Transcript How We Came to Understand Confinement ()

How
we
cam
to
understand
”How We Came
confinement
to Understand
Confinement”
The Ubiquitous Little Proton



From Chemistry,
the “Hydrogen Ion”
Tastes rather sour;
“lemonade”
The small round dot
of Ernest
Rutherford
P
Form Factors, More than
Fudge Factors
Observed
Amplitude(
M)
All Measured
 a fudge
factor

a
fudge
factor
Amplitude(
M
 

form

factors
Model
M
M) Model

A form factor is a GENERAL expansion…

Sum over all possible irreps of relevant groups!
What Rosenbluth Did
 p',s'|J EM |ps  u( p',s') [ e 






2
2
F 1(Q )  i 2m eF 2 (Q )
] u( p,s)
Lorentz symmetry:
(1/2,0)+(0,1/2)
->(1/2,1/2)
P, T
Gauge Singlet
Chirality +, -
P
P’
Form factors are observable
matrix elements

Once measured, use
it forever.

Know your operator!!
…”any deviation from Rosenbluth
cannot be attributed to our ignorance of
the strong coupling..
Matrix Elements and
Factorization

Once a matrix
element is
measured, you
must get the
same value in a
new measurement
P’
P
Q
Factorization: amplitudes
multiply
e

It is the same
Itmatrix
is the element
same
matrix element
perturbatively
measured again
measured again in
perturbatively in
atomic physics
EM part of pp
scattering
e’
p
P

p, D, n*…
e
…do not neglect
resonant interference
quantum mechanics is more
than diagrams
QuickTime™ and a
Animation decompressor
are needed to see this picture.
Interpretation ca 1960

Assuming an instantaneous
point-like probe, static charge
distribution r(x),
2
3
iQ
x
GE (Q )   d x r(x ) e
Analyticity, i.e. Causality
Q
F(Q2 ) 
1
2i
F(Q'2 )
2
 dQ' 2 2 ;
Q' Q
2
1
Im[
F
(Q'
)]
2
2
Re[F(Q )]  P  dQ'
;

Q'2 Q2
xx
r =770
x
+-150 MeV
 =780 +-10 MeV
VMD
THUS, an internally
self-consistent
theory existed
already 40 years
…which has ago
nearly faded into
oblivion
The point like probe
…what changed everything forever,
is the point-like probe
Factorization and form
factors of quarks
quark
proton
same
quark same
proton

ixp
z


(x,b)  dz e  p,s| (z ,b;z 0) (0) | p,s
 
Parton distributions are
integrated form factors

Forward scattering is
integrated over
transverse separation b


Functions of
Feynman x
(x,b)   dzeixp z  p,s | (z,b;z  0) (0) | p,s 

2

2
2
q(x,Q )  (x,b 1/Q )
An era of great discoveries
and confidence in pQCD…
 Factorization for
 …until it seemed
exclusive could
everything
x1
reactions
be calculated
from
…andfirst
at first
x
2
with
principles…
1- x 1 - x
correspondingly
2
high ambitions…
.…and needing next to
about the
no information
hadrons
themselves…
( Fade to black )
What Jlab Taught Us



Magnificent
Structure
functions in
Resonance Region
No Longer in
Denial
Osipenko et al ‘03
What
Jlab Taught
N->D Transition
versus Q Us
2
Just as often
wrong as right
Frolov
99not the
 It is
Stoler 02
fault of “pQCD”

and see
Carlson
JLAB delivers…



Color transparency
A =10-100
A (e,e’p) matrix
elements are form
factors!!
Garrow
et al ‘01
Dutta et
al ‘03
Proton QF2/F1 aversus Q^2
What Jlab Taught Us


Just as often
wrong as right
It is not the
fault of “pQCD”
Gayou et al PRL ‘02
Jones et al PRL ‘01
What Jlab Taught Us

Explain?
Walker ‘94
Arrington’ 03
Read carefully…
Combined Fit
2/dof \sim 1

Arrington’ 03
GM
/G
n
D
the neutron:
surprises?



12 GeV
Xu et al, PRC ‘20
(M. Jones et al ,
private comm.)
Valence Models, Pretty Good


Miller and Frank
Agrees with pQCD
that F2/F1 due to
quark
Orbital
Angular
Momentum,
aka “OAM”
Every theorist had to take a
pledge to reform

“perturbaholics anonymous”

It is not the fault of “pQCD”
How it works in pQCD
Ambition:
Some
Lower
High
Ambition:
Outrageous
Predictability:
Some
Lower
High
Predictability:
High++
Safety:
Higher
Safety:None
0

Ambition:
Low
Model
Dependence:
Even
Model Dependence:
 Predictability:
Higher
Moderate
Remains
Low
 Safety: High
 Model
Dependence:
Very High
GPD’s are Unobservable
DJ = 1
…yet
capable
pQCD
…yet
pQCD
predictions
…yetcapable
capable of
of of
pQCD
predictions
model independent;
Scaling
predictions:
F2 from
OAM
Azimuthal
asymmetries;
Scaling
Probably the Proton is not a
small ROUND dot…
M(bT ) 
d
2
kT e
 e
im
ikT bT
M(kT )
Mm (b)
m

Orbital Angular Momentum: light cone
SO(2) |m; J2>
Ask not how big your theory is..
Ask what it tells us about
confinement


No one scheme
is supposed to
predict
everything
An infinite
number of
factorizations
 It’s
(about) the
3-Dimensional
structure of
hadrons
What Jlab can do:
the three dimensional structure of
confinement


Point-like
Probes: =
large
virtuality
With LOW
momentum
transfer t,
Deeply Virtual Exclusives

The ability to
isolate the
transverse,
Lorentz
invariant,
structure of
hadrons
by
bx
How the transverse
coordinate Works
M(bT )   d D e
2
ib D
 p,s |T[J(Q)J(k)] | p  D,s'
…a non-relativistic acting sub-world
of light cone geometry
Confinement is observable

The interior of a
“quantum black hole
of color”
…confinement!
QuickTime™ and a
Animation decompressor
are needed to see this picture.
Physics based on observables


GPD’s, while exciting, are
unobservable
Observable matrix elements maintain
the priority

 






 p,s| T(J (z ,b Db;z 0) J (z ',bDb,z 0)
|p',s'
Transverse Structure 100%
Observable
Method of observation



Use any large
vituality pointlike
probe
Measure the D
dependence, D2t,
0<|t|<1 GeV2
If you have an
amplitude: good!



Take the Fourier
transform: D-> b
Square the result
Result: a true
window into
confining system
Deeply Virtual Exclusives
DVET:Deeply
Virtual Transitions
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
DVEW: Deeply
(Burkert;
E93-050
Virtual
Hall
A) semi
Electroweak

Z
ZZ
ZZ
Z
Interpretation Holds

Assuming an instantaneous
point-like electroweak probe,
P
2
3
iQ
x
Gweak(Q )   d x rweak (x ) e
P’
We share high-minded
goals. Theorists are united:
JLAB-12 GeV
will measure the confining
three-dimensional structure
of hadrons
Theory and experiment in
partnership
o JLAB-
12 GeV
: the ultimate
confinement
explorer
o
ENGAGE