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 22 June 2005 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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=2.792847, mn=-1.913043, l=5.6, t= Q2/4M2 Axial-vector form factor FA FA(Q2)=-1.2617/(1+Q2/MA2)2 22 June 2005 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

(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 M.Sakuda@NuFact05

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 looked finite. But, no one needed better accuracy than that with dipole forms, untill Neutrino physics need it recently. 22 June 2005 M.Sakuda@NuFact05

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 22 June 2005 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05 Q2 (GeV/c)2 Q2 (GeV/c)2

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 M.Sakuda@NuFact05 Reconstructed Q2 (GeV/c)2

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 M.Sakuda@NuFact05

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 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 Reconstructed Q2 22 June 2005 1 Track M.Sakuda@NuFact05 2 Track QE 2 Track nQE

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 22 June 2005 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

Comparison of MA obtained by other experiments stat error total error (H2O) This experiment 1.06 +/- 0.03 stat +/- 0.14 syst. Dipole Form Factors Q2min. = 0.2 (GeV/c)2 Deuterium MAQE 1.0 22 June 2005 M.Sakuda@NuFact05

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. 22 June 2005 M.Sakuda@NuFact05

Benhar et al., hep-ph/0506116, PRD, -Comparison of FG, SP, SP+FSI validated by electron scattering data FG SP SP+FSI 22 June 2005 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

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 0.5 1.0 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 M.Sakuda@NuFact05

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 M.Sakuda@NuFact05

Single Pion Production Cross Section Prediction = Rein-Sehgal MA=1.2 GeV/c2 MS@nuint01 1x10-381.0 (cm2) 0.0 22 June 2005 M.Sakuda@NuFact05