Measurement of F2 and sL/sT on Nuclear-Targets in the Nucleon Resonance Region - E03-110 First Stage of a Program to Investigate Quark Hadron Duality in Electron and Neutrino Scattering on Nucleons and Nuclei

1
Measurement of F2 and sL/sT on Nuclear-Targets
in the Nucleon Resonance Region - E03-110First
Stage of a Program to Investigate Quark Hadron
Duality in Electron and Neutrino Scattering on
Nucleons and Nuclei

• A. Bodek (spokesperson), S. Manly, K. McFarland,
  (J. Chovjka, G.B. Yu- PhD students), (D. Koltun,
  L. Orr, S. Rajeev - Collaborating theorists) -
  University of Rochester, Rochester, NY 14627
• M.E. Christy, W. Hinton, C. Keppel
  (spokesperson), E. Segbea - Hampton University,
  Hampton, VA
• P. Bosted, S. E. Rock - University of
  Massachusetts, Amherst, MA
• I. Niculescu - James Madison University,
  Harrisonburg, VA
• R. Ent, D. Gaskell, M. Jones, D. Mack, S. Wood -
  Thomas Jeerson National Accelerator Facility,
  Newport News, VA
• J. Arrington - Argonne National Laboratory,
  Argonne, IL
• H. Gallagher - Tufts University, Medford, MA
• This Presentation in Response to Email from PAC24
  Readers --gt Focus on the Physics, Detailed Run
  Plan in Proposal

2
Neutrino cross sections at low energy?

• Many dedicated neutrino oscillation experiments
  (K2K, MINOS, CNGS, MiniBooNE, and at JHF) are in
  the few GeV region.
• Neutrino cross section models at low energy are
  crucial for precise next generation neutrino
  oscillation experiments.
• The high energy region of neutrino-nucleon
  scatterings (30-300 GeV) is well understood at
  the few percent level in terms of the
  quark-parton mode constrained by data from a
  series of e/m/n DIS experiments.
• However, neutrino cross sections in the low
  energy region are poorly understood. (
  especially, resonance and low Q2 DIS
  contributions).
• Renewed Interest of the High Energy Physics
  Community in QCD/Nucleon Structure at Low
  Energies.

3
Neutrino cross sections at low energy

• Quasi-Elastic / Elastic (WMn)
• nm n m- p
• Input from both Electron and Neutrino Experiments
  and and described by form factors
• Resonance (low Q2, Wlt 2)
• nm p m- p p
• Can be well measured in electon scattering but
  poorly measured in neutrino scattering (fits by
  Rein and Seghal
• Deep Inelastic
• nm p m- X
• well measured in high energy experiments and
  well described by quark-parton model (pQCD with
  NLO PDFs, but doesnt work well at low Q2).

Issues at few GeV

• Resonance scattering and low Q2 DIS contribution
  meet, (difficult to avoid double counting problem
  ).
• Challenge to describe all these three processes
  at all neutrino (or electron) energies.

4
Need to Build up a model for all Q2 for both
nucleon vector and axial structure in electron
and neutrino scattering

• Need to build up a model to describe all Q2 from
  high down to very low energies ?
• DIS, resonance, photo-production(Q20)
• Describe them in terms of quark-parton model, and
  also in terms of elastic and resonance form
  factors
• With PDFS, it is straightforward to convert
  charged-lepton scattering cross sections into
  neutrino cross section. (just matter of different
  couplings)
• With Form Factors, use isospin relations, CVC
  I1/2 and 13/2
• Need Rvector, Raxial and Axial form factors and
  structure functions at low Q2
• Need nuclear effects in vector and axial
  structure functions and form factors

F2
GRV94 LO
Challenges

• Understanding of high x PDFs
• at very low Q2?
• - Requires understanding of non-perturbative
  QCD effects, though SLAC, JLAB data.
• Understanding of Quasielastic resonance
  scattering in terms of quark-parton model, form
  factors (Need to understand duality, QCD, Low Q2
  sum rules, transition between DIS and resonance)

5
How are PDFs Extracted from global fits to High
Q2 Deep Inelastic e/m/n Data
Note additional information on Antiquarks from
Drell-Yan and on Gluons from p-pbar jets also
used.

