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High-Energy Hadron Physics
at J-PARC
Shunzo Kumano
High Energy Accelerator Research Organization (KEK)
Graduate University for Advanced Studies (GUAS)
[email protected]
http://research.kek.jp/people/kumanos/
Sixth International Conference on Perspectives in Hadronic Physics
ITCP, Trieste, Italy
May 12 – 16, 2008
(Talk on May 16)
Contents
1. Introduction to high-energy hadron physics at J-PARC
• Introduction to the J-PARC facility
• Possible projects with 30 – 50 GeV proton beam
2. Structure functions
Possible roles of J-PARC projects in
• Unpolarized and Polarized
parton distribution functions (PDFs), Nuclear PDFs
• Fragmentation functions
• Tensor structure functions
Part I
Introduction to
High-Energy Hadron Physics
at J-PARC
J-PARC Facility
J-PARC Location
J-PARC
(Japan Proton Accelerator
Research Complex)
http://j-parc.jp/index-e.html
Joint facility of JAEA and KEK.
JAEA (Japan Atomic Energy Agency)
KEK (High Energy Accelerator
Research Organization)
Bird’s-eye view
Particle and Nuclear Physics
High-Intensity Frontier of Proton Accelerator
High-intensity proton beam
 High-intensity secondary beams
(Neutrino, Kaon, Pion, Neutron …)
Strangeness nuclear physics (1st experiment) Efforts are needed
to get approval
Exotic hadrons
for projects after
Hadrons in nuclear medium
strangeness physics.
Hard processes
(50 GeV recovery)
Nucleon spin
(proton polarization)
Quark-hadron matter (heavy ion)Theorist’s contributions
are crucial for the 2nd projects.
New nuclei with strangeness
New hadronic many-body system
by extending the flavor degrees of freedom.
Baryon interactions with strangeness
(New aspect of low-energy QCD)
LL, X nuclei
–2
–1
S=0
L,S,K nuclei
• No data for YY interactions
, in nuclei
Ordinary
nuclei
Z
?
N
• Some data
for YN interactions (~ 40)
• Plenty of data
for NN interactions (~ 4,000)
+1
J-PARC (K–, K+) for X and LL nuclei, YN scattering
(K–, π±), (π±, K+) for L nuclei, YN scattering
Aerial photograph on January 28, 2008
Hadron facility
Hadron Facility in May 2007
and a possible schedule for beam lines
Hadron Facility on April 11, 2008
High-Momentum Beam Line (30, 50 GeV Proton)
This beam line should be interesting
for the audience of this workshop.
General comments on J-PARC projects
with 30 – 50 GeV proton beam
J-PARC workshops on hadron physics
• J-PARC-HS05,
http://www-conf.kek.jp/J-PARC-HS05/program.html
• J-PARC-NP07,
http://www-conf.kek.jp/NP_JPARC/program.html
• J-PARC-NP08, http://j-parc.jp/NP08/
Refs. My talks on “Possible Hadron Physics at J-PARC”
in Trieste (2006) http://www.pg.infn.it/hadronic06/
in Ghent (2007)
http://inwpent5.ugent.be/workshop07/
in Mito (2008)
http://j-parc.jp/NP08/
Haron Physics at J-PARC
Strangeness nuclear physics (1st experiment)
Exotic hadrons
Kaon and pion beams
Hadrons in nuclear medium
Proton beam
Hard processes
(50 GeV recovery)
Nucleon spin
(proton polarization
Quark-hadron matter
(heavy ion)
My talk is related to
Hadron physics with 30 – 50 GeV proton beam
30 GeVJ/ production
Transition: Hadron  Quark degrees of free
Hadron interactions in nuclear medium
Short-range NN interactions
GPDs
…
50 GeVDrell-Yan (unpolarized PDFs)
Single spin asymmetries
Tensor structure at 50 GeV (Spin-1 hadrons)
Fragmentation functions (Hadron production
…
Proton-beam polarization
Drell-Yan: Double asymmetries (Polarized PD
Complimentary to RHIC-Spin (large-x physi
…
Hadron facilities
e.g. Drell-Yan: x1 x2 
s
x:
 s  ( p1  p2 )
x1
2
m
x:
2
m
m 
s
J-PARC:
RHIC:
LHC:
3

