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hube
rg@
ureg
ina.
ca
Elec
tron
Sca
tterin
g an
d H
adro
nSt
ruct
ure
Gar
th H
uber
Uni
vers
ity o
f Man
itoba
, Dec
embe
r 1, 2
006.
hube
rg@
ureg
ina.
ca
Qua
rks,
Lep
tons
and
thei
rFu
ndam
enta
l Int
erat
ions
The
grou
nd
stat
e of
m
atte
r.
hube
rg@
ureg
ina.
ca
The
gluo
ns o
f QC
D
carr
y co
lor c
harg
e an
d in
tera
ct s
tron
gly
(in c
ontr
ast t
o th
e ph
oton
s of
QED
).
QED
QC
D
Qua
ntum
Ele
ctro
dyna
mic
sQ
uant
um C
hrom
odyn
amic
s
hube
rg@
ureg
ina.
ca
QC
Ds
Dua
l Nat
ure
Sho
rt D
ista
nce
Inte
ract
ion:
Qua
rks
insi
de p
roto
ns b
ehav
e as
if th
ey
are
near
ly u
nbou
nd.
Asy
mpt
otic
Fre
edom
.S
hort
dist
ance
qua
rk-q
uark
inte
ract
ion
is
feeb
le.
per
turb
ativ
eQ
CD
(pQ
CD
).
Long
Dis
tanc
e In
tera
ctio
n:Q
uark
s ar
e st
rong
ly b
ound
with
in
hadr
ons.
Col
or c
onfin
emen
t.Q
CD
cal
cula
tions
are
com
plex
.Q
CD
-bas
ed m
odel
s ar
e of
ten
used
.L
attic
e Q
CD
hol
ds m
uch
prom
ise.
hube
rg@
ureg
ina.
ca
The
Scie
nce
Prob
lem
The
Scie
nce
Prob
lem
Qua
ntum
Q
uant
um C
hrom
odyn
amic
sC
hrom
odyn
amic
s(Q
CD
) in
the
(QC
D) i
n th
eco
nfin
emen
tco
nfin
emen
t reg
ime:
regi
me:
How
doe
s it
wor
k?H
ow d
oes
it w
ork?
W
hat d
o w
e kn
ow?
Wha
t do
we
know
?Q
CD
wor
ks in
the
QC
D w
orks
in th
e pe
rturb
ativ
epe
rturb
ativ
e(w
eak)
regi
me
(wea
k) re
gim
eM
any
expe
rimen
tal t
ests
led
to th
is c
oncl
usio
n, e
xam
ple:
!P
roto
n is
not
poi
nt-li
ke; E
last
ic e
lect
ron
scat
terin
g (N
obel
Priz
e: H
ofst
adte
r, 19
61).
!Q
uark
s an
d gl
uons
/Par
tons
are
the
cons
titue
nts;
Dee
p In
elas
tic e
lect
ron
Sca
tterin
g (N
obel
priz
e: F
riedm
an, K
enda
ll an
d Ta
ylor
, 199
0).
Theo
ry c
eleb
rate
d re
cent
lyA
sym
ptot
ic fr
eedo
m (N
obel
priz
e: G
ross
, Pol
itzer
and
Wilc
zek,
200
4), b
utQ
uant
itativ
e Q
CD
des
crip
tion
of th
e nu
cleo
ns
prop
ertie
sQ
uant
itativ
e Q
CD
des
crip
tion
of th
e nu
cleo
ns
prop
ertie
s(i.
e. u
nder
stan
ding
of t
he c
onfin
emen
t reg
ime)
rem
ains
a p
uzzl
e!(i.
e. u
nder
stan
ding
of t
he c
onfin
emen
t reg
ime)
rem
ains
a p
uzzl
e!
hube
rg@
ureg
ina.
ca
Ph
ysic
s P
rob
lem
s fo
r th
e N
ext
Mill
enn
ium
Sele
cted
by:
Micha
el D
uff,
Dav
id G
ross
, Ed
ward
Witte
nSt
ring
s 20
00
1.Si
ze o
f di
men
sion
less
par
amet
ers.
2.
Ori
gin
of t
he U
nive
rse.
3.Li
feti
me
of t
he P
roto
n.4.
Is N
atur
e Su
pers
ymm
etri
c?
5.W
hy is
the
re 3
+1 S
pace
-tim
e di
men
sion
s?
6.Co
smol
ogic
al C
onst
ant
prob
lem
. 7.
Is M
-the
ory
fund
amen
tal?
8.
Blac
k H
ole
Info
rmat
ion
Para
dox.
9.Th
e we
akne
ss o
f gr
avit
y.
10.Q
uark
con
fine
men
t an
d th
e st
rong
for
ce.
hube
rg@
ureg
ina.
ca
Why
ele
ctro
n sc
atte
ring
expe
rimen
ts?
Why
ele
ctro
n sc
atte
ring
expe
rimen
ts?
Wha
t qua
ntiti
es d
o w
e m
easu
re?
Wha
t qua
ntiti
es d
o w
e m
easu
re?
!!H
adro
nH
adro
nfo
rm fa
ctor
sfo
rm fa
ctor
s: p
ion,
nuc
leon
. [S
yste
m re
spon
ds c
oher
ently
]
!!N
ucle
on s
truct
ure
func
tions
Nuc
leon
stru
ctur
e fu
nctio
ns: [
Sys
tem
resp
onds
inco
here
ntly
]
Tran
sitio
n fro
m
Tran
sitio
n fro
m p
QC
DpQ
CD
to
to S
trong
QC
DS
trong
QC
Dne
eds
data
with
ne
eds
data
with
hig
h pr
ecis
ion
high
pre
cisi
on
for a
qua
ntita
tive
unde
rsta
ndin
g of
con
finem
ent.
for a
qua
ntita
tive
unde
rsta
ndin
g of
con
finem
ent.
Lum
inos
ity:
(SLA
C, 1
978)
~ 8
x 1
031cm
-2-s
-1
(JLa
b, 2
000)
~ 4
x 1
038
cm-2
-s-1
22
(GeV
/c)
101.0
fm1.01
−=
⇔→
=Q
d
1990
s a
dvan
cemen
ts:
Inte
nse
CW e
lect
ron
beam
s.
Pola
rize
d ta
rget
s/po
lari
met
ry.
