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Axial-vector mass M A and K2K Q 2 distribution

Axial-vector mass M A and K2K Q 2 distribution. Makoto Sakuda (Okayama) 22 June, 2005 @ NuFact05 Outline 1. M A 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

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Axial-vector mass M A and K2K Q 2 distribution

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  1. Axial-vector mass MA and K2K Q2 distribution Makoto Sakuda (Okayama) 22 June, 2005 @ 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 M.Sakuda@NuFact05

  2. MAanalysis 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 M.Sakuda@NuFact05

  3. 1. Quasi-elastic cross sectionnmnm-p and form factors Form Factors F1V,F2V,and FAand (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=2.792847, mn=-1.913043, l=5.6, t= Q2/4M2 • Axial-vector form factorFA • FA(Q2)=-1.2617/(1+Q2/MA2)2 M.Sakuda@NuFact05

  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 M.Sakuda@NuFact05

  5. MA=1.2 GeV MA=1.1 GeV MA=1.0 GeV ddq2(10-38cm2/(GeV/c)2) Q2(GeV/c)2 MA=1.0 GeV MA=1.1 GeV MA=1.2 GeV Shape only Q2(GeV/c)2 dQE/dQ2 distribution at En = 1.3 GeV Absolute Cross-section (includes normalization) M.Sakuda@NuFact05

  6. Nucleon Vector Form Factors Gourdin@Phys.Rep.C11(‘74) • 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 lookedfinite. But, no one needed better accuracy than that with dipole forms, untill Neutrino physics need it recently. M.Sakuda@NuFact05

  7. Updated Nucleon Vector Form Factors de Jager@PANIC02 • 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 M.Sakuda@NuFact05

  8. Eν = 1.0 MA= 1.1 +5% -4% 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 < 1% different, GEn is ~2% different, both largest at low Q2 Changes MA fit value by -0.05 M.Sakuda@NuFact05

  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? M.Sakuda@NuFact05

  10.  θ p ２．Reconstruction of Quasi-Elastic Neutrino Interactions from measured lepton angle and lepton momentum q Axial vector form factor depends on MA and Q2 M.Sakuda@NuFact05

  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 M.Sakuda@NuFact05

  12. Event Selection  n-> - p 2 track event 1 track event Neutrino interaction in H2O target (+ 20% Aluminum) Typical two-track event showing the muon and second track M.Sakuda@NuFact05

  13. - (E, p) p  Expected proton assuming QE interaction  Dq distribution of 2 track events: QE and nonQE +n ->-+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 M.Sakuda@NuFact05

  14. Basic Distributions, Pm, qm for Scifi Detector Overall agreement is good Pm qm Muon momentum Muon angle One-track events (60% QE) M.Sakuda@NuFact05

  15. Reconstructed Q2 distribution in SciFi detector Make DIS correction (Bodek/Yang) and reducedCoherent Pion production (Marteau) 2 track non-QE 1 track sample 2 track QE enhanced M.Sakuda@NuFact05 Q2 (GeV/c)2 Q2 (GeV/c)2 Q2 (GeV/c)2

  16. -> Q2 cut Most significant uncertainties due to Pauli blocking and choice of nuclear model, coherent pion, correction to DIS Monte Carlo best fit Quasi Elastic fraction QE signal and inelastic background are treated the same way Reconstructed Q2 (GeV/c)2 Fit only Q2 > 0.2 region M.Sakuda@NuFact05

  17. Free nucleon (no Pauli Blocking) 210 kf = 225 235 MeV/c We Cut here Uncertainty in QE cross section due to Pauli Blocking in the Q2 < 0.2 region a Fermi-gas model with different Fermi-momenta kf M.Sakuda@NuFact05

  18. Fit the 1track, 2track (QE), and 2track (nonQE) simultaneously K2K-I 8114 events total 4310 Q2>0.2 in fit K2K-IIa 5967 events total 2525 Q2>0.2 in fit 1 Track 2 Track QE 2 Track nQE 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 M.Sakuda@NuFact05

  19. 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 M.Sakuda@NuFact05

  20. 1.06 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. Zero Coherent pion Lowers MA by 0.10 better Pauli Blocking 0.10 effect at Q2min=0.0 K2K-I data, MA-1p = 1.1 Standard Cut 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. M.Sakuda@NuFact05

  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 M.Sakuda@NuFact05

  22. MAQE 1.0 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 M.Sakuda@NuFact05

  23. 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 (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 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. e+Ce+X. June 25 (WG2) • Benhar, Varverde,BarbaroBetter calculation over the entire q2 region. • Benhar et.al,hep-ph/0506116, to appear in PRD. M.Sakuda@NuFact05

  24. Benhar et al., hep-ph/0506116, PRD,-Comparison of FG, SP, SP+FSI validated by electron scattering data FG SP SP+FSI M.Sakuda@NuFact05

  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 M.Sakuda@NuFact05

  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 M.Sakuda@NuFact05

  27. Pauli Bloching effect 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% 0.5 1.0 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 M.Sakuda@NuFact05

  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(nmpm+n) s(nmnm-p) 1.0 1x10-381.0 (cm2) Pauli effect ~8% 0.1 1.0 10. 50. 0. 0.1 1. 10. M.Sakuda@NuFact05

  29. Single Pion Production Cross Section Prediction = Rein-Sehgal MA=1.2 GeV/c2 MS@nuint01 1x10-381.0 (cm2) 0.0 M.Sakuda@NuFact05

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