 0.3
10
s
3

 0.02
200
3

 0.0002
14000
p  p(A)       X (qq      )
2
2
 m  3 GeV
x2
s  10 GeV
s  200 GeV
s  14 TeV
J-PARC
Large-x facility
(Medium-x)
RHIC
LHC
Small-x facility
Flavor asymmetric antiquark distributions: u / d
J.-C. Peng’s talk
E866
J-PARC
E906
J-PARC proposal, M. Bai et al. (2007)
This project is suitable for probing
“peripheral structure” of the nucleon.
http://www.acuonline.edu/academics
/cas/physics/research/e906.html
SK, Phys. Rep. 303 (1998) 183;
G. T. Garvey and J.-C. Peng,
Prog. Part. Nucl. Phys. 47 (2001) 203.
Elastic Scattering: A+B  C+D at large pT
Brodsky@J-PARC-HS05
Transition from hadron degrees of freedom
to quark-gluon d.o.f.
 p   n
Constituent counting rule
H. Gao
d
(AB  CD) : s 2n f ( c.m. )
dt
n = nA + nB + nC + cD
(total number of interacting
elementary particles)
d
s
dt
7
J-PARC: p + p  p + p
L.Y. Zhu et al.,
PRL 91 (2003) 022003
Color Transparency
“Probe of dynamics of elementary reactions”
At large momentum transfer, a small-size component of the hadron
wave function should dominate. This small-size hadron could freely
pass through nuclear medium. (Transparent)
Brodsky, Strikman@J-PARC-HS05
Investigate p A  p p (A-1)
A
Nuclear transparency: T 
A N
Hadron size ~ 1 / hard scale
Color transparency:
T  larger, as the hard scale  larger
(BNL-EVA) J. Aclander et al.,
PRC 70 (2004) 015208
Possibility at J-PARC
0.8
T
12C
0.4
(p,2p) at J-PARC
0
10
30
50
Incident energy (GeV)
Generalized Parton Distributions (GPDs)
q
*
k+q

q –
p  p
P
,   p  p
2
k +
k
Bjorken variable
GPDs are defined as correlation
of off-forward matrix.
Q2
x
2pq
Momentum transfer squared
p
t = 2
p= p +
t  2
p  p 

 
Skewdness parameter   

p  p
2P

dz  ixP z 
1 
i    


e
p

(
z
/
2)


(z
/
2)
p

H(x,

,t)u(
p
)

u(
p)

E(x,

,t)u(
p
)
u(
p)



r

 4
z   0, z  0
2P  
2M



dz ixP z 
1  %


%  , t)u( p )  5  u( p) 
e
p

(
z
/
2)



(z
/
2)
p

H(x,

,t)u(
p
)


u(
p)

E(x,


r

5
5

 4
z  0, z  0
2P  
2M

H(x,  ,t)   t  0 
Forward limit: PDFs
First moments: Form factors
Dirac and Pauli form factors F1 , F2
Axial and Pseudoscalar form factors GA , GP
Second moments: Angular momenta
Sum rule: J q 
f (x),
%  ,t)
H(x,
 f (x)
t0
%
There is no analog in E and E.
 dx H(x,  , t)  F (t),  dx E(x,  , t)  F (t)
%  ,t)  G (t),
%  , t)  G (t)
 dx H(x,
 dx E(x,
1
2
A
P
1
1


dx
x
H
(x,

,
t

0)

E
(x,

,
t

0)
,
J

q  Lq
q
q
 q

2
2
GPDs in different x regions and GPDs at J-PARC
 x
  x

1
1  x  
x 
 x    0, x    0
Quark distribution
  x  
x 
 x
0
x 

1
  x 1
 x    0, x    0
Emission of antiquark with momentum fraction -x
Absorption of antiquark with momentum fraction -x-
p
p
qq
Meson distribution amplitude
Antiquark distribution
 x    0, x    0
t ? mN2
Emission of quark with momentum fraction x+
Absorption of quark with momentum fraction x-
Emission of quark with momentum fraction x+
Emission of antiquark with momentum fraction -x
x
p
GPDs