• MRSR2 PDFs

xq is the probability
that a Parton q carries fractional momentum x
Q2/2Mn in the nucleon (x is the Bjorken
Variable)
At high x, deuteron binding effects introduce an
uncertainty in the d distribution extracted from
F2d data (but not from the W asymmetry data).
XQ2/2Mn Fraction momentum of quark
6
Quasielastic Scattering C.H. Llewellyn Smith
(SLAC). SLAC-PUB-0958 Phys.Rept.3261,1972
Non zero
7
UPDATE Replace by GEV GEP-GEN
UPATE Replace by GMV GMP-GMN
Q2-q2
gA1.267,MA need to Be updated
Fp important for Muon neutrinos only at Very Low
Energy
From C.H. Llewellyn Smith (SLAC). SLAC-PUB-0958
Phys.Rept.3261,1972
8
Resonance Models

• Current Matrix Elements from a Relativistic Quark
  Model - Phys. Rev. D 3, 27062732 (1971)
• R. P. Feynman, M. Kislinger, and F. Ravndal
• Lauritsen Laboratory of Physics, California
  Institute of Technology, Pasadena, California
  91109
• Received 17 December 1970
• A relativistic equation to represent the
  symmetric quark model of hadrons with harmonic
  interaction is used to define and calculate
  matrix elements of vector and axial-vector
  currents. Elements between states with large mass
  differences are too big compared to experiment,
  so a factor whose functional form involves one
  arbitrary constant is introduced to compensate
  this. The vector elements are compared with
  experiments on photoelectric meson production,
  Kl3 decay, and omega --gt pi gamma .
  Pseudoscalar-meson decay widths of hadrons are
  calculated supposing the amplitude is
  proportional (with one new scale constant) to the
  divergence of the axial-vector current matrix
  elements. Starting only from these two constants,
  the slope of the Regge trajectories, and the
  masses of the particles, 75 matrix elements are
  calculated, of which more than 3 / 4 agree with
  the experimental values within 40. The problems
  of extending this calculational scheme to a
  viable physical theory are discussed.
• Resonance Models D. Rein and L. M. Sehgal,
  Annals Phys. 133 79 (1981) D. Rein, Z. Phys. C.
  35, 43 (1987) R. P. Feynman, M. Kislinger and
  F. Ravndal, Phys. Rev. D 3, 2706 (1971).

9
Duality, QCD Sum Rules and Current Algebra Sum
Rules.

• Local duality and Global duality appears to work
  for Q2 gt 1.5 GeV2 in electron scattering This
  is basically a consequence of the fact that
  higher twists are small and QCD sum rules are
  approximately true for Q2 gt 1.5 GeV2 .
• (e.g. momentum sum rule - quarks carry about 1/2
  of the proton momentum) F2P, F2N are related to
  PDFs weighted by quark charges).

10
MRSR2 or CTEQ4M predictions using NLO TM
higher twist describe the data reasonably well -
Bodek/Yang Phys. Rev. Lett 82, 2467 (1999)
Phys. Rev. Lett. 84, 3456 (2000)
F2
R
11
Very high x F2 proton data (DIS resonance)(not
included in the original fits Q21. 5 to 25 GeV2)
Q2 25 GeV2 Ratio F2data/F2pQCD
F2 resonance Data versus F2pQCDTMHT
Q2 1. 5 GeV2
pQCD ONLY
Q2 3 GeV2
Q2 25 GeV2 Ratio F2data/ F2pQCDTM
pQCDTM
Q2 15 GeV2
Q2 9 GeV2
Q2 25 GeV2 Ratio F2data/F2pQCDTMHT
pQCDTMHT
Q2 25 GeV2
pQCDTMHT
x ????
x ????
Aw (w, Q2 ) will account for interactions with
spectator quarks

• (Bodek/Yang) NLO pQCD x TM higher twist
  describes very high x DIS F2 and resonance F2
  data well. (duality works) Q21. 5 to 25 GeV2

12
F2, R comparison with NNLO QCD (Bodek/Yang)
Eur. Phys. J. C13, 241 (2000)
Size of the higher twist effect with NNLO
analysis is really small (a2-0.009(NNLO) vs
0.1(NLO)
13
When does duality break down Momentum Sum Rule
has QCDnon- Perturbative Corrections (breaks
down at Q20) but ADLER sum rule is EXACT
(number of Uv minus number of Dv is 1 down to
Q20).
Q2 0.07 GeV2
Q2 0.22 GeV2
Elastic peak
Q2 0.8 5 GeV2
Q2 1. 4 GeV2
Q2 9 GeV2
DIS high Q2 Integral F2p
Q2 3 GeV2