Impr
ovem
ent
in p
olar
ized
e s
ourc
es.
hube
rg@
ureg
ina.
ca
Elas
tic F
orm
Fac
tors 22
obje
ctpo
int
)(Q
Fdd
dd⎟ ⎠⎞
⎜ ⎝⎛Ω
=⎟ ⎠⎞
⎜ ⎝⎛Ω
σσ 2
/3
()
()
iqx
FQ
xe
dx
ρ=∫
!! i#
!
Spi
n 0
mes
ons
(π+ ,K
+ ): e
lect
ric c
harg
e fo
rm fa
ctor
(F) o
nly.
Spi
n ½
Nuc
leon
:ele
ctric
(GE)
and
mag
netic
(GM) f
orm
fact
ors.
→al
tern
ate
repr
esen
tatio
n in
term
s of
spi
n no
n-fli
p (F
1) a
nd
spin
flip
(F2)
form
fact
ors.
The
mea
sure
men
ts a
llow
us
to te
st o
ur u
nder
stan
ding
of
The
mea
sure
men
ts a
llow
us
to te
st o
ur u
nder
stan
ding
of
hadr
onic
hadr
onic
stru
ctur
e by
com
paris
on to
QC
Dst
ruct
ure
by c
ompa
rison
to Q
CD
-- bas
ed p
redi
ctio
ns.
base
d pr
edic
tions
.
In th
e ca
se o
f an
infin
itely
mas
sive
targ
et, t
he fo
rm fa
ctor
is
sim
ply
the
Four
ier t
rans
form
of t
he c
harg
e di
strib
utio
n.
In g
ener
al, t
he e
last
ic s
catte
ring
cros
s se
ctio
n fro
m a
n ex
tend
ed ta
rget
is
hube
rg@
ureg
ina.
ca
An
early
pQ
CD
Pred
ictio
n:-D
imen
sion
al S
calin
g at
Lar
ge M
omen
tum
At i
nfin
ite m
omen
tum
, qua
rks
At i
nfin
ite m
omen
tum
, qua
rks
are
asym
ptot
ical
ly fr
ee.
are
asym
ptot
ical
ly fr
ee.
E
quiv
alen
t to
turn
ing
off t
he
stro
ng in
tera
ctio
n.
The
hadr
onbe
com
es a
co
llect
ion
of fr
ee q
uark
s w
ith
equa
l lon
gitu
dina
l mom
enta
.
12
2
)(
1)
(−
∝n
FS.
J. B
rods
ky, G
.P. L
epag
eP
ertu
rbat
ive
QC
D,
A.H
. Mue
ller,
ed.,
1989
.
Dim
ensi
onal
ana
lysi
s of
the
Dim
ensi
onal
ana
lysi
s of
the
hadr
onha
dron
scat
terin
g am
plitu
de in
term
s of
the
scat
terin
g am
plitu
de in
term
s of
the
parti
cipa
ting
field
s yi
elds
parti
cipa
ting
field
s yi
elds
hube
rg@
ureg
ina.
ca
Tran
sitio
n to
pQ
CD
at o
nly
Q2 ≈
1 G
eV2 ?
Con
side
r a p
QC
Dca
lcul
atio
n at
ver
y hi
gh Q
2
for p
seud
osca
larm
eson
(JP=0
-)fo
rm fa
ctor
s (e
.g. p
ion)
∫+
=+
dpq
pp
QF
)(
)(
)(
*2
ππ
πφ
φ
In q
uant
um fi
eld
theo
ry,
F πis
the
over
lap
inte
gral
φ soft
φ soft
γ*
(1−
x)
xy
g
(1−
y)
At l
arge
Q2 ,
pertu
rbat
ive
QC
D (p
QC
D) c
an b
e us
ed:
234
2
1 0
1 02
22
)(
)(
32)
(
xyQ
g
yx
xyQg
dydx
QF
sπα
φφ
π
==∫
∫+
(q-γ
coup
ling
cons
t)2vi
rtual
ityof
exc
hang
ed g
luon
As
Q2 →
∞, o
nly
the
hard
por
tion
rem
ains
)1(
6)
(x
xf
x−
→π
πφ
f π=13
2 M
eVπ+→
µ+ν
coup
ling
cons
tant
.Q
CD
Asy
mpt
otic
Lim
it
2
22
2
8(
)s
Q
fF
ππ
πα→
∞→
hube
rg@
ureg
ina.
ca
At e
xper
imen
tally
acc
essi
ble
Q2 ,
both
the
hard
and
soft
par
ts
of th
e pa
rton
dist
ribu
tion
func
tion
cont
ribu
te.
→→no
cle
ar a
nsw
er fr
om th
eory
(yet
) on
rela
tive
cont
ribut
ions
.no
cle
ar a
nsw
er fr
om th
eory
(yet
) on
rela
tive
cont
ribut
ions
.
The
trans
ition
from
the
Soft
to H
ard
QC
D re
gim
e is
bes
t obs
erve
d ex
perim
enta
lly w
ith si
mpl
e sy
stem
s suc
h as
the
π+fo
rm fa
ctor
.
hube
rg@
ureg
ina.
ca
Pio
nan
d K
aon
Cha
rge
Form
Fac
tor
Dat
a
hube
rg@
ureg
ina.
ca
Spin
0: π
and
KEl
ectr
omag
netic
For
m F
acto
rs
()
φσ
εφ
σε
εσ
σε
φσπ
2co
sco
s1
22
dtddtd
dtddtd
dtdd
TTLT
TL
++
++
=
),
()
()
(2
22
22
tQ
Ft
gm
ttQ
dtdN
NL
ππ
π
σ−−
∝300
GeV
expe
rimen
t at
CERN
SPS
mea
sure
s π+
(K+ )
cha
rge
radi
i:
To a
cces
s hi
gher
To
acc
ess
high
er QQ
22on
e m
ust u
se a
n ex
perim
enta
lly u
ncle
an:
mov
ing
virtu
al ta
rget
ε=
[1+2
(1+τ
)tan2 (
θ /2
)]-1
At l
ow
At l
ow QQ
22 <0.