B
GPDs at J-PARC:
SK, M. Strikman, K. Sudoh,
in progress.
Short-range NN interaction
Ciofi degli Atti@J-PARC-NP07
Strikman@INPC07
E. Piasetzky et al.,
PRL97 (2006) 162504
• Short-range repulsive core, Tensor force
• Quark degrees of freedom
• Cold dense nuclear matter, Neutron star
V(r)
Nuclei do not collapse  Short-range repulsive core
0.4 fm
Nucleon size r ≈ 0.8 fm
Average nucleon separation in a nucleus: R ≈ 2 fm ~ 2r
The short-range part is important as the density becomes larger
(neutron star).
A(p, 2pN)X experiment for short range correlation
p
n
p
initial
final
p
r
Single spin asymmetry
Sivers effect
AN : f1T  D1
–
(No polarized proton beam is needed!)
Nucleon
Quark
(Sivers function  Unpolarized fragmentation)
Burkardt
@J-PARC-HS05

Probe of angular
momentum
The Sivers function describes unpolarized quark
in the transversely polarized nucleon.
Collins effect
  
AN  
  
–

–
AN : T q  H1 (Transversity  Collins fragmentation function)
The transversity distribution describes transverse quark polarization
in the transversely polarized nucleon.
The Collins fragmentation function describes a fragmentation of polarized quark
into unpolarized hadron.
 Higher-twist
Qiu, Sterman; Koike@J-PARC-HS05
Part II
Parton Distribution Functions
and
Fragmentation Functions
in connection with J-PARC
Unpolarized Parton Distribution Functions (PDFs) in the nucleon
The PDFs could be obtained from
http://durpdg.dur.ac.uk/hepdata/pdf.html
1
Gluon distribution / 5
Q 2 = 2 Ge V 2
0.8
xuv
xg/5
0.6
0.4
xd v
xd
0.2
Valence-quark
distributions
xs
0
0.00001 0.0001
0.001
0.01
x
xu
0.1
1
PDF uncertainty
CTEQ6 (J. Pumplin et al.),
JHEP 0207 (2002) 012
other PDF
CTEQ6
u
d
CTEQ5M1
MRS2001
CTEQ5HJ
g
Important x region for finding an “exotic
event” in a high-pT region at LHC
J-PARC x region
If processes are well understood theoretically
including pQCD terms, J-PARC measurements
are important for finding new physics at LHC
or possibly in cosmic rays.
Nuclear
Parton Distribution Functions
http://research.kek.jp/people/kumanos/nuclp.html
Experimental data: total number = 1241
(1) F2A / F2D
896 data
p, He, Li, C, Ca
He, Be, C, Al,
Ca, Fe, Ag, Au
EMC:
C, Ca, Cu, Sn
E665:
C, Ca, Xe, Pb
BCDMS: N, Fe
HERMES: N, Kr
(2) F2A / F2A’
Q2 (GeV 2)
NMC:
SLAC:
293 data
NMC: Be / C, Al / C,
Ca / C, Fe / C,
Sn / C, Pb / C,
C / Li, Ca / Li
(3) DYA /  DYA’ 52 data
E772:
E866:
C / D, Ca / D,
Fe / D, W / D
Fe / Be, W / Be
500
100
NMC (F2A/F2D)
HERMES
S LAC
NMC (F2A/F2A')
EMC
E772/E886 DY
E665
NMC (F2D/F2p)
BC DMS
10
1
0.001
0.01
0.1
x
1
Functional form
Nuclear PDFs “per nucleon”
If there were no nuclear modification
Au A x  Zu p x Nun x, Ad A x  Zd p x Nd n x
Isospin symmetry： un  d p  d,
 u A x  
Zu x   Nd x 
,
A
p = proton, n = neutron
dn  u p  u
d A x  
Zd x   Nu x 
A
Take account of nuclear effects by wi (x, A)
Zuv x   Ndv x 
Zd x   Nuv x 
, dvA x   wdv x, A  v
A
A
Zu x   Nd x 
Zd x   Nu x 
u A x   wq x, A 
,
d A x   wq x, A 
A
A
s A x   wq x, A s x 
uvA x   wuv x, A 
g A x   wg x, A g x 
at Q2=1 GeV2 ( Q02 )
Functional form of wi (x, A)
fi A (x,Q02 )  wi (x, A) fi (x,Q02 )
i  uv , dv , u, d, s, g
1  ai  bi x  ci x 2  di x 3

wi (x, A)  1   1   

A 
(1  x)
Note: The region x > 1 cannot be
described by this parametrization.
x
A simple function = cubic polynomial
Three constraints
1 A
1 A
2 A
A
A
Nuclear charge: Z  A  dx  u  u  d  d  s  s A
3
3
3
1
1
1
Baryon number: A  A  dx  u A  u A  d A  d A  s A  s A
3
3
3
Momentum:

