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ARIE BODEK University of Rochester (in collaboration with R. Bradford, H. Budd and J. Arrington)

Vector and Axial Form Factors Applied to Neutrino Quasi-Elastic Scattering. ARIE BODEK University of Rochester (in collaboration with R. Bradford, H. Budd and J. Arrington) MILOS May 2006. Outline.

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ARIE BODEK University of Rochester (in collaboration with R. Bradford, H. Budd and J. Arrington)

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  1. Vector and Axial Form Factors Applied to Neutrino Quasi-Elastic Scattering ARIE BODEK University of Rochester (in collaboration with R. Bradford, H. Budd and J. Arrington) MILOS May 2006 Arie Bodek, Univ. of Rochester

  2. Outline • Review of BBA2003 and BBBA2005 vector-form factors from electron scattering • Reanalyze the previous neutrino-deuterium quasi-elastic data by calculating MA with their assumptions and with BBBA2006-form factor to extract a new value of MA • Compare to MA from pion electro-production • Use the previous deuterium quasi-elastic data to extract FA and compare axial form factor to models • Future: Look at what MINERnA can do • See what information anti-neutrinos can give Arie Bodek, Univ. of Rochester

  3. Vector and axial form factors Arie Bodek, Univ. of Rochester

  4. Vector Axial dipole approx Vector dipole approx Arie Bodek, Univ. of Rochester

  5. BBA2003-Form Factors and our constants Our Constants Arie Bodek, Univ. of Rochester

  6. Neutron GMN is negative Neutron (GMN/ GMNdipole ) Neutron (GMN/ GMNdipole ) At low Q2 Ratio to Dipole similar to that nucl-ex/0107016 G. Kubon, et al Phys.Lett. B524 (2002) 26-32 Arie Bodek, Univ. of Rochester

  7. Neutron, GENis positive - Imagine N=P+pion cloud Neutron GEN is positive New Polarization data gives Precise non zero GEN hep-ph/0202183(2002) show_gen_new.pict (GEN)2 Galster fit Gen Krutov Neutron (GEN/ GEPdipole ) Arie Bodek, Univ. of Rochester

  8. Functional form and Values of BBA2003 Form Factors • GEP.N (Q2)=  {e i q . r r(r) d3r } = Electric form factor is the Fourier transform of the charge distribution for Proton And Neutron (therefore, odd powers of Q should not be there at low Q) Poor data cannot constrain Gen very well Arie Bodek, Univ. of Rochester

  9. New innovation - Kelly Parameterization – J. Kelly, PRC 70 068202 (2004) • Fit to sanitized dataset favoring polarization data. • Employs the following form (Satisfies power behavior of form factors at high Q2): --> introduce some theory constraints Gep, Gmp, and Gmn But uses old form for Gen Arie Bodek, Univ. of Rochester

  10. Kelly Parameterization • Still not very well constrained at high Q2. Arie Bodek, Univ. of Rochester Source: J.J. Kelly, PRC 70 068202 (2004).

  11. BBBA2005 ( Bodek, Budd, Bradford, Arrington 2005) • Fit based largely on polarization transfer data. • Dataset similar to that used by J. Kelly. • Functional form similar to that used by J. Kelly (satisfies correct power behavior at high Q2): use a0=1 for Gep, Gmp, Gmn, and a0=0 for Gen. • Employs 2 additional constraints from duality to have a more constrained description at high Q2. 4 parameters for Gep, Gmp, and Gmn. 6 parameters for Gen. Arie Bodek, Univ. of Rochester

  12. Constraint 1: Rp=Rn (from QCD) • From local duality R for inelastic, and R for elastic should be the same at high Q2: • We assume that Gen > 0 continues on to high Q2. • This constraint assumes that the QCD Rp=Rn for inelastic scattering, carries over to the elastic scattering case. This constraint is may be approximate. Extended local duality would imply that this applies only to the sum of the elastic form factor and the form factor of the first resonance. (First resonance is investigated by the JUPITER Hall C program) at high Q2. Arie Bodek, Univ. of Rochester

  13. Constraint 2: From local duality:F2n/F2p for Inelastic and Elastic scattering should be the same at high Q2 • In the limit of →∞, Q2→∞, and fixed x: • In the elastic limit: (F2n/F2p)2→(Gmn/Gmp)2 We ran with d/u=0, .2, and .5. Arie Bodek, Univ. of Rochester