3 G
eV<0
.3 G
eV2 2
the
π+ (K
+ ) fo
rm fa
ctor
can
be
mea
sure
dex
actly
usi
ng h
igh
ener
gy π
+ (K
+ ) s
catte
ring
from
ato
mic
elec
trons
.
fm03
1.0
560
.0fm
008
.067
2.0
±=
±=
Krr π
hube
rg@
ureg
ina.
ca
θ π
π+
φ π
γ v
W2=
(pγ+
pp)2
e’
e
nReact
ion P
lane
2 =(p
e−
pSca
ttering P
lane
e2 ’)
t=(p
γ−p
2 ) π−
Q
()
φσ
εφ
σε
εσ
σε
φσπ
2co
sco
s1
22
dtddtd
dtddtd
dtdd
TTLT
TL
++
++
=
1.1.N
eed
to ta
ke d
ata
at sm
alle
st a
vaila
ble
Nee
d to
take
dat
a at
smal
lest
ava
ilabl
e tt
, so
, so
σσ LLha
s max
imum
con
tribu
tion
has m
axim
um c
ontri
butio
n fr
om th
e fr
om th
e ππ++
pole
. po
le.
!Fo
r giv
en Q
2 , hi
gher
Wal
low
s sm
alle
r |t m
in|.
2.2.Ex
tract
ion
of
Extra
ctio
n of
FFππ
requ
ires
requ
ires
tt dep
ende
nce
of
depe
nden
ce o
f σσLL
to b
e kn
own.
to
be
know
n.
!O
nly
thre
e of
Q2 ,
W, t
, θπ
are
inde
pend
ent.
!V
ary θ π
to m
easu
re t
depe
nden
ce.
!Si
nce
non-
para
llel d
ata
need
ed, L
T an
d TT
mus
t als
o be
det
erm
ined
.
hube
rg@
ureg
ina.
ca
PIO
N C
harg
e Fo
rm F
acto
r:
Ext
ract
ion
of fo
rm fa
ctor
from
σLda
ta
p(e,
eπ+
)nda
ta a
re o
btai
ned
som
e di
stan
ce fr
om th
e t=
mπ2
pole
.
!N
o re
liabl
e ph
enom
enol
ogic
al
extra
pola
tion
poss
ible
.
A m
ore
relia
ble
ap
pro
ach
is t
o A
mor
e re
liab
le a
pp
roac
h is
to
use
a m
odel
inco
rpor
atin
g th
e u
se a
mod
el in
corp
orat
ing
the
ππ+
+ p
rod
uct
ion
mec
han
ism
an
d
pro
du
ctio
n m
ech
anis
m a
nd
th
e `s
pec
tato
rth
e `s
pec
tato
r n
ucl
eon
to
nu
cleo
n t
oex
trac
t ex
trac
t FF
ππ((QQ
22 ) f
rom
)
from
σσLL..
hube
rg@
ureg
ina.
ca
Ext
ract
ion
of fo
rm fa
ctor
from
σLda
ta
KA
ON
Cha
rge
Form
Fac
tor:
K+
pole
is lo
cate
d ev
en fu
rther
aw
ay fr
om th
e ex
perim
enta
lly
acce
ssib
le re
gion
.
Onl
y lo
w Q
2el
astic
sca
tterin
g da
ta a
vaila
ble.
Tria
l ext
ract
ion
of K
+fo
rm fa
ctor
vi
a p(
e,e
K+)Σ
0 ,Λ0
near
Q
2 =2
GeV
2 at
Jeff
erso
n La
b.
Ope
n qu
estio
n w
heth
er σ
Lda
ta
are
suff
icie
ntly
sens
itive
to K
+
pole
.0
0.0
40.0
80.1
20.1
6Q
2 [G
eV
2]
0.6
0.7
0.8
0.9
1.0
|FK(Q2)|
2
hube
rg@
ureg
ina.
ca
Jeffe
rson
Lab
Fπ
Col
labo
ratio
nR
. Ent
, D. G
aske
llD
. Gas
kell,
M.K
. Jon
es, D
. Mac
kD
. Mac
k, D
. Mee
kins
, J. R
oche
, G. S
mith
, W. V
ulca
n,
G. W
arre
n, S
.A. W
ood
Jeffe
rson
Lab
, New
port
New
s, V
A , U
SA
E.J.
Bra
sh, G
.M. H
uber
G.M
. Hub
er, V
. Kov
altc
houk
, G.J
. Lol
os, S
. Vid
akov
ic, C
. Xu
C. X
uU
nive
rsity
of R
egin
a, R
egin
a, S
K, C
anad
a
H. B
lok
H. B
lok,
V. T
vask
isV
rije
Uni
vers
iteit,
Am
ster
dam
, Net
herla
nds
E. B
eise
E. B
eise
, H. B
reue
r, C
.C. C
hang
, T. H
orn
T. H
orn,
P. K
ing,
J. L
iu, P
.G. R
oos
Uni
vers
ity o
f Mar
ylan
d, C
olle
ge P
ark,
MD
, US
A
W. B
oegl
in, P
. Mar
kow
itz, J
. Rei
nhol
dFl
orid
a In
tern
atio
nal U
nive
rsity
, FL,
USA
J. A
rrin
gton
, R. H
olt,
D. P
otte
rvel
d, P
. Rei
mer
, X. Z
heng
Argo
nne
Nat
iona
l Lab
orat
ory,
Arg
onne
, IL,
USA
H. M
krtc
hyan
, V. T
adev
osya
nY
erev
an P
hysi
cs In
stitu
te, Y
erev
an, A
rmen
ia
S. J
in, W
. Kim
Kyu
ngoo
k N
atio
nal U
nive
rsity
, Tae
gu, K
orea
M.E
. Chr
isty
, C. K
eppe
l, L.
G. T
ang
Ham
pton
Uni
vers
ity, H
ampt
on, V
A, U
SA
J. V
olm
erD
ES
Y, H
ambu
rg, G
erm
any
A. M
atsu
mur
a, T
. Miy
oshi
, Y. O
kaya
suTo
huku
Uni
vers
ity, S
enda
i, Ja
pan
B. B
arre
tt, A
. Sar
tyS
t. M
ary
s U
nive
rsity
, Hal
ifax,
NS
, Can
ada
K. A
niol
, D. M
arga
ziot
isC
alifo
rnia
Sta
te U
nive
rsity
, Los
Ang
eles
, CA,
USA
L. P
entc
hev,
C. P
erdr
isat
Col
lege
of W
illia
m a
nd M
ary,
Willi
amsb
urg,
VA
, US
A
E. G
ibso
n, I.