2 A 1 A 
  A  dx  3 uv  3 dv 

1 A 1 A 

A
dx
  3 uv  3 dv 


 
 


 
 

A  A  dx u A  u A  d A  d A  s A  s A  g 


 A  dx uvA  dvA  2 u A  d A  s A  g 
Analysis conditions
MRST98 [ LQCD = 174 MeV (LO), 300 MeV (NLO) ]
· Nucleonic PDFs:
· Total number of parameter：12
· Total number of data： 1241 ( Q2≧1 GeV2 )
896 (F2A/F2D) + 293 (F2A/F2A´) + 52 (Drell-Yan)
· Subroutine for 2 analysis： CERN-Minuit
2  

Ridata  Ritheo
 

2
data 2
i
i
F2A
R D,
F2
 idata 
F2A
 pA
,
A
F2
 pA 
 isys    istat 
2
2
2min ( /d.o.f.) = 1653.3 (1.35) ….. LO
= 1485.9 (1.21) ….. NLO
· Error estimate： Hessian method
F(x) 1 F(x)
H ij
 F(x)   


 j
i, j
i
2
2
H ij  Hessian
i  parameter
Comparison with F2Ca/F2D & DYpCa/ DYpD data
LO analysis
NLO analysis
1.2
F2Ca/F2D
EMC
H
E136
1.1
NMC
E665
H H
1
H
H
0.9
H
HH
0.8
2
2
Q = 10 GeV
0.7
0.001
0.01
0.1
1
x
R= F2Ca/F2D, DYpCa/ DYpD
(Rexp-Rtheo)/Rtheo at the same Q2 points
0.2
0
-0.2
0.001
EMC
H
E139
NMC
F
E665
F
F
0.2
E772
F
H
F
0.01
0.1
x
F
H
HH
H HH
0
1
-0.2
x
Results & Future experiments
Fermilab
J-PARC
J-PARC proposal
J. Chiba et al. (2006)
E866
J-PARC
RHIC
E906
LHC
eLIC
eRHIC
JLab
Fermilab
J-PARC
GSI
Factory
MINARA
RHIC
LHC
eLIC
eRHIC
(HKN07)
Polarized
Parton Distribution Functions
http://spin.riken.bnl.gov/aac/
Nucleon Spin
Naïve Quark Model
S  uv  dv  1
Electron / muon scattering
S  0.1 ~ 0.3
Almost none of nucleon spin
is carried by quarks!
QCD
Sea-quarks and gluons?
Orbital angular momenta ?
Gluon: G
Lq , Lg
Sea-quarks: qsea
Recent data indicate
G is small at x ~ 0.1.

Future experiments

1 1
 uv  dv  qsea  G  Lq  Lg
Nucleon Spin:
2 2 1 4 44 2 4 4 43
S
Current polarized data are
Q2
Q2
x
;
kinematically limited.
2 p  q ys
(from H1 and ZEUS, hep-ex/0502008)
Q2
1
fixed target: min(x) 

2M N Elepton 2Elepton (GeV)
if Q 2  1 GeV2
1
for Elepton (SMC)  190 GeV, min(x) 
 0.003
400
100
E130(p)
E143(p)
(GeV2
)
E155(p)
EMC(p)
g1 data
SMC(p)
HERMES(p)
E143(d)
10
E155(d)
SMC(d)
E142(n)
E154
HERMES(n)
1
0.001
0.01
(from AAC04)
0.1
1
x
region of g1 data
F2 data
General strategies for determining polarized PDFs
2x 1  R
Spin asymmetry A1 ; g1
F2
R
FL
F  2xF1
 2
2xF1
2xF1
1 dy


1
 s (Q 2 )
2
2
2
 q(x / y,Q )  q(x / y,Q )   (1  y) 
g1 (x,Q )   eq 
Cq (y)   
x y
2 q
2


2
1
+ eq2
2

dy
 s (Q 2 )
2 
g(x
/
y,Q
)
n
C
(y)


g
 f 2

x y


1
Leading Order (LO)
eq2 
1
nf
Next to Leading Order (NLO)
Cq (Cg )  quark (gluon) coefficient function


dy
 s (Q 2 ) (2)
2
2
 q(x / y,Q )  q(x / y,Q )  (1  y) 
F2 (x,Q )  x e 
Cq (y)  
x y
2
q