  14. Constraint 2 • In the elastic limit: (F2n/F2p)2→(Gmn/Gmp)2 . We use d/u=0, This constraint assumes that the F2n/F2p for inelastic scattering, carries over to the elastic scattering case. This constraint is may be approximate. Extended local duality would imply that this applies only to the sum of the elastic form factor and the form factor of the first resonance. (First resonance is investigated by the JUPITER Hall C program) Arie Bodek, Univ. of Rochester

  15. Neutrino Oscillations experiments need to know the precise energy dependence of low energy neutrino interactions: Need to Understand both vector and axial form factors, and nuclear corrections Arie Bodek, Univ. of Rochester

  16. BBBA2005… NuInt05 ep-ex/0602017 • We have developed 6 parameterizations: • One for each value of (d/u)=0, 0.2, 0.5 (at high x) • One each for Gen>0 and Gen<0 at high Q2. • Our preferred parameterization is for • Gen > 0 at high Q2 • d/u=.2, so (Gmn/Gmp)=.42857 (if d/u=.2 as expected from QCD) • Following figures based on preferred parameterization. Arie Bodek, Univ. of Rochester

  17. Results BBBA2005: use Kelly fit for Gep ; use New fit for Gmp , New constrained fit for GmnNew constrained fit for Gen Arie Bodek, Univ. of Rochester

  18. 0.25 (d/u=0.0) 0.42875 (d/u=0.2) Constraints: Gmn/Gmp Questions: would including the first resonance make local duality work at lower Q2? Or is d/u --> 0 (instead of 0.2) which implies F2n/F2p= 0.25 instead of 0.43? Arie Bodek, Univ. of Rochester

  19. Constraints: (Gep/Gmp)2=(Gen/Gmn)2` Arie Bodek, Univ. of Rochester

  20. BBBA Kelly Comparison with Kelly Parameterization Arie Bodek, Univ. of Rochester

  21. Summary - Vector Form Factors • We have developed new parameterizations of the nucleon form factors BBA2005. • Improved fitting function • Additional constraints extend validity to higher ranges in Q2 (assuming local duality) • Ready for use in simulations.... • Further tests to be done by including new F2n/F2p and Rp and Rn data from the first resonance (from new JUPITER Data) Arie Bodek, Univ. of Rochester

  22. BBBA2005 Fit Parameters (Gen>0, d/u=0.2) hep-ex/0602017 Arie Bodek, Univ. of Rochester

  23. Rextract Fa from neutrino data using updated vector form factors modern ga Miller 1982: We type in their d/dQ2 histogram. Fit with our best Knowledge of their parameters : Get MA=1.116+-0.05 (A different central value, but they do event likelihood fit And we do not have their the events, just the histogram. If we put is BBBA2005 form factors and modern ga, then we get MA=1.086+-0.05 or DMA= -0.030. So all the Values for MA from this expt. should be reduced by 0.030 Arie Bodek, Univ. of Rochester

  24. Do a reanalysis of old neutrino data to get DMA to update using latest ga+BBBA2005 form factors. (note different experiments have different neutrino energy Spectra, different fit region, different targets, so each experiment requires its own study). If Miller had used Pure Dipole analysis, with ga=1.23 (Shape analysis) - the difference with BBA2003 form factors would Have been --> DMA = -0.050 (I.e. results would have had to be reduced by 0.050) But Miller 1982 did not use pure dipole (but did use Ollson with Gen=0) so their result only needs to be reduced by DMA = -0.030 Reanalysis of FOUR different neutrino experiments (they mostly used D2 data with Olsson vector form factors and and older value of Ga) yields DMA VARYING From -0.022 (FNAL energy) to -0.030 (BNL energy) Arie Bodek, Univ. of Rochester

  25. Determining mA , Baker et al. – 1981 BNL deuterium • The dotted curve shows their calculation using their fit value of 1.07 GeV • They do unbinned likelyhood to get MA No shape fit • Their data and their curve is taken from the paper of Baker et al. • The dashed curve shows our calculation using MA = 1.07 GeV using their assumptions • The 2 calculations agree. • If we do shape fit to get MA • With their assumptions -- MA=1.079 GeV • We agree with their value of MA • If we fit with BBA Form Factors and our constants - MA=1.050 GeV. • Therefore, we must shift their value of MA down by -0.029 GeV. • Baker does not use a pure dipole- They used Ga=-1.23 and Ollson Form factors • The difference between BBBA2005-form factors and dipole form factors is -0.055 GeV Arie Bodek, Univ. of Rochester

