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Arie Bodek, Univ. of Rochester1 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

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Arie Bodek, Univ. of Rochester2 Review of BBA2003 and BBBA2005 vector-form factors from electron scattering Reanalyze the previous neutrino-deuterium quasi- elastic data by calculating M A with their assumptions and with BBBA2006-form factor to extract a new value of M A Compare to M A from pion electro-production Use the previous deuterium quasi-elastic data to extract F A and compare axial form factor to models Future: Look at what MINER A can do See what information anti-neutrinos can give Outline

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Arie Bodek, Univ. of Rochester3 Vector and axial form factors

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Arie Bodek, Univ. of Rochester4 Vector Axial dipole approx Vector dipole approx

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Arie Bodek, Univ. of Rochester5 Our Constants BBA2003-Form Factors and our constants

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Arie Bodek, Univ. of Rochester6 Neutron G M N is negative Neutron (G M N / G M N dipole ) At low Q2 Ratio to Dipole similar to that nucl-ex/0107016 G. Kubon, et al Phys.Lett. B524 (2002) 26-32 Neutron (G M N / G M N dipole )

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Arie Bodek, Univ. of Rochester7 Neutron G E N is positive New Polarization data gives Precise non zero G E N hep-ph/0202183(2002) Neutron, G E N is positive - Imagine N=P+pion cloud Neutron (G E N / G E P dipole ) Krutov (G E N ) 2 show_gen_new.pict Galster fit Gen

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Arie Bodek, Univ. of Rochester8 Functional form and Values of BBA2003 Form Factors G E P.N (Q 2 ) = {e i q. r (r) d 3 r } = 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

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Arie Bodek, Univ. of Rochester9 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 Q 2 ): --> introduce some theory constraints G ep, G mp, and G mn But uses old form for Gen

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Arie Bodek, Univ. of Rochester10 Kelly Parameterization Still not very well constrained at high Q2. Source: J.J. Kelly, PRC 70 068202 (2004).

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Arie Bodek, Univ. of Rochester11 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 Q 2 ): use a 0 =1 for G ep, G mp, G mn, and a 0 =0 for G en. Employs 2 additional constraints from duality to have a more constrained description at high Q 2. 4 parameters for G ep, G mp, and G mn. 6 parameters for G en.

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Arie Bodek, Univ. of Rochester12 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 G en > 0 continues on to high Q 2. 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 Q 2.

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Arie Bodek, Univ. of Rochester13 Constraint 2: From local duality: F 2n /F 2p for Inelastic and Elastic scattering should be the same at high Q 2 In the limit of →∞, Q 2 →∞, and fixed x: In the elastic limit: (F 2n /F 2p ) 2 →(G mn /G mp ) 2 We ran with d/u=0,.2, and.5.

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Arie Bodek, Univ. of Rochester14 Constraint 2 In the elastic limit: (F 2n /F 2p ) 2 →(G mn /G mp ) 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)

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Arie Bodek, Univ. of Rochester15 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

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Arie Bodek, Univ. of Rochester16 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 G en >0 and G en <0 at high Q 2. Our preferred parameterization is for –G en > 0 at high Q 2 –d/u=.2, so (G mn /G mp )=.42857 (if d/u=.2 as expected from QCD) Following figures based on preferred parameterization.

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Arie Bodek, Univ. of Rochester17 Results BBBA2005: use Kelly fit for G ep ; use New fit for G mp, New constrained fit for G mn New constrained fit for Gen

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Arie Bodek, Univ. of Rochester18 Constraints: G mn /G mp 0.42875 (d/u=0.2) 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? 0.25 (d/u=0.0)

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Arie Bodek, Univ. of Rochester19 Constraints: (G ep /G mp ) 2 =(G en /G mn ) 2`

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Arie Bodek, Univ. of Rochester20 Comparison with Kelly Parameterization Kelly BBBA

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Arie Bodek, Univ. of Rochester21 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 Q 2 (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)

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Arie Bodek, Univ. of Rochester22 BBBA2005 Fit Parameters (Gen>0, d/u=0.2) Observable a1a1 a2a2 b1b1 b2b2 b3b3 b4b4 Use Kelly for G ep G mp 0.0150 ± 0.0312 11.1 ± 0.103 19.6 ± 0.281 7.54 ± 0.967 G en 1.25 ± 0.368 1.30 ± 1.99 9.86 ± 6.46 305 ± 28.6 -758 ± 77.5 802 ± 156 G mn 1.81 ± 0.402 14.1 ± 0.597 20.7 ± 2.54 68.7 ± 14.1 hep-ex/0602017