• In proton
• QPM Integral of F2p
• 0.17(1/3)20.34(2/3)2 0.17 (In
  neutron0.11)
• Where we use the fact that
• 50 carried by gluon
• 34 u and 17 d quarks

Q2 1 5 GeV2
Q2 2 5 GeV2
Adler sum rule (valid to Q20) is the integral Of
the difference of F2/x for Antineutrinos and
Neutrinos on protons (including elastic)
14
Note that in electron scattering the quark
charges remain But at Q20, the neutron elastic
form factor is zero)
Momentum sum rule breaks down and all QCD sum
rules break down below Q21. However. the Adler
sum rule, which comes from Current Algebra (which
includes the elastic part) is exact and is equal
to the NUMBER of Uv-Dv 1. -gt (F2(x)/x) . It is
valid all the way to Q20.
F2(elastic) proton
F2(elastic) Neutron
Q2
15
Tests of Local Duality at high x, high Q2 vs.
Q20 Electron Scattering Case

• INELASTIC High Q2 x--gt1.
• QCD at High Q2 Note d refers to d quark in the
  proton, which is the same as u in the neutron.
  d/u0.2 x1.
• F2 (e-P) (4/9)u(1/9)d (4/91/45) u (21/45)
  u
• F2(e-N) (4/9)d(1/9)u (4/455/45) u (9/45)
  u
• DIS LIMIT High Q2
• F2(e-N) /F2 (e-P) 9/210.43

• Elastic/quasielastic resonance at high Q2
  dominated by magnetic form factors which have a
  dipole form factor times the magnetic moment
• F2 (e-P) A G2MP(el) BG2MP (res c1)
• F2 (e-N) AG2MN (el) BG2MN (res c0)
• TAKE ELASTIC TERM ONLY
• F2(e-N) /F2 (e-P) (elastic High Q2)
• ?2? N ?? ?2? P ????????????????? 2 0.47
• Close if we just take the elastic/quasielastic
  x1 term.
• Different at low Q2, where Gep,Gen dominate.
• F2(e-N) /F2 (e-P) (Q20) 0 Since Gep0.

Q2 0 Limit
16
On neutrons both quasielastic And resonanceDIS
production possible.
NEUTRINOS Only scatter on d quarks
m-
?
m-
?
NEUTRINOS On Neutrons
? - d
W
W
u 2/3 possible
d -1/3
Puud or Res Both quasiRes
Nudd
m-
?
m-
?
W
NEUTRINOS On Protons
? - u
W
???? uuu Res only state
Puud
Not possible 5/3
u 2/3
On protons only resonance DIS production
possible.
17
On neutrons both quasielastic And resonanceDIS
production possible. First resonance has
different mixtures of I3/2 And I1/2 terms.
Neutrino and electron induced production are
Better related using Clebsch Gordon Coeff.. (Rein
Seghal model etc)
NEUTRINOS On nucleons
m-
?
m-
?
NEUTRINOS On Neutrons

W
Puud or ?? Both quasiRes
X 1 quasielastic
Nudd
1st reson
m-
?
0
W
NEUTRINOS On Protons
???? uuu Res only state
Puud
X 1 zero
On protons only resonance DIS production
possible.
1st reson
18
On Protons both quasielastic And resonanceDIS
production possible.
ANTI-NEUTRINOS Only scatter on u quarks
m
? bar
m
? bar
ANTINEUTRINOS On Protons
W-
W-
d -1/3
u 2/3
Nudd or ??
Puud
m?
? bar
m
? bar
ANTINEUTRINOS On Neutrons
W-
W-
??? ddd
Nudd
Not possible
d
On Neutrons only resonance DIS production
possible.
-1/3
-4/3
19
Tests of Local Duality at high x, High Q2
Neutrino Charged Current Scattering Case

• Elastic/quasielastic resonance at high Q2
  dominated by magnetic form factors which have a
  dipole form factor times the magnetic moment
• F2 (? -P) -gt A 0 (no quasiel) B(Resonance
  c2)
• F2(? -N) -gt A Gm ( ? quasiel) B(Resonance
  c1)
• F2 (? bar -P) -gt A Gm ( ? quasiel) B(Resonance
  c0)
• F2(? bar-N) -gt A 0( no quasiel) B(Resonance
  c-1)
• Quasi ELASTIC TERM ONLY
• F2(? -P) /F2 (? -N) 0
• F2(? -P) /F2 (? bar-P) 0
• F2(? -P) / F2(? bar-N) 0/0
• F2(? -N) /F2 (? bar-P) 1
• FAILS TEST MUST TRY TO COMBINE Quasielastic and
  first resonance)