  26. Kitagaki et al. 1983 FNAL deuterium • The dotted curve shows their calculation using their fit value of MA=1.05 GeV • They do unbinned likelyhood, no shape fit. • The dashed curve shows our calculation using MA=1.05 GeV and their assumptions • The solid curve is our calculation using their fit value MA=1.05 GeV • The dash curve is our calculation using our fit value of MA=1.19 GeV with their assumption • However, we disagree with their fit value. • Our fit value seem to be in better agreement with the data than their fit value. • We get MA=1.172 GeV when we fit with our assumptions • Hence, -0.022 GeV should be subtracted from their MA. • They used Ga=-1.23 and Ollson Form factors Arie Bodek, Univ. of Rochester

  27. Barish 1977 et al. ANL deuterium • Dotted curve – their calculation MA=0.95 GeV is their unbinned likelyhood fit • The dashed curve – our calculation using their assumption • We agree with their calculation. • The solid curve – our calculation using theirs shape fit value of 1.01 GeV. • We are getting the best fit value from their shape fit. • The dashed curve is our calculation using our fit value MA=1.075 GeV. • We slightly disagree with their fit value. • We get MA=1.046 GeV when we fit with BBA2005 – Form Factors and our constants. • Hence, -0.029 GeV must be subtracted from their value of MA • They used Ga=-1.23 and Ollson Form factors Arie Bodek, Univ. of Rochester

  28. Miller 1982– ANL deuterium DESCRIBED EARLIER • Miller is an updated version of Barish with 3 times the data • The dotted curve – their calculation taken from their Q2 distribution figure, MA=1 GeV is their unbinned likely hood fit. • Dashed curve is our calculation using their assumptions • We don't quite agree with their calculation. • Their best shape fit for MA is 1.05 • Dotted is their calculation using their best shape MA • Our MA fit of using their assumptions is 1.116 GeV • Our best shapes agree. • Our fit value using our assumptions is 1.086 GeV • Hence, -0.030 GeV must be subtracted from their fit value. • They used Ga=-1.23 and Ollson Form factors Arie Bodek, Univ. of Rochester

  29. Kitagaki 1990 They used Ollson, Mv=0.84 and Ga=-1.254. We get that Ma should be corrected by -0.031 GeV Arie Bodek, Univ. of Rochester

  30. Summary of Results for 5 neutrino experiments on Deuterium Updated value 1.039+-0.06, 0.981+-0.09, 1.02+-0.05, 1.028+-0.14, 1.039+-0.043 0.898+-0.076 FNAL Kitagaki (1990) 1.07+-0.040-0.045 TBA TBA -0.031 -0.051 Mann (1973) 0.95+-0.076 TBA TBA -0.052 -0.052 Take average of Deuterium data to get neutrino world average value of MA Get: Average Deuterium Corrected --> MA = 1.016+-0.026 Vs. Average Pion Electro-production Corrected--> MA = 1.014+-0.016 Arie Bodek, Univ. of Rochester

  31. Hep-ph/0107088 (2001) From Neutrino quasielastic Neutrinos D only corrected 1.016+-0.026-=MA average From charged Pion Electroproduction Average value of 1.069->1.014 when corrected for theory hadronic effects to compare to neutrino reactions Propane -0.030 D Freon -0.029 D Freon -0.029 D -0.030 D -0.022 D C use for High Q C use for High Q -0.030 D For updated MA we reanalyzed neutrino expt with new gA, and BBBA2005 form factors Difference in Ma between Electroproduction And neutrinos is understood =1.014 +_0.016 when corrected for hadronic effects Arie Bodek, Univ. of Rochester

  32. Conclusion of Reanalysis of neutrino data • Using BBBA2005-form factors we derive a new value of mA = 1.016 GeV+-0.026 From the world average of Neutrino expt. On Deuterium • agrees with the results from pion electroproduction: • mA = 1.014+-0.016 GeV • We now understand the Low Q2 behavior of FA • ~7-8% effect on the neutrino cross section from the new value mA and with the updated vector form factors • MINERnA can measure FA and determine deviations from the dipole form at high Q2. Can extract FA from neutrino data on ds/dq2 • The anti-neutrinos at high Q2 serves as a check on FA Arie Bodek, Univ. of Rochester