Nic
ules
cu, V
. Pun
jabi
hube
rg@
ureg
ina.
ca
F π-1
and
Fπ-
2 Ex
perim
ents
at J
effe
rson
Lab
Exp
Q2
(GeV
2)W
(G
eV)
|tmin|
(Gev
2)E e
(GeV
)
Fπ-1
0.6-
1.6
1.95
0.03
-0.1
502.
445-
4.04
5
Fπ-2
1.6,
2.45
2.22
0.09
3,0.
189
3.77
9-5.
246
Exp
erim
ent:
Exp
erim
ent:
Ext
ract
Fπ
via
L/T/
LT/T
T Ro
senb
luth
se
para
tion
in p
(e,e
π+)n
.
Coi
ncid
ence
mea
sure
men
t be
twee
n ch
arge
d pi
ons
in H
MS
and
elec
tron
s in
SO
S.D
ata
acqu
ired
: Fπ-
1: 19
97,F
π-2:
2003
.
FF ππ-- 2
2 G
oals
:G
oals
: E
xten
sion
of
our
earl
ier
FEx
tens
ion
of o
ur e
arlie
r F ππ
-- 1 t
o th
e 1
to t
he
high
est
high
est
QQ22
poss
ible
wit
h po
ssib
le w
ith
JLab
JLab
6 6 Ge
VGe
Vel
ectr
on b
eam
elec
tron
bea
m..
Hig
her
Hig
her
WWab
ove
reso
nanc
e re
gion
.ab
ove
reso
nanc
e re
gion
. R
epea
t Re
peat
QQ22 =
1.60
GeV
=1.6
0 Ge
V22cl
oser
to
t=m
clos
er t
o t=
mππ
pole
.po
le.
!!re
duce
d m
odel
unc
erta
inti
es.
redu
ced
mod
el u
ncer
tain
ties
.SO
S:1.
7 G
eV/c
HM
S:7
GeV
/c
Ope
rate
d by
Jeff
erso
n Sc
ienc
e A
ssoc
iate
s for
the
U.S
. Dep
artm
ento
f En
ergy
Tho
mas
Jef
fers
on N
atio
nal A
ccel
erat
or F
acili
ty
Page
Two
Col
d S
uper
cond
uctin
g Li
nacs
Con
tinuo
us P
olar
ized
Ele
ctro
n B
eam
E →
6 G
eV>
100
µAup
to 8
0% p
olar
izat
ion
conc
urre
nt to
3 H
alls
Firs
t bea
m d
eliv
ered
in 1
994
AB
C
hube
rg@
ureg
ina.
ca
p(e,
eπ+ )
nEv
ent S
elec
tion
C
oinc
iden
ce m
easu
rem
ent b
etw
een
char
ged
pion
s in
HM
S an
d el
ectr
ons
in S
OS.
π+
dete
cted
in H
MS
A
erog
el C
eren
kov
and
Coi
ncid
ence
tim
e fo
r PID
.
El
ectro
ns in
SO
S
iden
tifie
d by
Cer
enko
v /C
alor
imet
er.
A
fter P
ID c
uts,
alm
ost n
o ra
ndom
coi
ncid
ence
s re
mai
n.
Mis
sing
mas
s cu
t as
sure
s ex
clus
ivity
.
hube
rg@
ureg
ina.
ca
Kin
emat
icC
over
age
θ π=0
θ π=+
3θ π
=-3
-t=0
.1
-t=0
.3Q
2 =1.
60,
High ε
M
easu
rem
ents
ove
r 0<φ
<2π
are
requ
ired
to d
eter
min
e LT
, TT
cont
ribut
ions
ver
sus
-t.
HM
S s
ettin
gs ±
3ole
ft an
d rig
ht o
f the
q-
vect
or a
re u
sed
to o
btai
n go
od
φ-co
vera
ge o
ver a
rang
e of
t.
Te
chni
que
dem
ands
goo
d kn
owle
dge
of s
pect
rom
eter
acc
epta
nces
.
O
verla
ppin
g da
ta a
t hig
h an
d lo
wε
are
requ
ired
for L
/T se
para
tion.
D
iam
ond
cuts
def
ine
com
mon
(W
,Q2 )
cove
rage
at b
oth ε.
Radi
al co
ordi
nate
(Ra
dial
coor
dina
te ( --tt )
) A
zim
utha
lA
zim
utha
l coo
rdin
ate
(co
ordi
nate
( φφ).).
hube
rg@
ureg
ina.
ca
O
ver
Ove
r --co
nstr
aine
d co
nstr
aine
d p(
e,e’
pp(
e,e’
p ))re
actio
n an
d re
actio
n an
d ee ++
1212C
reac
tions
use
d to
C
reac
tions
use
d to
ca
libra
te s
pect
rom
eter
acc
epta
nces
, ca
libra
te s
pect
rom
eter
acc
epta
nces
, mom
enta
mom
enta
, offs
ets,
etc
., o
ffset
s, e
tc.
B
eam
ene
rgy
and
spec
trom
eter
mom
enta
dete
rmin
ed to
<0.
1%.
Sp
ectr
omet
er a
ngle
s to
~0.
5 m
r.
Agr
eem
ent w
ith p
ublis
hed
p+e
elas
tics
cros
s se
ctio
ns <
2%.
Pe
r dat
a Pe
r dat
a tt -- b
inbin
(F(Fππ--
2)2)::
Ty
pica
l sta
tistic
al e
rror
:1-
2%.
U
ncor
rela
ted
syst
. unc
. in
σ UN
S co
mm
on to
all
tbin
s:1.
8(1.
9)%
.
Add
ition
al u
ncor
rela
ted
unc.
als
o un
corre
late
d in
t:1.
1(0.
9)%
.
Tota
l cor
rela
ted
unce
rtain
ty:
3.5%
.