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Arie Bodek, Univ. of Rochester23 Miller 1982: We type in their d /dQ2 histogram. Fit with our best Knowledge of their parameters : Get M A =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 g a, then we get M A =1.086+-0.05 or M A = -0.030. So all the Values for M A from this expt. should be reduced by 0.030 Rextract F a from neutrino data using updated vector form factors modern g a

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Arie Bodek, Univ. of Rochester24 Do a reanalysis of old neutrino data to get M A 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 --> M A = -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 M A = -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 M A VARYING From -0.022 (FNAL energy) to -0.030 (BNL energy)

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Arie Bodek, Univ. of Rochester25 The dotted curve shows their calculation using their fit value of 1.07 GeV They do unbinned likelyhood to get M A No shape fit Their data and their curve is taken from the paper of Baker et al. The dashed curve shows our calculation using M A = 1.07 GeV using their assumptions The 2 calculations agree. If we do shape fit to get M A With their assumptions -- M A =1.079 GeV We agree with their value of M A If we fit with BBA Form Factors and our constants - M A =1.050 GeV. Therefore, we must shift their value of M A 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 Determining m A, Baker et al. – 1981 BNL deuterium

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Arie Bodek, Univ. of Rochester26 The dotted curve shows their calculation using their fit value of M A =1.05 GeV They do unbinned likelyhood, no shape fit. The dashed curve shows our calculation using M A =1.05 GeV and their assumptions The solid curve is our calculation using their fit value M A =1.05 GeV The dash curve is our calculation using our fit value of M A =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 M A =1.172 GeV when we fit with our assumptions Hence, -0.022 GeV should be subtracted from their M A. They used Ga=-1.23 and Ollson Form factors Kitagaki et al. 1983 FNAL deuterium

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Arie Bodek, Univ. of Rochester27 Dotted curve – their calculation M A =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 M A =1.075 GeV. We slightly disagree with their fit value. We get M A =1.046 GeV when we fit with BBA2005 – Form Factors and our constants. Hence, -0.029 GeV must be subtracted from their value of M A They used Ga=-1.23 and Ollson Form factors Barish 1977 et al. ANL deuterium

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Arie Bodek, Univ. of Rochester28 Miller is an updated version of Barish with 3 times the data The dotted curve – their calculation taken from their Q 2 distribution figure, M A =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 M A is 1.05 Dotted is their calculation using their best shape M A Our M A 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 Miller 1982– ANL deuterium DESCRIBED EARLIER

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Arie Bodek, Univ. of Rochester29 Kitagaki 1990 They used Ollson, Mv=0.84 and Ga=-1.254. We get that Ma should be corrected by -0.031 GeV

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Arie Bodek, Univ. of Rochester30 Summary of Results for 5 neutrino experiments on Deuterium 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 M A Get: Average Deuterium Corrected --> M A = 1.016+-0.026 Vs. Average Pion Electro-production Corrected--> M A = 1.014+-0.016 FNAL 1.039+-0.06, 0.981+-0.09, 1.02+-0.05, 1.028+-0.14, 1.039+-0.043 0.898+-0.076 Updated value

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Arie Bodek, Univ. of Rochester31 Hep-ph/0107088 (2001) Difference in Ma between Electroproduction And neutrinos is understood -0.029 D Neutrinos D only corrected 1.016+-0.026-=M A average From Neutrino quasielasti c From charged Pion Electroproduction Average value of 1.069->1.014 when corrected for theory hadronic effects to compare to neutrino reactions =1.014 +_0.016 when corrected for hadronic effects For updated M A we reanalyzed neutrino expt with new g A, and BBBA2005 form factors -0.029 D -0.030 D -0.022 D -0.030 D C use for High Q Freon Propane

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Arie Bodek, Univ. of Rochester32 Conclusion of Reanalysis of neutrino data Using BBBA2005-form factors we derive a new value of m A = 1.016 GeV+-0.026 From the world average of Neutrino expt. On Deuterium agrees with the results from pion electroproduction: m A = 1.014+-0.016 GeV We now understand the Low Q2 behavior of F A ~7-8% effect on the neutrino cross section from the new value m A and with the updated vector form factors MINER A can measure F A and determine deviations from the dipole form at high Q2. Can extract F A from neutrino data on d /dq 2 The anti-neutrinos at high Q 2 serves as a check on F A

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Arie Bodek, Univ. of Rochester33 Theory predictions for F A some calculations predict that F A is may be larger than the Dipole predictions at high Q 2 1.Wagenbrum - constituent quark model (valid at intermediate Q 2 ) 2.Bodek - Local duality between elastic and inelastic implies that vector=axial at high Q 2 3.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 F A /Dipole

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Arie Bodek, Univ. of Rochester34 Current Neutrino data on F A vs MINERvA For inelastic (quarks) axial=vector Therefore, local duality implies that At high Q 2, 2xF 1 - elastic Axial and Vector are the same. Note both F 2 and 2xF 1 - elastic Axial and Vector are the same at high Q2 - when R-->0.