• INELASTIC High Q2, x--gt1. QCD at High Q2 Note
  d refers to d quark in the proton, which is the
  same as u in the neutron. d/u0.2 x1.
• F2 (? -P) 2xd
• F2(? -N) 2xu
• F2 (? bar -P) 2xu
• F2(? bar-N) 2xd
• In the DIS LIMIT
• F2(? -P) /F2 (? -N) d/u 0.2
• F2(? -P) /F2 (? bar-P) d/u0.2
• F2(? -P) / F2(? bar-N) 1
• F2(? -N) /F2 (? bar-P) 1

20
Adler Sum rule EXACT all the way down to Q20
includes W2 quasi-elastic S. Adler, Phys. Rev.
143, 1144 (1966) Exact Sum rules from Current
Algebra. Valid at all Q2 from zero to infinity.

• b- W2 (Anti-neutrino -Proton)
• b W2 (Neutrino-Proton) q0n

AXIAL Vector part of W2
gA(Q2) 1.267 at Q20 gA(Q2) 0 at Q20
Adler is a number sum rule at high Q2
1 is
Vector(Q2)1 at Q20 Vector (Q2) 0 at high Q2
F2- F2 (Anti-neutrino -Proton) n W2
?F2 F2 (Neutrino-Proton) n W2 we use
d ?q0) d (n????? n )d ??????
Vector Part of W2
see Bodek and Yang hep-ex/0203009 and
references therein
at fixed q2 Q2
21
S. Adler, Phys. Rev. 143, 1144 (1966) Exact Sum
rules from Current Algebra. Valid at all Q2 from
zero to infinity.
22
b- W2 (Anti-neutrino -Proton) b
W2 (Neutrino-Proton) q0n
?- W1 (Anti-neutrino -Proton) ?
W1 (Neutrino-Proton)
?- W3 (Anti-neutrino -Proton) ?
W3 (Neutrino-Proton)
W1 Sum rules, and others on this page have not
been investigated.
23
F. Gillman, Phys. Rev. 167, 1365 (1968) Adler
like Sum rules for electron scattering.
24

• Outline of Multi-Year Program Starting with
  E03-110
• Update Vector form factors and Rvector of the
  large number of resonances in the
  Rein-Seghal-Feynman Quark Oscillator model by
  fitting all F2 and R Electron Resonance data
  (SLAC photoproduction) and new Jlab Datafrom
  E02-109 on for H and D E94-110, E02-109
• Improve on Inelastic continuum in for vector F2
  and R using a formalism like Bodek/Yang (next few
  slides) with Jlab H and D data and
  photoproduction
• Convert EM Vector to Weak Vector form factors -
  use the Various isospin rules I1/2 and I3/2
  of elastic, resonance and inealstic form Factors
  (using (H and D data) E94-110, E02-109
• Check that Models fitted for Vector scattering
  satisfy Adler Vector sum rules (reasonable
  Quasielsatic and high Q2 DIS data, but poorer
  resonances And low Q2 DIS data exist(H and D) -
  E94-110, E02-109
• Check that the Models assumptions/parameters for
  Axial scattering satisfy the Adler Axial sum
  rules (H and D). E94-110, E02-109
• Apply nuclear corrections for DIS and resonance
  region to predict Neutrino and Antineutrino data
  on nuclei from E03-110 - Requires 5 days of
  running and also use E99-118 and SLAC E140. for
  DIS
• Compare to existing low statistics neutrino data
  and to new precise neutrino data to become
  available available in a couple of years
  (MINERva, and JHF- Japan)
• In parallel - Final states in nuclear targets to
  be investigated in a collaboration with Hall B
  experiments.