Mag
netic
Spe
ctro
met
er C
alib
ratio
nsM
agne
tic S
pect
rom
eter
Cal
ibra
tions
Unc
orre
late
d un
certa
intie
s in
U
ncor
rela
ted
unce
rtain
ties
in σσ
UN
SU
NS
are
are
ampl
ified
by
ampl
ified
by
1/1/∆ε∆ε
in L
in L
-- T s
epar
atio
n.T
sepa
ratio
n.S
cale
unc
erta
inty
pro
paga
tes
dire
ctly
into
sep
arat
ed c
ross
sec
Sca
le u
ncer
tain
ty p
ropa
gate
s di
rect
ly in
to s
epar
ated
cro
ss s
ectio
n.tio
n.
hube
rg@
ureg
ina.
ca
Exp
erim
enta
l Cro
ss S
ectio
n D
eter
min
atio
nE
xper
imen
tal C
ross
Sec
tion
Det
erm
inat
ion
C
ompa
re e
xper
imen
tal y
ield
s to
M
onte
Car
lo o
f the
exp
erim
ent:
R
adia
tive
effe
cts,
pio
n de
cay,
en
ergy
loss
, mul
tiple
sca
tterin
g
CO
SY
mod
el fo
r spe
ctro
met
er
optic
s.
E
xtra
ct σ
Lby
sim
ulta
neou
s fit
usin
g m
easu
red
azim
utha
l ang
le
(φπ) a
nd k
now
ledg
e of
pho
ton
pola
rizat
ion
(ε).
MC
MC
dtt
QW
dYY
dtt
QW
d⎟⎟ ⎠⎞
⎜⎜ ⎝⎛=
⎟⎟ ⎠⎞⎜⎜ ⎝⎛
),,
,(
),,
,(
2ex
p
exp
2ϕ
σφ
σ
Fπ-2
dat
a: P
RL
97(2
006)
1920
01.
()
22
21
cos
cos2
TLT
TTL
dd
dd dt
ddt
dtd d
dt
tσ
σσ
σπ
εε
εσ
φε
φφ
=+
++
+
Onl
y S
tatis
tical
Unc
erta
intie
s S
how
n.
hube
rg@
ureg
ina.
ca
Erro
r bar
s in
dica
te s
tatis
tical
and
rand
om (p
t-pt)
syst
emat
ic un
certa
intie
s in
qua
drat
ure.
Yello
w ba
nd in
dica
tes
the
corre
lated
(sca
le) a
nd p
artly
cor
relat
ed (t
-cor
r)
syst
emat
ic un
certa
intie
s.
Λπ2 =
0.51
3, 0
.491
GeV
2 , Λρ2 =
1.7
GeV
2 .
22
11
/F
Qπ
π=
+Λ
Fit t
o σ L
to m
odel
giv
es Fπ
at e
ach
Q2 .
Fπ-2 data: PRL 97(2006)192001.
Fe
ynm
an p
ropa
gato
r
repl
aced
by π
and ρ
Reg
gepr
opag
ator
s.
Rep
rese
nts
the
exch
ange
of a
ser
ies
of p
artic
les,
com
pare
d to
a s
ingl
epa
rticl
e.
Mod
el p
aram
eter
s fix
ed fr
om p
ion
phot
opro
duct
ion.
Fr
ee p
aram
eter
s: Λ
π, Λρ
(traj
ecto
ry
cuto
ff).
[Van
derh
aegh
en, G
uida
l, La
get,
PRC
57(
1998
)145
4]21
tm
π
⎛⎞
⎜⎟
−⎝
⎠
Erro
r bar
s in
dica
te s
tatis
tical
and
rand
om (p
t-pt)
syst
emat
ic un
certa
intie
s in
qua
drat
ure.
Yello
w ba
nd in
dica
tes
the
corre
lated
(sca
le) a
nd p
artly
cor
relat
ed (t
-cor
r)
syst
emat
ic un
certa
intie
s.
Afte
r A
fter σσ
L L is
det
erm
ined
, is
det
erm
ined
, a
mod
ela
mod
elis
requ
ired
to e
xtra
ct
is re
quire
d to
ext
ract
FFππ((
QQ22 ))
VG
L V
GL
Reg
geR
egge
Mod
elM
odel
::
Mod
el in
corp
orat
es
Mod
el in
corp
orat
es ππ
++pr
oduc
tion
mec
hani
sm a
nd s
pect
ator
neu
tron
effe
cts:
prod
uctio
n m
echa
nism
and
spe
ctat
or n
eutro
n ef
fect
s:
hube
rg@
ureg
ina.
ca
Com
paris
on w
ith Q
CD
-bas
ed C
alcu
latio
ns
Dis
pers
onD
ispe
rson
Rela
tion
wit
h Q
CD C
onst
rain
t:Re
lati
on w
ith
QCD
Con
stra
int:
[B.V
. Ges
hken
bein
, Phy
s.Rev
.D61
(200
0)03
3009
]
Use
s co
nstra
ints
pos
ed b
y ca
usal
ity a
nd
anal
ytic
ityto
rela
te th
e tim
elik
ean
d sp
acel
ike
dom
ains
of t
he p
ion
form
fact
or
on th
e co
mpl
ex p
lane
.R
elat
ivel
y m
odel
-inde
pend
entb
ut⇒
inco
mpl
ete
unde
rsta
ndin
g of
all
the
pole
s in
the
timel
ike
regi
on c
reat
es
unce
rtain
ties.
Add
ition
al c
onst
rain
ts, s
uch
as b
ehav
ior
of F
πin
asy
mpt
otic
regi
on im
pose
d.
FF ππ-- 2
resu
lts in
a re
gion
of
2 re
sults
in a
regi
on o
f QQ22
whe
re m
odel
cal
cula
tions
beg
in to
div
erge
.w
here
mod
el c
alcu
latio
ns b
egin
to d
iver
ge.
Still
far
fro
m h
ard
QCD
pre
dict
ion.
Still
far
fro
m h
ard
QCD
pre
dict
ion.
[A.P
. Bak
ulev
et
al, P
hys.R
ev.D
70(
2004
)033
014.
]
hube
rg@
ureg
ina.
ca
The
role
of S
oft a
nd H
ard
term
s in
Fπ
QCD
Sum
Rul
es:
QCD
Sum
Rul
es:
[V.A
. Nes
tere
nko
and
A.V.
