1. Hadron-structure studies at a neutrino factory
Shunzo Kumano
Saga University
Talk at the workshop on neutrino factory
Sept , 2000, KEK, Japan
Sept. 14, 2000

2. - Contents - (1) Introduction: current status on
unpolarized parton distributions
(2) What can be done at a neutrino
factory?
(3) Summary
References

3. Introduction: current status
Parton distributions are determined
by fitting various experimental data.
electron/muon
neutrino
Drell-Yan
direct photon
...
(1)
(3)
(2)

4. Available data for determining
parton distributions
(Ref. MRST, hep/ph ) 

5. Determination of each distribution Valence quark
neutrino deep inelastic scattering

6. Sea quark e/ scattering Drell-Yan (lepton-pair production) projectile
target

7. Gluon
scaling violation of F2
direct photon
J/ production

8. Recent unpolarized distributions
CTEQ5, Eur. Phys. J. C12 (2000) 375
GRV98, Eur. Phys. J. C5 (1998) 461
MRST99, Eur. Phys. J. C14 (2000) 133
Neutrino data are important for determining
valence-quark distributions in the “nucleon”.
However, the used CCFR target is iron!?

9. What can be done at a  factory?
unpolarized distributions in the nucleon
in parton model
parity-violation
terms
valence-quark distributions

10. Charged current
Neutral current

11. Fe target  p, d, 3He targets with intense  beam
kinematical range
Fe target  p, d, 3He targets
with intense  beam
accurate determination of uv and dv
in the “nucleon”
accurate determination of and g
important for finding any exotic signature beyond current theoretical framework

12. parton distributions in nuclei
Nuclear modification of F2A / F2A is
well known in electron/muon scattering.
However, little is known about F3
(namely valence-quark) modification
at small x due to lack of accurate
deuteron data.

13. Theoretical predictions of F3A/F3D
(1) Q2 rescaling & recombination
Q2 rescaling:
Recombination:
anti-shadowing ?

14. (2) vector-meson type shadowing ?
e.g. Frankfurt-Liuti-Strikman, PRL, 65, 1725 (1990)
shadowing ?

15. Experimental restriction from F2
neglect NLO s effects
assume
baryon-number conservation

16. Comparison
Both results are allowed at this stage.

17. Valence-quark distributions in nuclei
Nuclear modification of F3 cannot be investigated at this stage due to lack of accurate deuteron data.
accurate F3A/F3D data are valuable
for determining the shadowing model
for determining accurate nuclear parton
distributions  application to heavy-ion
physics

18. polarized parton distributions
status of proton-spin issue
polarized e/-proton scattering
 measurement of g1
proton, deuteron, 3He g1 data
with isospin symmetry
 valence and sea polarization
quark spin content
experimentally
rest of the spin ???

19. Initial parton distributions
D fi (x,Q02) = Ai xi (1+i xi) fi (x,Q02)
(i=uv , dv , q, g) Ai , i , i , i : free
positivity
flavor-symmetric distributions at initial Q02
first moments uv , dv are fixed
 F = ± 0.008, D = ± 0.008
uv = 0.986, dv=  
uv and dv are determined so as
to satisfy these conditions.
We determine 14 parameters by theχ2 fitting !

20. [proton, neutron (3He), deuteron]
2 fitting to the data
[proton, neutron (3He), deuteron]
which is minimized by the subroutine MINUIT
We analyzed with the following conditions.
Unpolarized PDF GRV98
Initial Q Q02 = 1 GeV 2
Number of flavor Nf = 3
QCD LO = 204 MeV
NLO = 299 MeV

21. - Results - Spin asymmetry A1p Total 2 LO 2/d.o.f. = 322.6 / 360
NLO 2 /d.o.f. = / 360
Total data 375
Spin asymmetry A1p

23. Parton distributions (Q2=1 GeV2 )

24. Role of  measurements new parity-violating
polarized structure functions
Polarized valence-quark and sea-quark
(strange, charm) distributions can be
investigated in detail.

25. Quark spin content at a  factory

26. Drell-Yan p-n asymmetry (NA51, E866)
Gottfried sum
Drell-Yan p-n asymmetry (NA51, E866)
(from hep-ex/ )

27. see SK, Phys. Rep. 303 (1998) Sec 5.5

28. Isospin symmetry violation at a  factory
see SK, Phys.Rep. -- Sec 4.5 & 5.6
The isospin symmetry is usually taken
for granted in parton distributions.

29. Polarized distributions & other topics
At this stage, are
fixed by semi-leptonic decays.
not undoubtedly obvious whether such
small-Q2 data can be used in connection
with DIS data
independent determination
at a  factory
understand accurate polarized valence-
quark distributions
 accurate determination of antiquark
distributions

30. Summary In general,  measurements are
important for finding the non-singlet
part of structure functions and s(x).
However, if the data are accurate enough,
there are other interesting topics.
accurate p, d, 3He data
valence-quark distributions in the nucleon
nuclear modification of V(x)
 determination of shadowing model
polarizated distributions and other topics
valence-quark contributions to nucleon spin
new polarized structure functions
determination of quark spin content
(polarized) light-antiquark flavor asymmetry
(polarized) strange and charm distributions
isospin symmetry

31. References Unpolarized parton distributions Nuclear distributions, F3
MRST99, Eur. Phys. J. C4 (1998) 463; C14 (2000).
Nuclear distributions, F3
R. Kobayashi, SK, and M. Miyama,
Phys. Lett. B354, 465 (1995).
Polarized distributions
Y. Goto et al. (AAC), Phys. Rev. D62 (2000)
B. Lampe and E. Reya, Phys. Rep. 332 (2000) 1.
Light-antiquark flavor asymmetry, Isospin
SK, Phys. Rep. 303 (1998) 183.
 factory in general
C. Albright et al., hep-ex/