25
Example Modeling of Continuum Region

• Modeling in Leading Order from Q20 to very high
  Q2
• A. Bodek and U. K.Yang, hep-ex/0203009,
  Nucl.Phys.Proc.Suppl. 11270-76,2002. - GRV98
  and x w
• A. Bodek and U. K.Yang, hep-ex/0301036 - GRV98
  and x w
• Bodek, U. K. Yang, hep-ex/0210024 , J. Phys. G.
  Nucl. Part. Phys. 29, 1 (2003) - GRV94 and Xw
• Based on QCD NLO and NNLO studies for Q2gt1 GeV2
• Studies in NLO TM HT - Yang and Bodek Phys.
  Rev. Lett 82, 2467 (1999) Phys. Rev. Lett. 84,
  3456 (2000)
• Studies in NNLO TM HT - Yang and Bodek Eur.
  Phys. J. C13, 241 (2000))

26
Initial quark mass m I and final mass ,mFm
bound in a proton of mass M -- Summary INCLUDE
quark initial Pt) Get x scaling (not xQ2/2Mn
)for a general parton Model
qq3,q0

• x Is the correct variable which is Invariant in
  any frame q3 and P in opposite directions.

• x

PF PF0,PF3,mFm
PF PI0,PI3,mI
P P0 P3,M
Special cases (1) Bjorken x, xBJQ2/2Mn?,? x,
-gt x ?For m F 2 m I 2 0 and High n2, (2)
Numerator m F 2 Slow Rescaling x as in charm
production (3) Denominator Target mass
term ???x? Nachtman Variable x Light Cone
Variable x Georgi Politzer Target Mass
var. (all the same x )

• Most General Case (Derivation in Appendix)
• ????????x w Q2 B / Mn (1(1Q2/n2)
  ) 1/2 A (with A0, B0)
• where 2Q2 Q2 m F 2 - m I 2 ( Q2m F 2
  - m I 2 ) 2 4Q2 (m I 2 P2t) 1/2
• Bodek-Yang Add B and A to account for effects
  of additional ? m2
• from NLO and NNLO (up to infinite order) QCD
  effects. For case x w with P2t 0
• see R. Barbieri et al Phys. Lett. 64B, 1717
  (1976) and Nucl. Phys. B117, 50 (1976)

27
Pseudo NLO approach

• Original approach (NNLO QCDTM) was to
  explain the non-perturbative QCD effects at low
  Q2, but now we reverse the approach Use LO PDFs
  and effective target mass and final state
  masses to account for initial target mass, final
  target mass, and missing higher orders

q
mfM (final state interaction)
PM
Resonance, higher twist, and TM
x
Q2mf2O(mf2-mi2)
Xbj Q2 /2 Mn
Mn (1(1Q2/n2) ) 1/2
A initial binding/target mass effect
plus higher order terms B final state mass mf2 ,
Dm2, and photo- production limit (Q2 0)
x w Q2B / Mn (1(1Q2/n2)1/2 ) A
28
Modified GRV98 PDFs
Fit with xw and Kval and Ksea
Only 5 parameters for all DIS data at all Q2
A, B, Csea, C2V and C1V

• Different K factors for valence and sea
• Ksea Q2/Q2Csea
• Kval 1- GD 2 (Q2)
• Q2C2V / Q2C1V
• where GD2 (Q2) 1/ 1Q2 / 0.71 4
• (elastic nucleon dipole form factor
  )
• (Form Motivated by Adler Sum Rule)
• Do a fit to SLAC/NMC/BCDMS F2 P, D low x
  HERA/NMC F2 data. Very good fits are obtained
• A0.418, B0.222, Csea 0.381
• C1V 0.604, C2V 0.485
• ?2/DOF 1268 / 1200

• 1. GRV98 LO (Q2min0.80 GeV2 )
• - describe F2 data at high Q2
• 2. Replace the X with a new scaling, X Q2 /
  2Mn
• xw Q2B / Mn (1(1Q2/n2)1/2 ) A
• 3. Multiply all PDFs by a K factor of for photo
  prod. limit and higher twist
• s(g) 4pa/Q2 F2(xw, Q2)
• 4. Freeze the evolution at Q2 Q2min
• - F2(x, Q2 lt 0.80) K F2(xw, Q20.80)