2
1 dy
  (Q ) (2)

 x eq2 
g(x / y,Q 2 )  n f s
Cg (y)  
x y
2


2
2
q
1
Unpolarized PDFs
e
2
q
q
Description of 0 production
Parton interactions
Fragmentation functions
Parton distribution functions
 :
2
2
f
(x
,Q
)

f
(x
,Q
)
 a a
b
b
a,b,c
 ö(ab  cX ) 
Dc (z,Q 2 )
g  g  q(g)  X processes are dominant at small pT
q  g  q(g)  X
at large pT
The 0 production process is suitable
for finding the gluon polarization g.
Gluon and antiquark distributions
have large uncertainties at large x.
Situation of polarized PDFs


0.5
0.4
Q2 = 1 GeV
0.6
2
AAC06
GRSV
0.4
BB
0.3
0.2
xg(x)
LSS
0.2
xu (x)
v
0
0.1
0
0.001
0.01
0.1
1
0
-0.2
0.001
0.01
0.1
1
J-PARC
0.01
0
xdv(x)
-0.1
-0.01
AAC06
GRSV
-0.02
BB
LSS
-0.2
0.001
-0.03
0.01
0.1
x
1
Q2 = 1 GeV2
xq(x)
-0.04
0.001
0.01
0.1
x
1
Fragmentation Functions
http://research.kek.jp/people/kumanos/ffs.html
Purposes of investigating fragmentation functions
Semi-inclusive reactions have been used for investigating
・origin of proton spin
r
r r
e  p  e  h  X (e.g. HERMES), p  p  h  X (RHIC-Spin)
Quark, antiquark, and gluon contributions to proton spin
(flavor separation, gluon polarization)
・properties of quark-hadron matters A  A  h  X (RHIC, LHC)
Nuclear modification
(recombination, energy loss, …)


a,b,c
f a (xa ,Q 2 )  fb (xb ,Q 2 )
 ö(ab  cX ) 
Dc (z,Q 2 )
Fragmentation Function
e+
q
, Z
q
e–
Fragmentation: hadron production
from a quark,
antiquark, or gluon
h
Fragmentation function is defined by
 
1
d

(e
e  hX)
h
2
F (z,Q ) 
 tot
dz
 tot  total hadronic cross section
z
Eh
2Eh Eh


,
Q
Eq
s /2
s  Q2
Variable z
• Hadron energy / Beam energy
• Hadron energy / Primary quark energy
A fragmentation process occurs from quarks, antiquarks, and gluons,
so that Fh is expressed by their individual contributions:
 z 2 h
F (z,Q )   
Ci  ,Q  Di ( y,Q 2 )
z y
y

i
Non-perturbative
(determined from experiments)
Calculated in perturbative QCD
h
2
1 dy
Ci (z,Q 2 )  coefficient function
Dih (z,Q 2 )  fragmentation function of hadron h from a parton i
Comparison with pion data
F

 

1
d

(e
e


X)
(z,Q2 ) 
 tot
dz
Our fit is successful to
reproduce the pion data.
The DELPHI data deviate
from our fit at large z.
Our NLO fit
with uncertainties
Rational difference
between data and theory
F

(z,Q )data  F
2

(z,Q 2 )theory

F  (z,Q 2 )
theory
Fragmentation functions
at J-PARC Gluon and light-quark
fragmentation functions
have large uncertainties.
Large differences between
the functions of various
analysis groups.
s
sˆ
sˆ  x a xb s ~ (0.4)2 (10 GeV)2
sˆ  0.4  10  4 GeV
pT
p
z~
 T ~ 1 (large z)
2
sˆ / 2
Global analysis
results for 
J-PARC
Exotic hadron search
by fragmentation functions
f0(980) as an example
Criteria for determining f0 structure
by its fragmentation functions
Possible configurations of f0 (980)
1
(1) ordinary u, d - meson
(uu  dd )
2
(2) strange meson,
ss
(3) tetraquark (KK),
(4) glueball
Contradicts with experimental widths
 theo ( f0   )  500  1000 MeV
?  exp  40  100 MeV
 theo ( f0   )  1.3  1.8 keV
?  exp  0.205 keV
1
(uuss  ddss )
2
Contradicts with lattice-QCD estimate
gg
mlattice ( f0 )  1600 MeV
? mexp  980 MeV
Discuss 2nd moments and functional forms (peak positions)
of the fragmentation functions for f0 by assuming
the above configurations, (1), (2), (3), and (4).
Tensor Structure at High-Energies
For Spin-1 Hadrons
Note: Proton-beam polarization is not needed.
Polarized deuteron target is enough at J-PARC!
http://www-conf.kek.jp/J-PARC-HS05/program.html
Tensor Structure in High-energy Reactions
(Note: No polarized proton beam is needed!)
L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557.
P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571.
Structure
Functions
F1  d
(in e scattering)
g1  d , 1  d , 1