  33. Theory predictions for FA some calculations predict that FA is may be larger than the Dipole predictions at high Q2 • Wagenbrum - constituent quark model (valid at intermediate Q2) • Bodek - Local duality between elastic and inelastic implies that vector=axial at high Q2 • However, local duality may fail. We need to measure both elastic and first resonance vector and axial form factors. We can then test for Adler sum rule for vector and axial form scattering separately- MINERvA and JUPITER FA /Dipole Arie Bodek, Univ. of Rochester

  34. Current Neutrino data on FA vs MINERvA For inelastic (quarks) axial=vector Therefore, local duality implies that At high Q2, 2xF1- elastic Axial and Vector are the same. Note both F2 and 2xF1- elastic Axial and Vector are the same at high Q2 - when R-->0. Arie Bodek, Univ. of Rochester

  35. Supplemental Slides Arie Bodek, Univ. of Rochester

  36. Nuclear correction uses NUANCE calculation • Fermi gas model for carbon. Include Pauli Blocking, Fermi motion and 25 MeV binding energy • Nuclear binding on nucleon form factors as modeled by Tsushima et al. • Model valid for Q2 < 1 • Binding effects on form factors expected to be small at high Q2. Arie Bodek, Univ. of Rochester

  37. Neutrino quasi-elastic cross section Most of the cross section for nuclear targets low Arie Bodek, Univ. of Rochester

  38. Anti-neutrino quasi-elastic cross section Mostly on nuclear targets Even with the most update form factors and nuclear correction, the data is low Arie Bodek, Univ. of Rochester

  39. Effects of form factors on Cross Section • A comparison of the Q2 distribution using 2 different sets of form factors. • The data are from Baker • The dotted curve uses Dipole Form Factors with mA=1.10 GeV. • The dashed curve uses BBA-2003 Form Factors with mA=1.05 GeV. • The Q2 shapes are the same • However the cross sections differ by 7-8% • Shift in mA – roughly 4% • Nonzero GEN - roughly 3% due • Other vector form factor – roughly 2% at low Q2 Arie Bodek, Univ. of Rochester

  40. Effect of Form Factors on Cross Section • Previously K2K used dipole form factor and set mA=1.11 instead of nominal value of 1.026 • This plot is the ratio of BBA with mA=1 vs dipole with mA =1.11 GeV • This gets the cross section wrong by 12% • Need to use the best set of form factors and constants Arie Bodek, Univ. of Rochester

  41. Extracting the axial form factor I • These plots show the contributions of the form factors to the cross section. • This is d(ds/dq)/dff % change in the cross section vs % change in the form factors • The form factor contribution neutrino is determined by setting the form factors = 0 • The plots show that FA is a major component of the cross section. • Also shows that the difference in GEP between the cross section data and polarization data will have no effect on the cross section. Arie Bodek, Univ. of Rochester

  42. Measure FA(q2) • We solve for FA by writing the cross section as • a(q2,E) FA(q2)2 + b(q2,E)FA(q2) + c(q2,E) • if (ds/dq2)(q2) is the measured cross section we have: • a(q2,E)FA(q2)2 + b(q2,E)FA(q2) + c(q2,E) – (ds/dq2)(q2) = 0 • For a bin q12 to q22 we integrate this equation over the q2 bin and the flux • We bin center the quadratic term and linear term separately and we can pull FA(q2)2 and FA(q2) out of the integral. We can then solve for FA(q2) • Shows calculated value of FA for the previous experiments. • Show result of 4 year Minerna run • Efficiencies and Purity of sample is included. Arie Bodek, Univ. of Rochester

  43. FA/dipole • For Minerna - show GEP for polarization/dipole, FA errors , FA data from other experiments. • For Minerna – show GEP cross section/dipole, FA errors. • Including efficiencies and purities. • Showing our extraction of FA from the deuterium experiments. • Shows that we can determine if FA deviates from a dipole as much as GEP deviates from a dipole. • However, our errors, nuclear corrections, flux etc., will get put into FA. • Is there a check on this? Arie Bodek, Univ. of Rochester