29
?2 1268 / 1200 DOF DashedGRV98LO QCD F2 F2QCD
(x,Q2) Solidmodified GRV98LO QCD F2 K(Q2)
F2QCD(x w, Q2) SLAC, NMC,BCDMS (H,D)
HERA 94 Data ep
Fit with xw modified GRV98 PDFs
30
Fit with xw Predictions modified GRV98 PDFs
Photo-production (P)
F2(P) resonance
Neutrino Xsection on iron at 55GeV (CCFR)
31
Fit with xw Predictions modified GRV98 PDFs
F2(d) resonance
Photo-production (d)
32
Correct for Nuclear Effects measured in e/m expt.
Comparison of Fe/D F2 data In resonance region
(JLAB) Versus DIS SLAC/NMC data In ?TM (However,
what happens At low Q2? Is it versus ?W ).
33
From D. Casper, UC Irvine K2K NUANCE MC 2003
W, Final Hadronic Mass Comparison on Water
------ Bodek/Yang modified x?w scaling GRV98
PDFs 2003
En2 GeV
------ D. Rein and L. M. Sehgal, Annals Phys.
133, 79 (1981) Resonance Non Resonance model
En3 GeV
En5 GeV
34
Q2 Comparison on Water
------ Bodek/Yang modified x?w scaling GRV98
PDFs 2003 First assume VA V0 at Q20
------ D. Rein and L. M. Sehgal, Annals Phys.
133, 79 (1981) Resonance Non Resonance
model Vector not equal Axial At Very low
Q2 Ga1.27 Gv1.0
35
DIS Resonance Summary and Plan (Bodek/Yang)

• Our modified GRV98LO PDFs with the scaling
  variable ?w describe all SLAC/BCDMS/NMC/HERA
  DIS data.
• Predictions in resonable agreement with resonance
  data (down to Q2 0) , photo-production data,
  and with high-energy neutrino data on iron.
• This model should also describe a low energy
  neutrino cross sections reasonably well.
  However, need separate modeling of quasielastic
  and resonance region especially in the Delta
  region, AND Axial contribution

Things can be learned from electron scattering
Things cant be added from electron scattering

• Resonance form factors, A(w) from Jlab data.
• Nuclear effects on various targets in res, and
  quasielastic region
• Rvectror sL/sT

• Axial vector contribution at low Q2
• Different nuclear effects in neutrino scatt.
• Raxial different from Rvector

Collaborative approach between High Energy and
Nuclear Physics community
High x and low Q2 PDFs for e/neutrino, resonance
form factors, nuclear corrections 1.Electron
scattering exp. at JLAB E03-110 - 5 Days of DATA
and -gt Lots of analysis 2.New Near Detector
neutrino exp. at Fermilab-NUMI/JHF - --gtYears of
data MINERVA
36
References
Sum Rules S. L. Adler, Phys. Rev. 143, 1144
(1966) F. Gilman, Phys. Rev. 167, 1365
(1968). Resonance Models D. Rein and L. M.
Sehgal, Annals Phys. 133 79 (1981) D. Rein, Z.
Phys. C. 35, 43 (1987) R. P. Feynman, M.
Kislinger and F. Ravndal, Phys. Rev. D 3, 2706
(1971). Coherent nuclear effects. R. Belusevic
and D. Rein, Phys. Rev. D 46, 3747
(1992) Modeling A. Bodek and U. K.Yang,
hep-ex/0203009, Nucl.Phys.Proc.Suppl.11270-76,200
2. A. Bodek and U. K.Yang, hep-ex/0301036 A.
Bodek, U. K. Yang, hep-ex/0210024 , J. Phys. G.
Nucl. Part. Phys. 29, 1 (2003) and references
therein.
37
Backup Slides of Neutrino data at low Energy
38
What about the fact that Adler sum rule is for
Uv-Dv as measured in vector and axial scattering,
on light quarks, what about Strangeness Changing

• One could gets the factors for Dv and Uv
  separately by using the Adler sum rules for the
  STRANGNESS CHANGING (DS-1 proportional to sin2
  of the Cabbibo angle )(where he gets 4, 2) if
  one knew the Lambda and Sigma form factors (F1v,
  F2v, Fa) as follows. Each gives vector and axial
  parts here cosTC and SinTc are for the Cabbibo
  Angle.
• F2nub-p (DS0)/cosTc u dbar (has Neutron
  final state udd quasielastic)
• F2nu-p (DS0)/(costTc d ubar (only
  inelastic final states continuum only)
• F2nub-p (DS-1)/sinTc u sbar (has Lambda and
  Sigma0 uds quasielastic)
• F2nu-p (DS-1)/sinTc s ubar (making uud sbar
  continuum only))
• F2nub-n (DS-1) d sbar (has Sigma- dds
  quasielastic)
• F2nu-n (DS-1)s ubar (making udd sbar
  continuum only))
• A. strangeness conserving is Equations 1 minus 2
  Uv-DV 1V1A 2 (and at Q20 has Neutron
  quasielastic final state) (one for vector and
  one for axial)
• B. strangeness changing on neutrons is
  Equation 5 minus 6 Dv 1V1A 2(and at Q20
  has Sigma- quasielastic)
• strangeness changing on protons is Equation 3
  minus 4 Uv 2V2A 4 (and at Q20 has both
  Lambda0 and Sigma0 qausielastic.
• Note according to Physics reports article of
  Llwellyn Simth - DeltaI1/2 rule has cross
  section for Simga0 at half the value of Sigma).
  