Rad
yush
kin,
Phy
s.Let
t. B1
15(1
982)
410]
Int
erpo
latio
n be
twee
n pe
rturb
ativ
ean
d no
n-pe
rtuba
tive
sect
ors
usin
g di
sper
sion
re
latio
n m
etho
ds in
com
bina
tion
with
the
Ope
rato
r Pro
duct
Exp
ansi
on.
Not
rigo
rous
ly d
eriv
ed fr
om Q
CD
, but
an
intu
itive
brid
ge b
etw
een
low
and
hig
h en
ergy
pro
perti
es o
f QC
D.
HA
RD
:sim
ple
mod
el b
ased
on
the
inte
rpol
atio
n be
twee
n th
e Q
2 =0
valu
e (r
elat
ed b
y W
ard
iden
tity
to
O(α
s) te
rm o
f 2-p
oint
cor
rela
tor)
an
d th
e as
ympt
otic
beh
avio
r.
SOFT
:QC
D S
um R
ules
use
d to
gi
ve a
loca
l qua
rk-h
adro
ndu
ality
es
timat
e w
ith n
o fre
e pa
ram
eter
s.
2/32
0
20
)/
41(
/6
11
Qs
Qs
Fso
ft
++−
=π
)2/
1(1
02
sQ
Fs
hard
+=
παπ
22
20
GeV
0.
74
:In
terv
alD
ualit
y ≈
=π
πf
s
hube
rg@
ureg
ina.
ca
Latti
ce Q
CD
(LQ
CD
)
Lat
tice
disc
retiz
atio
ner
rors
.
Use
impr
oved
LQ
CD
act
ions
.C
hira
lext
rapo
latio
n of
LQ
CD
resu
lts in
the
pion
mas
s.Q
uenc
hing
err
ors.
N
eed
to in
clud
e di
scon
nect
ed q
uark
loop
s.
Past
:LQ
CD
cal
cula
tions
con
fined
onl
y to
the
heav
y qu
ark
sect
or.
Now
: A
dvan
ces
in c
ompu
tatio
nal t
echn
ique
s m
ay p
erm
it th
eir
appl
icat
ion
to th
e lig
ht q
uark
sec
tor w
ith g
reat
er a
utho
rity.
Futu
re:L
QC
D h
as g
reat
pot
entia
l to
revo
lutio
nize
our
und
erst
andi
ng o
fQ
CD
and
allo
w p
reci
sion
pre
dict
ions
of h
adro
nic
prop
ertie
s to
be
mad
e.
Latti
ce Q
CD
pro
mis
es to
ove
rcom
e th
eore
tical
unc
erta
intie
s at
loLa
ttice
QC
D p
rom
ises
to o
verc
ome
theo
retic
al u
ncer
tain
ties
at lo
w
w QQ
22 ..
All
QC
D-b
ased
mod
els
requ
ire c
onfin
emen
t to
be p
ut in
by
hand
.
Latti
ce Q
CD
allo
ws
the
calc
ulat
ion
to p
roce
ed fr
om fi
rst p
rinci
ples
.
Non
ethe
less
, LQ
CD
invo
lves
a n
umbe
r of a
ppro
xim
atio
ns:
Non
ethe
less
, LQ
CD
invo
lves
a n
umbe
r of a
ppro
xim
atio
ns:
hube
rg@
ureg
ina.
ca
Latti
ce Q
CD
exa
mpl
e:F π
(Q2 )
Rec
ently
, fou
r diff
eren
t lat
tice
grou
ps
have
pur
sued
Fπ
calc
ulat
ions
.G
oal:
to p
erfo
rm c
alcu
latio
n w
ith s
igni
fican
tly
smal
ler q
uark
mas
ses
than
bef
ore,
and
ev
entu
ally
atta
in la
rger
val
ues
of Q
2 .
Low
er p
ion
mas
s →
Larg
er N
sxN
sxN
sxN
tla
ttice
. →
Mor
e ra
pidl
y co
nver
ging
act
ion
and
fast
er C
PU
.H
ighe
r Q2→
Fine
r lat
tice
spac
ing.
→
Impr
oved
pio
nop
erat
ors.
The
first
LQ
CD
cal
cula
tions
of F
π(1
980
s) u
sed
mπ~
1 G
eV.
C
alcu
latio
n up
to Q
2 =1
GeV
2co
nsis
tent
with
pio
nch
arge
radi
us,
with
in (l
arge
) erro
r.
hube
rg@
ureg
ina.
ca
Bes
t Cal
cula
tion:
Unq
uenc
hed
Latti
ce Q
CD
F. B
onne
t et a
l, PR
D 7
2(20
05)0
5450
6.pQ
CD
Unq
uenc
hed
dom
ain-
wall
acti
on c
alcu
lati
on
by L
atti
ce H
adro
nPh
ysic
s Co
llabo
rati
on(J
Lab/
Regi
na/Y
ale)
.
Now
:LQ
CD
cal
cula
tions
are
con
sist
ent w
ith e
xper
imen
tal d
ata,
with
inla
rge
stat
istic
al a
nd s
yste
mat
ic (c
hira
lext
rapo
latio
n) e
rrors
.
Prim
ary
aim
is to
test
pro
of-o
f-prin
cipl
e of
var
ious
cal
cula
tion
tech
niqu
es.
Nex
t dec
ade:
hope
to s
ee d
ynam
ical
(unq
uenc
hed)
cal
cula
tions
of F
πw
ith p
ion
mas
s su
ffici
ently
low
to y
ield
sm
all c
hira
lext
rapo
latio
n un
certa
intie
s.
Hig
her Q
2da
ta a
re re
quire
d to
val
idat
e ne
w L
QC
D m
etho
ds.