d 1  d 1
b1  d 0  
2

Parton
Model
q

H

1
F1   ei 2 qi  qi
2 i


1 1
qi  qi  qi 0  qi 1
3

x,Q 
2
1
g1   ei 2 qi  qi
2

1
b1   ei 2  qi   q i
2 i


qi  qi 1  qi 1
1
1
q

q
i
 qi  qi 0  i
2

Tensor Structure in Proton-Deuteron Drell-Yan
(Note: No polarized proton beam is needed!)
b1 for spin-1 particles
1st measurement of b1:
(HERMES) A. Airapetian et al.,
PRL 95 (2005) 242001.
b1 = 0
only in S-wave
Polarized proton-deuteron Drell-Yan
(Theory) S. Hino and SK,
PR D 59 (1999) 094026,
D 60 (1999) 054018.
(Experiment) None  J-PARC
Spin asymmetries
ALL


2
 qa xA qa xB  qa xA qa xB 
e
a
a

2
 qa xA qa xB  qa xA qa xB 
e
a
a
2
sin 2  cos 2   a ea  T qa xA T qa xB  T qa xA T qa xB 
ATT 
1  cos2 
 a ea2 qa xA qa xB  qa xA qa xB 
AUQ0
e  q x  q x  q x  q x 


 e q x q x  q x q x 
2
a
a
a
2
a a
A
a
A
a
B
a
A
a
B
a
A
a
a
B
B
Note:   transversity in my notation
Unpolarized proton
+ Tensor polarized deuteron
Unique advantage of J-PARC ( q measurement)
AUQ0 large xF
e q x  q x 


 e q x q x 
2
a
a
a
2
a
a
a
A
A
a
a
B
B
qi 1  qi 1
 qi  qi 
2
0
D
 dx b1 (x)  0 
F. E. Close and SK, PRD42, 2377 (1990)
Gottfried:


1
Q   Q
9
sea
dx
1 2
 F2p (x)  F2n (x)     dx  u  d 
x
3 3
Our works related to this talk
(1) Overview on “Possible Hadron Physics at J-PARC”
SK, Nucl. Phys. A782 (2007) 442.
(2) ubar/dbar
SK, Phys. Rep. 303 (1998) 183.
(3) Nuclear PDFs
M. Hirai, SK, and M. Miyama, Phys. Rev. D 64 (2001) 034003;
M. Hirai, SK, and T.-H. Nagai, Phys. Rev. C 70 (2004) 044905; C 76 (2007) 065207.
(4) Polarized PDFs, Asymmetry Analysis Collaboration (AAC)
Y. Goto et al., Phys. Rev. D 62 (2000) 034017;
M. Hirai, SK, N. Saito, Phys. Rev. D 69 (2004) 054021; D 74 (2006) 014015.
(5) Global analyses for FFs of , K, and p + their uncertainties
M. Hirai, SK, T.-H. Nagai, and K. Sudoh, Phys. Rev. D75 (2007) 094009;
Exotic hadron search by using FFs e.g. for f0(980)
M. Hirai, SK, M. Oka, and K. Sudoh, Phys. Rev. D77 (2008) 017504.
(6) Sum rule for b1(x)
F. E. Close and SK, Phys. Rev. D 42 (1990) 2377.
General formalism for polarized proton+deuteron Drell-Yan
S. Hino and SK, Phys. Rev. D 59 (1999) 094026; D 60 (1999) 054018.
Summary
J-PARC will be an important facility
in hadron and nuclear physics communities.
In high-energy hadron physics
 Structure functions of hadrons
 Fragmentation
 Hadron interactions in nuclear medium
 Short-range NN interactions
 Hadron  Quark degrees of freedom
 Hadron spin
 …
I introduced some topics. More contributions
are needed for the hadron project at J-PARC!
Need to discuss possible topics with 30 GeV,
50 GeV, and 50 GeV polarized proton beams.
The End
The End