.
39
Examples of Current Low Energy Neutrino Data
Quasi-elastic cross section
?tot/E
40
Examples of Low Energy Neutrino Data Total
(inelastic and quasielastic) cross section

• E GeV

41
Examples of Current Low Energy Neutrino Data
Single charged and neutral pion production
Old bubble chamber language
42
Reanalysis of
43
?quasi-elastic neutrinos on Neutrons-( -
Calculated ?quasi-elastic Antineutrinos on
Protons - Calculated From H. Budd -U of
Rochester (NuInt02) (with Bodek and Arrington)
DATA - FLUX ERRORS ARE 10
Even with the most Up to date Form Factors The
agreement With data is not spectacular
Antineutrino data mostly on nuclear targets-
Nuclear Effects are important
44
Backup Slides on Importance for Neutrino
Experiments
45
nm Charged Current Processes is of Interest
Charged - Current both differential cross
sections and final states

• Neutrino mass DM2 -gt Charged Current Cross
  Sections and Final States are needed
• The level of neutrino charged current cross
  sections versus energy provide the baseline
  against which one measures DM2 at the oscillation
  maximum.

• Measurement of the neutrino energy in a detector
  depends on the composition of the final states
  (different response to charged and neutral pions,
  muons and final state protons (e.g. Cerenkov
  threshold, non compensating calorimeters etc).

??muon response
??
W
??0 EM shower EM response
N
N nucleon response
?? response
46
Nm Neutral Current Processes is of Interest
Neutral - Current both differential cross
sections and final states

• SIGNAL ?????e transition 0.1 oscillations
  probability of ????? e.

• Backgrounds Neutral Current Cross Sections and
  Final State Composition are needed
• Electrons from Misidentified ??? in NC events
  without a muon from higher energy neutrinos are a
  background

e- -gt EM shower
? m ?? ? e in beam
W
??
N
??
P
??
Z
??
??
Z
??0 EM shower FAKE electron
N
N
??0
N
N
background
SIGNAL ??
47
Importance of Precision Measurements of
P(nm-gtne) Oscillation Probability with nm and
nm Superbeams
?

• Conventional superbeams of both signs (e.g.
  NUMI) will be our only windows into this
  suppressed transition
• Analogous to Vub in quark sector (CP phase
  d?could be origin of matter-antimatter asymmetry
  in the universe?
• (The next steps m sources or b beams are too
  far away)

Studying P(nm-gtne) in neutrinos and
anti-neutrinos gives us magnitude and phase
information on Ue3 http//www-numi.fnal.gov/fnal
_minos/ new_initiatives/loi.html A.Para-NUMI
off-axis http//www-jhf.kek.jp/NP02 K.
Nishikawa JHF off-axis http//www.pas.rochester.ed
u/ksmcf/eoi.pdf K. McFarland (Rochester) -
off-axis near detector NUMI http//home.fnal.gov/
morfin/midis/midis_eoi.pdf). J. Morfin (FNAL-
)Low E neutrino reactions in an on-axis near
detector at MINOS/NUMI
nm
nm
48
Event Spectra in NUMI Near Off-Axis, Near
On-Axis and Far Detectors (The miracle of the
off-axis beam is a nearly mono-energetic neutrino
beam making future precision neutrino
oscillations experiments possible for the first
time
Far 0.7o OA
Far 0.7o OA
Near 0.7o OA (LE)
Near On-Axis (LE)
Near 0.7o OA (ME)
Near On-Axis (ME)
1 2 3 4 5 6 GeV Neutrino
Energy
1 2 3 4 5 6 GeV Neutrino
Energy