Ope
rate
d by
Jeff
erso
n Sc
ienc
e A
ssoc
iate
s for
the
U.S
. Dep
artm
ento
f En
ergy
Tho
mas
Jef
fers
on N
atio
nal A
ccel
erat
or F
acili
ty
Page
CH
LC
HL --
22
Upg
rade
mag
nets
U
pgra
de m
agne
ts
and
pow
er
and
pow
er
supp
lies
supp
lies
Enh
ance
equ
ipm
ent i
n E
nhan
ce e
quip
men
t in
exis
ting
halls
exis
ting
halls
Add
new
hal
lA
dd n
ew h
all
12 G
eVU
pgra
de
CD
1 gr
ante
d: F
eb/0
6Fi
rst 1
2 G
eVbe
am: m
id-2
013
Ope
rate
d by
Jeff
erso
n Sc
ienc
e A
ssoc
iate
s for
the
U.S
. Dep
artm
ento
f En
ergy
Tho
mas
Jef
fers
on N
atio
nal A
ccel
erat
or F
acili
ty
Page
Expe
rimen
tal H
all C
At t
he p
rese
nt 6
GeV
Bea
m E
nerg
yA
fter t
he 1
2 G
eV U
pgra
de
Hal
l Cs
Hig
h M
omen
tum
Spe
ctro
met
er,
Shor
t Orb
it Sp
ectr
omet
er a
nd
spec
ializ
ed e
quip
men
t for
stu
dyin
g:T
he s
tran
ge q
uark
con
tent
of t
he p
roto
n.F
orm
fact
ors
of s
impl
e qu
ark
syst
ems.
The
tran
sitio
n fr
om h
adro
ns to
qua
rks.
Nuc
lei w
ith a
str
ange
qua
rk e
mbe
dded
.
Add
a S
uper
-Hig
h M
omen
tum
(12
GeV
) Sp
ectr
omet
er fo
r stu
dyin
g:S
uper
-fast
(hig
h x B
) qua
rks.
For
m fa
ctor
s of
sim
ple
quar
k sy
stem
s.T
he tr
ansf
orm
atio
n of
qua
rks
into
had
rons
.Q
uark
-qua
rk c
orre
latio
ns.
hube
rg@
ureg
ina.
ca
12 G
eV:S
tudy
ing
the
trans
ition
to H
ard
QC
D
Ano
ther
impo
rtant
issu
e in
the
phys
ics
of c
onfin
emen
t is
A
noth
er im
porta
nt is
sue
in th
e ph
ysic
s of
con
finem
ent i
s
unde
rsta
ndin
g th
e tra
nsiti
on o
f the
beh
avio
r of Q
CD
from
low
un
ders
tand
ing
the
trans
ition
of t
he b
ehav
ior o
f QC
D fr
om lo
w QQ
22to
to
hi
gh
high
QQ22 .
. Th
e Th
e pi
onpi
onis
one
of t
he s
impl
est Q
CD
sys
tem
s av
aila
ble
for
is o
ne o
f the
sim
ples
t QC
D s
yste
ms
avai
labl
e fo
r st
udy,
and
the
mea
sure
men
t of i
ts e
last
ic fo
rm fa
ctor
is th
e be
sst
udy,
and
the
mea
sure
men
t of i
ts e
last
ic fo
rm fa
ctor
is th
e be
s t h
ope
t hop
e fo
r see
ing
this
tran
sitio
n ex
perim
enta
lly.
for s
eein
g th
is tr
ansi
tion
expe
rimen
tally
.-U
.S. N
ucle
ar S
cien
ce A
dvis
ory
Com
mitt
ee (2
002)
.
JLabProposal: 12-06-101
hube
rg@
ureg
ina.
ca
Nuc
leon
Ele
ctric
and
Mag
netic
Form
Fac
tor D
ata
hube
rg@
ureg
ina.
ca
Spin
½: E
last
ic e
lect
ron
scat
terin
g fr
om n
ucle
ons
pQC
DD
imen
sion
al S
calin
g R
ule:
F 1
(Q2 )
∼1/Q
4(n
=3).
F 2
(Q2 )
∼1/Q
6(n
=3 w
ith sp
in fl
ip).
!Q
2 F2/F
1∼co
nsta
nt.
D
ata
indi
cate
ons
et o
f pQ
CD
scal
ing
at o
nly
Q2 ≈
2 G
eV2 .
Wor
ld p
roto
n da
ta s
et, 1
997.
Mag
netic
con
tribu
tion
dom
inat
es
cros
s se
ctio
n at
hig
h Q
2 :!
F 1da
ta o
f fai
rly g
ood
qual
ity.
Ele
ctric
con
tribu
tion
at fe
w %
leve
l:!
F 2di
fficu
lt to
mea
sure
.!
Sys
tem
atic
erro
r iss
ues.
)(
)(
22
2Q
GQ
GdQd
ME
elτ
εσ
+→ τ=
Q2 /4
M2
ε=
[1+2
(1+τ
)tan2 (
θ /2
)]-1
hube
rg@
ureg
ina.
ca
Pol
ariz
atio
n tra
nsfe
r tec
hniq
ue
e
e’
γp
θ e
NLT
h
Te
chni
que
deve
lope
d at
Nov
osib
irsk.
R
equi
res
an in
tens
e po
lariz
ed e
lect
ron
beam
and
Foc
al P
lane
P
olar
imet
erto
mea
sure
the
pola
rizat
ion
of th
e re
coil
nucl
eon.
S
imul
tane
ous
mea
sure
men
t of t
rans
vers
e an
d lo
ngitu
dina
l S
imul
tane
ous
mea
sure
men
t of t
rans
vers
e an
d lo
ngitu
dina
l po
lariz
atio
n co
mpo
nent
s pr
ovid
es a
n ac
cura
te m
easu
rem
ent o
f po
lariz
atio
n co
mpo
nent
s pr
ovid
es a
n ac
cura
te m
easu
rem
ent o
f th
e fo
rm fa
ctor
ratio
.th
e fo
rm fa
ctor
ratio
.
⎟ ⎠⎞⎜ ⎝⎛
+−
=2
tan
2'
e
lt
ME
mEE
ppGG
θ
hube
rg@
ureg
ina.
ca
2004
JLab
Sup
erR
osen
blut
h
(e,p
)cro
ss se
ctio
ns d
ata
agre
e w
ell w
ith g
loba
l cro
ssse
cton
fit.
(I.A
. Qat
tan
et a
l, PR
L 94
(05)
1423
01)
The
prot
on: r
ecoi
l pol
ariz
atio
n vs
. cro
ss s
ectio
ns
Lik
ely
culp
rit:
2-γ
exch
ange
impa
cts c
ross
sect
ion
data
.(P
. Blu
nden
et a
l, PR
L 91
(03)
1423
04)
can
be d
irect
ly te
sted
with
σ(
e+ )/ σ
(e- )
(Nov
osib
irsk,
JLab
).