  44. Do we get new informationfrom anti-neutrinos? • d(ds/dq2)/dff is the % change in the cross section vs % change in the form factors • Shows the form factor contributions by setting ff=0 • At Q2 above 2 GeV2 the cross section become insensitive to FA • Therefore at high Q2, the cross section is determined by the electron scattering data and nuclear corrections. • Anti-neutrino data serve as a check on FA. Arie Bodek, Univ. of Rochester

  45. Errors on FA for antineutrinos • The overall errors scale is arbitrary • The errors on FA become large at Q2 around 3 GeV2 when the derivative of the cross section wrt to FA goes to 0 • Bottom plot shows the % reduction in the cross section if FA is reduced by 10% • At Q2 =3 GeV2 the cross section is independent of FA Arie Bodek, Univ. of Rochester

  46. Propane *D-todo 1 Freon D-used OK Freon Pin C C D-usedOK D-used-ok D D-used-ok C C *D-todo 2 Al We should use on 6 D data expts only, Correct for vector form factors And form a new Ma average- Need to add Two more D experiments and have more Fa vs Q2 data. Add 2 P in C expt at high Q2 to look at Fa vesus Q2 Freon Propane summary Arie Bodek, Univ. of Rochester

  47. Neutrino data on Carbon • Carbon ) Measurement Of Neutrino - Proton And Anti-Neutrino - Proton Elastic Scattering. • L.A. Ahrens et al. Print-86-0919 (PENN), BNL-E-734-86-1, (Received Jul 1986). 117pp. • Published in Phys.Rev.D35:785,1987 • TOPCITE = 250+ • References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 251 times | More Info • ADS Abstract Service • Phys. Rev. D Server • EXP BNL-E-0734 | Reaction Data (Durham) | IHEP-Protvino Data • 6) A Study Of The Axial Vector Form-Factor And Second Class Currents In Anti-Neutrino Quasielastic Scattering. • L.A. Ahrens et al. 1988. • Published in Phys.Lett.B202:284-288,1988 • References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 48 times | More Info • ADS Abstract Service • Science Direct • EXP BNL-E-0734 | IHEP-Protvino Data Arie Bodek, Univ. of Rochester

  48. Antineutrino data on Carbon • A study of the axial-vector form factor and second-class currents in antineutrino quasielastic scattering • L. A. Ahrens, S. H. Aronson, B. G. Gibbard, M. J. Murtagh and D. H. White1 • J. L. Callas2, D. Cutts, M. Diwan, J. S. Hoftun and R. E. Lanou • Y. Kurihara3 • K. Abe, K. Amako, S. Kabe, T. Shinkawa and S. Terada • Y. Nagashima, Y. Suzuki and Y. Yamaguchi4 • E. W. Beier, L. S. Durkin5, S. M. Heagy6 and A. K. Mann • D. Hedin7, M. D. Marx and E. Stern8 • Physics Department, Brookhaven national Laboratory, Upton, NY 11973, USA • Department of Physics, Brown University, Providence, RI 02912, USA • Department of Physics, Hiroshima University, Hiroshima 730, Japan • National Laboratory for high Energy Physics (KEK), Tsukuba, Ibaraki-ken 305, Japan • Department of Physics, Osaka University, Toyonaka, Osaka 560, Japan • Department of Physics, University of Pennsylvania, Philadelphia, PA 19104, USA • Department of Physics, State University of New York at Stony Brook, Stony Brook, NY 11794, USA • Received 23 November 1987. Available online 19 December 2002. • Abstract • The antineutrino quasielastic reaction Image has been studied in the Q2 range up to 1.0 (GeV/c)2 at the Brookhaven AGS. The value of the axial vector mass MA in the dipole parametrization of the from factor was determined from the shape of the Q2 distribution to be 1.09±0.03±0.02 GeV/c2. A search for second-class currents was also conducted. No significant effect was found. • 12) Determination Of The Neutrino Fluxes In The Brookhaven Wide Band Beams. • L.A. Ahrens et al. 1986. • Published in Phys.Rev.D34:75-84,1986 • References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 24 times | More Info • ADS Abstract Service • Phys. Rev. D Server • EXP BNL-E-0723 • EXP BNL-E-0734 | IHEP-Protvino Data Arie Bodek, Univ. of Rochester

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