/4(|FA|2 + |FV1|2 + Q2/4M2|xFV2|2).
Historically, we used
Vector Form factors
　GEp=D, GMp=mpD, GMn=mnD, GEn=-mnt/(1+lt)D,
D=1/(1+Q2/MV2)2, MV=0.843 (GeV/c2)
mp= , mn= , l=5.6, t= Q2/4M2
Axial-vector form factor FA
FA(Q2)= /(1+Q2/MA2)2
22 June 2005

4. Nucleon Form Factors　　　
Electromagnetic current (Jaem) and weak hadronic charged current (JaCC=Va1+i2–Aa1+i2) is written in terms of form factors: e e q N N
22 June 2005

5. (includes normalization)
dQE/dQ2 distribution at En = 1.3 GeV
ddq2(10-38cm2/(GeV/c)2)
MA=1.2 GeV
MA=1.1 GeV
MA=1.0 GeV
Absolute
Cross-section
(includes normalization)
Q2(GeV/c)2
MA=1.0 GeV
MA=1.1 GeV
MA=1.2 GeV
Shape only
Q2(GeV/c)2
22 June 2005

6. Nucleon Vector Form Factors
A simple dipole form
GD = (1+Q2/MV2)-2, MV=0.843
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.
22 June 2005

7. Updated Nucleon Vector Form Factorsde
A simple dipole form
D=(1+Q2/MV2)-2, MV=0.843
GMnGMp  GEp
Curve – Bosted, PRC51,409,’95
Curve=(1+a1Q+a2Q2+.+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
22 June 2005

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.
Eν = 1.0
MA= 1.1
+5%
-4%
New cross section is smaller at low Q2 and larger at higher Q2
~5% overall difference in dsQE/dQ2
Fp is < 1% different, GEn is ~2% different, both largest at low Q2
Changes MA fit value by -0.05
22 June 2005

9. 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?
22 June 2005

10. ２．Reconstruction of Quasi-Elastic Neutrino Interactions
from measured lepton angle and lepton momentum   θ q p
Axial vector form factor depends on MA and Q2
22 June 2005

11. 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 > 600 MeV/c
Recoil proton threshold is
three layers in SciFi
pproton > ~ 600 MeV/c
1-track events with muon only
2-track events with muon plus either proton or pion
22 June 2005

12. Event Selection  n-> - p
Typical two-track event showing the muon and second track
1 track event
2 track event
Neutrino interaction in H2O target (+ 20% Aluminum)
22 June 2005

13. Dq distribution of 2 track events: QE and nonQE
 + n -> -+p -
(E, p)  p
Expected proton
assuming QE interaction 
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
22 June 2005

14. Basic Distributions, Pm, qm for Scifi Detector
Overall agreement is good Pm qm
Muon momentum
Muon angle
One-track events (60% QE)
22 June 2005

15. Reconstructed Q2 distribution in SciFi detector
Make DIS correction (Bodek/Yang) and reduced Coherent Pion production (Marteau)
1 track sample
2 track QE enhanced
2 track non-QE
22 June 2005
Q2 (GeV/c)2
Q2 (GeV/c)2
Q2 (GeV/c)2

16. Fit only Q2 > 0.2 region Most significant uncertainties due
to Pauli blocking
and choice of
nuclear model,
coherent pion,
correction to DIS
-> Q2 cut
Monte Carlo best fit
Quasi Elastic fraction
QE signal
and inelastic background
are treated the same way
22 June 2005
Reconstructed Q2 (GeV/c)2

17. Uncertainty in QE cross section due to Pauli Blocking
in the Q2 < 0.2 region
a Fermi-gas model with different Fermi-momenta kf
Free nucleon (no Pauli Blocking)
210
kf = 225
235
MeV/c
We Cut here
22 June 2005

18. Preliminary MA fit with K2K-I and K2K-IIa data
MA = / stat +/ syst
Bodek/Yang DIS correction and Marteau Coherent Pi cross-section
Fit the 1track, 2track (QE), and 2track (nonQE) simultaneously
K2K-I events total 4310 Q2>0.2 in fit
K2K-IIa events total 2525 Q2>0.2 in fit
Reconstructed Q2
22 June 2005
1 Track
2 Track QE
2 Track nQE

19. Systematic Errors in combined fit
Flux and Normalization
Energy scale
LG density
Escale/LG correlation
Escale-MA correlation
MA-1pi
nQE/QE
Statistics
Total error
22 June 2005

20. MA vs Q2 cut value -- We use data for Q2>0.2
At low Q2 there are large nuclear effects (Pauli blocking)
also uncertainty in coherent pion and multi-pion interactions.
1.06
Zero Coherent pion
Lowers MA by 0.10
better
Pauli Blocking
0.10 effect at
Q2min=0.0
Standard
Cut
K2K-I data,
MA-1p = 1.1
statistical errors
and energy spectrum
uncertainty
Result is stable and consistent with MA=1.06 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.
22 June 2005

21. 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 MA=1.06 (GeV/c2) at each energy.
1.06
Q2 cut = 0.2
statistical errors only
22 June 2005

22. Comparison of MA obtained by other experiments
stat error
total error
(H2O) This experiment
1.06 +/ stat +/ syst.
Dipole Form Factors
Q2min. = 0.2 (GeV/c)2
Deuterium
MAQE
1.0
22 June 2005

23. Conclusions
We present the preliminary analysis of MAQE with SciFi detector ( )
MA = / stat. +/ syst.
Here, we use Fermi Gas modl, the dipole form (MV=0.843) for vector form factors,
and only data with Q2 > 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
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. e+Ce+X.
June 25 (WG2)
Benhar, Varverde,BarbaroBetter calculation over the entire q2 region.
Benhar et.al,hep-ph/ , to appear in PRD.
22 June 2005

24. Benhar et al., hep-ph/ , PRD, -Comparison of FG, SP, SP+FSI validated by electron scattering data FG SP
SP+FSI
22 June 2005

25. 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
22 June 2005

26. 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
22 June 2005

27. Pauli Bloching effect En=1.3 GeV，kF=220 MeV/c ds/dQ2 n m-
Nuclear effects are large in the low Q2 region, where the cross section is large.
En=1.3 GeV，kF=220 MeV/c
ds/dQ2 n m-
Quasi-elastic q
W/o Pauli effect n p P p
W/ Pauli effect
Total 8%
ds/dQ2
If P <kF , suppressed. n m-
D production
10-15% suppression
At low Q2
Total 3% reduction q p D P p P p W
22 June 2005

28. Charged-Current Quasi-elastic Scattering
This is the simplest and the most important reaction. Calculation by Ch.L.Smith et al. with MA=1.0. _
s(nm pm+ n)
s(nm nm- p)
1.0
1x10-381.0
(cm2)
Pauli effect ~8% 0.
0.1
1.0
10.
50.
0.1 1.
10.
22 June 2005

29. Single Pion Production Cross Section
Prediction = Rein-Sehgal MA=1.2 GeV/c2
1x10-381.0
(cm2)
0.0
22 June 2005