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Arie Bodek, Univ. of Rochester35 Supplemental Slides

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Arie Bodek, Univ. of Rochester36 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 Q 2 < 1 Binding effects on form factors expected to be small at high Q 2.

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Arie Bodek, Univ. of Rochester37 Neutrino quasi-elastic cross section Most of the cross section for nuclear targets low

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Arie Bodek, Univ. of Rochester38 Anti-neutrino quasi-elastic cross section Mostly on nuclear targets Even with the most update form factors and nuclear correction, the data is low

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Arie Bodek, Univ. of Rochester39 A comparison of the Q 2 distribution using 2 different sets of form factors. The data are from Baker The dotted curve uses Dipole Form Factors with m A =1.10 GeV. The dashed curve uses BBA-2003 Form Factors with m A =1.05 GeV. The Q 2 shapes are the same However the cross sections differ by 7-8% Shift in m A – roughly 4% Nonzero GEN - roughly 3% due Other vector form factor – roughly 2% at low Q 2 Effects of form factors on Cross Section

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Arie Bodek, Univ. of Rochester40 Previously K2K used dipole form factor and set m A =1.11 instead of nominal value of 1.026 This plot is the ratio of BBA with m A =1 vs dipole with m A =1.11 GeV This gets the cross section wrong by 12% Need to use the best set of form factors and constants Effect of Form Factors on Cross Section

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Arie Bodek, Univ. of Rochester41 These plots show the contributions of the form factors to the cross section. This is d(d /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 F A is a major component of the cross section. Also shows that the difference in G E P between the cross section data and polarization data will have no effect on the cross section. I Extracting the axial form factor

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Arie Bodek, Univ. of Rochester42 We solve for F A by writing the cross section as a(q 2,E) F A (q 2 ) 2 + b(q 2,E)F A (q 2 ) + c(q 2,E) if (d /dq 2 )(q 2 ) is the measured cross section we have : a(q 2,E)F A (q 2 ) 2 + b(q 2,E)F A (q 2 ) + c(q 2,E) – (d /dq 2 )(q 2 ) = 0 For a bin q 1 2 to q 2 2 we integrate this equation over the q 2 bin and the flux We bin center the quadratic term and linear term separately and we can pull F A (q 2 ) 2 and F A (q 2 ) out of the integral. We can then solve for F A (q 2 ) Shows calculated value of F A for the previous experiments. Show result of 4 year Miner a run Efficiencies and Purity of sample is included. Measure F A (q 2 )

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Arie Bodek, Univ. of Rochester43 For Miner a - show G E P for polarization/dipole, F A errors, F A data from other experiments. For Miner a – show G E P cross section/dipole, F A errors. Including efficiencies and purities. Showing our extraction of F A from the deuterium experiments. Shows that we can determine if F A deviates from a dipole as much as G E P deviates from a dipole. However, our errors, nuclear corrections, flux etc., will get put into F A. Is there a check on this? F A /dipole

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Arie Bodek, Univ. of Rochester44 d(d /dq 2 )/dff is the % change in the cross section vs % change in the form factors Shows the form factor contributions by setting ff=0 At Q 2 above 2 GeV 2 the cross section become insensitive to F A Therefore at high Q 2, the cross section is determined by the electron scattering data and nuclear corrections. Anti-neutrino data serve as a check on F A. Do we get new information from anti-neutrinos?

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Arie Bodek, Univ. of Rochester45 Errors on F A for antineutrinos The overall errors scale is arbitrary The errors on F A become large at Q 2 around 3 GeV 2 when the derivative of the cross section wrt to F A goes to 0 Bottom plot shows the % reduction in the cross section if F A is reduced by 10% At Q 2 =3 GeV 2 the cross section is independent of F A

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Arie Bodek, Univ. of Rochester46 Pin C D Al Freon Propane summary D-used-ok D-usedOK *D-todo 2 *D-todo 1 C C C Freon Propane 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

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Arie Bodek, Univ. of Rochester47 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

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Arie Bodek, Univ. of Rochester48 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

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