WH
AT
THIS
ME
AN
S: E
last
ic
cros
s se
ctio
ns a
re a
ccur
ate,
but
the
pola
rizat
ion
trans
fer m
easu
rem
ents
be
tter r
epre
sent
GEp .
O. Gayouet al, PRL 88(02)092301.
hube
rg@
ureg
ina.
ca
Jeffe
rson
Lab
Pro
ton
F 2/F
1D
ata
JL
abda
ta s
how
that
Q2
scal
ing
was
pre
mat
ure
.
The
data
inst
ead
show
a re
mar
kabl
e sc
alin
g w
ith Q
, whi
ch w
as n
ot
antic
ipat
ed.
H
ighe
r tw
ist a
nd o
ther
sof
t con
tribu
tions
pro
duce
ln(Q
2 )co
rrect
ions
w
hich
giv
e ris
e to
Q-li
ke s
calin
g (B
elits
ky, J
i, Y
uan,
PR
L 91
(03)
092
003)
.
hube
rg@
ureg
ina.
ca
Neu
tron
ela
stic
form
fact
ors
O
btai
ning
goo
d in
form
atio
n on
the
neut
ron
Obt
aini
ng g
ood
info
rmat
ion
on th
e ne
utro
n s e
lect
rom
agne
tic st
ruct
ure
is
s ele
ctro
mag
netic
stru
ctur
e is
pr
oble
mat
ic, b
ut si
gnifi
cant
pro
gres
s has
bee
n m
ade
in re
cent
ye
prob
lem
atic
, but
sign
ifica
nt p
rogr
ess h
as b
een
mad
e in
rece
nt y
e ars
.ar
s.!
Nuc
lear
targ
ets
[2 H (d
), 3 H
e] a
re re
quire
d.
!In
trodu
ces
nucl
ear w
ave
func
tion
unce
rtain
ties.
Rec
ent 2
-and
3-N
ca
lcul
atio
ns h
ave
redu
ced
the
theo
retic
al u
ncer
tain
ties
due
to ta
rget
.
GGMM
nnca
n be
det
erm
ined
from
d(e
,en
)/d(e
,ep
)cro
ss se
ctio
n ra
tio m
easu
rem
ents
or
from
elec
tron
spin
asy
mm
etry
in k
inem
atic
s whe
re th
e ne
utro
n co
ntrib
utio
n do
min
ates
..!
New
resu
lts a
ppro
ach
the
prec
isio
n of
pro
ton
data
(5%
) up
to Q
2 =5
GeV
2 .
GGeenn
is sm
all,
so th
e ro
le o
f pio
ncl
oud
or
co
mpo
nent
s are
enh
ance
d.!
Two
rece
nt J
Lab
doub
le p
olar
izat
ion
expe
rimen
ts
now
pro
vide
the
first
mea
sure
men
ts a
bove
Q2 =
1 G
eV2 .
GE
(Q2 =
0):
1 (p
)0
(n
)__
____
____
____
____
____
____
____
____
____
____
____
__
GM
(Q2 =
0):
2.79
µN
(p)
-1.9
1 µ N
(n)
qq(
,'
),
(
,'
)d
ee
np
de
en
p$!!
!!
3(
,')
He
ee
$$$!!
hube
rg@
ureg
ina.
ca
Glo
bal a
naly
sis
of p
and
nFo
rm F
acto
rsG
loba
l ana
lysi
s of
pan
d n
Form
Fac
tors
char
ge
prot
onne
utro
n
mag
netiz
atio
nJL
abpo
lariz
atio
n da
ta
show
dep
letio
n of
ch
arge
in p
roto
n in
terio
r.
J.J. K
elly
, PR
C66
(200
2) 0
6520
3
hube
rg@
ureg
ina.
ca
App
rove
dE
01-1
09
SH
MS
in H
all C
at 1
1 G
eV
full:
Lom
onda
shed
:Mill
er
12 G
eV: P
robe
the
Cha
rge
and
Cur
rent
Dis
trib
utio
ns in
the
Prot
on a
t <0.
1 fm
hube
rg@
ureg
ina.
ca
Plan
ned
Neu
tron
GM
nM
easu
rem
ents
ed
e
n(p s)
epeπ
+ n
hube
rg@
ureg
ina.
ca
Sum
mar
y
The
past
10
year
s ha
ve s
een
good
pro
gres
s in
dev
elop
ing
a qu
antit
ativ
e un
ders
tand
ing
of th
e el
ectro
mag
netic
st
ruct
ure
of th
e lig
htes
t mes
ons
and
the
nucl
eon.
M
uch
cred
it go
es to
the
cont
inuo
us e
lect
ron
beam
pro
vide
d by
the
Jeffe
rson
Lab
sup
erco
nduc
ting
linac
, and
adv
ance
s in
pol
ariz
atio
n te
chni
ques
in e
lect
ron
scat
terin
g.
New
puz
zles
hav
e em
erge
d as
a re
sult
of th
e im
prov
ed
leve
l of p
reci
sion
of t
he d
ata.
In th
e ne
xt fe
w y
ears
, we
look
forw
ard
to:
R
esul
ts fo
r the
pion
form
fact
or a
nd p
ossi
bly
the
Kao
n.
Dee
per u
nder
stan
ding
of t
he p
roto
ns
char
ge a
nd m
agne
tism
and
th
e ro
le o
f qua
rk o
rbita
l ang
ular
mom
entu
m.
hube
rg@
ureg
ina.
ca
Long
er te
rm V
iew
Ove
r the
long
er te
rm, w
e lo
ok fo
rwar
d to
con
tinue
d de
velo
pmen
t of L
attic
e Q
CD
tech
niqu
es fo
r the
ligh
t qua
rk
sect
or:
U
nque
nche
d ca
lcul
atio
ns.
U
sage
of r
ealis
tic p
ion
mas
s an
d be
tter C
hira
lext
rapo
latio
ns.
V
ery
prom
isin
g, b
ut n
ot y
et p
rove
n.
2012
+:JL
ab12
GeV
upgr
ade
will
pro
vide
new
insi
ghts
:
Stru
ctur
e of
the
nucl
eon.
Tr
ansi
tion
betw
een
the
hadr
onic
and
quar
k/gl
uon
desc
riptio
ns o
f mat
ter.
M
any
parts
of p
rogr
am n
ot d
iscu
ssed
her
e.
