arie bodek university of rochester (in collaboration with r. bradford, h. budd and j. arrington)
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Arie Bodek, Univ. of Rochester 1
Vector and Axial Form Factors Applied to
Neutrino
Quasi-Elastic ScatteringARIE BODEK
University of Rochester(in collaboration with R. Bradford, H. Budd and
J. Arrington)
MILOS
May 2006
Arie Bodek, Univ. of Rochester 2
• 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 MINERA can do• See what information anti-neutrinos can give
Outline
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
Our Constants
BBA2003-Form Factors and our constants
Arie Bodek, Univ. of Rochester 6
Neutron GMN is negative Neutron (GM
N / GM
N dipole )
At low Q2 Ratio to Dipole similar to that nucl-ex/0107016 G. Kubon, et alPhys.Lett. B524 (2002) 26-32
Neutron (GMN / GM
N dipole )
Arie Bodek, Univ. of Rochester 7
Neutron GEN is positive New
Polarization data gives Precise non
zero GEN hep-ph/0202183(2002)
Neutron, GEN is positive -
Imagine N=P+pion cloud
Neutron (GEN / GE
P dipole )
Krutov
(GEN)2
show_gen_new.pict
Galster fit Gen
Arie Bodek, Univ. of Rochester 8
Functional form and Values of BBA2003 Form Factors•GE
P.N (Q2) = {e i q . 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
( )∑
∑+
=
=
+= 2
1
02
1n
k
kk
n
k
kk
b
aqG
τ
τ
( ) ( )22
1QG
b
aQG Den τ
τ
+=
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.
Source: J.J. Kelly, PRC 70 068202 (2004).
Arie Bodek, Univ. of Rochester 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.
( )∑
∑+
=
=
+= 2
1
02
1n
k
kk
n
k
kk
b
aqG
τ
τ 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)
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟
⎟⎠
⎞⎜⎜⎝
⎛
mn
en
mp
ep
GG
G
G
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
udud
F
F
G
G
p
n
mp
mn
+
+≈⎟
⎟⎠
⎞⎜⎜⎝
⎛≈⎟
⎟⎠
⎞⎜⎜⎝
⎛⇒
4
412
2
2
2
We ran with d/u=0, .2, and .5.
( )xfexF ii
i∑= 22
Arie Bodek, Univ. of Rochester 14
Constraint 2
• In the elastic limit: (F2n/F2p)2→(Gmn/Gmp)2
udud
F
F
G
G
p
n
mp
mn
+
+≈⎟
⎟⎠
⎞⎜⎜⎝
⎛≈⎟
⎟⎠
⎞⎜⎜⎝
⎛⇒
4
412
2
2
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 Gmn New constrained fit for Gen
Arie Bodek, Univ. of Rochester 18
Constraints: Gmn/Gmp
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)
Arie Bodek, Univ. of Rochester 19
Constraints: (Gep/Gmp)2=(Gen/Gmn)2`
Arie Bodek, Univ. of Rochester 20
Comparison with Kelly Parameterization
Kelly
BBBA
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)
Observable
a1 a2 b1 b2 b3 b4
Use Kelly for
Gep
Gmp0.0150 ± 0.0312
11.1± 0.103
19.6± 0.281
7.54± 0.967
Gen1.25± 0.368
1.30± 1.99
9.86± 6.46
305± 28.6
-758± 77.5
802± 156
Gmn1.81± 0.402
14.1± 0.597
20.7± 2.54
68.7± 14.1
hep-ex/0602017
Arie Bodek, Univ. of Rochester 23
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 MA= -0.030. So all the
Values for MA from this expt. should be reduced by 0.030
Rextract Fa from neutrino data using updated vector form factors modern ga
Arie Bodek, Univ. of Rochester 24
Do a reanalysis of old neutrino data to get MA to update using latest ga+BBBA2005 form factors.
(note different experiments have different neutrino energySpectra, 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 --> MA = -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 MA = -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 MA VARYING From -0.022 (FNAL energy)
to -0.030 (BNL energy)
Arie Bodek, Univ. of Rochester 25
• 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
Determining mA , Baker et al. – 1981 BNL deuterium
Arie Bodek, Univ. of Rochester 26
• 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
Kitagaki et al. 1983 FNAL deuterium
Arie Bodek, Univ. of Rochester 27
• 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
Barish 1977 et al. ANL deuterium
Arie Bodek, Univ. of Rochester 28
• 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
Miller 1982– ANL deuteriumDESCRIBED EARLIER
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
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
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
Arie Bodek, Univ. of Rochester 31
Hep-ph/0107088 (2001)
Difference in Ma between Electroproduction And neutrinos is understood
-0.029 D
Neutrinos D only corrected 1.016+-0.026-=MA average
From
Neutrino
quasielastic
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 MA we reanalyzed neutrino expt with new gA, and BBBA2005 form factors
-0.029 D
-0.030 D-0.022 D
-0.030 D
-0.030 D
C use for High Q C use for High Q
Freon
Freon
Propane
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
•MINERA can measure FA and determine deviations from the dipole form at high Q2. Can extract FA from neutrino data on d/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
1. Wagenbrum - constituent quark model (valid at intermediate Q2)
2. Bodek - Local duality between elastic and inelastic implies that vector=axial at high Q2
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
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 sectionMost of the cross section for nuclear
targets low
Arie Bodek, Univ. of Rochester 38
Anti-neutrino quasi-elastic cross sectionMostly on nuclear targetsEven with the most update form
factors and nuclear correction, the data is low
Arie Bodek, Univ. of Rochester 39
• 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
Effects of form factors on Cross Section
Arie Bodek, Univ. of Rochester 40
• 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
Effect of Form Factors on Cross Section
Arie Bodek, Univ. of Rochester 41
• 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 FA is a major component of the cross section.
• Also shows that the difference in GE
P between the cross section data and polarization data will have no effect on the cross section.
IExtracting the axial form factor
Arie Bodek, Univ. of Rochester 42
• 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 (d/dq2)(q2) is the measured cross section
we have: • a(q2,E)FA(q2)2 + b(q2,E)FA(q2) +
c(q2,E) – (d/dq2)(q2) = 0 • For a bin q1
2 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 Minera run• Efficiencies and Purity of sample is
included.
Measure FA(q2)
Arie Bodek, Univ. of Rochester 43
• For Minera - show GEP for
polarization/dipole, FA errors , FA data from other experiments.
• For Minera – 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 GE
P deviates from a dipole.
• However, our errors, nuclear corrections, flux etc., will get put into FA.
• Is there a check on this?
FA/dipole
Arie Bodek, Univ. of Rochester 44
• d(d/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.
Do we get new information from anti-neutrinos?
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
Pin CD
Al
FreonPropanesummary
D-used-ok
D-used-ok
D-usedOK
D-used OK
*D-todo 2
*D-todo 1
C
C
C
Freon
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
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
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